well control problems associated with gas solubility in
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Louisiana State UniversityLSU Digital Commons
LSU Historical Dissertations and Theses Graduate School
1988
Well Control Problems Associated With GasSolubility in Oil-Based Drilling Fluids.Patrick Leon O'bryanLouisiana State University and Agricultural & Mechanical College
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O rder N u m b er 8819965
Well control problems associated w ith gas solubility in oil-based drilling fluids
O’Bryan, Patrick Leon, Ph.D.
The Louisiana State University and Âgricnltnral and Mechanical CoL, 1988
C opyrigh t © 1989 by O ’B ry a n , P a trick Leon. A ll rights reserved.
UMISOON. Zeeb Rd.Ann Aibor, MI 48106
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WELL CONTROL PROBLEMS ASSOCIATED WITH GAS SOLUBILITY IN OIL-BASED DRILLING FLUIDS
A Dissertation
Submitted to the Graduate Faculty of the Louisiana State University and
Agricultural and Mechanical College in partial fulfillment of the
requirements for the degree of Doctor of Philosophy
in
The Department of Petroleum Engineering
by
Patrick L. O'Bryan B.S., Mississippi State University, 1983 M.S., Louisiana State University, 1985
May 1988
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©1989
PATRICK LEON O',BRYAN
All Rights Reserved
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ACKNOWLEDGMENT
The author wishes to thank Dr. A.T. Bourgoyne, Jr., under whose
guidance this work was conducted, for his encouragement and sug
gestions, and the many opportunities he provided this student through
out the course of his graduate career.
A special thanks goes to Drs. Teresa Monger, Zaki Bassiouni, Bill
Holden, Rex Pilger, and Ahmed El-Amawy for serving on the examining
committee.
The financial assistance provided by Amoco, Arco, British
Petroleum, Chevron, Cities Service, Conoco, Exxon, Tenneco, and Union
oil companies for this project is greatly appreciated.
The author would like to thank Debra Kopsco for her assistance in
completing the phase behavior study, Allen Kelly for his assistance in
completing the full-scale well experiments, and Jan Easley for typing
this document.
The author thanks the good Lord for making all of this possible
and blessing the author and his family with so much.
To his wife Pam and son Taylor, the author would like to say thank
you for the love and support you provided him during the course of this
study and his graduate career. We made it!
Finally, the author is indebted to his parents for providing the
opportunity to attend graduate school and always being very supportive.
In particular, the author thanks his father for teaching him early in
life how to use his head for something other than a hat rack and would
like to dedicate this work to him.
ii
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TABLE OF CONTENTS
Page
ACKNOWLEDGMENT............................................. li
LIST OF TABLES............................................. v
LIST OF FIGURES............................................ vii
ABSTRACT................................................... x
CHAPTER I INTRODUCTION............................ 1
CHAPTER II LITERATURE REVIEW....................... 9
CHAPTER III AN EXPERIMENTAL AND THEORETICAL STUDY OF METHANESOLUBILITY IN OIL-BASED DRILLING FLUIDS.... 15
3.1 Purpose of Study................... 15
3.2 Experimental Apparatus and Procedure 15
3.3 Experimental Results..... 27
3.4 Equation of State Modeling......... 28
CHAPTER IV ADDITIONAL GAS SOLUBILITY DATA......... 33
4.1 Experimental Apparatus and Procedure.... 33
4.2 Experimental Results.............. 33
4.3 Solubility of Other Gases......... 41
CHAPTER V GAS SOLUBILITY APPROXIMATION........... 44
5.1 Solubility of Gas in Base Oil. 45
5.2 Solubility of Gas in Water.... 47
5.3 Solubility of Gas in Oil-Based DrillingFluids............................ 53
5.4 Experimental Verification of the Correlation....................... 53
CHAPTER VI GAS MISCIBILITY......................... 55
6.1 First Contact Miscibility......... 55
6.2 Methane Miscibility with No. 2 Diesel Oil 55
iii
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6.3 Effects of Other Gases on MethaneMiscibility............................ 61
6.4 Field Application...................... 61
CHAPTER VII SWELLING OF OIL-BASED DRILLING FLUIDS DUE TODISSOLVED GAS............................... 65
7.1 Oil Swelling Calculations.............. 65
7.2 Pit Gain Calculations................. 66
7.3 Field Application..................... 71
7.4 Example Calculations.................. 77
7.5 Drilling Fluid Density Calculations 81
CHAPTER VIII HANDLING DRILLED-GAS IN OIL-BASED DRILLINGFLUIDS...................................... 83
8.1 Drilled-Gas Concentration............. 83
8.2 Circulating Time to Gas Evolution..... 84
8.3 Calculation of the Decrease in BottomholePressure Due to Gas Evolution.......... 87
8.4 Drilling Fluid Expelled Due to GasEvolution and Surface Gas Rate......... 92
8.5 Experimental Verification of CalculationProcedure .......................... 92
8.6 Evaluation of Field Procedures........ 94
CHAPTER IX CONCLUSIONS................................. 108
CHAPTER X RECOMMENDATIONS.............................. 110
CHAPTER XI REFERENCES................................... Ill
APPENDIX A PENG-ROBINSON EQUATION OF STATE............. 113
APPENDIX B FULL SCALE EXPERIMENTS...................... 117
APPENDIX C GAS FREE DRILLING FLUID PRESSURE CALCULATIONS 125
APPENDIX D TWO-PHASE PRESSURE GRADIENT CALCULATIONS 129
VITA....................................................... 131
iv
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LIST OF TABLES
Page
TABLE 2.1 Methane Solubility in No. 2 Diesel Oil atT = 100®F (Thomas, Lea, and Turek).......... 10
TABLE 2.2 Methane Solubility in Unweighted Oil-BasedDrilling Fluid at T = 100°F (Thomas, Lea, and Turek).................................. 10
TABLE 3.1 Base Oil Molar Compositions.................. 17
TABLE 3.2 Composition of 13 Ibm/gal Oil-Based DrillingFluid (Salisbury)........................... 18
TABLE 3.3 Experimentally Measured Versus PREOS PredictedMethane Solubility in Mentor 28 Oil......... 29
TABLE 3.4 Experimentally Measured Versus PREOS PredictedMethane Solubility in 13 Ibm/gal Oil-Based Drilling Fluid.............................. 31
TABLE 4.1 Natural Gas Composition........ 34
TABLE 5.1 Empirical Correlation Constants.............. 46
TABLE 5.2 Gas Solubility in Water Curve Fits........... 52
TABLE 5.3 Experimentally Measured Versus PredictedBubble Point Pressure for Natural Gas/13-lbm/gal Oil-Based Drilling Fluid......... 54
TABLE 6.1 API Average Bottomhole Circulating Temperature 62
TABLE 7.1 Base Oil Critical Properties................. 67
TABLE 7.2 Comparison of Experimentally Measured andComputed Values of Volume Factor, Bo, for Methane in No. 2 Diesel Oil at 100°F........ 68
TABLE 7.3 Comparison of Experimentally Measured andPredicted Pit Gains in 6000 ft. ExperimentalWell........................................ 72
TABLE 8.1 Comparison of Experimental Observations andTheoretical Predictions..................... 93
TABLE 8.2 Volume of Drilling Fluid Expelled Due to GasEvolution................................... 100
TABLE A.1 Peng-Robinson Equation of State BinaryInteraction Coefficients.................... 116
V
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TABLE B.l
TABLE B.2
TABLE B.3
Full Scale Experimental Gas Composition.
Full Scale Experimental Conditions.....
Full Scale Experimental Measurements....
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Vi
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LIST OF FIGURES
FIGURE 1.1
FIGURE 1.2
FIGURE 1.3
FIGURE 1.4
FIGURE 2.1
FIGURE 2.2
FIGURE 3.1
FIGURE 3.2
FIGURE 3.3
FIGURE 3.4
FIGURE 3.5
FIGURE 3.6
FIGURE 3.7
FIGURE 3.8
FIGURE 3.9
FIGURE 4.1
FIGURE 4.2
FIGURE 4.3
FIGURE 4.4
Gas Kick Versus Drilled-Gas.
Gas Kick Detection In Water-Versus Oil-Based Drilling Fluids............ .................
Drilled-Gas Contamination of Water-Based Drilling Fluids.........................
Drilled-Gas Contamination of Oil-Based Drilling Fluids.......................
Methane Solubility in No. 2 Diesel Oil (Thomas, Lea, and Turek)..............
Carbon Dioxide, Hydrogen Sulfide, and Methane Solubility in No. 2 Diesel Oil (Matthews)....
Experimental Apparatus......................
Sample Experimental Pressure Versus Volume Plot
Experimental Procedure Verification.........
Methane Solubility in Mentor 28 Oil.........
Methane Solubility in Emulsifier............
Methane Solubility in 13 Ibm/gal Oil-Based Drilling Fluid..............................
Methane Solubility in Mentor 28 Oil, Emulsifier, and Brine (T = 100°F)....
Methane Solubility in No. 2 Diesel, Mentor 28, and Conoco LVT Base Oils (T = 100°F)........
Pressure Versus Density for Methane/13-blm/gal Oil-Based Drilling Fluid Mixture..
Ethane Solubility in Mentor 28 Base Oil.
Ethane Solubility in 13 Ibm/gal Oil-Based Drilling Fluid...........................
Carbon Dioxide Solubility in Mentor 28 Base Oil...............................
Carbon Dioxide Solubility in 13 Ibm/gal Oil-Based Drilling Fluid...............
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v ix
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FIGURE 4.5 Natural Gas Mixture Solubility in Mentor 28Base Oil....................................
FIGURE 4.6 Natural Gas Mixture Solubility in 13 Ibm/galOil-Based Drilling Fluid....................
FIGURE 4.7 Gas Solubility in Mentor 28 Base Oil(T = 100°F).................................
FIGURE 5.1 Methane Solubility in Pure Water (McCain)....
FIGURE 5.2 Carbon Dioxide Solubility in Pure Water(Crawford, et. al.).........................
FIGURE 5.3 Water Salinity Correction for MethaneSolubility in Water (McCain)................
FIGURE 5.4 Water Salinity Correction for Carbon DioxideSolubility in Water (Crawford, et. al.).....
FIGURE 6.1 Pressure-Composition Diagram................
FIGURE 6.2 Methane/No. 2 Diesel Oil Miscibility PressuresVersus Temperature..........................
FIGURE 6.3 Locus of Cricondenbars for Methane and No. 2Diesel Oil..................................
FIGURE 6.4 Pit Gain Per 1000 SCF Méthane Kick in Oil- andWater-Based Drilling Fluids.................
FIGURE 6.5 Methane Miscibility Depth Versus No. 2 DieselOil-Based Drilling Fluid Density...... ......
FIGURE 7.1 Gas/Oil-Based Drilling Fluid Downhole Mixing.
FIGURE 7.2 No. 2 Diesel Oil Swelling Due to DissolvedMethane (T = 100°F).........................
FIGURE 7.3 No. 2 Diesel Oil Swelling Due to DissolvedMethane (T = 200°F) ........................
FIGURE 7.4 No. 2 Diesel Oil Swelling Due to DissolvedMethane (T = 300°F).........................
FIGURE 7.5 No. 2 Diesel Oil Swelling Due to DissolvedMethane (T = 400°F).........................
FIGURE 7.6 Downhole Oil-Based Drilling Fluid DensityChanges Due to Dissolved Methane............
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FIGURE 8.1 Circulating Gas Contaminated Drilling Fluid Out of Well................................. 85
FIGURE 8.2 Annular Velocity Profiles Due to Laminar Flow and Hole Eccentricity....................... 88
FIGURE 8.3 Computer Model Wellbore Geometry............ 89
FIGURE 8.4 Effect of Penetration Rate and Drilling Fluid Density on Drilled-Gas Concentration (D = 8000 Feet)....................................... 95
FIGURE 8.5 Effect of Penetration Rate and Drilling Fluid Density on Drilled-Gas Concentration (D = 15000 Feet)................. ■..................... 96
FIGURE 8.6 Effect of Drilled-Gas Concentration on Circulation Time to Gas Evolution........... 97
FIGURE 8.7 Effect of Penetration Rate and Gas Sand Thickness on Bottomhole Pressure Reduction... 99
FIGURE 8.8 Effect of Gas Send Thickness on Gas Volume in Well........................................ 101
FIGURE 8.9 Effect of Pump Rate and Drilled-Gas Concentration on Peak Surface Gas Rate...... 102
FIGURE 8.10 Rotating Head - Separator Flow Arrangement for No Free Gas in Wellbore................. 104
FIGURE 8.11 Rotating Head Pressure Rating Required to Keep Gas in Solution............ ........... 105
FIGURE 8.12 Rotating Head - Separator Flow Arrangement with Free Gas in Wellbore................... 106
FIGURE B.l Full Scale Experimental Test Well........... 118
FIGURE B.2 Experiment No. 1 Measured Data.............. 122
FIGURE B.3 Experiment No. 2 Measured Data.............. 123
FIGURE B.4 Experiment No. 3 Measured Data.............. 124
FIGURE C.l Friction Factors for Frictional Pressure Loss
Ix
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ABSTRACT
Gas contamination of an oil-based drilling fluid during drilling
operations, whether it be by the flow of formation gas into the
wellbore (gas kick) or by the drilling of gas-bearing formations
(drilled-gas), poses a potential hazard to the drilling equipment,
environment, and personnel. This danger is the greatest when
bottomhole conditions are such that the gas will completely dissolve
into the drilling fluid and rapidly evolve as the gas-cut drilling
fluid is circulated up the well.
This work summarizes a study of well control problems associated
with gas solubility in oil-based drilling fluids. The solubilities of
various gases (i.e., methane, ethane, carbon dioxide, etc.) in base
oils used in oil-based drilling fluid preparation as well as an
oil-based drilling fluid over a range of pressures and temperatures
were measured and a method for predicting the solubility of a gas
mixture containing methane, ethane, and carbon dioxide in an oil-based
drilling fluid is pesented. In addition, methods for predicting the
pit gain to be expected for a given gas kick taken while drilling with
an oil-based drilling fluid and for predicting the annular behavior to
be expected when drilled-gas contaminates an oil-based drilling fluid
during drilling were developed. Both methods were verified using data
measured during experiments conducted in a 6000 ft test well.
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CHAPTER I
INTRODUCTION
Oil-based drilling fluids, or muds as they are often referred to by
drilling personnel, are an alternative to the standard water-based
drilling fluids commonly used in the petroleum industry. Several
factors including reduced formation damage, better lubricity of both
surface and subsurface drilling equipment, better borehole stability,
and better drilling fluid stability at high pressures and temperatures
have led some companies to use oil-based drilling fluids exclusively
when drilling water sensitive production formations and/or deep, hot
wells. However, the use of oil-based drilling fluids have presented
several problems with respect to well control when the drilling fluid is
contaminated by gas.
Figure 1.1 illustrates how a drilling fluid can become contaminated
by formation gas. In Figure 1.1a the gas sand pressure is greater than
the circulating bottomhole pressure in the wellbore resulting in gas
flow from the sand into the well. This flow of formation gas is often
referred to as a "gas kick". Also notice in Figure 1.1a that the gas in
the wellbore displaces drilling fluid from the well resulting in an
increase in the volume of drilling fluid in the surface tanks or pits.
This is referred to as a "pit gain" and is the most commonly used and
most reliable method for detecting a kick in the well.
Figure 1.1b shows another way by which gas contaminates the
drilling fluid. In this case no gas flows from the sand because the
circulating bottomhole pressure in the well is greater than the gas sand
pressure. However, the gas contained in the pore space of the sand
1
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Mud Inj
0Bottom Hole Pressure Less thtn 6aa Sand Formation Pressure
@)Gas Flows into Wellbore
@ Gas Kick in Wellbore
0)6as Kick Displaces Mud from Wellbore (P it Gain)
(§)Gos Send
(a ) GAS KICK
Mud In
rk
•
(D Bottom Hole Pressure Greater than Gas Sand Formation Pressure
©Me Gas Flow into Wellbore
©Dispersed Gas Bubbles from Gas Sand Destroyed by Bit in Wellbore
® No Mud Displaced from Wellbore
® Gas Sand
(b ) DRILLED GAS
Figure 1.1 - Gas Kick Versus Drilled-Gas.
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destroyed by the bit will mix with the drilling fluid. This gas is
referred to as "drilled-gas".
When a gas kick is taken while drilling, it is imperative that the
kick be detected early enough to allow the proper well control
procedures to be implemented in order to reduce the risk of damage to
the environment, equipment, and personnel due to a "blowout", which is
the uncontrolled flow of formation fluids into the wellbore. As
previously mentioned, the most reliable indicator of a gas kick in the
wellbore is the surface pit gain. However, the pit gain observed for a
given gas kick size will be a function of several variables, one of
which is the type of drilling fluid being used (i.e., water- or
oil-based). Figure 1.2 schematically shows the difference between the
observed pit gain for a gas kick taken while drilling with water- and
oil-based drilling fluids.
When the gas kick enters the wellbore while drilling with a
water-based drilling fluid (Figure 1.2a), the volume of drilling fluid
displaced from the wellbore is proportional to the volume the gas kick
occupies at the pressures and temperatures existing in the well.
However if the gas kick is taken in an oil-based drilling fluid (Figure
1.2b), the volume of drilling fluid displaced from the well is much
less due to gas being more soluble in oil-based drilling fluids than in
water-based drilling fluids. The volume of drilling fluid displaced
from the well in this case is a function of the volume of gas dissolved
in the oil-based drilling fluid and tha swelling of the drilling fluid
due to the dissolved gas at wellbore pressures and temperatures.
As with gas kicks the well response associated with drilled-gas
contamination of the drilling fluid is a function of the drilling fluid
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Mud In
riS
I
m 90 Gas Flows Into Wellbore
(§)G&t Kick exists as Free Gas
d) Pit Gain Equal to Gas Kick Volume at Bottomhole Pressure and Temperature
Gos Sand
(a ) GAS KICK IN W ATER-BASED MUD
Mud InI
0 Gas Flows into Wellbore
0 Gas Dissolves into Oil Mud No initial Free Gas in Wellbore
0 Pit Gain Equal to Swelling of Oil Mud Due to Dissolved Gas
Gos Sond
(b) GAS KICK IN OIL-BASED MUD
Figure 1.2 - Gas Kick Detection In Water-Versus Oil-Based Drilling Fluids.
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type being used. For drilled-gas in water-based drilling fluids (Figure
1.3), the buoyancy of the gas bubbles and the relative insolubility of
the gas in the water causes the gas to migrate up the wellbore. This
migration of the gas causes the concentration of gas per volume of
water-based drilling fluid to be very low and in most cases has no
adverse effect on the drilling process.
For the case where drilled-gas contaminates an oil-based drilling
fluid (Figure 1.4), the solubility of the gas in the drilling fluid
causes the gas to remain concentrated as the gas/oil drilling fluid
mixture is circulated up the well. Once the bubble point depth of the
gas/drilling fluid mixture is reached in the well, the gas will evolve
from the drilling fluid usually very close to the surface. The bubble
point depth is defined as the depth at which the wellbore pressure and
temperature are such that the first bubble of gas appears. A
significant amount of gas and drilling fluid will be spewed out of the
well exposing the drilling rig personnel to hazardous conditions and a
reduction of the bottomhole pressure will occur due to the removal of
drilling fluid from the well which could possibly allow formation fluids
to flow from exposed subsurface formations.
Currently in the petroleum industry, computer models are used to
train field personnel in the proper well control procedures to be used
in the eve-t a gas contaminates the drilling fluid while drilling and
how the well will behave. However, these models are greatly simplified
and in most cases only model gas kicks taken while drilling with
water-based drilling fluids. It is the purpose of this study to extend
existing published data for the solubility of various gases in oils used
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CD■DOQ.CgQ.
■DCD
C/)C/)
DRILLED GAS IN W ATER-BASED MUDS
8■D
CD
3.3"CD
CD■DOQ.CaO3"Oo
CDQ.
■DCD
Mud In
Ir-q
i-
Mud In
\
X D
Gas Send
0 Drilled Gas Enters Well as Bubbles and Migrates up Wsllbore«
Gos Sond
0 Drilled Gae Concentration Substantially Reduced by Bubble Migration.
(D L ittle or No Bottom Hole Pressure Rsduetlsn*
C/)(/)
Figure 1.3 - Drilled-Gas Contamination of Water-Based Drilling Fluids.os
CD"OOQ.CsQ.
"OCDC/)o'3O
8"O(O'
3.3"CD
O"OOQ.CaO3■DO
CDQ.
■DCD(/)(/)
Mud In
t
DRILLED GAS IN O IL-B ASED MUDS
Mud In
1Mud in
i
Gas Sand
0 Drilled Gaa Enters Well and Dissolves Into Oil Mud.
Gas Sand
No Migration.
rc%
*v *
Gas Sand
0 Violant Gao Expanolon noar Surfaea* 0 Bottomhole Prooouro Rodvctlonf
Figure 1.4 - Drilled-Gas Contamination of Oil-Based Drilling Fluids.
in oil-based drilling fluid preparation and an oil-based drilling fluid.
This data will be used to develop models that will allow the expected
well behavior to be predicted when gas contaminates an oil-based
drilling fluid during the drilling process. Models developed will focus
on gas kick detection in oil-based drilling fluids as well as the
effects of drilled-gas dissolved in oil-based drilling fluids on well
behavior.
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CHAPTER II
LITERATURE REVIEW
In 1981, O'Brien first reported the results of a study of well
control problems caused by gas solubility in oil-based drilling fluids.
Although the author made no experimental measurements, he concluded that
at the same pressure and temperature, the solubility of gas in an
oil-based drilling fluid would be 10 to 100 times greater than the
solubility in water-based fluids.
O'Brien also stated that the use of a drilling fluid-gas separator
at the surface where any dissolved gas in an oil-based drilling fluid
could be removed from the drilling fluid would reduce the hazard of any
gas being released on the drilling rig floor. No design criteria as to
the size of the separator required was presented.
In 1984, Thomas, Lea, and Turek presented nine experimentally
measured data points for methane solubility in No. 2 Diesel oil and
three for methane solubility in an unweighted oil-based drilling fluid
all at 100°F. The units used to express gas solubility are standard
cubic feet (SCF) per surface barrel (STB). A summary of the data
presented by the authors is shown in Tables 2.1 and 2.2. In this study
it was shown that methane solubility in the oil-based drilling fluid was
less than the solubility of methane in pure No. 2 Diesel oil. It was
stated that this difference in methane solubilities in the two liquids
was caused by the presence of brine, emulsifier, and solids in the
drilling fluid. Also presented were curves from computer predictions
using the Redlich-Kwong equation of state for methane solubility in No.
2 Diesel oil over a range of temperatures (i.e., 100 to 600°F). These
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10
Table 2.1 - Methane Solubility in No. 2 Diesel Oil at T = 100°F (Thomas, Lea, and Turek)
Pressure, psia Methane Solubility, SCF/STB
805 1261000 1691682 2802065 3442405 4273635 6384820 8505790 1066
Table 2.2 - Methane Solubility in Unweighted Oil-Based Drilling Fluid at T = 100°F (Thomas, Lea, and Turek)
Pressure, psia Methane Solubility, SCF/STB
1555 1672570 3353585 502
Composition of oil-based drilling fluid used:Component Weight Percent
No. 2 Diesel Oil 51.31Calcium-Based Surfactant 2.17Lignite 2.61Slaked Lime 2.61Burite 10.17Kengel (Oil-wetting Bentonite) 0.52NaCl Saturated Brine 30.61
Z = 100.00
Density of oil-based drilling fluid at 14.7 psia and 78°F = 1.0985 gm/cm^.
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11
curves are shown in Figure 2.1. No experimental data was presented
pertaining to the swelling of the base oil or drilling fluid due to the
dissolved methane.
In addition, Thomas, Lea, and Turek addressed the surface responses
(i.e., annular flow rate and pit gain) due to a gas kick taken while
drilling with an oil-based drilling fluid. They did this study with the
aid of a proprietary computer model and concluded that pit gain was the
most reliable indicator of a gas kick m both oil- and water-based
drilling fluids. It is interesting to note that to predict the swelling
of the oil-based drilling fluid due to dissolved gas, the authors used
the Standing correlation which was developed for gas dissolved in
California crude oils.
In a follow-up paper, Thomas and Lea provided further computer
simulation studies for gas kicks taken in both oil- and water-based
drilling fluids. They stated that the well response to a gas kick in an
oil-based drilling fluid is dampened by the solubility of gas in the
drilling fluid. The authors recommended that a consistent procedure for
kick detection based on pit gain measurements be developed.
In 1984, Matthews presented solubility curves for methane, carbon
dioxide, and hydrogen sulfide in No. 2 Diesel oil at 250° F. For
equivalent volumes of the three gases in a mixture at some temperature,
the author concluded that as pressure is decreased, methane would come
out of solution first followed by carbon dioxide and then hydrogen
sulfide. This is to say that hydrogen sulfide is the most soluble gas
of the three gases studied with methane being the least soluble in No. 2
diesel oil. The curves presented in this work are shown in Figure 2.2.
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12
10
8 -
10PRESSURE (MPa)
20 30 40TT - r T
CVICD lOCO lO
B BIL ILo 0o oo o(0 in
îc09r:N
IOCNÎ
50 60T Tiq o>g 2ro lO
ÜJ O
1.81.6
5.4
1.2
I0.80.60 .4
0.2
W
§ = !ë °to -Jë S
w Ul s o
ro ro E Ed 0: H y en û-
2 0 0 0 4 0 0 0 6 0 0 0PRESSURE (psic)
8 0 0 0
Figure 2.1 - Methane Solubility In No. 2 Diesel Oil (Thomas, Lea, and Turek).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
13
PRESSURE (MPa) 20 30 5040
T = 250*F (l2rC)
üJ _l _ILÜ men3 ü J
CMCM
O
0.8 (j) omm 0.6
0.4
0.2
2000 4000 6000PRESSURE (psia)
8000
Figure 2.2 - Carbon Dioxide, Hydrogen Sulfide, and Methane Solubility In No. 2 Diesel Oil (Matthews).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14
Matthews also presented simplified curves for estimating the depth
at which methane, carbon dioxide, and hydrogen sulfide would break out
of solution for various drilling fluid weights. He also advocated the
use of a rotating head to divert gas contaminated drilling fluid from
the rig floor to a drilling fluid-gas separator although no design
criteria was presented.
In 1985, Ekrann and Rommetveit presented an outline for a simulator
for gas kicks in oil-based drilling fluids. Their work dealt primarily
with the numerical solution techniques used in their model and no
results pertaining to the effects of gas solubility in oil-based
drilling fluids on drilling operations were reported.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER III
AN EXPERIMENTAL AND THEORETICAL STÜDY OF METHANE SOLUBILITY IN On.-BASED DRILLING FLUIDS
The author’s research work in the area of well control problems
associated with gas solubility in oil-based drilling fluids began during
the course of completing requirements for the Master of Science Degree
in Petroleum Engineering. This chapter summarizes that work.
3.1 Purpose of Study
The purpose of this study was to extend the existing data
pertaining to methane solubility in oil-based drilling fluids to a wider
range of pressures and temperatures and base oils used in oil-based
drilling fluid preparation than previously presented. More data about
methane solubility in oil-based drilling fluids was desired because it
is the most common gas encountered in the field.
In addition, it vas desired to apply an equation of state to
predict methane solubility in a specified oil-based drilling fluid at a
given pressure and temperature as well as the density of the oil-based
drilling fluid with dissolved methane. The ability to accurately
predict the solubility of methane in oil-based drilling fluids and the
resulting densities would allow models to be developed for predicting
the well behavior to be expected when methane contaminates an oil-based
drilling fluid during drilling.
3.2 Experimental Apparatus and Procedure
The base oils chosen for use in this study were No. 2 Diesel,
Mentor 28, and Conoco LVT oils. The composition of these three oils is
15
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16
shown in Table 3.1. The composition shown for No. 2 Disel oil was
reported by Thomas, Lea, and Turek while the compositions for the Mentor
28 and Conoco LVT oils were obtained from chromatographic analysis. In
addition to the base oils, methane solubility was measured in an
emulsifier used in rll-based drilling fluid preparation and a 13
pound-per-gallon (Ibm/gal) oil-based drilling fluid having a composition
as shown in Tahle 3.2
To measure the solubility of methane in the base oils, emulsifier,
and oil-based drilling fluid, an experimental apparatus was constructed.
Figure 3.1 shows a diagram of the experimental apparatus used. The
system has a 250 cm^ positive displacement pump used to displace mercury
into a blind pressure-volume-temperature (PVT) cell. Mercury is used
for pressurizing the mixture being studied. Pressure is monitored using
a 10,000 psi bourdon tube gauge. The PVT cell is heated with a heating
mantle and heat losses to the atmosphere are minimized by the addition
of extra insulation. The temperature of the system is monitored using a
digital thermometer with a platinum resistance probe placed between the
PVT cell and heating mantle. The PVT cell is mounted on a stand that
allows rotation of the cell during experiments which facilitates
mechanical mixing of the fluids being studied.
After each experiment, a commercial computer model was then used to
calibrate the raw experimental data. The model takes into account the
expansion and compressibility of the PVT cell, pump manifold, and
mercury due to changes in temperature and pressure. The calibrated data
was then plotted as pressure versus volume as shown in Figure 3.2. The
break in the isotherm indicates the bubble point pressure of the
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17
Table 3.1 - Base Oil Molar Compositions
Mole PercentCarbon Number
8 9
10
11
12
13
14
15
16
17
18
19
20 21
22
23
24
Z =
No. 2 Diesel
0.22 0.88 3.79
10.68
13.45
13.73
16.01
15.18
9.10
8.53
4.19
2.40
1.16
0.42
0.12 0.11
+ 0.03
100.00
Mentor 28
1.4187
2.2240
6.0817
10.6920
9.4953
31.8370
28.1870
+ 10.0710
Conoco LVT
1.1736
11.2037
24.1092
16.5396
11.8951
17.6742
15.2455
1.4253
+ 0.7333
100.0000 100.0000
Molecular Weight (Ib/lb-mole)
Density @ 60°F (Ibm/gal)
199.0
6.932
252.0
7.117
177.4
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18
Table 3.2 - Composition of 13 Ibm/gal Oil—Based Drilling Fluid (Salisbury)
Component Volume, cc Weight, gm
Mentor 28 225 -
Lime — 4.5
Primary Emulsifier 12 -
Filtration Agent - 5
Water 50 -
Gelling Agent - 4.5
Secondary Emulsifier 6 -
Calcium Chloride - 23
Barite - 292
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CD"OOQ .CgQ.
"OCD
C/)C/)
8"O
CD
3.3"CD
CD"OOQ.CaO3"OO
CDQ.
"OCD
BURRET
SAMPLEBOTTLES
TEMPERATURE CONTROLLER- + PROBE HIGH
PRESSUREBOTTLESPVT CELL
VACUUMPUMP
MERCURY PUMP
C/)C/)
Figure 3.1 - Experimental Apparatus.
20
2500
2000
COo
s. 1500LÜ(T3COCOLÜg 1000
rm
0 ^
BUBBLE ^ “ POINT PRESSUR500
300 400 500 600SAMPLE VOLUME, cc
Figure 3.2 - Sample Experimental Pressure Versus Volume Plot.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CD"OOQ.CgQ.
"OCD
</)C/)
CD
8"O( O '
CD"OOQ.CaO3"OO
CDQ.
"OCD
(/)(/)
5 1200 jO S.t>*
600
CD 400 3O(/)
wz<XHLÜS
200 -
1000 -O-JUJwWS 800 -aCM6zz
>-
Pressurepsia Thomos et. ol.CurrentStudy
720 130605 126 -
1000 169 -
1220 - 2331475 - 2581682 280 .
2065 3442405 427 -
2545 4673635 6383795 - 6954080 - 8214820 850 -
5790 1066 -
□ Currant Study O Thomos et.ol. T= lOO'F
1000 50002000 3000 4000PRESSURE, psia
Figure 3.3 - Experimental Procedure Verification.
6000
N>
22
500 Pressurepsia
Temperature Methane Solubility degree F s c f/b b i
j O
S 400
COOJ
trO 300 -
LÜs
*-_i 200m3Ow
LÜZ<XI -LÜ
775 100 1261200 100 1901985 too 3172315 100 3712825 too 4 4 3
670 200 851340 200 1751950 200 2652325 2 00 3212660 2 00 377
980 300 1121315 300 1551780 3 00 2132190 300 2732670 300 341
D T = ! 00®FO T = 2 0 0 ‘»FA T =300®F
100 -
1000 2000 PRESSURE , psiG
3 0 0 0
Figure 3.4 - Methane Solubility In Mentor 28 Oil.
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23
400 r Pressure Temperature Methane Sal.psia degree F set/bbl
.o 900 100 83JO I8 6 0 100 188
2 8 0 0 100 315
u 770 200 73(0 1725 2 0 0 159
3215 2 0 0 315Œ 300 7 5 0 3 0 0 63UJ 1745 3 0 0 159ÛZ 3 2 0 0 3 0 0 267
CO D T= IOO®FO 7= 2 00® F
3 A T = 3 0 0 « F
UJ
2 200>K
ffi3w 100wz<UJ
1000 2000PRESSURE, psia
3000 4000
Figure 3.5 - Methane Solubility In Emulsifier.
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24
600 r Pressure Temperature psio degree F
Methane Sol. scf/bbi
500 -jb
o <0O 3sd 400 o
1360 100 1583250 100 3794575 100 5441660 200 1562595 200 2684160 200 4032660 300 2 6 03325 300 3004700 30 0 396
O T = IOO*F0 T = 2 0 0 “ F6 T =300°F
lO
>I -
CD3_lO(0UJz<XI -w
300 -
200 -
<00 -
1000 2 00 0 3000P R E S S U R E , psio
4000 5000
Figure 3.6 - Methane Solubility In 13 Ibm/gal Oil-Based Drilling Fluid.
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25
500 r
400
tu 200
UJ
o MENTOR 28 OIL O 300.000 PPM BRINE A EMULSIFIER
100
40003000200010000P R E S S U R E , psio
Figure 3.7 - Methane Solubility In Mentor 28 Oil, Emulsifier, and Brine (T = 100°F).
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26
500
400
300
aa
oz>I -
CO3_l 200LÜZ<I►-111z
100
METHANE SOLUBILITY, SCF/bbl Pressure No. 2 Diesel Conoco Mentor 28
psio LVT
395 720 775 875 1200 1220
1345 1475 1985
2 0 8 0 2315 2545 2825
□ MENTOR 28 OIL O DIESEL OIL A CONOCO LVT OIL
233
258
67 -
126166 —
- 190
258 -
3174 5 3 —
- 371
443
1000 2000 PRESSURE, psio
3000J
4000
Figure 3.8 - Methane Solubility In No. 2 Diesel, Mentor 28, and Conoco LVT Base Oils (T = 100°F).
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27
mixture. Above the bubble point the mixture is all liquid and below the
bubble point the mixture is both gas and liquid.
Figure 3.3 shows a plot of methane solubility in No. 2 Diesel oil
versus pressure at 100°F for data obtained using the experimental
apparatus and procedures described previously and data published by
Thomas, Lea, and Turek. Note tht both sets of data lay along the same
trend indicating that the experimental procedures of the current study
were correct.
3.3 Experimental Results
Figures 3.4-3.6 summarize the solubility data obtained for methane
dissolved in Mentor 28 oil, emulsifier, and the 13 Ibm/gal oil-based
drilling fluid at 100, 200, and 300°F. Notice that in all figures,
methane solubility in the experimental liquid decreases with increasing
temperature for the range of pressures studied. Also notice that at a
given pressure and temperature, methane is more soluble in the Mentor 28
oil than in the emulsifier and 13 Ibm/gal oil-based drilling fluid.
Figure 3.7 shows a plot of methane solubility in Mentor 28 oil,
emulsifier, and brine which are the only components of an oil-based
drilling fluid in which a gas can dissolve. The solubility of methane
in brine was determined from correlations presented by McCain. Notice
that methane is the most soluble in the Mentor 28 oil followed by
emulsifier and brine. It was concluded, as it was in the study of
Thomas, Lea, and Turek, that brine, emulsifier, and solids in the
drilling fluid reduce the solubility of methane in the drilling fluid by
diluting the base oil volume in a give volume of drilling fluid.
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28
Figure 3.8 shows the solubility of methane in the three base oils
studied at 100°F. Notice that at methane concentrations less than about
200 SCF/STB, methane solubility is not greatly effected by the base oil
type. However at methane concentrations greater than 200 SCF/STB, the
solubility of methane in the base oil is strongly effected by base oil
type.
3.4 Equation of State Modeling
It was shown in this study that methane solubility in an oil-based
drilling fluid is controlled by the volume fractions of base oil, brine,
and emulsifier in the drilling fluid. However, since the volume of
emulsifier in a drilling fluid is small and its volume fraction in the
drilling fluid difficult to determine, it can be neglected for the
purposes of calculating the solubility of methane in an oil-based
drilling fluid.
The solubility of methane in an oil-based drilling fluid can
accurately be determined at a given pressure and temperature by,
R = f R + f R .............................(3.1)sm o so w swwhere R is the solubility of methane in the drilling fluid, basesm,o,woil, and water in SCF/STB and f is the volume fraction of oil ando,wwater in the drilling fluid.
The Peng-Robinson equation of state (PREOS) was used to predict the
solubility of methane in the base oil Table 3.3 shows a comparison of
experimentally measured and predicted methane solubilities in Mentor 28
base oil at 100, 200, and 300®F. The solubility of methane in water was
determined from correlations presented by McCain.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
29
Table 3.3 - Experimentally Measured Versus PREOS Predicted Methane Solubility in Mentor 28 Oil
Methane Solubility, SCF/STB Pressure, psia T = 100 F 200 F 300 F
775 126 (114)1200 190 (184)1985 317 (329)2315 371 (397)2825 443 (510)670 - 85 (78)1340 - 175 (167)1950 - 265 (260)2325 - 321 (324)2660 - 377 (386)980 - - 112 (107)1315 - - 155 (150)1780 - - 213 (214)2190 - - 273 (278)2670 - - 341 (363)
( ) - PREOS Predicted Methane Solubility
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30
Table 3.4 shows a comparison of experimentally measured and
predicted methane solubilities in the 13 Ibm/gal oil-based drilling
fluid used in this study.
The PREOS was also used to predict the density of methane/oil-based
drilling fluid mixtures. Figure 3.9 shows a comparison of
experimentally measured versus predicted single— and two-phase densities
for a mixture of 379 SCF of methane and one STB of 13 Ibm/gal oil-based
drilling fluid. Notice that the PREOS predicts densities less than
those experimentally measured. This is commonly reported in the
literature when the PREOS is used.
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31
TABLE 3.4 — Experimentally Measured Versus PREOS Predicted Methane Solubility in 13 Ibm/gal Oil-based Drilling Fluid
Methane Solubility, SCF/STB Pressure, psia T = 100°F 200°F 300°F
1360 158 (138)
3250 379 (398)
4575 544 (666)
1660 - 156 (140)
2595 - 258 (243)
4160 - 403 (485)
2660 - - 206 (234)
3325 - - 300 (325)
( ) - PREOS Predicted Methane Solubility
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I32
6 0 0 0
5 0 0 0
4 0 0 0
<AO.w(r3COU)wccCL
3 0 0 0 -
2000
1000
3 79 SCF Methane/bbI Oil Mud = 13 lb/go!
T = IOO®F * — Bubble Point □ — Experimentol A — Computer Predicted ^ .
_L _L9 II
DENSITY, Ib/gol13
Figure 3.9 - Pressure Versus Density For Methane/13-lbm/gal Oil-Based Drilling Fluid Mixture.
rReproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER IV
The ultimate goal of this work is to study the effects of gas
solubility in oil-based drilling fluids on the drilling process.
Although methane is the most common gas encountered during drilling it
is not the only gas present. Further data is needed for the solubility
of other gases in base oils and oil-based drilling fluids before
definitve conclusions can be made. In this chapter, a summary of
additional measurements of the solubility of ethane, carbon dioxide, and
a natural gas mixture in Mentor 28 oil and a 13 Ibm/gal oil-based
drilling fluid will be presented.
4.1 Experimental Apparatus and Procedure
As mentioned previously, the base oil used was Mentor 28 oil. The
13 Ibm/gal oil-based drilling fluid had a composition as shown in Table
3.2. The composition of the natural gas used is shown in Table 4.1.
Measurements of gas solubility in the base oil and drilling fluid
were made at 100, 200, and 300°F using the apparatus and procedures
outlined in Chapter III.
4.2 Experimental Results
Figures 4.1-4.6 summarize the data obtained from these gas
solubility experiments. Notice that in all of the figures, as
pressure is increased the solubility of the gas in the oil and drilling
33
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34
Table 4.1 - Natural Gas Composition
Component Mole Percent
Nitrogen 0.28
Carbon Dioxide 0.89
Methane 90.18
Ethane 4.84
Propane 2.05
i-Butane 0.49
n-Butane 0.53
i-Pentane 0.23
n-Pentane 0.15
Hexanes 0.14
Heptanes + 0.22
Z = 100.00
Natural Gas Specific Gravity = 0.62
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35
6 0 0 r
Pressure Temperature Ethane Sol. psia degree F scf/bbi2 40 100 121360 100 2474 50 100 3 6 8575 100 5 0 56 10 100 681
2 05 200 794 5 0 2 00 1546 5 0 2 0 0 2357 0 0 2 0 0 331
1050 2 0 0 443
290 300 1037 3 0 300 154840 3 00 2 66
1055 300 3551180 3 0 0 4 3 3
-2 r = too®O T = 2 0 0 "A T = 300®
5 0 0 1000
PRESSURE, psIa1500
Figure 4.1 - Ethane Solubility In Mentor 28 Base Oil.
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36
300 rjaJO
o(A
O3S
O 2 00 -ocr
fO
100 -
m
ocoUJ
<XHLÜ
Pressuri Ttmptrature Ethane Soi.psio degree F sef/bbi2 0 9 100 8 63 7 0 100 1755 5 5 100 2 8 3
2 4 3 2 0 0 754 0 3 2 0 0 1395 5 9 2 0 0 207
169 3 0 0 36362 3 0 0 85621 3 0 0 144
O T = IO O * F O T = 2 0 0 *F A T = 3 0 0 * F
5 0 0 1000
PRESSURE , psia1500
Figure 4.2 - Ethane Solubility In 13 Ibm/gal Oil-Based Drilling Fluid.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
37
3000r Pressure Temperature Carbon Dioxide Sol.
- 2500
CO CMg 2000gzUJs
psio degree F s c f / l725 100 3 6 7
1030 100 7 8 91140 100 12971200 100 17941295 100 2839
270 200 1067 7 0 2 0 0 2 60
1080 2 00 4 2 51240 2 0 0 5 4 01420 200 7056 00 300 141
1140 3 0 0 3 031400 300 418I8 6 0 3 0 0 5 0 91910 3 0 0 659
c T = IOO»Fo T = 2 0 0 “ F4 T = 300®F
m3_JOC/5
1500 -
O 1000 §
Om(T<Ü 500 -
500 1000PRESSURE , psia
1500 2000
Figure 4.3 - Carbon Dioxide Solubility In Mentor 28 Base Oil.
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38
400 r Pressure Tëmperefure Corbon Dioxide psia degree F Sol.,scf/bbl
aao(A
O3z-I 300 -
260 too 61585 100 162700 100 219430 200 68900 200 15 1
1100 200 245590 300 84900 300 139
1400 300 379
O T= IOO®FO T= 200 °FA T = 300°F
200 ->i—
003_jOWUJO 100Xo
zomoc<u
1000 2000 PRESSURE, psia
3000
Figure 4.4 - Carbon Dioxide Solubility In 13 Ibm/gal Oil-Based Drilling Fluid.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
_ 800 A
o(0
Pressure Temperoture Noturol Gas Sol. psio degree F s c f/b b i
600 -O00CM
(rezUJ
— 400 >-
CD
3oCO
CO<CO
6 2 5 100 1161040 100 1881775 100 3092 7 5 0 100 4 9 737 1 0 100 698
810 200 1281440 200 2051990 200 3032500 200 4 3 33475 20 0 616
8 0 0 300 9 31580 300 1972310 3 0 0 3163 030 300 4613 8 0 0 30 0 6 3 2
D T = IOO»F0 T = 2 0 0 ° F4 T = 3 0 0 ° F
200
<a:3
1000 2000PRESSURE . psia
3000 4000
Figure 4.5 - Natural Gas Mixture Solubility In Mentor 28 Base Oil.
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40
_ 4 0 0 r
o(A
O32UO"5
2ro
PressurepsioI I I O
2080 3115
Temperature degree F
100100!00
Noturol Gos Sol scf/bbl
3 0 0 -
1090 2001900 2002 6 0 0 200
1025 3001800 3002735 300
O T = :00»F o T = 200"F A T = 3 0 0 "F
Z 2 0 0 -
>-H_iCO3_jOV)CO<o
<oc3
1000 2000 PRESSURE, psio
3 0 0 0 4 0 0 0
Figure 4.6 - Natural Gas Mixture Solubility In 13 Ibm/gal Oil-Based Drilling Fluid.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
fluid increases and as temperature is increased gas solubility decreases
at constant pressure.
Figure 4.7 shows a plot of gas solubility versus pressure for
methane, ethane, carbon dioxide, and the natural gas mixture dissolved
in Mentor 28 oil at 100*F. Notice that ethane is the most soluble while
methane is the least soluble in the base oil of the four gases. For
hydrocarbon gases the solubility of the gas increases with increasing
gas specific gravity. It can further be concluded that for a mixture of
equal parts of methane, ethane, and carbon dioxide dissolved in the base
oil at constant temperature, as the pressure is decreased, methane would
break out of solution first followed by carbon dioxide, and then ethane.
4.3 Solubility of Other Gases
From the results of the solubility experiments, it was concluded
that it would not be practical to measure the solubility of hydrocarbon
gases heavier than ethane (i.e., propane, n-butane, etc.) in base oil
and drilling fluid. This is because ethane is very soluble in base oils
and drilling fluids, and as previously shown an increase in hydrocarbon
specific gravity increases gas solubility at constant pressure and
temperature.
For most conditions existing in a wellbore, hydrocarbon gases
heavier than ethane will not breakout of solution, if at all, until the
gas contaminated drilling fluid has reached the surface. It can
therefore be reasonably assumed that the effects of hydrocarbon gases
heavier than ethane, in terms of existing in the well as a free gas
phase, is negligible and these gases can be assumed to exist as solution
gas.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42
800r
u(0_ J
GO
ITO&—ZbJZ 400 z
CD 3 200 C| (SPGR=.55)
N GAS(SPGR*.64) 02 (SPGR=I.058Î CO2 (SPGR= 1.518)
OV)CO<CD
40003000200010000PRESSURE, psio
Figure 4.7 - Gas Solubility In Mentor 28 Base Oil (T = 100“F).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
43
Hydrogen sulfide solubility was not measured due to the high
toxicity of this gas. However, it is recommended that this gas be
studied, if the proper facilities are available, because this gas is
common in deep hot well.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER V
GAS SOLUBIILTY APPROXIMATION
In Chapter III an equation of state model was outlined for
predicting the solubility of methane in an oil-based drilling fluid.
However, considerable computer time (1 computer processing unit minute
per 11 data points) is required to solve for methane solubility in a
drilling fluid at a given pressure and temperature. Any increase in the
number of components in the gas to be mixed with the oil-based drilling
fluid will increase the ratio of computer-time-required-to-solve-for-
the-gas-solubility-to-number-of-data-points. As pointed out previously,
it is the obj ective of this study to determine the effects of gas
contamination of an oil-based drilling fluid on the drilling process.
To satisfy this objective, a model requiring the calculation of the
solubility of a gas in an oil-based drilling fluid quickly and
accurately will be needed. Also, a method for predicting gas solubility
in an oil-based drilling fluid which is easy to use yet accurate will
aid in the training of field personnel as to how much gas could go into
solution for given well conditions.
It is the purpose of this chapter to summarize a method for
approximating the solubility of a gas mixture containing methane,
ethane, and carbon dioxide in an oil-based drilling fluid. The method
will allow quick, direct calculations of the solubility of a gas mixture
containing these components in an oil drilling fluid based on
experimental observations.
44
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45
5.1 Solubility of Gas in Base Oil
From the results of the experimental studies previously discussed,
the following empirical equation for predicting the solubility of
methane, ethane, and carbon dioxide in a base oil was developed,
+ cl' « • »
where is the gas solubility in the base oil in SCF/STB, P is the
pressure in psia, T the temperature in °F, and a, b, c, and n constants
determined from Table 5.1.
Equation 5.1 also takes into account the variations of methane
solubility in base oil due. to base oil composition which was pointed out
in Chapter III. The trend observed for variations of methane solubility
in base oils of differing composition was used in accounting for
variations of ethane solubility in different base oil types since both
methane and ethane are hydrocarbon gases and no data existed for ethane
solubility in different base oils. No adjustment of carbon dioxide
solubility variation due to base oil composition was made since no such
data was generated and carbon dioxide is not a hydrocarbon gas.
Equation 5.1 is valid for carbon dioxide solubility in Mentor 28 base
oil only.
It should be pointed out that the inverse proportionality of
methane solubility to temperature is based on experimental observations
made over the range of pressures and temperatures studied. However,
the curves of Figure 2.1 presented by Thomas, Lea, and Turek indicate
that at high pressures this observation reverses and methane solubility
increases with increasing temperature. This behavior is calculated at
pressures near and above the cricondenbar in the single phase region
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46
Table 5.1 - Empirical Correlation Constants.
Gas Type a b c______________________ n________Methane 1.922 0.2552 4.94 e(-00081P+.00177T) q .8922 y
o-.7521Ethane 0.033 0.8041 0 0.8878 y^
Dioxide 0.059 0.7134 0.3352e^’°^°^^“'°^^^'^ 1.0
where, T = temperature, “F
P = pressure, psia
y^ = base oil specific gravity
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
where methane and oil are miscible in all proportions. Equation 5.1
takes this phenomena into account.
To calculate the solubility of a gas mixture containing methane,
ethane, and carbon dioxide in a base oil, in SCF/STB, the following
equation is used,
so " ^sCg^Cg ^sCOg^COg.............
where f is the volume fraction of methane (Cj), ethane (Cg), and carbon
dioxide (COg) in the gas mixture and R^ for each gas component is
determined by equation 5.1.
5.2 Solubility of Gas in Water
For most cases, the solubility of gas in the internal water phase
of an oil-based drilling fluid can be neglected because of the small
contribution made to the overall solubility of a gas in the drilling
fluid. However, if it is desired to account for gas solubility in the
water phase, R ^ in SCF/STB, it can be calculated as,
^sw " \Cj^Cj ^sCg^Cg ^sC02^C02............
where f is the volume fraction of methane (C^), ethane (Cg) and carbon
dioxide (COg) in the gas mixture and R^ the solubility of each component
in water determined from Figures 5.1 and 5.2, and corrected for water
salinity using Figures 5,3 and 5.4. For convenience these figures have
been fitted to equations shown in Table 5.2.
A correlation of ethane solubility in water was not found in the
literature and since the solubility of a hydrocarbon gas in water is
small, it is assumed that the solubilities of methane and ethane in
water are equivalent.
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48
teLJ 64
56UJ
48
-X
24U.
- 1,000
- 600- r 200 r
O 60 ICO 140 180 220 260 300 340TEMPERATURE (*F )
Figure 5.1 - Methane Solubility In Pure Water (McCain).
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!(D
IOOZ;I
f5
awf,ord. et.
«sV)
50
UJZq:es
CO<o_J<(TIDH<l l
O
OS3OCO
w 1.00Q90 -0.80 -
0.70 -
020 -
O 0.15 CO 0 10 20 30TOTAL DISSOLVED SOLIDS (%)
Figure 5.3 - Water Salinity Correction For Methane Solubility In Water (McCain).
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51
I O r
0.9
35,000 PPM
100,000 PPM
% 0.7
0.6
Uioc 0 5
2 0 0 ,0 0 0 PPM
0.4
0.370005 0 0 0 6 0 0 01000 2 0 0 0 3 0 0 0 4 0 0 0
PRESSURE, psio
Figure 5.4 - Water Salinity Correction For Carbon Dioxide Solubility In Water (Crawford, et. al.).
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52
Table 5.2 - Gas Solubility In Water Curve Fits.
Carbon Dioxide:2 3Rsco = (A + BP + CP + DP ) X Salinity Correction
A = 95.08 - .931 + 2.28E - 03T^
B = 0.1626 - 4.025E - 04T + 2.5E - 07T^
C = -2.62E - 05 - 5.39E - 08T + 5.13E - lOT^
D = 1.39E - 09 + 5.94E - 12T - 3.61E - 141^
Salinity Correction = .92 - .0229 % Solids
Hydrocarbon Gas:
^sHC ~ (A + BT + CT^) X Salinity Correction
A = 5.5601 + 8.49E - 03P - 3.06E - 07P^
B = -0.03484 - 4.0E - 05P
C = 6.0E - 05 + 1.5102E - 07P
Salinity Correction = EXP[(-.06 + 6.69E - 05T)
X (% Solids)]
where, P = pressure, psia
T = temperature, ®F
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53
P
5.3 Solubility of Gas in Oil-Based Drilling Fluids
For a given drilling fluid volume, the relative volumes of base oil
and water in the drilling fluid can be determined from a standard retort
analysis. Once the volume fractions of and the solubility of the gas in
the oil and water in the drilling fluid are known, the solubility of a
gas in the oil-based drilling fluid can be determined by Equation 3.1.
5.4 Experimental Verification of the Correlation
Using an iterative calculation procedure, the bubble point
pressures of the natural gas/13-lbm/gal oil-based drilling fluid mixture
studied in Chapter IV were predicted using the equations developed in
this chapter. The predicted bubble point pressures were compared with
the experimentally measured bubble point pressures. The results are
shown in Table 5.3. An average error of -0.5% was obtained indicating
good agreement between the predicted and measured bubble point pressures
for the data compared.
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54
Table 5.3 - Experimentally Measured Versus Predicted Bubble Point Pressure For Natural Gas/13-lbm/gal Oil-Based Drilling Fluid.
Natural Gas Bubble Point Pressure, psiaSolubility, SCF/STB T, °F Measured Predicted Error, %
125 100 1110 1105 - .45248 100 2080 2187 +5.14346 100 3115 2968 -4.72
102 200 1090 1037 —4.86190 200 1900 1933 +1.74282 200 2600 2771 +6.58
84 300 1025 906 -13.13172 300 1800 1866 +3.67268 300 2735 2773 +1.39
Average % Error = -0.5
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CHAPTER VI
GAS MISCIBILITY
In this chapter the concept of gas miscibility will be introduced
as it relates to the behavior of a gas kick taken while drilling with an
oil-based drilling fluid under certain well conditions. Although the
conclusions of this chapter are not based on the experimental
observations of this study, they will provide a basis from which further
studies into this complex phase behavior phenomena can be extrapolated.
For the purposes of this discussion methane and No. 2 Diesel oil will be
considered since published data in the miscible region exists for this
mixture.
6.1 First Contact Miscibility
Stalkup defines a fluid that is "first contact miscible" as being a
fluid that will mix directly with an oil in all proportions and that
their mixtures will remain single phase. For this to occur, the fluid
and oil mixture must be exposed to pressures above the cricondenbar, as
determined from a Pressure-Composition (P-X) diagram for the fluid and
oil mixture (Figure 6.1). Methane is a gas that is first contact
miscible with an oil.
6.2 Methane Miscibility with No. 2 Diesel Oil
From Figure 2.1, the miscibility pressure as a function of
temperature can be determined for methane and No. 2 Diesel oil. The
miscibility pressure is represented by the pressure at which the curves
of Figure 2.1 become vertical indicating infinite methane solubility in
55 ■
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56
(OQ.
UJa:3COcoLUû:CL
Gos Miscible in Ail Proportions with Oil Cricondenbar
Pressure
Single- Phose Region
Ploit^ Point
Tw o-Phose Envelope
MOLE FRACTION OF GAS IN GAS-OIL MIXTURE
Figure 6.1 - Pressure-Composition Diagram.
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57
No. 2 Diesel oil. Figure 6.2 shows a plot of miscibility pressure
versus temperature for this mixture as determined from Figure 2.1.
A better understanding of this phenomena as it relates to the
wellbore can be obtained from Figure 6.3 which shows the locus of
cricondenbars for a mixture of methane and No. 2 Diesel oil. If a
methane kick enters the wellbore at point (P^, T^), the methane will
exist as a gas and dissolve into a diesel oil-based drilling fluid.
However, if a methane kick enters the wellbore at point (P,, T^), the
methane will exist as a miscible fluid because the mixture is above the
cricondenbar pressure and will mix in all proportions with the drilling
fluid.
Figure 6.4 represents the pit gain to be expected per thousand
standard cubic feet (MSCF) of a methane kick versus depth for a well
having a depth of 15,000 feet. The drilling fluid is a 15.5 Ibm/gal,
diesel oil-based drilling fluid having an oil-water ratio of 80:20. A
comparison is made between the oil-based drilling fluid and a
water-based one. Point A represents the transition from a miscible
fluid to a gas for the oil-based drilling fluid case. Notice that at
depths greater than 10,000 feet the pit gain resulting from the methane
kick in the oil-based drilling fluid is essentially the same as a
methane kick in a water-based drilling fluid when little or no natural
mixing takes place. However, at depths less than 10,000 feet the
methane will go into solution and the pit gain in the oil-based drilling
fluid case is less than the water-based drilling fluid. If the methane
mixed with the oil-based drilling fluid to give a gas-drilling fluid
ratio of 1000 SCF/STB, the methane would break out of solution at point
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58
I0 0 0 0 r
UJ 8000
6000
O 4000
2000
300 400 500TEMPERATURE, *F
600
Figure 6.2 - Methane/No. 2 Diesel Oil Miscibility Pressures Versus Temperature.
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59
Locus of Cricondenbors * Critical Points10000r
8 0 0 0
Q. 6 0 0 0
W 4 0 0 0
2000
NO. 2 Diesel Oil^^y/^Nethone800200 4 0 0 6 0 00-200
TE M P E R A TU R E . »F
Figure 6.3 - Locus of Cricondenbars For Methane and No. 2 Diesel Oil.
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CD■DOQ .CgQ .
’f
■DCD
C/)C/)
8■D
3.3"CD
CD■DOQ .CaO3"Oo
CDQ .
■DCD
C/)C/)
PIT GAIN PER MSCF OF METHANE KICK VOLUME, BBL
1 2 3 4
5000 -
XHO.uo
CIRCULATING TEMPERATURE,®F 0 100 200
10,000 -
OIL-BASED MUD WATER-BASED MUD
KICK SIZE : 1000 SCF ® 15.5 LB/GAL
♦ b a s e o il » No. 2 DIESEL OIL-WATER RATIO « 8 0 : 20 3 0 0 ,0 0 0 ppm CoClg BRINE
15,000*-
Figure 6.4 - Pit Gain Per 1000 SCF Methane Kick In Oil- and Water-Based Drilling Fluids. ONO
61
B. If on the other hand, the gas-drilling fluid ratio was only 100
SCF/STB, the methane would not break out of solution until point C was
reached.
6.3 Effects of Other Gases On Methane Miscibility
Stalkup states that hydrocarbon gases heavier than methane mixed
with oil will have a lower miscibility pressure than methane. It can be
concluded that any addition of hydrocarbon gases heavier than methane to
pure methane will lower the pressure at which the gas mixture will
become miscible with a diesel oil-based drilling fluid below the
miscibility pressure of mixtures of pure methane and diesel oil-based
drilling fluids.
6.4 Field Application
For field applications, the miscibility pressure for pure methane
and No. 2 Diesel oil-based drilling fluids will be the highest pressures
above which gas miscibility in a wellbore can exist. Using American
Petroleum Institute (API) charts (Western Engineers Handbook) for
estimating the average bottomhole circulating temperature as a function
of the geothermal gradient and assuming an incompressibile oil-based
drilling fluid, the maximum depth above which gas miscibility in a
wellbore as a function of diesel drilling fluid density can be
determined.
First, the depth at which an assumed circulating temperature exists
for a given geothermal gradient can be determined from the regression
equations for the API circulating temperature charts as shown in Table
6.1. Next, the methane/diesel miscibility pressure corresponding to the
assumed temperature is determined from Figure 6.2. The drilling fluid
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62
Table 6.1 - API Average Bottomhole Circulating Temperature
SECT = A X EXP(B x D)
where, BHCT = Bottomhole Circulating Temperature, °F
D = Depth, ft
A = 109.28 - 40.44 + 11.83
B = 5.48E - 05
G^ = Geothermal Gradient, °F/100 feet
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63
density corresponding to the depth and methane/diesel miscibility
pressure is calculated as,
- W - 0 5 2 0 ..................................where is the drilling fluid density in Ibm/gal, is the
methane/diesel miscibility pressure in psi, and D is the depth
corresponding to the assumed temperature in feet.
Figure 6.5 shows a plot of methane miscibility depth versus No. 2
Diesel oil-based drilling fluid density for a range of geothermal
gradients. These curves represent the upper limit above which gas
miscibility can exist in a wellbore.
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64
15000
14000
12000
% 13000h~Q.W0>- H
müen2 II 0 0 0
UJz<1l- 10000 ÜJ
9000
8000 _L9 II 13 15 17 19NO. 2 DIESEL OIL-BASED DRILLING FLUID DENSITY
lb /gal
Figure 6.5 - Methane Miscibility Depth Versus No. 2 Diesel Oil-Based Drilling Fluid Density.
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CHAPTER VII
SWELLING OF OIL-BASED DRILLING FLUIDS DUE TO DISSOLVED GAS
In this chapter, a method is presented for estimating the swelling
of oil-based drilling fluids due to dissolved gas. Ths method can be
applied both (1) when the gas is fully miscible with the drilling fluid,
and downhole mixing is limited and (2) when gas initially contacts the
drilling fluid in volumes above the solution gas-drilling fluid ratio,
and mixing is enhanced by the initial development of gas bubbles.
Experimental PVT data were used to verify the calculation method
presented for a range of compositions and pressures at 100°F. The
method was also verified by experiments in a 6000-foot test well.
Examples are presented showing typical computed values for swelling
volumes at various depths, drilling fluid densities, and gas
concentrations. Pit gain comparisons are made with water-base drilling
fluids for a wide range of conditions. These examples illustrate
situations in which it is difficult to detect a gas kick in an oil-based
drilling fluid.
In addition to determining the amount of the dissolved gas present
in a given field situation, the method can also be used to determine the
sensitivity requirements of kick-detection equipment for any specified
hole geometry. The method applies to both surface and subsurface
kick-detection equipment.
7.1 Oil Swelling Calculations
The Peng-Robinson equation of state model described in Chapter III
was used to calculate the swelling of base oil due to dissolved gas.
65
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66
The equations used are presented in Appendix A. Critical pressures,
critical temperatures, and acentric factors, needed for the equation of
state model, are shown in Table 7.1 for carbon numbers typically found
in base oils commonly used in oil-based drilling fluid preparation.
In order to calibrate the equation of state model, the use of an
adjusted molecular weight for the gas-free oil phase was found to be
necessary. The value, G that must be added to the gas-free oil phase
molecular weight is determined as,
G = 26.41 - 1.607E -02 R + I.641E - 07 R ^___ (7.1)so sowhere R^^ is the solution gas-base oil ratio in SCF/STB. Equation 7.1
was obtained empirically based on experimental data. Use of an adjusted
average molecular weight for the base oil was found to decrease the
error in the calculation of subsurface oil-phase swelling from about 10%
to less than 1%. Shown in Table 1-2 is a comparison of equation of
state calculations to experimentally obtained PVT data for methane and
No. 2 Diesel oil mixtures.
7.2 Pit Gain Calculations
The pit gain associated with a given standard volume of gas is
typically less in an oil-based drilling fluid than in a water-based
drilling fluid because the gas occupies less volume in solution than in
a free-gas phase. A closer average molecular spacing is permitted
because of high forces of attraction between the molecules of the gas
phase and the oil phase. The pit gain in an oil-based drilling fluid
also depends on the volume of drilling fluid in which the gas is mixed.
The volume of drilling fluid displaced from the well by a given standard
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67
Table 7.1 - Base Oil Critical Properties
Carbon AcentricNo. Tc, °R Pc, psia Factor
8 1007.5 381.8 .3329 1049.9 350.4 .37310 1090.8 326.4 .41111 1125.4 304.7 .44812 1156.7 285.4 .48413 1185.7 268.1 .51814 1212.4 253.4 .55115 1237.7 244.4 .58216 1261.6 227.1 .61217 1283.2 216.4 .64118 1303.9 207.1 . 66819 1323.5 197.7 .69420 1342.2 190.7 .71921 1360.7 182.4 .74422 1378.7 175.4 .76723 1395.3 169.0 .78924 1410.6 163.0 .81125 1426.5 157.0 .832
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68
Table 7.2 - Comparison of Experimentally Measured and Computed Values of Volume Factor, Bo, for Methane in No. 2 Diesel Oil at 100°F
Gas-OilRatio
(SCF/STB)Pressure(psia)
Molecular Weight Correction
(G)_______
ExperimentalBo
(bbl/STB)
PredictedBo
(bbl/STB)
3320377547054940
26.2 .993.991.987.986
.993
.991
.987
.986
234 12251585220
23.0 1.0701.0601.053
1.0641.0601.054
259 1475212526903365
22.5 1.0691.0541.0491.045
1.0701.0631.0581.052
467 254526253710
18.5 1.1371.1271.117
1.1311.1301.119
695 3825412046605305
15.2 1.1971.1911.1861.182
1.1991,1951.1891.182
821 4075426544905070
13.5 1.2541.2431.2331.225
1.2461.2431.2401.230
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69
volume of gas tends to decrease as the volume of drilling fluid in which
it is dissolved increases.
When a kick is taken, the volume of drilling fluid that the gas
contacts is controlled to a great extent by the rate at which drilling
fluid is being circulated past the bit (Figure 7.1). The initial
gas-drilling fluid ratio, in SCF/STB, when the kick is being taken
can be computed using,
V i " % .......................................
where is the gas flow rate from the formation in SCF per minute
(SCF/min) and is the circulation rate of the pump in STB per minute
(STB/min). If this initial gas-drilling fluid ratio is less than the
solution gas-drilling fluid ratio for existing bottomhole conditions,
then little additional mixing will take place as the gas goes into
solution. However, if the initial gas-drilling fluid ratio is greater
than the solution gas-drilling fluid ratio, then free-gas bubbles will
tend to rise into the previously uncontacted drilling fluid above and go
into solution (Figure 7.1). Natural mixing due to bubble rise will
cause new drilling fluid to be contacted until the gas-drilling fluid
ratio is approximately equal to the solution gas-drilling fluid ratio.
The pit gain volume in barrels per 1000 SCF of gas kick, V^, can be
estimated using,
' ' g ’ 5 ^ ' V V V > ............................................................(7 -3 )
where f is the volume fraction of the oil in the drilling fluid, B and o oB are the volume factors of the oil-phase without and saturated with oggas in volume per surface volume, and R^^ is the gas-drilling fluid
ratio in SCF/STB.
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70
MUDCIRCULATION
PITGAIN
FREE GAS BUBBLES WILL RISE AND CAUSE NATURAL MIXING
FORCED MIXING DUE TO MUD CIRCULATION
GAS FLOW
Figure 7.1 - Gas/Oil-Based Drilling Fluid Downhole Mixing.
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71
The volume factors can be determined for any gas mixture and base oil
using the Peng-Robinson equation of state model as outlined in Appendix
A. Equation 7.3 neglects the solubility of the gas in the water phase
due to the small effect the swelling of water saturated with gas has on
the overall pit gain.
The pit gain calculation procedure was tested by conducting two gas
kick experiments in a 6000 foot well. Appendix B summarizes the
experimental procedures, facilities used, and the conditions of each
experiment. A comparison of the observed and predicted pit gains for
each experiment is shown in Table 7.3. Note that good agreement between
the predicted and observed pit gains for both experiments was attained.
7.3 Field Application
As stated in previous chapters, most natural gas kicks are
predominantly methane in composition. In order to develop a method that
will allow field personnel to estimate the pit gain to be expected for a
given gas kick volume, the equation of state model outlined in Appendix
A and the gas solubility correlation presented in Chapter V were used to
generate Figures 7.2-7.5 which show No. 2 Diesel oil swelling as a
function of pressure, temperature, and methane solubility in the base
oil. Using these curves along with Equation 7.3, the pit gain to be
expected for a given kick volume can be estimated. Although the curves
were generated for No. 2 Diesel oil, they also provide a close
approximation for other base-oils when used in conjunction with equation
7.3 since this equation is sensitive only to the change in volume
factors caused by the dissolved gas.
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72
Table 7.3 - Comparison of Experimentally Measured and Predicted Pit Gains in 6000 ft. Experimental Well
Gas-Mud Mud Flow Measured Pit Predicted Pit Kick Size Ratio Rate Gain Gain
Experiment (SCF) (SCF/STB) (Gal/min) (bbl) (bbl)
1 4978 185 81.9 1.20 1.13
2 8132 178 119.7 2.20 1.96
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CD■DI8Û.
■DCD
C/)(go"3
CD
8■DC5-
3CD
C3.
CD"OSÛ.CaO3T33
(DQ .
OC
"OCD
mI— if)
CDCD
Om
oo
<ü
Eo>
1.400 deg F No. 2 Diesel
MethaneOilGas
1.3
1.2
800
600.1
400
200G
Miscibility Pressure
0.9 18 2 014 164 6 8Pressure, (1000's psia)
121020
Figure 7.2 - No. 2 Diesel Oil Swelling Due to Dissolved Methane (T = 100°F). •vjw
74
a > ( N £
l - O O
815/188 O p D Ja i u n i o A
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CD■DOQ.CgQ.
■DCD
C/)C/)
8■D
CD
3.3"CD
CD■DOQ.CaO3"OO
CDQ.
■DCD
C / )C / )
1.4 rm
(/)T = 3 0 0 deg F Oil = No. 2 Diesel Cas = Methane
—I 1.3 -æCD
m 1.2 -
0)
E 1.0o>
0.9
Miscibility Pressure
J I I I I I L j I4 6 8 10 12 14 16Pressure, (1000's psia)
18 20
Figure 7.4 - No. 2 Diesel Oil Swelling Due to Dissolved Methane (T = 300®F).Ln
■oâgÛ.
" OCD
C/)C/)
5'3
CD
85(5'
i3CD
C§CD
CD-OOQ .
O3
O3"
8.
OC■oCD
(/)o"3
T = 4 0 0 deg F Oil = No. 2 Diesel Cas = Methane
Miscibility Pressure
Figure 7.5
4 6 8 10 12 14 16P r e s s u r e , (1000‘s p s ia )
No, 2 Diesel Oil Swelling Due to Dissolved Methane (T = 400°F) o>
77
7.4 Example Calculations
The use of Figures 7.2-7.5 for simplified pit gain estimations is
best illustrated using examples. Three examples will be discussed. The
first example illustrates a situation in which gas initially contacts
the drilling fluid in concentrations below the allowable gas solubility.
The second example illustrates a situation in which gas initially
contacts the drilling fluid in concentrations above the allowable gas
solubility, and natural mixing will occur due to the rise of gas
bubbles. The third example illustrates a situation in which the gas and
drilling fluid are miscible in all proportions, and natural mixing due
to rise of gas bubbles cannot occur.
Example #1:
A 17.5-in. hole is being drilled at a depth of 4000 ft when gas
begins to enter the well on bottom at a rate of 2000 SCF/min. The 9.0
Ibm/gal drilling fluid has an oil volume fraction of 0.76, a water
fraction of 0.19, and a solids fraction of 0.05 and is being circulated
at 20 STB/min. At the bottomhole pressure of 1900 psia and the
bottomhole temperature of 100*F, the gas deviation factor is 0.85.
Estimate the pit gain expected per 1000 SCF of gas which enters the
borehole.
Solution - Using Eqn. (7.2), the initial gas-drilling fluid mixture is
2000/20 = 100 SCF/STB.
Since the volume fraction of oil is 0.76, the initial gas-oil ratio is
(100/0.76) = 132 SCF/STB.
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78
Entering Figure 7.2 at 1900 psia, it can be seen that the solubility of
the gas in the base oil is 300 SCF/STB (value of solution gas at bubble
point curve), which is more than the gas-drilling fluid ratio. Thus,
all of the gas can go into solution in the oil. Also from Figure 7.2,
the volume factor of the gas-free oil is 1.005, and the volume factor of
the 132 SCF/STB gas-oil solution is 1.037. Using these values in
Equation 7.3 yields
1000/100 [0.76 (1.037-1.005)] = 0.24 STB/1000 SCF or4.11 MSCF/STB
The volume of the gas in a free-gas phase prior to going into solution
can be determined using the gas law as
1000 (14.7/1900) (560/520) (0.85/5.615) = 1.26 STB/1000 SCFor 0.79 MSCF/STB
Thus, for these conditions, the amount of gas in the well when a kick is
detected would be about 400% more in an oil-base drilling fluid than in a
water-base drilling fluid.
Example #2:
A 12.5-in. hole is being drilled at a depth of 8000 ft when gas
begins to enter the well on bottom at a rate of 6000 SCF/min. The 12.0
Ibm/gal drilling fluid has an oil volume fraction of 0.64, a water
fraction of 0.16, and a solids fraction of 0.20, and is being criculated
at 10 STB/min. The bottomhole pressure is 5000 psia, the bottomhole
temperature of 200°F, and the gas deviation factor is 1.03. Estimate
the pit gain expected per 1000 SCF of gas which enters the borehole.
Also, repeat the calcultions assuming the gas enters the well on bottom
at a rate of 600 SCF/min.
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79
Solution - Using Equation 7.2, the initial gas-drilling fluid mixture is
6000/10 = 600 SCF/STB.
Since the volume fraction of oil is 0.64, the initial gas-oil ratio is
(600/0.64) = 938 SCF/STB.
Entering Figure 7.3 at 5000 psia, it can be seen that the solubility of
the gas in the base oil is 670 SCF/STB (value of solution gas at bubble
point curve), which is less than the gas-oil ratio. This means that gas
bubbles can form and invade the previously uncomtaminated drilling fluid
region above until the gas-oil ratio is lowered to the solution gas-oil
ratio of 670 SCF/STB. This would yield a gas-drilling fluid ratio of
0.64 (670) = 429 SCF/STB.
Also from Figure 7.3, the volume factor of the gas-free oil is 1.012,
and the volume factor of the 670 SCF/STB gas-oil solution is 1.239.
Using these values in Equation 7.3 yields
1000/429 [0.64 (1.239-1.012)] = 0.34 STB/1000 SCF or2.95 MSCF/STB
The volume of the gas in a free-gas phase prior to going into solution
can be determined using the gas law as
1000 (14.7/5000) (660/520) (1.03/5.615) = 0.68 STB/1000 SCFor 1.46 MSCF/STB
Thus, for these conditions, the amount of gas in the well when a kick is
detected would be about 100% more in an oil-base drilling fluid than in
a water-base drilling fluid.
Repeating the calculations at a gas rate of 600 SCF/min gives a
gas-drilling fluid ratio of 60 SCF/STB and a gas-oil ratio of 94
SCF/STB. Use of Equation 7.3 yields
1000/60 [0.64 (1.034 - 1.012)] = 0.23 STB/1000 SCF or4.26 MSCF/STB
which is about 300% more than for a water base drilling fluid.
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80
Example #3:
An 8.5-in. bit is withdrawn from a 15,000 ft. borehole when gas
begins to enter the well on bottom at a rate of 5000 SCF/min. The 15.0
Ibm/gal drilling fluid has an oil volume fraction of 0.52, a water
fraction of 0.13, and a solids fraction of 0.35. At the bottom-hole
pressure of 11,700 psia and the bottom-hole temperature of 300°F, the
gas deviation factor is 1.20. Estimate the pit gain expected per 1000
SCF of gas which enters the borehole.
Solution - Since no drilling fluid was being circulated when the kick
was taken, forced gas-drilling fluid mixing was not significant.
Entering Figure 7.4 at 11,700 psia, it can be seen that the pressure is
above the value (6,500 psia) at which the gas is miscible with the oil
phase of the drilling fluid in all proportions. This implies that gas
bubbles will not form to create an efficient natural mixing process.
Thus, the gas region below the drilling fluid is thought to behave
essentially as a free-gas phase with a transition mixed zone separating
it from the drilling fluid above. The volume of the gas in a free-gas
phase can be determined using the gas law as
1000 (14.7/11,700) (760/520) (1.20/5.615) = 0.39 STB/1000 SCFor 2.55 MSCF/STB
Thus, for these conditions, the initial gain observed would be
approximately the same for oil-based and water-based drilling fluids.
However, this would not be true if forced mixing cccured. For example,
if the gas contacted sufficient mud to result in a gas-oil ratio of 500
SCF/STB and a gas drilling fluid ratio of 260 SCF/STB, then the pit gain
for the oil-based drilling fluid would be.
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81
1000/260 [0.52 (1.130-1.001)] = 0.26 STB/1000 SCF
or 3.88 MSCF/STB
which Is about 50% more gas per STB gained than for a water-based
drilling fluid.
7.5 Drilling Fluid Density Calculations
The volume factors used to estimate subsurface drilling fluid
swelling can also be used to determine drilling fluid density. The
drilling fluid density in Ibm/bbl is equal to the mass in one surface
barrel of drilling fluid plus the mass of dissolved gas divided by the
volume factor of the drilling fluid. Thus, techniques presented in this
chapter can also be used to assist field personnel in estimating changes
in subsurface oil-based drilling fluid density due to changes in
temperature, pressure, and gas concentration.
One possible early kick detection scheme being currently
investigated is through the use of a measurements-while-drilling (MWD)
tool to detect changes in drilling fluid density just above the bit.
The required sensitivity of such a device was estimated for the well
conditions of Examples 1 and 2 presented previously, and the results are
shown in Figure 7.6. Note that the required sensitivity is greater in
the surface hole example.
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82
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CHAPTER VIII
HANDLING DRILLED-GAS IN OIL-BASED DRILLING FLUIDS
This chapter presents techniques for estimating the amount of
drilled-gas entering an oil-based drilling fluid and for predicting the
behavior of the gas-drilling fluid mixture in the annulus as it is
circulated to the surface. Using the methods presented, the depth at
which gas would begin evolving from the drilling fluid and the resulting
loss in hydrostatic pressure can be calculated. The volime of drilling
fluid that would be expelled from the well and the associated gas rate
can also be estimated. The calculation procedures presented were
verified by experiments conducted in a 6000 foot well. Also, methods
for handling drilled-gas in oil-based drilling fluids were investigated
by means of the calculation procedures developed.
8.1 Drilled-Gas Concentration
The concentration of drilled gas entering the drilling fluid at
bottomhole depends primarily on the penetration rate of the bit, the
diameter of the bit, the circulation rate of the drilling fluid, and the
formation pore pressure. The gas influx rate, in SCF/min can be
estimated using,
p.. dj ♦ S„ R-S - 310.97 z 4 « • «
where is the bottomhole pressure in psi, d^ is the bit diameter in
inches, <l> is the formation porosity expressed as a fraction, is the
formation gas saturation expressed as a fraction, R is the penetration
83
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84
rate of the bit in ft/hr, z is the gas deviation factor, and T,, is theD£l
bottomhole circulating temperature in °R.
The resulting drilled-gas-drilling fluid ratio, in SCF/STB is
approximated using,
*3. - 42 ....................................
where is the drilling fluid flow rate in gal/min. In Equation 8.2,
it is assumed that the drilled-gas goes into solution at the bit and no
upward migration of gas bubbles occurs. This assumption is reasonable
since the value of R calculated from Equation 8.2 is small (i.e., <sm100 SCF/STB) as will be shown later in this chapter.
The total volume of drilled-gas entering the well, in SCF can be
calculated as.
V = 60 -#— ................................... (8.3)'g R
where h is the formation thickness in feet.
8.2 Circulating Time to Gas Evolution
The circulating time to gas evolution is an important parameter to
know because it allows drilling to continue for a time before the well
should be shut-in and the gas contaminated drilling fluid circulated out
of the well if it is not allowable to have free gas in the wellbore.
Current practice in the petroleum industry is to shut-in and circulate
bottoms-up (Figure 8.1) to remove possible gas contaminated oil-based
drilling fluid associated with a drilling break (the sudden increase or
decrease in penetration rate due to a change in lithology)
(Billingsley). However, significant costs can be incurred because of
the lost drilling time that is a consequence of this practice.
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SEA LEVEL
CHOKE LINE
MUD LINEGAS CONTAMINATED MUD
Figure 8.1 - Circulating Gas Contaminated Drilling Fluid Out of Well.00Cn
86
To calculate the circulating time to gas evolution, the depth at
which the gas will begin to breakout of solution has to be determined.
For a given drilled-gas-drilling fluid ratio, an iterative procedure
having the following steps must be used:
1. Calculate the frictional and the hydrostatic pressure
gradients as outlined by Bourgoyne et. al. (Appendix C) for
gas free drilling fluid as this fluid will be above the gas
contaminated drilling fluid.
2. Move down-hole one length step. The distance moved is equal
to the length step size selected.
3. Calculate the pressure using the gradients from Step 1 and the
circulating temperature (Table 6.1) at this depth.
4. Using the gas solubility equations presented in Chapter V,
calculate the solution gas-drilling fluid ratio at the
pressure and temperature from Step 3.
5. If the solution gas-drilling fluid ratio calculated in Step 4
is equal to the given drilled-gas-drilling fluid ratio the
depth is the bubble point depth. If not, repeat Steps 2-4.
Once the bubble point depth has been determined, the bottoms-up
circulating time to this depth, t in minutes is,
t = (L-D, )/60 V ............................... (8.4)op awhere is the bubble point depth in feet, L is the vertical length of
the well in feet, and is the average annular velocity in ft/sec for a
concentric hole.
In most drilling applications, laminar flow in the annulus is
required to provide efficient drilled cuttings transport. Also most
wells drilled are not concentric but rather eccentric. The combination
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87
of laminar flow and hole eccentricity results in the development of
velocity profiles in the annulus (Figure 8.2) and will cause Equation
8.4 to over-estimate the circulating time to gas evolution. To account
for the velocity profiles in the annulus. Equation 8.4 should be divided
by 1.5 for a concentric wellbore where the annular velocity will be the
smallest and by 2.5 for a fully eccentric wellbore where the annular
velocity will be the greatest as recommended by lyoho and Azar. These
two extreme cases are conveniently assumed since the eccentricity of a
wellbore is seldom known in actual practice and will allow the upper and
lower limits of the circulation time to gas evolution to be available.
8.3 Calculation of the Decrease in Bottomhole Pressure Due to Gas
Evolution
Knowledge of the decrease in bottomhole pressure due to drilled-gas
evolution will allow field personnel to determine whether or not
wellbore conditions will be such that gas may flow into the well from an
exposed gas sand. In addition, the volume of drilling fluid that will
be expelled from the well when the drilled gas breaks out of solution
can be estimated so that surface equipment can be designed to accomodate
the excess drilling fluid flow from the well.
To calculate the circulating bottomhole pressures with and without
gas, a computer model was developed. The program was written in FORTRAN
and was executed on an IBM Time Sharing Option Mainframe Computer. The
wellbore geometry modelled is shown in Figure 8.3.
The circulating bottomhole pressure, in psi is calculated as,
P,, = P, + AP- + P ............................. (8.4)bh hs f s
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88
ISO VELOCITY
/5’/\VZ
DEPTH
Figure 8.2 - Annular Velocity Profiles Due to Laminar Flow and Hole Eccentricity.
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89
A Drill Pipe OD
Casing Shoe ^ -----
Diameter
Casing ID
Figure 8.3 - Computer Model Wellbore Geometry.
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90
where is the hydrostatic pressure due to the annular fluids in psi,
AP^ is the annular frictional pressure losses in psi, and P^ is the
surface pressure in psi.
For the case where no drilled gas has contaminated the well, the
hydrostatic pressure is due to the drilling fluid and drilled cuttings
in the annulus. For the purposes of this study, the effects of drilled
cuttings on the hydrostatic pressure is neglected. The annular
frictional pressure losses are calculated using the power law model to
approximate the apparent Newtonian viscosity of the oil-based drilling
fluid (Appendix C).
To calculate the circulating bottomhole pressure when the top of
gas contaminated drilling fluid reaches the surface which corresponds to
the maximum decrease in bottomhole, an iterative method was used. The
steps used are:
1. Start at the surface where the pressure and temperature is
known.
2. Move down-hole one length step. The distance moved is equal
to the length step size selected.
3. Assume a pressure and calculate the circulating temperature
(Table 6.1) at this depth.
4. Using an average pressure and temperature, calculate the free
gas rate and density, and the density of the oil-based
drilling fluid containing dissolved gas.
5. Calculate the hydrostatic and frictional pressure gradients
and sum these values to get the total pressure gradient over
the length step.
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91
6. Using the calculated pressure gradient, calculate the pressure
and compare with the assumed pressure. If the two pressures
compare favorably continue to the next step. If not, use the
new pressure and repeat Steps 4-6.
7. Calculate the volume of free and dissolved gas contained in
the annular section associated with the selected length step.
8. Repeat Steps 2-7 until the sum of the volume of free and
dissolved gas contained in the annular sections equals the
volume of gas that entered the well as calculated using
equation 8.3
9. Use the frictional pressure gradient and hydrostatic gradient
calculated for gas free drilling fluid to calculate the
pressure due to a column of gas free drilling fluid that may
exist below the region of gas contaminated drilling fluid.
10. The sum of the last pressure calculated in Step 6 and the
pressure calculated in Step 9 will be the circulating
bottomhole pressure.
The solution gas-drilling fluid ratios are calculated as outlined
in Chapter V and the oil-based drilling fluid densities are calculated
as outlined in Chapter VII and Appendix A. The frictional and
hydrostatic pressure gradients of the gas-drilling fluid mixture were
determined as recommended by Langlinais, et. al. and is outlined in
Appendix D.
Once the circulating bottomhole pressures have been calculated for
gas free and contaminated drilling fluid, the decrease in bottomhole
pressure due to gas evolution is simply the difference between the two
pressures.
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92
8.4 Drilling Fluid Expelled Due to Gas Evolution and Surface Gas Rate
The maximum volume of drilling fluid that will be expelled from the
well due to gas evolution, in surface barrels can be estimated as,
\ - aPg/.052 ..................... (8.5)where AP^ is the decrease in bottomhole pressure due to gas evolution in
psi, is the oil-based drilling fluid density in Ibm/gal, and is
the annular capacity in bbl/ft.
The surface gas rate, in SCF/Day can be estimated as,
Qg - 34-3 4m*sm.................................. (*'*)where is the drilling fluid rate in gal/min and is the
drilled-gas-drilling fluid ratio in SCF/STB.
8.5 Experimental Verification of Calculation Procedure
The experimental well and procedures as described in Appendix B
were used to veryify the calculation procedure. The loss in bottomhole
pressure due to gas evolution and the circulation time before gas
evolution occurred were noted for each experiment and compared to the
theoretical calculations. The first evolution of gas could be detected
by observing a sharp change in the bottomhole pressure, pump pressure,
pump speed, and pit gain. A comparison between the experimental results
and the theoretical calculations are shown in Table 8.1. Note that
there was good agreement between the observed and calculated results for
both the loss in bottomhole pressure and in the circulation time to gas
evolution.
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Table 8.1 - Comparison of Experimental Observations and Theoretical Predictions
Theoretical Predictions Observed ResultsCirculating Circulating
Time TimeGas-mud Pump Change To Cas Change To CasRatio, Rate, In BHP*, Evolution, In BHP, Evolution,SCF/STB STB/MIN psla mln psla mln
185 1.95 170 54 177 53
178 2.85 112 40 114 36
235 1.05 376 51 385 48
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8.6 Evaluation of Field Procedures
Sensitivity analyses were made to determine the effects of a number
of drilling variables on the severity of the problems caused by
drilled-gas dissolving in an oil base drilling fluid. The effect of the
most important parameters affecting the initial gas concentration
dissolving in the drilling fluid are shown in Figures 8.4 and 8.5.
Shown in Figure 8.4 are the effects of penetration rate and formation
pore pressure for a well drilling at 8000 ft with a 12.25-in. bit. It
is assumed that the drilling fluid density used is near the formation
pore pressure. Note that for the well conditions assumed, the initial
drilled-gas concentration could sometimes be as high as 40 SCF/STB.
The effect of increasing well depth on initial drilled-gas
concentration can be seen by comparing Figures 8.4 and 8.5. Note that
for a typical well plan of decreasing hole size with increasing well
depth, the maximum anticipated drilled-gas concentration would tend to
decrease with depth.
Figure 8.6 shows the calculated circulating time to gas evolution
as a function of the drilled-gas-drilling fluid ratio for a concentric
hole (eccentricity = 0) and for a fully eccentric hole (eccentricity =
1) for the conditions shown. Note that as the gas-drilling fluid ratio
increases the circulating time to gas evolution decreases. This is to
be expected since the bubble point pressure increases as the
gas-drilling fluid ratio increases resulting in the bubble point depth
occuring deeper in the well. Also note that the circulating time to gas
evolution is much less for the eccentric hole than for the concentric
hole. This is due to the higher annular velocities associated with the
fully eccentric hole.
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m 50 Q,„ «306gpm ( Vo=l F T / S )Tbh= 130'FTEMPERATURE GRADIENT » 1.2 “F / 100 FTSfl « 8 0 % _______________________________to
4 0
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100
Figure 8.4 - Effect of Penetration Rate and Drilling Fluid Density on Drilled-Gas Concentration (D = 8000 Feet). VOU1
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Figure 8.5 - Effect of Penetration Rate And Drilling Fluid Density on Drilled-Gas Concentration (D » 15000 Feet). VO
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Depth « 8 0 0 0 ftHole Diometer « 12.25 InCosing Diameter « 15.124 inDrill Pipe Diometer = 5 inOm * 3 0 6 gpmPm " I2ppq (O W R -75-.25)Tômporoture Grad. = I.2 ® F /I0 0 ft
10 15 2 0 25 3 0 35G A S -M U D RATIO, SCF/STB
4 0 45 50
Figure 8,6 - Effect of Drilled-Gas Concentration on Circulation Time To Gas Evolution. VO
98
Figure 8.7 shows the effect of penetration rate on the decrease In
bottomhole pressure due to gas evolution for a range of sand thicknesses
and the conditions shown. Notice that for a given sand thickness, at
low penetration rates the sand will appear Infinite and a worst case of
gas contaminated drilling fluid throughout the entire annular section
will exist (Point A). However, as the penetration Is Increased this
apparent Infinite sand thickness will not exist rather the actual sand
thickness will be realized (Point B). For both Point A and B, the
decrease In bottomhole pressure Increases with an Increase In
penetration rate. A further increase In penetration rate will cause a
decline In the rate with which the bottomhole pressure decreases (Point
C). This Is because the higher gas-drllllng fluid ratios associated
with the higher penetration rates Increases the free gas rate causing
the majority of the drilled gas to slip past the drilling fluid and to
exist in the upper portion of the well.
Table 8.2 shows the calculated volumes of drilling fluid that can
be expelled from the hole for the conditions shown In Figure 8.7. Note
that as the sand thickness increases the volume of drilling fluid that
can be expelled from the well increases which is to be expected since
the decrease In bottomhole pressure increases with increasing sand
thickness as shown In Figure 8.7. This happens because the volume of
gas In the well Is Increasing as the sand thickness Increases as uhown
in Figure 8.8.
Shown in Figure 8.9 are the effects of drilled-gas concentration
and pump rate on the required surface gas handling rate. This figure
shows that gas flow rates from the well in the range of .5 to 1.5
MMSCF/Day can occur for typical drilled-gas concentrations. This
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3 0 0
Flgurfi 8.7 “ Effect of Penetration Rate and Gas Sand Thickness on Bottomhole Pressure Reduction. VO
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Table 8.2 - Volume of Drilling Fluid Expelled Due to Gas Evolution
V , bbls inR, ft/hr
50
100
150
200 250
300
h, ft = 25
2 21
49
56
59
61
50
3
22
50
77
84
89
150
12
24
52
81
109
138
500
12
45
79
88115
143
>500
12
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79
93
127
166
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4
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0 200 2 5 0 3 0 0100 ISO50GAS SAND THICKNESS, Ft.
Figure 8.8 - Effect of Gas Sand Thickness on Gas Volume In Well.
102
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103
suggests the need for a flowllne degasser or separator capable of
handling these rates that is placed upstream of the shale-shaker. It
also indicates the need for a rotating head to prevent gas from being
vented at the rig floor reducing an explosion hazard to the rig
personnel. This design was suggested by O ’Brien and Matthews as pointed
out previously.
As pointed out in Chapter III, the solubility of gas in an
oil-based drilling fluid is a function of the volume fraction of oil in
the drilling fluid. For a constant gas-drilling fluid ratio and
temperature, the bubble point pressure for the mixture will increase
with a decrease in the volume fraction of oil in the drilling fluid.
If it is desired to prevent any gas from breaking out of solution
in the wellbore, a rotating head can be used to exert a backpressure on
the well equal to the bubble point pressure of the gas-drilling fluid
mixture (Figure 8.10). Figure 8.11 shows a plot of rotating head
pressure needed to keep gas in solution versus gas-drilling fluid ratio
for various volume fractions of oil in the drilling fluid. Note that a
considerable backpressure is needed to keep typical values of drilled
gas in solution for low volume fractions of oil in the drilling fluid.
The high backpressures needed to keep drilled gas in solution make
this approach unattractive since it requires rig personnel to work with
a well under pressure and requires rotating heads with working pressure
ratings in excess of those commonly available. The most safe design
appears to be a rotating head operated at a low pressure to prevent gas
from being expelled on the rig floor and a flowline degasser or
separator downstream of the rotating head but before the shale-shaker as
shown in Figure 8.12. The separator, gas vent line, and drilling fluid
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5
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DISSOLVED GAS
Figure 8.12 - Rotating Head - Separator Flow Arrangement With Free Gas in Wellbore.
oa\
107
flow Unes should be sized such that excessive backpressures are not
placed on the well when the gas and drilling fluid are expelled from the
well. This will prevent the risk of fracturing exposed subsurface
formations.
Note that in the design of Figure 8.12, some free gas will exist in
the wellbore. Use of the calculation methods presented will allow the
effects of the free gas in the well to be determined and the proper
rotating head pressure rating and drilling fluid density to be selected
to minimize the effects of the free gas in the well.
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CHAPTER IX
CONCLUSIONS
1. A method for estimating the solubility of gas in an oil-based
drilling fluid has been developed.
2. Curves for estimating the upper limit depth of gas miscibility in
the wellbore has been presented.
3. The Peng-Robinson equation of state model has been calibrated using
PVT data, and curves for predicting the swelling of base oils used
in drilling fluid preparation due to dissolved gas have been
generated.
4. A method for predicting the pit gain to be expected for given field
conditions has been developed.
5. The standard volume of gas in the borehole when a given pit gain is
observed at the surface:
a) tends to be greater in an oil-based drilling fluid than in a
water-based drilling fluid.
b) tends to increase as the gas is mixed in increasingly larger
volumes of oil-based drilling fluid.
c) can be as much as 400% more than for a water-based drilling
fluid.
6. A technique has been presented for calculating the annular behavior
of drilled-gas in an oil-based drilling fluid.
7. Drilled-gas concentration in oil-based drilling fluids is
controlled primarily by bit size- penetration rate, drilling fluid
flow rate and formation pore pressure and usually varies from 5-40
SCF/STB.
108
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109
I-
8. Drllled-gas concentrations decrease with increasing depth for
typical wells where hole size decreases with depth.
9. The decrease in hottomhole pressure due to drilled-gas evolution
increases with increasing penetration rate and gas sand thickness.
10. Design criteria for determining the proper rotating head pressure
rating and separator size to be used when handling drilled-gas in
oil-based drilling fluids have been presented.
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CHAPTER X
RECOMMENDATIONS
1. Data should be generated for the solubility of hydrogen sulfide in
base oils over a range of temperatures (i.e., 100, 200, and 300°F)
and pressures.
2. Using the data from 1., a correlation should be developed for
predicting the solubility of hydrogen sulfide in base oils.
3. Experimental data for gas/oil-based drilling fluid miscibility is
needed to further define this complex phase behavior as it relates
to the wellbore.
4. Experimental data for the time rate of gas solubility will be
useful in determining how gas bubbles migrate up the well when the
initial gas-drilling fluid ratio is in excess of the allowable
bottomhole gas-drilling fluid ratio.
5. Experimental data on how gas dissolved in an oil-based drilling
fluids affects the drilling fluid properties would be of interest.
Particularly of interest would be the effects of gas solubility on
barite settling in the wellbore when the well is shut in for a
considerable period of time after a gas kick has been detected.
110
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CHAPTER XI
REFERENCES
Billingsley, J.L., Tenneco Oil Exploration and Production, personal communication.
Bourgoyne, A.I., Jr., Millheim, K.K., Chenevert, M.E., and Young, F.S., Jr., Applied Drilling Engineering, Society of Petroleum Engineering, 1986, pp. 152-155.
Brill, J.P. and Beggs, H.D., Two-Phase Flow In Pipes, University of Tulsa, 1982, pp. 3-11-3-18.
Craft, B.C. and Hawkins, M.F., Applied Petroleum Reservoir Engineering, Prentice Hall, 1959, p. 131.
Crawford, H.R., Neill, G.H., Lucy, B.J., and Crawford, P.D., "Carbon Dioxide - A Multipurpose Additive for Effective Well Stimulation," JPT, March 1963.
Ekrann, S. and Rommetveit, R., "A Simulator for Gas Kicks In Oil-Based Drilling Muds," SPE 14182, Presented at the 60th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Las Vegas, NV, September 22-25, 1985.
Hagedom, A.R. and Brown, K.E., "Experimental Study of Pressure Gradients Occurring During Continuous Two-Phase Flow in Small Diameter Vertical Conduits," JPT, April 1965, pp. 475-483.
lyoho, A.W. and Azar, J.J., "An Accurate Slot Flow Model for Non- Newtonian Fluid Flow Through Eccentric Annuli," SPEJ, October 1981, pp. 565-572.
Katz, D.L. and Firoozabadi, A., "Predicting Phase Behavior of Condensate/Crude-Oil Systems Using Methane Interaction Coefficients," JPT, November 1978, pp. 1649-1655.
Langlinais, J.P., Bourgoyne, A.T., and Holden, W.R.,: "FrictionalPressure Losses for Annular Flow of Drilling Mud and Mud Gas Mixtures", Transactions of the ASME, Vol. 107, March 1985, pp. 142-151.
Lee, A.L., Gonzalez, M.H., and Eakin, B.E., "The Viscosity of Natural Gases," JPT, August 1966, pp. 997-1000.
McCain, William D., The Properties of Petroleum Fluids, Penn Well, Tulsa, OK (1973), pp. 284-285.
Matthews, W.R., "How to Handle Acid Gas H^S and CO^ Kicks," Petroleum Engineer International, 15 November 1984, pp. 22-29.
Ill
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
112
O’Brien, T.B., "Handling Gas in an Oil Mud Takes Special Precautions," World Oil, January 1981, pp. 83-86.
Peng, D.Y. and Robinson, D.B.: "A New Two Constant Equation ofState", Ind. Eng. Chem. Fund., Vol. 15, No. 1, 1976, pp. 59-64.
Salisbury, D.P., Milchem Incorporated, personal communication.
Stalkup, F.I., Miscible Displacement, Society of Petroleum Engineers, Dallas, TX, 1983, pp. 3, 4, 99, 100, 140.
Standing, M.B., Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, Society of Petroleum Engineers, Dallas, TX, 1977, pp. 40-42.
Thomas, D.C., Lea, J.F. Jr., and Turek, E.A., "Gas Solubility in Oil- Base Drilling Fluids: Effects on Kick Detection," JPT, June 1984, pp.959-974.
Thomas, D.C. and Lea, J.F., Jr., "Blowouts - A Computer Simulation Study," lADC/SPE 11375, Presented at the 1983 I ADC/SPE Drilling Conference, New Orleans, LA, February 20-23.
The Western Company of North America, Engineers Handbook, Fort Worth, TX, p. 7-19.
Whitson, C.H., "Characterizing Hydrocarbon Plus Fractions," SPEJ, August, 1983, pp. 683-694.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX A
PENG-ROBINSON EQUATION OF STATE
In its general form, the Peng-Robinson equation of state is given
as,
p = H _________a(T)v-b v(v+b) + b(v—b)
where P is the pressure in psia, T is the temperature in °R, v is the
molar volume in ft^/lb-mole, R is the universal gas constant, 10.73
psia • ft^/lb-mole • °R, a(T) is the Peng-Robinson molecular
attraction parameter which is a function of temperature, and b is the
Peng-Robinson molecular repulsion parameter.
Rewritten, Equation A.1 becomes.
where.
- (l-B)z^ + (A-3B^-2B)z - (AB-B^-B^) = 0 (A.2)
A = (A.3)R T
B - g (A.4)
Pv ^ RT (A. 5)
with z being the deviation factor. Equation A.2 yields one or three
real roots, and for liquids, the smallest positive root is desired.
Equation A.5 is then used to calculate the molar volume, v, in barrels
per pound-mole. Knowing the molar volume and n, the pound-moles of
liquid, the volume of liquid in barrels at a given pressure and
temperature can be determined as,
V = V • n (A. 6)
113
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114
To determine the molecular attraction parameter, a(T) and the
molecular repulsion parameter b for use in Equations A.3 and A.4,
parameters a(T) and b are evaluated at the critical pressure, and
temperature, for the component of interest as,
R^T 2a(T^) = 0.45724 (A. 7)
c
RTb(T^) = 0.0778 (A.8)
c
Parameter a(T^) is corrected to the temperature of interest by
aCT) = a(T ) • a(T^,w) (A.9)c rwhere.
a = [1 + (.37464 + 1.54226w - .269920)^) (1-T^^) (A. 10)
with being the reduced temperature defined as the temperature of
interest divided by the component critical temperature, both being in
absolute temperature units and w being the component acentric factor.
To calculate parameters a(T) and b for a mixture, mixing rules
given as,
a = Z Z X . X . a(T).. (A.11)i j ^
b = Z X. b . (A.12)i ^
where x^ and x^ are the i- and j-component mole-fractions respectively
and b^ is the i-component repulsion parameter defined by Equation A. 8.
The parameter a(T)^^ is calculated as,
a(T) = (1-C ) aCT) a(T)^ (A. 13)-J 1 3
where a(T)^ and a(T)j are the i- and j-component attraction parameters
calculated by Equations A.7 and A.9 and is the binary interaction
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115
parameter for the 1- and j-component binary. Commonly used binary
interaction coefficients are listed in Table A.I.
Once the volume of a mixture at a given pressure and temperature is
determined by Equation A.6, the volume factor, can be calculated as,
B = V/V (A. 14)o scwith the units of B^ being volume at pressure and temperature per volume
at standard conditions (i.e., pressure = 15.025 psia and temperature =
60°F).
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116
Table A.1: Peng-Robinson Equation of State Binary InteractionCoefficients
CarbonNo.
Methane Binary* Interaction Coefficient
23
n4n5n6n789
1011121314151617181920 21 22232425
00
.0200
.0200
.0250
.0250
.0381
.0407
.0427
.0442
.0458
.0473
.0488
.0502
.0512
.0523
.0500
.0537
.0544
.0551
.0558
.0565
.0571
.0575
Binary MixtureInteractionCoefficient*
Nitrogen + Hydrocarbon .1200Carbon Dioxide + Hydrocarbon .1500Hydrogen Sulfide + Hydrocarbon .1200Ethane + Hydrocarbon .0100Propane + Hydrocarbon .0100
*-Carbon numbers 8 - 2 5 methane binary interaction coefficients from Whitson. All other interaction coefficients from Katz and Firoozabadi.
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APPENDIX B
FULL SCALE EXPERIMENTS
Experiments were conducted in a 6000 foot test well in which gas
was injected into an oil-based drilling fluid and the well monitored for
pit gain, circulation time to gas evolution, and decrease in bottomhole
pressure due to gas evolution. Figure B.l shows the flow arrangement
used.
The experimental test well is designed to simulate drilling 3000
feet below the seafloor in 3000 feet of water. The drillstring is
modelled using 2.875 inch tubing set at 6000 feet. Gas can be injected
into the bottom of the well through 1.315 inch tubing run concentrically
inside the drillstring. Gas storage and compression wells permit 0.62
specific gravity natural gas (Table B.l) to be injected at any desired
bottomhole pressure, up to a maximum of 5500 psi, and at any desired
bottomhole feed rate, up to a maximum of about 3 STB/min. The choke and
kill lines to the simulated subsea blowout preventer stack are modelled
using 2.375 inch tubing.
To conduct each experiment, the well was circulated at a given rate
while gas was injected down the 1.315 inch gas injection line.
Bottomhole pressure, pit gain, pump pressure, and pump speed were
monitored during the course of each experiment.
The conditions and results of the experiments are summarized in
Tables B.2 and B.3. Figures B.2 - B.4 are plots of the measured data
versus time for each experiment. Pit gain was not recorded for
Experiment No. 3 (Figure B.4) due to difficulty with the pit gain
monitoring equipment during the experiment.
117
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Figure B.l - Full Scale Experimental Test Well.
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119
TABLE B.l: Full Scale Experimental Gas Composition
Component Mole Percent
Nitrogen 0.28
Carbon Dioxide 0.89
Methane 90.18
Ethane 4.84
Propane 2.05
i-Butane 0.49
n-Butane 0.53
i-Pentane 0.23
n-Pentane 0.15
Hexanes 0.14
Heptanes+ 0.22
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TABLE B.2; Full Scale Experimental ConditionsOil Mud Data Mud Gas Volume GMR,
Exp. No. Pm* PP8 o m up, cp Y.P., lb/100 ft^ Rate, bpm Injected, SCF SCF/STB
1 8.2 64:36 22 16 1.95 4,978 185
2 8.1 64:36 21 12 2.85 8,132 178
3 7.85 64:36 21 12 1.08 10,274 235
Surface Temperature: 80®FSurface Pressure: 15.025 psia Geothermal Gradient: 1.3°F/100 ft
Measured kill line and drill pipe pressure losses:
Pump Speed, SPM
0 50
60
70
Kill Line AP, pslg
0140
215
300
Drill Pipe AP, pslg
0760
1,025
1,280
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o-o Bottom Hole Minimum
Circulating Bottom Hole Circulating
Exp. No..Pressure
(No Gas), pslgPressure Due
To Gas Evolution, pslgCirculating Time
To Gas Evolution, mlnPitGas
Gain Before Evolution, bbl
1 2,695 2,518 53 1.2
2 2,824 2,710 36 2.2
3 2,487 2,102 48 -
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APPENDIX C
GAS FREE DRILLING FLUID PRESSURE CALCULATIONS
To calculate the frictional pressure losses in an annulus, the
average annular velocity, V in ft/sec, is calculated as,
’ * 2.448 ............................where is the drilling fluid rate in gal/min, d^ is the hole diameter
in inches, and d^^ is the drill-pipe diameter in inches.
The apparent Newtonian viscosity of the drilling fluid, in
centipoise (cp) is calculated as,
Kf^h-^dp)^ , 2 + 1/n f 2)
where,
and.
'"a 144 ÿ(l-n) ' 0.0208
n = 3.32 log ©6oo/®300.......................... (^.3)
K = 510 Qgog/Sll^............................... (C.4)
K is known as the consistency index of the drilling fluid having units
of equivalent centipoise and n is the flow behavior index which is
dimensionless. ©goQ ®3QG the 600 and 300 rpm readings from a
Fann Viscometer.
The Reynolds number, N^^ is used as the flow regime, either laminar
or turbulent, criteria. It is given as,
. , , . 3,
Re
If N^^ is less than the critical Reynolds number for the given n value,
flow is laminar. If it is greater then the critical Reynolds number for
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126
the given n value, flow is turbulent. The critical Reynolds number for
values of n can be determined from Figure C. 1 as well as the friction
factor, f for turbulent flow calculations.
If flow is laminar, the frictional pressure loss, AP^ in psi is
calculated as,
u V LA P , ...... (C.6)
1000 (d^-djp)"
If flow is turbulent, the frictional pressure is calculated as,
f v \•f - 21— (d^-d^p)AP, = ™ — 3— r ............................ (C.7)
To calculate the hydrostatic pressure due to a column of gas free
oil-based drilling fluid, an iterative calculation technique is used to
account for the compressibility and expansion of the drilling fluid
caused by pressure and temperature. The steps are:
1. Start at the surface where the pressure and temperature is
known.
2. Move down-hole one length step. The distance moved is equal
to the length step size selected.
3. Assume a pressure and calculate the circulating temperature
(Table 6.1) at this depth.
4. Calculate the drilling fluid density using the PREOS model
described in Appendix A.
5. Using an average density over the length step and the
frictional gradient as determined above, calculate the
pressure due to a column of drilling fluid associated with the
length step size selected and compare with the assumed
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127
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128
pressure. If the two pressures compare favorably continue to
the next step. If not, use the new pressure and repeat Steps
4 and 5.
6. Repeat Steps 2-5 until bottomhole is reached with the last
pressure calculated being the bottomhole pressure for a column
of gas free drilling fluid.
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APPENDIX D
TWO-PHASE PRESSURE GRADIENT CALCULATIONS
The procedure outlined by Langlinais, et. al. for calculating
flowing pressure gradients for two-phase annular flow uses the Hagedom
and Brown correlation with an equivalent diameter defined by the
hydraulic diameter concept and the power law model to define the
apparent Newtonian viscosity of the drilling fluid. The hydraulic
diameter, in inches is given as,
*e = 'Hi ■ 'dp.................. (D'l)where d, is the hole diameter and d, is the drill pipe diameter both in h dpinches.
The Hagedom and Brown correlation for calculating the two-phase
pressure gradient, CdP/dz)^^^ in psi is given as,
CdP/dz)^^^ = (dP/dz)j + (dP/dz)g^.............. (D.2)
where.
and.
(dP/dz) - = g/g [p H + p (1-H )]........... (D.3)61 c in m g m
. 2(dP/dz). = -------------------------- (D.4)
2.9652 X lOr p^ dg
(dP/dz)^^ and (dP/dz)^ are the pressure gradients due to elevation and
friction respectively.
Equation D.4 was rewritten by Brill and Beggs as,
f p.(dP/dz) = f (D.5)
f 2 8c dgwhere,
V , = V + V ............................... fD.6)mix sm sg
129
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130
and,
%s = = Vg ...........................3
In Equations D.3-7, is the drilling fluid density in Ibm/ft
calculated using the Peng-Robinson equation of state as outlined in3
Appendix A, is the gas density in Ibm/ft , is the H a g e d o m and
Brown liquid holdup expressed as a fraction, f is the friction factor,
d^ is the hydraulic diameter in inches defined b y Equation D.l, w is the
mass flow rate in Ibm/day, is the two-phase mixture superficial
velocity in ft/s, is the superficial drilling fluid velocity in
ft/s, is the superficial gas velocity in ft/s, is the two-phase
mixture viscosity in cp, is the power law apparent Newtonian
viscosity for the drilling fluid in cp as calculated in Appendix C, y^
is the gas viscosity in cp as determined using the Lee, et. al.
correlation.3
In Equation D.5, p^ in Ibm/ft is defined as,
Pg = Pjj /Pg................................... (D.8)where.
and.». - ...................
p = p H + p ( 1 — H ) ........................................................... (D. IO)s in m ^ Ts
Note that in Equation D.l, the pressure gradient due to
acceleration are neglected. This is commonly done in practice due to
the small contribution in the total pressure gradient made by
acceleration of the fluid.
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VITA
Patrick Leon O'Bryan is the son of Mr. and Mrs. L. K. O’Bryan of
Brandon, MS. He was b o m in Hattiesburg, MS on August 17, 1961. He is
married to the former Pamela Elizabeth Bramlett, also from Brandon, and
they have a son, Taylor Patrick. Patrick graduated from Brandon High
School in 1979 and then attended Mississippi State University where he
received a Bachelor of Science degree in Petroleum Engineering in May,
1983. He then began graduate studies at Louisiana State University
where he received a Master of Science degree, also in Petroleum
Engineering in December, 1985. He began work towards the Doctor of
Philosophy degree in Petroleum Engineering at Louisiana State
University in January, 1986.
131
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w
DOCTORAL EXAJVnNATION AND DISSERTATION REPORT
Candidate; Patrick Léon O’Bryan
Major Field: Petroleum Engineering
Title of Dissertation: Well Control Problems Associated With Gas Solubility InOil-Based Drilling Fluids
Date of Examination:
April 26, 1988
Approved:
Major Professor a6l c64irmtm
Dean of the Graduate/School
EXAMINING COMMITTEE:
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