Before passing on to the specific models for the various coefficients, we state here several general constraints (independent of any modeling assumptions) on the geomechanical constants a_{ij}. Note that in order to measure the a_{ij}'s in the laboratory, we need only consider an isolated sample immersed in a ``reservoir'' characterized by three control parameters: p_{c}, p_{f}^{(1)}, and p_{f}^{(2)}; i.e., gradients in these quantities and the subsequent flow induced by those gradients do not enter the definition of the a_{ij}'s.
The constraints are obtained from the limiting case in which the rate at which p_{c}, p_{f}^{(1)}, and p_{f}^{(2)} are all changing is much slower than the rate at which internal fluid equilibration can take place. In this ``long-time limit'', we are always in the quasi-static state where
p_{f}^{(1)} = p_{f}^{(2)}. | (18) |