production system analysiss3.amazonaws.com/noteswap-sid-1/2/5/0/4/25045dd60dbfc3d...production...

Production System Analysis

Production System Analysis

Nodal Analysis

• An analytical tool used in forecasting the performance of the various elements comprising the completion and production comprising the completion and production system. This concept is based on the a well having one flow rate implied by fixed end pressures.

Nodal Analysis

• This procedure consist of selecting a division

point (node) in the well and dividing the

system at this point.

•The locations of the

most commonly used

nods are shown:

Nodal Analysis

• Once a node is selected, i.e. bottom hole

pressure, the pressure is calculated from both

directions (upstream and downstream from

the node). the node).

– Inflow to the node:

– Outflow from the node:

noderppp )components (upstream =∆−

nodeFWHppp )components m(downstrea =∆+

Nodal Analysis

• The pressure drop, Δp, in any component

varies with flow rate, q. Therefore, a plot of

node pressure versus flow rate will produce

two curves, the intersection of which will give two curves, the intersection of which will give

the conditions satisfying requirements 1 and

2, given previously. The procedure is

illustrated graphically in Fig. 1-3.

Determination of Flowing Capacity

Nodal Analysis

• Using a simple producing system and selecting

the wellhead as the node


pppp =∆−∆−


whtbgresrpppp =∆−∆−

whflowlinesep ppp =∆+

• The effect of the flow capacity of changing the

tubing size and the effect of a change in

flowline size.

Nodal Analysis

• Frequently used is the procedure to select the

node between the reservoir and the piping

system.



whresrppp =∆−

wftbgflowlinesep pppp =∆+∆+

•The effect of a change in tubing size on the

total system producing capacity when pwf is the

node pressure.

•A case in which the well performance is controlled by

the inflow is below. In this case, the excessive pressure

drop could be caused by formation damage or

inadequate perforations.

•A qualitative example of selecting the optimum

tubing size for a well that is producing both gas

and liquids is shown below

Procedure for Apply Nodal Analysis

1. Determine which components in the system can be

changed. Changes are limited in some cases by

previous decisions. For example, once a certain hole

size is drilled , the casing size and , therefore, the

tubing size is limited.tubing size is limited.

2. Select one component to be optimized.

3. Select the node location that will best emphasize the

effect of the change in the selected component. This

is not critical because the same overall result will be

predicted regardless of the node location .

Procedure for Apply Nodal Analysis

4. Develop expressions for the inflow and outflow .

5. Obtain required data to calculate pressure drop

versus rate for all the components. This may require

more data than is available, which may necessitate

per- the analysis over possible ranges of conditions.

6. Determine the effect of changing th e characteristics

of the selected component by plotting inflow versus

outflow and reading the intersection.

7. Repeat the procedure for each component that is to

be optimized.

Reservoir Performance

WELL PERFORMANCE EQUATIONS

• To calculate the pressure drop occurring in a

reservoir, an equation that expresses the

energy or pressure losses due to viscous shear

or friction forces as a function of velocity or or friction forces as a function of velocity or

flow rate is required. Although the form of the

equation can be quite different for various

types of fluids, the basic equation on which all

of the various forms are based is Darcy's law.

• Linear Flow (constant area flow)

– Oil

– Gas

×+

×=−

−

− 2

2132

321

1008.9

10127.1 A

LBq

Ak

LBqpp oo

o

o

ooo

βρµ

×+

=−

−

2

16

22

2

2

1

10247.193.8

A

LZTLq

Ak

LTZqpp

g

sc

g

sc

γβµ– Gas

+

=−221

Aq

Akqpp sc

g

sc

p1 = upstream pressure, psia Z = gas deviation factor

p2 = downstream pressure, psia T = flowing temperature, oR

μo = oil viscosity, cp γg = gas gravity (air=1)

Bo = oil formation volume factor, bbl/stb qsc= gas flow rate, scf/day

L = Length of flow path, ft μg = gas viscosity, cp

Ko = permeability of oil, md Kg = permeability of gas, md

= velocity coefficient, ft-1 A = area open to flow, ft2

qo = oil flow rate, stb/dayβ

• Radial Flow

–Oil

–Gas

SrrB

pphkq

weoo

wfeo

o +

−=

)/ln(

)(00708.0

µ

)(10703 6

wfRg pphkq

−×=

−

–Gas

pe = pressure at r=re, psia Z = gas deviation factor

pwf = well flowing pressure, psia T = flowing temperature, oR

μo = oil viscosity, cp pR = avg. reservoir pressure, psia

Bo = oil formation volume factor, bbl/stb qsc= gas flow rate, scf/day

ko = permeability of oil, md μg = gas viscosity, cp

rw = wellbore radius, ft Kg = permeability of gas, md

re = well drainage area, ft h = reservoir thickness, ft

qo = oil flow rate, stb/day qsc = gas flow rate, Mscfd

S = skin factor

)/472ln(.

)(10703

weg

wfRg

scrrZT

qµ

−×=

Linear Flow Radial flow

Productivity Index (J)

• The relationship between well inflow rate and

pressure drawdown has often been expressed

in the form of a Productivity Index J,

q

wfR

o

pp

qJ

−=

qo = oil flow rate, stb/day

pR = avg. reservoir pressure, psia

pwf = well flowing pressure, psia

Permeability Alteration and

Turbulence

• The magnitude of the pressure change due to the skin and turbulence, defined as:

SBqp ooo

′=∆

µ2.141

• A value for S’ (skin factor due to permeability change) can be obtained from analysis of various types of pressure transient tests.

hk

SBqp

o

oooskin

′=∆

µ2.141

Factors Affect Productivity Index

• Phase Behavior in Reservoirs

• Relative Permeability Behavior

• Oil Viscosity Behavior

• Oil Formation Volume Factor Behavior• Oil Formation Volume Factor Behavior

–

scsc T ,p ,conditions stock tankat oil of Volume

T p,at gas dissolved its plus oil of Volume=oB

Phase Behavior Diagram

Relative Permeability Behavior

Oil Viscosity Behavior

Oil Formation Volume Factor Behavior

Factors Affecting Inflow Performance

• For oil reservoirs

1. Decrease in kro as gas saturation increases.

2. Increase in μo as pressure decreases and gas is

evolved.evolved.

3. Shrinkage of the oil as gas is evolved when pressure

on the oil decreases.

4. Formation damage or stimulation around the well

bore

5. An increase in the turbulence as oil flow rate

increases.

Drive Mechanisms

• The source of pressure energy to cause

the oil and gas to flow into the well bore

has a substantial effect on both the

performance of the reservoir and the performance of the reservoir and the

total production system

Dissolved Gas Drive

• A dissolved-gas-d rive reservoir is closed from

any outside source of energy, such as water

encroachment. Its pressure is initially above

bubblepoint pressure, and, therefore, no free bubblepoint pressure, and, therefore, no free

gas exists. The only source of material to

replace the produced fluids is the expansion

of the fluids remaining in the reservoir.

Dissolved Gas Drive

Gas Cap Drive







of the fluids remaining in the reservoir. Some

small but usually negligible expansion of the

connate water and rock may also occur.

Gas Cap Drive

Water Drive







of the fluids remaining in the reservoir. Some

small but usually negligible expansion of the

connate water and rock may also occur.

Water Drive

Combination Drive

• In many cases, an oil reservoir will be both

saturated and in contact with an aquifer. In

this case, all three of the previously described

mechanisms may be contributing to the mechanisms may be contributing to the

reservoir drive. As oil is produced, both the

gas cap and aquifer will expand and the gas/oil

contact will drop as the oil/water contact

rises, which can cause complex production

problems.

Drawdown

• The difference between the average reservoir pressure and the flowing bottomholepressure.

• The effects of drawdown on inflow • The effects of drawdown on inflow performance differs for a well with zero skin factor. The effects of both positive and negative skin factors will then be discussed.

Positive Skin

Negative Skin

Effect of Depletion

• In any reservoir in which the average reservoir

pressure is not maintained above the bubble point

pressure, gas saturation will increase in the entire

drainage volume of the wells. This will cause a

decrease in the pressure function in the form of decrease in the pressure function in the form of

decreased kro, which will cause an increase in the

slope of the pressure profile and the IPR. Therefore

to maintain a constant inflow rate to a well, it will be

necessary to increase the drawdown as pR declines

from depletion

Depletion on the Pressure Profile

Depletion on the IPR

Predicting Present Time IPR’s

Vogel Method

• Vogel developed and empirical equation for

the case of a depletion drive reservoir, in

which the reservoir pressure is everywhere which the reservoir pressure is everywhere

below the bubble point pressure. He arrived

at the the following relationship between

dimensionless flow rate and pressure: 2

(max)

8.02.01

−−=

R

wf

R

wf

o

o

p

p

p

p

q

q

Vogel’s Equation

• pwf = well flowing pressure, psia

2

(max)

8.02.01

−−=

R

wf

R

wf

o

o

p

p

p

p

q

q

• pwf = well flowing pressure, psia

• pR = avg. reservoir pressure, psia

• qo = oil flow rate, stb/day

Note: qo(max) is a fictitious value of production representing a maximum drawdown, corresponding to pwf=0.

Constant Productivity Index

• The dimensionless IPR for a well with a

constant productivity index can be calculated

from:

−= wfpq

−=

R

wf

o

o

p

p

q

q1

(max)

Vogel Method

• The tangent of the curve represents 1/J.

Therefore, the J is the negative derivative of q

with respect to P. The negative sign is due to

the fact that the slope of the curve is negative the fact that the slope of the curve is negative

but the J is a positive quantity.

• Vogel’s equation should approximate Darcy’s

equation at very low flow rates.

oo

o

r B

HK

P

qJ

µ== max8.1(At Pwf=Pr)

Vogel Method

• One may want to predict a well’s behavior at some

future time when the reservoir pressures deplete.

futureoo

o

futurerfutureB

K

P

q

J

=

=µ

max8.1

• Simply solving for (qmax)future we obtain

presentoo

o

future

presentr

future

present

future

B

K

P

qJ

=

=

µmax8.1

( ) ( )( )( )

=

presentr

futurer

presento

oo

futureoo

o

presentfutureP

P

k

B

B

kqq

µµmaxmax

Predicting Future IPR’s for Oil Wells

• As the pressure in an oil reservoir declines from

depletion, the ability of the reservoir to transport oil

will also decline. This is caused from the decrease in

the pressure function as relative permeability to oil is

decreased due to increasing gas saturation. decreased due to increasing gas saturation.

• Planning the development of a reservoir with respect

to sizing equipment and planning for artificial lift, as

well as evaluating the project from an economics

standpoint, requires the ability to predict reservoir

performance in the future.

Standing Method

• Standing published a procedure that can be

used to predict the decline in the value of

qo(max) as gas saturation in the reservoir

increases from depletion. increases from depletion.

2

(max))( 8.02.01

−−=

RF

wf

RF

wf

FoFo

p

p

p

pqq

Fetkovich Method

• The method proposed by Fetkovich to

construct future IPR's consists of adjusting the

flow coefficient C for changes in

( )nppCq 22

−=

for changes in f(pr). He assumed that f(pr) was

a linear function of pr and, therefore, the

value of C can be adjusted as

)/( RPRFpF ppCC =

( )wfRo ppCq 2−=

Fetkovich Method

• A value of Cp is obtained from present time

production tests, that is, tests conducted

when pR = pRP. Fetkovich assumed that the

value of the exponent n would not change. value of the exponent n would not change.

• Future IPR's can thus be generated from

n

RPRFRPRFpFo ppppCq )/)(/(22

)( =

Well Completion Effects

• There are basically three types of

completions that may be made on a well

depending on the type of well, well

depth, and type of reservoir or depth, and type of reservoir or

formation.

– Open Hole Completions

– Perforated Completions

– Perforated, Gravel Packed Completions

Open Hole Completions

• The casing is set at the top of the producing

formation and the formation is not exposed to

cement. Also, no perforations are required

• The only effect of the completion on inflow • The only effect of the completion on inflow

performance of an open hole completion will

be caused by alteration of the reservoir

permeability by damage or stimulation.

Perforated Completions

• The most widely used completion method is

one in which the pipe is set through the

formation, and cement is used to fill the

annulus between the casing and the hole. annulus between the casing and the hole.

This, of course, requires perforating the well

to establish communication with the

producing formation. This type of completion

permits selection of the zones that are to be

opened.

Perforation

Perforated, Gravel Packed Completions

• In some reservoirs, the lack of cementing

material in the reservoir allows sand to be

produced into the well. When completing

wells in which the formation is incompetent or wells in which the formation is incompetent or

unconsolidated, a gravel pack completion

scheme is frequently employed. In this type of

completion, a perforated or slotted liner or a

screen liner is set inside the casing opposite

the producing formation.

Gravel-Pack

Well Flow Correlations

• One of the most important components in the

total well system is the well tubing. As much

as 80 percent of the total pressure loss can be

consumed in lifting the fluids from the bottom consumed in lifting the fluids from the bottom

of the hole to the surface. The flow may exist

in tubing or in the annulus between the

tubing and the casing. The wells may be

vertical of can be drilled at large deviation

angles, especially in the case of offshore wells

or wells drilled in urban areas.


• Many correlations have been developed over

the years to evaluate the pressure drop

resulting from the multiphase flow of fluids in

a vertical or deviated well.a vertical or deviated well.


1. Establish stable flow conditions at particular

values of qL , qg , pipe diameter, pipe angle,

etc.

2. In a test section of length ΔL , measure H and 2. In a test section of length ΔL , measure HL and

Δp. Methods for measuring HL include nuclear

densitometers, capacitance devices, quick

closing valves, etc. Flow pattern may be

observed if the test sectionis transparent.


3. Calculate mixture density and elevation

component.LgLLs

gdp

HH

Θ=

−+=

sin

)1(

ρ

ρρρ

4. Calculate and acceleration and friction

component.

c

s

el g

g

dL

dp Θ=

sinρ

accelel dL

dp

dL

dp

L

p

dL

dp

−

−

∆∆

=


5. Calculate a two phase friction factor

6. Change test conditions and return to step 2. H ,

fm

cTp

dL

dp

v

dgf

=2

2

ρ6. Change test conditions and return to step 2. HL,

fTP, and flow pattern should be obtained over a

wide range of conditions.

7. Develop empirical correlations for HL, FTP and

flow pattern as a function of variables that will be

known for design cases. These variables include

vsL, vsg, d, fluid properties, pipe angle, etc.

Choke Sizing

Choke Sizing for Liquid Flow

• Critical velocity is the velocity of sound in that

medium. This velocity is a limiting factor, so

the fluid cannot be accelerated to a large

velocity. velocity.

• The critical of any fluid is given by:

CV

ρ1.68

=∗

ρ = fluid density, lbm/ft3

C = isothermal compressibility of the fluid, psi

Choke Sizing

• Single Phase Liquid Flow

– Calculating the pressure drop across a choke is

relatively easy. However, flow through the choke is

liquid and gas since tubing pressure is usually liquid and gas since tubing pressure is usually

below the bubble point.

– If the exit velocity is below critical, the flow is:

ρP

Cdq c

∆= 22800

dc = choke throat diameter, in

ΔP = differential pressure across the choke, psi

C is given from the Flow Coefficient Graph

Graph of Flow Coefficients for flow

through chokes (Crane, 1957)

http://www.scribd.com/doc/21335619/Throug

h-valves-Pipes-and-Fittings

Reynolds number is given by

µρVd

&928

Re =

h-valves-Pipes-and-Fittings

Accessed Feb 24, 2010

Choke Sizing

• In the case of gas exiting an open-ended flow

line, the sonic velocity is given by:

kZT

T = temperature, oR

γg = gas specific gravity relative to air

Z = compressibility factor

k = ratio of gas specific heat at constant volume to constant pressure (k=cp/cv)

or obtained from Specific Heat Ratios for Hydrocarbon Vapors Graph

g

g

kZTV

γ4.41=∗

Choke Sizing

• The gas flow rate at critical velocity is given by

sceg

gZPT

TPdVQ

2122

2∗∗ =

Q = Gas flow rate, MMSCFD

T = Gas temperature, oR

P = Pressure, pisa

D = Pipe diameter, in

V*g = Sonic velocity in gas at P and T, ft/s

Z = Gas compressibility factor at P and T

sce

gZPT

Q2122

=

Choke Sizing for Gas Flow

• Gas flow through a small diameter exit can be

described by below.

[ ]kkkupdrr

kg

APCq /)1(/22

5.155 +−

= [ ]

g

rrk

gT

q1

2 −

−

=γ

Cd = Choke discharge coefficient

A = Choke throat area, in2

T = Inlet temperature, oR

Pup = Upstream gas pressure, psia

k = gas specific heat ratio, cp/cv

r = Pdn/Pup if ≥ ro

Choke Sizing for Two Phase Flow

• Choked flow for a gas liquid mixture is difficult to

mode, and only empirical correlations are available.

Two presently available are the Gilbert and the Ros

correlations, give asBRAq )(

C

B

pL

upd

RAqP

64

)(=

Pup = upstream pressure, psig (Gilbert), psia (Ros)

qL= liquid flow rate, bbl/day

d64 = choke diameter in 64ths”

Correlation A B C

Gilbert 10.00 0.546 1.89

Ross 17.40 0.500 2.00

Choke Sizing

• To ensure the flow is critical, the equation by

Wallis can be used to calculate the critical

velocity.

( )2/1−

λλ( )2/1

2*2*

−

∗

++=

LL

L

gg

g

ggLLVV

Vρλ

ρ

λλρλρ

V* = critical velocity

γ = in-situ volume fraction of each phase

ρ = density of gas and liquid, lbm/ft3

Flow in Pipes and Restrictions

(vertical wells)(vertical wells)

Two Phase Flow

• Variables

– Liquid Holdup- fraction of an element of pipe that

is occupied by liquid at some instant.

element pipe ain liquid of volume=

– Gas Holdup- relative in-situ volume of liquid and

gas expressed in terms of the volume fraction.

element pipe theof volume

element pipe ain liquid of volume=LH

Hg = 1- HL

Two Phase Flow

• Variables

– No-Slip Liquid Holdup-the ratio of the volume of

liquid in a pipe element that would exist if the gas

and liquid traveled at the same velocity (no and liquid traveled at the same velocity (no

slippage) divided by the volume of the pipe

element..

g

Lq+

=L

L

q

qγ

qL= sum of the in-situ oil and water

qg= the in-situ gas flow rate

Two Phase Flow

• Variables

– No-Slip Gas- gas void fraction can be defined as

q

g

Lgq+

=−=L

g

q

q1 λγ

qL= sum of the in-situ oil and water

qg= the in-situ gas flow rate

Two Phase Flow

• Variables

– Density- The density of an oil/water mixture may

be calculated from the oil and water densities and

flow rates if no slippage between the oil and water flow rates if no slippage between the oil and water

phases is assumed.

wwooL ff ρρρ +=

where

and fw = 1-fo

wo

oo

qq

qf

+=

Two Phase Flow

• Variables

– Velocity- the velocity that phase would exhibit if it

flowed through the total cross sectional area of

the pipe alone.gq=

the pipe alone.

AvL

gq=

•The actual area through which the gas flows is

reduced by the presence of the liquid to AHg.

Therefore, the actual gas velocity is calculated from:

g

gAH

vgq=

Two Phase Flow Patterns

• Whenever two fluids with different physical

properties flow simultaneously in a pipe, there

is a wide range of possible flow patterns. By

flow pattern, reference is made to the flow pattern, reference is made to the

distribution of each phase in the pipe relative

to the other phase.

•Two phase

vertical flow vertical flow

patterns

93-96 Effects of Variables on Well

Performance

• During the producing life of a well or field

many conditions can change that will affect

the well's flowing performance. Also,

conditions can change from well to well in a conditions can change from well to well in a

field at a given time, and conditions can

certainly vary among fields.

Effects of Variables on Well

Performance

• Some of these variables that can change

are…

1. Liquid Flow Rate

2. Gas/Liquid Ratio2. Gas/Liquid Ratio

3. Water/Oil Ratio or Water Cut

4. Liquid Viscosity

5. Tubing Diameter and Slippage

Liquid Flow Rate

• The effect of increasing liquid rate will be an

increase in both HL and fluid velocity. This will

cause an increase in both the hydrostatic and

friction. The effect may be seen graphically in friction. The effect may be seen graphically in

Figure 3-22 that was constructed by choosing

some general well conditions and holding

everything constant except qL.

Gas/Liquid Ratio

• The GLR has more effect on two-phase flowing pressure gradients than any other variable. In a depletion-type field the gas/oil ratio will usually increase with time until late in the life of the reservoir. The GLR may decrease if water cut reservoir. The GLR may decrease if water cut increases.

• The GLR has the most effect on the hydrostatic component of the pressure gradient equation because HL will decrease as GLR increases. However, the total flow rate will increase, and the friction loss depends on the flow rate squared.

Water/Oil Ratio or Water Cut

• The total pressure gradient in the well will

increase as fw increases. This results from an

increase in liquid density if the water is

heavier than the oil and also from a heavier than the oil and also from a

decreasing GLR, since the free gas in the

tubing comes primarily from the oil only. The

effect may be expressed graphically in Figures

3-25 and 3-26.

Figure 3-25 shows only the effect of increased liquid

density while the total effect is shown in Figure 3-26.

Liquid Viscosity

• The effects of liquid viscosity on pressure drop are very

difficult to isolate. This results from the fact that the

concept of a gas/liquid mixture viscosity has no

physical meaning. The liquid viscosity will affect HL to

some degree and will also increase the shearing some degree and will also increase the shearing

stresses in the liquid and, therefore, the friction

pressure drop. If an oil/water mixture is present,

dispersions or emulsions may form and cause a very

large increase in the pressure gradient. At the present

time, there is no method to accurately predict the

viscosity of an oil/water mixture, much less the

viscosity of a gas/oil/water mixture.

The combined effects of

decreasing API gravity

and increasing viscosity

for a gas/oil mixture are

shown qualitatively in

Liquid Viscosity

shown qualitatively in

Figure 3-27. If water

were present, the effects

would probably be even

more pronounced.

Tubing Diameter and Slippage

• The selection of the proper tubing size to install in a

well is one of the most critical and the most

neglected functions of a production engineer. In

many cases the tubing size will be selected based on

such criteria as what has been used in the past or such criteria as what has been used in the past or

what is available on the pipe rack. A total system

analysis, which combines the reservoir and piping

system performance, is required to select the proper

tubing size, but the effects of tubing size on velocity

and slippage will be discussed.

• As the tubing size increases, the velocity of the mixture

decreases and eventually the velocity will be too low to

lift the liquids to the surface. The well will then begin

to load up with liquids and may eventually die. The

tubing size at which a well will begin to load or the

maximum tubing size which will sustain flow can be

determined from a plot such as Figure 3-29.

Tubing Diameter

and Slippage

•The effect of declining production

rate and, therefore, velocity for a

particular tubing size can be shown

qualitatively in Figure 3-30. For a

particular tubing size, well depth,

wellhead pressure and as/liquid wellhead pressure and as/liquid

ratio, there will exist a minimum

production rate that will keep the

well unloaded.

•Figure 3-31 shows the effect of

tubing diameter on the minimum

rate. This type of information is

valuable in determining at what rate

a well will begin to load for various

tubing sizes.

Use of Prepared Pressure Traverse

Curves

• In some cases it is not feasible for the field engineer to conduct an involved computer study to calculate a traverse or to calculate the pressure drop in a tubing string for give field conditions. In some cases, it may be advantageous to construct some cases, it may be advantageous to construct a set of pressure traverse curves for hypothetical values of the variables such as qL ,GLR, d, fw , etc. These curves can then be used to estimate the pressure drop that would occur in a well producing under similar conditions.

production system analysiss3.amazonaws.com/noteswap-sid-1/2/5/0/4/25045dd60dbfc3d...production...

Documents