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Squirt aij Coefficients

To obtain the aij coefficients in the squirt model, we first note that these coefficients are defined under conditions where (no fluid passing between the porous grains and the principal porespace). Under these conditions, the rate of fluid depletion of a sample (rate of fluid volume being extruded from the principal pore space via the exterior sample surface as normalized by the sample volume) is due to the difference between the rate of dilatation of the principal porespace (denoted here as ) and the rate at which fluid in the pores is dilating . If we also perform a volume average of equation (3) over the porous grain space and use the notation that we obtain the following three equations
 (81) (82) (83)
The macroscopic dilatation of interest is . In order to obtain the macroscopic compressibility laws for porous-grain/principal-porespace composite, we introduce linear response laws of the form
 (84) (85)
where the ai and bi must be found. We note immediately that from the definition one has
 (86)
which must hold true for any variation of the independent pressure variables so that a1=1/v2, a2 = - v1/v2, a3 = 0.

To obtain the bi, we now combine the above into the macroscopic laws
 (87) (88) (89)
and use the fact that the coefficients of the matrix must be symmetric (aij = aji). With a11 = 1/K corresponding to the overall drained frame modulus of the composite (to be independently specified), we obtain v1 b1 = 1/K - 1/K2d, v1 b2 = -1/K + (1+v1)/K2d, and . The final aij coefficients are exactly
 (90) (91) (92) (93) (94) (95)
Reasonable models for K and Kd2 will be discussed shortly.

Next: Squirt Transport Up: SQUIRT-FLOW MODEL Previous: SQUIRT-FLOW MODEL
Stanford Exploration Project
10/14/2003