Page 304 - Principles of Applied Reservoir Simulation 2E

Part V: Technical Supplements 289

V - (27.12)
r
s
where
— compressional velocity
V p
= shear velocity
V s
K* = effective bulk modulus
fl* = effective shear modulus
= effective bulk density = (!-<J))p Ma +4^
p B
= density of grains (solid matrix material)
p ma
p, = fluid density = p 0S 0 +p wS w +p gS g
<j> = porosity
Gassman [1951] derived an expression for K* from the theory of elasticity of
porous media [Schon, 1996; McQuillin, et al., 1984]:

K

KB + (27
i K

where
- bulk modulus of empty reservoir, that is, dry rock or
K B
porous matrix material
= bulk modulus of grains (solid matrix material)
K G
= bulk modulus of fluid =
K F IIc f
c f = fluid compressibility = c 0 S 0 + c w S w + c g S g
The grain modulus K G equals the bulk modulus K B when porosity equals
zero. Figure 27-3 shows that bulk modulus and shear modulus are linear
functions of porosity for quartz sandstone [Murphy, et al., 1993] for porosity
less than 35%.
The WINB4D user must enter data that cannot be calculated from
traditional black oil simulator input data. In particular, the user must enter K B,
K G,\i*, and p ma. The references give values that may be used if the data are not