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Material Balance Equations
By : Dr. Ir. Dedy Kristanto, M.Sc
Petroleum Engineering Department UPN ”Veteran’ Yogyakarta
ENTER
Material Balance Equations
Introduction
INTRODUCTION MODELLING APPLICATION
Learning goals • Basic understanding of material balance
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.
SUMMARY
The handout “Material Balance Equations” can be downloaded from here:
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.
Introduction Application
Modelling
Summary Block diagram
Saturation
Material conservation
Equations Graph A
FAQ
REFERENCES
ABOUT
Graph B
Water influence
Plot 1
Plot 2
Initial gascap
Plot 3 HELP
Material Balance Equations
Block diagram of a producing reservoir
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation
The essence of material balance is described in the block diagram below.
Due to change in pressure, the pore volume as well as the fraction of the volume occupied by gas, oil & water will change.
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
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Principle of material conservation
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation
From the block diagram we get the expression below, which is the basis for the material balance formulas.
⎧Amount of fluids present⎫ ⎧ Amount of ⎫ ⎧Amount of fluids remaining⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ in the reservoir initially ⎬ − ⎨fluids produced⎬ = ⎨ in the reservoir finally ⎬ ⎪ ⎪ ⎪ ⎪ (st. vol.) ⎪ ⎪ (st. vol.) (st. vol.) ⎭ ⎭ ⎩ ⎩ ⎭ ⎩
APPLICATION SUMMARY
Note that “fluids produced” include all influence on the reservoir: • Production • Injection • Aquifer influx
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Formation Volume Factor in the Black Oil model
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation
The formation volume factors (FVF) tell how much the oil, gas and water is compressed at a given pressure.
APPLICATION
Bo = reservoir volume of oil / standard volume of oil
SUMMARY
Bg = reservoir volume of gas / standard volume of gas
The graphs below show how the FVF of oil, gas and water develop vs pressure. Click on the buttons to show the graphs.
Bw = reservoir volume of water / standard volume of water
Bo vs. P
Bg vs. P
Bo
Bw vs. P
Bg
P
Bw
P
P
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Solution Gas-Oil Ratio in the Black Oil model
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation APPLICATION
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.
Click on the button below to see the typical pressure dependency of the solution gas-oil ratio in the black oil model.
SUMMARY Rs = standard volume gas / standard volume oil
Rso vs. P
Rso
P Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
The complete black oil material balance equation
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation
The final material balance relationships is given below. How these expressions are derived can be studied in the Material Balance.
(
)
F = N E o + mE g + E f ,w + (Wi + We )Bw2 + Gi Bg2
APPLICATION SUMMARY
Where:
production terms are
[
(
) ]
F = N p Bo2 + R p − Rso2 Bg2 + W p Bw2 oil and solution gas expansion terms are
E o = (Bo2 − B o1 ) + (Rso1 − Rso2 )B g2 gas cap expansion terms are
⎛ B g2 ⎞ E g = B o1 ⎜⎜ − 1⎟⎟ ⎝ B g1 ⎠ and rock and water compression/expansion terms are
E f ,w = −(1 + m)Bo1
C r + C w S w1 1 − S w1
∆P
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Saturation and pressure development
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation APPLICATION SUMMARY
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.
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Application of Material Balance
INTRODUCTION MODELLING APPLICATION
In 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.
Initial gascap Plot 1 Plot 2 Water influence Plot 3
The animation below shows a producing reservoir with gas and water injection.
SUMMARY In the following pages ways of finding some of these values will be explained.
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Application of Material Balance Initial gas cap (Havlena and Odeh approach)
INTRODUCTION MODELLING APPLICATION
For 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 origo with 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.
Initial gascap Plot 1 Plot 2 Water influence Plot 3 SUMMARY
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:
(
)
F = N E o + mE g + E f ,w + (Wi + We )Bw2 + Gi Bg2
Assuming no water influence, gas injection and rock or water compression/expansion.
F = N (Eo + mE g )
(2)
Eg F = N + mN Eo Eo
(3)
Large version Plot 1 Large version Plot 2
Click to display symbols used
FAQ
REFERENCES
ABOUT
(1)
HELP
Material Balance Equations
Application of Material Balance Initial gas cap (Havlena and Odeh approach)
INTRODUCTION MODELLING APPLICATION
For 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 origo with a slope of N.
Initial gascap Plot 1 Plot 2 Water influence Plot 3 SUMMARY
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.
F = N (Eo + mE g )
(2)
Return
Large version Plot 2
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Application of Material Balance Initial gas cap (Havlena and Odeh approach)
INTRODUCTION MODELLING APPLICATION
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)
Initial gascap Plot 1 Plot 2 Water influence Plot 3
Assuming no water influence, gas injection and rock or water compression/expansion.
Eg F = N + mN Eo Eo
(3)
SUMMARY
Large version Plot 1 Return
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Application of Material Balance Water influence (Havlena and Odeh approach)
INTRODUCTION MODELLING APPLICATION
In 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)
Initial gascap Plot 1 Plot 2 Water influence Plot 3
General mass balance formula:
(
)
F = N E o + mE g + E f ,w + (Wi + We )Bw2 + Gi Bg2
(1)
Assuming no water or gas injection and Bw=1. 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.
SUMMARY
F = N (Eo + mEg + E f , w ) + We
(4)
Neglecting Ef,w due to it’s small influence and assuming no initial gascap.
F = NEo + We
(5)
W F =N+ e Eo Eo
(6)
Water influx model for radial aquifer shape:
(
)
We = (cw + c f )π re2 − ro2 fhφ∆p
(7)
Large version Plot 3
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Application of Material Balance Water influence (Havlena and Odeh approach)
INTRODUCTION MODELLING APPLICATION
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.
Initial gascap Plot 1 Plot 2 Water influence Plot 3
W F =N+ e Eo Eo
(6)
SUMMARY
Return
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Summary
INTRODUCTION MODELLING APPLICATION
MODELLING: 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.
SUMMARY
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. Block diagram 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 m∗N.
Saturation & pressure
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.
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
References
INTRODUCTION MODELLING APPLICATION
Jon Kleppe. Material balance. http://www.ipt.ntnu.no/~kleppe/SIG4038/02/matbal.pdf SUMMARY 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. Skjæveland (ed.) & Jon Kleppe (ed.) 1992. SPOR monograph : recent advances in improved oil recovery methods for North Sea sandstone reservoirs Norwegian Petroleum Directorate, Stavanger. 335 pp.
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
About this module
INTRODUCTION MODELLING APPLICATION
Title: Material Balance Equations SUMMARY 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: --
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Help Navigation tools in the module
INTRODUCTION MODELLING APPLICATION
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.
SUMMARY
The chapter you are currently viewing in is shown with this marker: , while the subchapter (when applicable) is highlighted in orange.
At bottom of the slide you’ll find a few standardised buttons which occur on every page (some may not be present in the module): REFERENCES
shows the list of references.
ABOUT
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BACK
Within the main frame (the white area), you’ll find text and illustrations as well as animations and videos etc. Many pictures have enlargement buttons near them.
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FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Symbols used in material balance equations
INTRODUCTION MODELLING APPLICATION
Bg
Formation volume factor for gas (res.vol./st.vol.)
Sg
Gas saturation
SUMMARY
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
T
Temperature
(pressure-1)
Cr
Pore compressibility
Cw
Water compressibility (pressure-1)
Vb
Bulk volume (res.vol.)
∆P
P2-P1
Vp
Pore volume (res.vol.)
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.)
Gi
Cumulative gas injected (st.vol.)
R
Density (mass/vol.)
Gp
Cumulative gas produced (st.vol.)
φ
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.)
P
Pressure
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)
Click to return to calculation
FAQ
REFERENCES
ABOUT
HELP
By : Dr. Ir. Dedy Kristanto, M.Sc
Petroleum Engineering Department UPN ”Veteran’ Yogyakarta
ENTER
Material Balance Equations
Introduction
INTRODUCTION MODELLING APPLICATION
Learning goals • Basic understanding of material balance
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.
SUMMARY
The handout “Material Balance Equations” can be downloaded from here:
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.
Introduction Application
Modelling
Summary Block diagram
Saturation
Material conservation
Equations Graph A
FAQ
REFERENCES
ABOUT
Graph B
Water influence
Plot 1
Plot 2
Initial gascap
Plot 3 HELP
Material Balance Equations
Block diagram of a producing reservoir
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation
The essence of material balance is described in the block diagram below.
Due to change in pressure, the pore volume as well as the fraction of the volume occupied by gas, oil & water will change.
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
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Principle of material conservation
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation
From the block diagram we get the expression below, which is the basis for the material balance formulas.
⎧Amount of fluids present⎫ ⎧ Amount of ⎫ ⎧Amount of fluids remaining⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ in the reservoir initially ⎬ − ⎨fluids produced⎬ = ⎨ in the reservoir finally ⎬ ⎪ ⎪ ⎪ ⎪ (st. vol.) ⎪ ⎪ (st. vol.) (st. vol.) ⎭ ⎭ ⎩ ⎩ ⎭ ⎩
APPLICATION SUMMARY
Note that “fluids produced” include all influence on the reservoir: • Production • Injection • Aquifer influx
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Formation Volume Factor in the Black Oil model
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation
The formation volume factors (FVF) tell how much the oil, gas and water is compressed at a given pressure.
APPLICATION
Bo = reservoir volume of oil / standard volume of oil
SUMMARY
Bg = reservoir volume of gas / standard volume of gas
The graphs below show how the FVF of oil, gas and water develop vs pressure. Click on the buttons to show the graphs.
Bw = reservoir volume of water / standard volume of water
Bo vs. P
Bg vs. P
Bo
Bw vs. P
Bg
P
Bw
P
P
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Solution Gas-Oil Ratio in the Black Oil model
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation APPLICATION
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.
Click on the button below to see the typical pressure dependency of the solution gas-oil ratio in the black oil model.
SUMMARY Rs = standard volume gas / standard volume oil
Rso vs. P
Rso
P Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
The complete black oil material balance equation
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation
The final material balance relationships is given below. How these expressions are derived can be studied in the Material Balance.
(
)
F = N E o + mE g + E f ,w + (Wi + We )Bw2 + Gi Bg2
APPLICATION SUMMARY
Where:
production terms are
[
(
) ]
F = N p Bo2 + R p − Rso2 Bg2 + W p Bw2 oil and solution gas expansion terms are
E o = (Bo2 − B o1 ) + (Rso1 − Rso2 )B g2 gas cap expansion terms are
⎛ B g2 ⎞ E g = B o1 ⎜⎜ − 1⎟⎟ ⎝ B g1 ⎠ and rock and water compression/expansion terms are
E f ,w = −(1 + m)Bo1
C r + C w S w1 1 − S w1
∆P
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Saturation and pressure development
INTRODUCTION MODELLING Block diagram Material conservation Graph A B Equations Saturation APPLICATION SUMMARY
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.
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Application of Material Balance
INTRODUCTION MODELLING APPLICATION
In 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.
Initial gascap Plot 1 Plot 2 Water influence Plot 3
The animation below shows a producing reservoir with gas and water injection.
SUMMARY In the following pages ways of finding some of these values will be explained.
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Application of Material Balance Initial gas cap (Havlena and Odeh approach)
INTRODUCTION MODELLING APPLICATION
For 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 origo with 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.
Initial gascap Plot 1 Plot 2 Water influence Plot 3 SUMMARY
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:
(
)
F = N E o + mE g + E f ,w + (Wi + We )Bw2 + Gi Bg2
Assuming no water influence, gas injection and rock or water compression/expansion.
F = N (Eo + mE g )
(2)
Eg F = N + mN Eo Eo
(3)
Large version Plot 1 Large version Plot 2
Click to display symbols used
FAQ
REFERENCES
ABOUT
(1)
HELP
Material Balance Equations
Application of Material Balance Initial gas cap (Havlena and Odeh approach)
INTRODUCTION MODELLING APPLICATION
For 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 origo with a slope of N.
Initial gascap Plot 1 Plot 2 Water influence Plot 3 SUMMARY
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.
F = N (Eo + mE g )
(2)
Return
Large version Plot 2
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Application of Material Balance Initial gas cap (Havlena and Odeh approach)
INTRODUCTION MODELLING APPLICATION
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)
Initial gascap Plot 1 Plot 2 Water influence Plot 3
Assuming no water influence, gas injection and rock or water compression/expansion.
Eg F = N + mN Eo Eo
(3)
SUMMARY
Large version Plot 1 Return
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Application of Material Balance Water influence (Havlena and Odeh approach)
INTRODUCTION MODELLING APPLICATION
In 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)
Initial gascap Plot 1 Plot 2 Water influence Plot 3
General mass balance formula:
(
)
F = N E o + mE g + E f ,w + (Wi + We )Bw2 + Gi Bg2
(1)
Assuming no water or gas injection and Bw=1. 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.
SUMMARY
F = N (Eo + mEg + E f , w ) + We
(4)
Neglecting Ef,w due to it’s small influence and assuming no initial gascap.
F = NEo + We
(5)
W F =N+ e Eo Eo
(6)
Water influx model for radial aquifer shape:
(
)
We = (cw + c f )π re2 − ro2 fhφ∆p
(7)
Large version Plot 3
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Application of Material Balance Water influence (Havlena and Odeh approach)
INTRODUCTION MODELLING APPLICATION
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.
Initial gascap Plot 1 Plot 2 Water influence Plot 3
W F =N+ e Eo Eo
(6)
SUMMARY
Return
Click to display symbols used
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
Summary
INTRODUCTION MODELLING APPLICATION
MODELLING: 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.
SUMMARY
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. Block diagram 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 m∗N.
Saturation & pressure
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.
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
References
INTRODUCTION MODELLING APPLICATION
Jon Kleppe. Material balance. http://www.ipt.ntnu.no/~kleppe/SIG4038/02/matbal.pdf SUMMARY 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. Skjæveland (ed.) & Jon Kleppe (ed.) 1992. SPOR monograph : recent advances in improved oil recovery methods for North Sea sandstone reservoirs Norwegian Petroleum Directorate, Stavanger. 335 pp.
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
About this module
INTRODUCTION MODELLING APPLICATION
Title: Material Balance Equations SUMMARY 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: --
FAQ
REFERENCES
ABOUT
HELP
Material Balance Equations
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INTRODUCTION MODELLING APPLICATION
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Material Balance Equations
Symbols used in material balance equations
INTRODUCTION MODELLING APPLICATION
Bg
Formation volume factor for gas (res.vol./st.vol.)
Sg
Gas saturation
SUMMARY
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
T
Temperature
(pressure-1)
Cr
Pore compressibility
Cw
Water compressibility (pressure-1)
Vb
Bulk volume (res.vol.)
∆P
P2-P1
Vp
Pore volume (res.vol.)
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.)
Gi
Cumulative gas injected (st.vol.)
R
Density (mass/vol.)
Gp
Cumulative gas produced (st.vol.)
φ
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.)
P
Pressure
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)
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