5- material balance

Material Balance Equations

ENTER

By : Dr. Ir. Dedy Kristanto, M.Sc

Petroleum Engineering Department UPN Veteran Yogyakarta

http://www.learningjournals.net/geoscience


REFERENCES ABOUT HELPFAQ

IntroductionINTRODUCTIONMODELLING

APPLICATIONLearning goals Basic understanding of material balance

The handout Material Balance Equations can bedownloaded from here:

To illustrate the simplest possible model we can have for analysis of reservoir behavior, we will start with derivation of so-called Material Balance Equations. This type of model excludes fluid flow inside the reservoir, and considers fluid and rock expansion/compression effects only, in addition, of course, to fluid injection and production.

This module is meant to be an extra help to the lectures in Reservoir recovery techniques by giving examples to the curriculum covered by the handout Material Balance Equations.

The structure of the model is shown below.

SUMMARY

IntroductionApplicationModelling

Summary

SaturationBlockdiagram

Waterinfluence

Materialconservation

Graph A Graph B

Equations

Initialgascap

Plot 1 Plot 2 Plot 3



Block diagram of a producing reservoirINTRODUCTIONMODELLING

Block diagramMaterial conservationGraph A BEquationsSaturation

Due to change in pressure, the pore volume as well as the fraction of the volume occupied by gas, oil & water will change.

The essence of material balance is described in the block diagram below.

From the initial stage oil, gas & water is produced. At the same time gas & water is (re)injected into the reservoir to maintain pressure. There is also an influx from the aquifer below the reservoir.

APPLICATION

SUMMARY

Click to display symbols used



Principle of material conservationINTRODUCTIONMODELLING


From the block diagram we get the expression below, which is the basis for the material balance formulas.

Amount of fluids presentin the reservoir initially

(st. vol.)

Amount of fluids produced

(st. vol.)

Amount of fluids remainingin the reservoir finally

(st. vol.)

=

APPLICATION

SUMMARY

Note that fluids produced include all influence on the reservoir: Production Injection Aquifer influx



Formation Volume Factor in the Black Oil modelINTRODUCTIONMODELLING


The graphs below show how the FVF of oil, gas and water develop vs pressure. Click on the buttons to show the graphs.

The formation volume factors (FVF) tell how much the oil, gas and water is compressed at a given pressure.

Bo = reservoir volume of oil / standard volume of oil

Bg = reservoir volume of gas / standard volume of gas

Bw = reservoir volume of water / standard volume of water

APPLICATION

SUMMARY

Bo vs. P Bg vs. P Bw vs. P

P

Bo

P

Bg

P

Bw




Solution Gas-Oil Ratio in the Black Oil modelINTRODUCTIONMODELLING


The Rso plot shows how the solution gas ratio develops vs pressure. When the pressure reaches the bubblepointpressure, it is no longer possible to solve more gas into the oil. Thus the gradient of the curve becomes zero.

Rs = standard volume gas / standard volume oil

Click on the button below to see the typical pressure dependency of the solution gas-oil ratio in the black oil model.

APPLICATION

SUMMARY

Rso vs. P

Rso

PClick to display symbols used



The complete black oil material balance equationINTRODUCTIONMODELLING


The final material balance relationships is given below. How these expressions are derived can be studied in the Material Balance.

( ) ( )F N E mE E W W B G Bo g f w i e w2 i g2= + + + + +,

Where: production terms are

( )[ ]F N B R R B W Bp o2 p so2 g2 p w2= + +

oil and solution gas expansion terms are

( ) ( )E B B R R Bo o2 o1 so1 so2 g2= +

gas cap expansion terms are

E BBB

1g o1g2

g1=

and rock and water compression/expansion terms are

( )E 1 m B C C S1 S

Pf w o1r w w1

w1, = +

+

APPLICATION

SUMMARY




Saturation and pressure developmentINTRODUCTIONMODELLING


View the animations below to see how the pressure and oil-, gas- and water-saturation typically develops in a reservoir initially above the bubblepoint develops versus time. Also included is how pressure might develop versus time.

The plot to the left shows how the saturations and the pressure in the reservoir develop vs time in a reservoir if there is small or no water injection.

The plot to the right shows the same for a reservoir with large water injecton.

APPLICATION

SUMMARY




Application of Material BalanceINTRODUCTIONMODELLING

APPLICATIONIn material balance calculations there are in most cases many uncertainties with regard to reservoir parametres. Uncertain values may for instance include the size of the initial gascap, the initial amount of oil in the reservoir and the influx of the aquifer.

In the following pages ways of finding some of these values will be explained.

The animation below shows a producing reservoir with gas and water injection.

Initial gascapPlot 1Plot 2

Water influencePlot 3

SUMMARY




Application of Material BalanceInitial gas cap (Havlena and Odeh approach)

INTRODUCTION

MODELLING

APPLICATIONFor gascap reservoirs the value of m is in most cases uncertain. The value of N can however usually be defined well through producing wells. In this case a good approach will be to plot F as a function of (Eo+mEg) for an assumed value of m. (eq. 2) For the correct value of m the slope will be a straight line passing through origowith a slope of N. For a too large value of m, the plot will deviate down and for a too small value it will deviate up.

If both the value of m and N are uncertain one should plot F/Eo as a function of Eg/Eo. This plot should be linear and will intercept the y axis at a value of N and have a slope of mN. (eq. 3)

General mass balance formula:Initial gascapPlot 1Plot 2 ( ) ( )F N E mE E W W B G Bo g f w i e w2 i g2= + + + + +, (1)

Water influencePlot 3 Assuming no water influence, gas injection and rock

or water compression/expansion.SUMMARY

( )go mEENF += (2)

o

g

o EE

mNNEF

+= (3)

Large version Plot 1






INTRODUCTION

MODELLING

APPLICATIONFor gascap reservoirs the value of m is in most cases uncertain. The value of N can however usually be defined well through producing wells. In this case a good approach will be to plot F as a function of (Eo+mEg) for an assumed value of m. (eq. 2) For the correct value of m the slope will be a straight line passing through origowith a slope of N.

For a too large value of m, the plot will deviate down and for a too small value it will deviate up.

Assuming no water influence, gas injection and rock or water compression/expansion.



SUMMARY ( )go mEENF += (2)

Return






INTRODUCTION

MODELLING

APPLICATIONIf both the value of m and N are uncertain one should plot F/Eo as a function of Eg/Eo. This plot should be linear and will intercept the y axis at a value of N and have a slope of mN. (eq. 3)

Assuming no water influence, gas injection and rock or water compression/expansion.


o

g

o EE

mNNEF

+=Water influencePlot 3

(3)

SUMMARY


Return




Application of Material BalanceWater influence (Havlena and Odeh approach)

INTRODUCTION

MODELLING

APPLICATIONIn water drive reservoirs the biggest uncertainty is in most cases the water influx, We. To find this we plot F/Eo vs We/Eo. In this plot We must be calculated with a known model. (e.g. eq. 7)

For a correct model of We we will get a straight line. For the wrong model the plot will deviate from a straight line as shown in plot 3.

General mass balance formula:Initial gascapPlot 1Plot 2 ( ) ( )F N E mE E W W B G Bo g f w i e w2 i g2= + + + + +, (1)Water influencePlot 3 Assuming no water or gas injection and Bw=1.

SUMMARY ( ) ewfgo WEmEENF +++= , (4)Neglecting Ef,w due to its small influence and assuming no initial gascap.

eo WNEF += (5)


o

e

o EWN

EF

+= (6)

( ) ( ) pfhrrccW oefwe += 22Water influx model for radial aquifer shape:

(7)




Application of Material BalanceWater influence (Havlena and Odeh approach)

INTRODUCTION

MODELLING

APPLICATIONFor a correct model of We we will get a straight line. For the wrong model the plot will deviate from a straight line as shown in plot 3. o

e

o EWN

EF

+= (6)Initial gascapPlot 1Plot 2


SUMMARY

Return




SummaryINTRODUCTIONMODELLING

APPLICATIONMODELLING: Block diagram: Material balance equations are based on a model with a know start- and end-point. Between the two stages oil, gas & water is produced and gas & water is (re)injected into the reservoir to maintain pressure. There is also an influx from the aquifer below the reservoir. Due to change in pressure, the pore volume as well as the fraction of the volume occupied by gas, oil & water will change.

Material conservation: Amounts of fluids in the reservoir at stage one is equal to the amount of fluids at stage two plus the amount of fluids produced.

Graph A: The formation volume factors (FVF) tell how much the oil, gas and water is compressed at a given pressure.

Graph B: The Rso plot shows how the solution gas ratio develops vs pressure. When the pressure reaches the bubblepointpressure, it is no longer possible to solve more gas into the oil. Thus the gradient of the curve becomes zero.

Equations: The material balance equations consist of a general part, oil and solution gas expansion terms, gas cap expansion terms and rock and water compression/expansion terms

Saturation: Pressure and saturations change versus time, depending on production/injection. See figure to the right.

APPLICATION: Initial gascap: In a gas drive reservoirs m may be calculated by plotting F as a function of (Eo+mEg). For the correct value of m the plot will be a straight line. Alternatively m & N may be calculated by plotting F/Eo vs Eg/Eo. The curve will intercept the y axis at a value of N and have a slope of mN.

Water influence: In a water drive reservoir the water influx, We, can be recovered by plotting F/Eo vs We/Eo. In this plot We must be calculated with a known model.

SUMMARY

Block diagram

Saturation & pressure



ReferencesINTRODUCTIONMODELLING

APPLICATIONJon Kleppe. Material balance. http://www.ipt.ntnu.no/~kleppe/SIG4038/02/matbal.pdf

L.P. Dake 1978. Fundamentals of reservoir engineering, Elsevier, Amsterdam, 443 pp.

L.P. Dake 1994. The practice of reservoir engineering, Elsevier, Amsterdam, 534 pp.

Svein M. Skjveland (ed.) & Jon Kleppe (ed.) 1992. SPOR monograph : recent advances in improved oil recovery methods for North Sea sandstone reservoirsNorwegian Petroleum Directorate, Stavanger. 335 pp.

SUMMARY



About this moduleINTRODUCTIONMODELLING

APPLICATIONTitle: Material Balance Equations

Author: Prof. Jon Kleppe

Assistant producer: Vidar W. Moxness

Size: 0.8 mb

Publication date: 24. July 2002

Abstract: The module describes the basics of material balance calculations.

Software required: PowerPoint XP/XP Viewer

Prerequisites: none

Level: 1 4 (four requires most experience)

Estimated time to complete: --

SUMMARY



HelpNavigation tools in the module

INTRODUCTION

MODELLING

APPLICATIONAt bottom of the slide youll find a few standardised buttons which occur on every page (some may not be present in the module):

On every page, you will find the title at the top, and a menu with the main chapters in bold to the left. These are hyperlinks which enable you choose the chapters in whichever order you wish to view them. Keep in mind that the module is set up in the order the author believes is most appropriate for study. These chapters are also represented with an illustration on the introduction slide linked to the appropriate chapter.

The chapter you are currently viewing in is shown with this marker: , while the subchapter (when applicable) is highlighted in orange.

Within the main frame (the white area), youll find text and illustrations as well as animations and videos etc. Many pictures have enlargement buttons near them.

SUMMARY

shows the list of references.REFERENCES

shows information about the module (e.g. author and assistant producer).

ABOUT

shows a list of frequently asked questions if there are any.FAQ

BACK takes you to previously viewed slide.

is linked to the previous chapter and slide, respectively.

Previous picture in an animation or sequence of pictures. is linked to the next chapter and slide, respectively.

Next picture in an animation or sequence of pictures.you may turn off the sound, or turn it on (when available).

HELP

ON OFF

you have figured it out!

will end your session with the current module.EXIT

If you have any problems, please let us know by sending an e-mail to [email protected]. Please include the title of module and description of the problem. We will respond as quickly as possible.

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Symbols used in material balance equationsINTRODUCTIONMODELLING

APPLICATION Bg Formation volume factor for gas (res.vol./st.vol.) Sg Gas saturation

Ef,w Rock and water expansion/compression term We Cumulative aquifer influx (st.vol.)

Eg Gas cap expansion term Wi Cumulative water injected (st.vol.)

Eo Oil & solution gas expansion term Wp Cumulative water produced (st.vol.)

P Pressure

Bo Formation volume factor for oil (res.vol./st.vol.) So Oil saturation

Bw Formation volume factor for water (res.vol./st.vol.) Sw Water saturation

Cr Pore compressibility (pressure-1) T Temperature

Cw Water compressibility (pressure-1) Vb Bulk volume (res.vol.)

P P2-P1 Vp Pore volume (res.vol.)

Gi Cumulative gas injected (st.vol.) R Density (mass/vol.)

Gp Cumulative gas produced (st.vol.) Porosity

m Initial gas cap size (res.vol. of gas cap)/(res.vol. of oil zone)

N Original oil in place (st.vol.)

Np Cumulative oil produced (st.vol.)

Pb Bubblepoint Pressure

Rp Cumulative producing gas-oil ratio (st.vol./st.vol.) = Gp/Np

Rso Solution gas-oil ratio (st.vol. gas/st.vol. oil)

SUMMARY

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5- material balance

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