Reservoir transport equations by compositional approach |
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Authors: | Sorab Panday MYavuz Corapcioglu |
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Institution: | (1) Department of Civil and Environmental Engineering, Washington State University, 99164-3001 Pullman, WA, USA |
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Abstract: | The objective of this paper is to present an overview of the fundamental equations governing transport phenomena in compressible reservoirs. A general mathematical model is presented for important thermo-mechanical processes operative in a reservoir. Such a formulation includes equations governing multiphase fluid (gas-water-hydrocarbon) flow, energy transport, and reservoir skeleton deformation. The model allows phase changes due to gas solubility. Furthermore, Terzaghi's concept of effective stress and stress-strain relations are incorporated into the general model. The functional relations among various model parameters which cause the nonlinearity of the system of equations are explained within the context of reservoir engineering principles. Simplified equations and appropriate boundary conditions have also been presented for various cases. It has been demonstrated that various well-known equations such as Jacob, Terzaghi, Buckley-Leverett, Richards, solute transport, black-oil, and Biot equations are simplifications of the compositional model.Notation List
B
reservoir thickness
- B
formation volume factor of phase
- Ci
mass of component i dissolved per total volume of solution
- C
i
mass fraction of component i in phase
- C
heat capacity of phase at constant volume
- Cp
heat capacity of phase at constant pressure
- D
i
hydrodynamic dispersion coefficient of component i in phase
- DMTf
thermal liquid diffusivity for fluid f
-
F
= F(x, y, z, t) defines the boundary surface
- fp
fractional flow of phase
-
g
gravitational acceleration
- Hp
enthalpy per unit mass of phase
- Jp
volumetric flux of phase
- krf
relative permeability to fluid f
- k0
absolute permeability of the medium
- Mp
i
mass of component i in phase
-
n
porosity
-
N
rate of accretion
- Pf
pressure in fluid f
- pca
capillary pressure between phases and =p-p
- Ri
rate of mass transfer of component i from phase to phase
- Ri
source
source rate of component i within phase
- S
saturation of phase
-
s
gas solubility
-
T
temperature
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t
time
-
U
displacement vector
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u
velocity in the x-direction
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v
velocity in the y-direction
- V
volume of phase
- Vs
velocity of soil solids
- Wi
body force in coordinate direction i
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x
horizontal coordinate
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z
vertical coordinate
Greek Letters p
volumetric coefficient of compressibility
- T
volumetric coefficient of thermal expansion
- ij
Kronecker delta
-
volumetric strain
- m
thermal conductivity of the whole matrix
-
internal energy per unit mass of phase
-
gf
suction head
-
density of phase
- ij
tensor of total stresses
- ij
tensor of effective stresses
-
volumetric content of phase
- f
viscosity of fluid f |
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Keywords: | Reservoir transport heat and mass tranfer macroscopic equations |
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