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 aij. Note that in order to measure the aij's in the laboratory, we need only consider an isolated sample immersed in a ``reservoir'' characterized by three control parameters: pc, pf(1), and pf(2); i.e., gradients in these quantities and the subsequent flow induced by those gradients do not enter the definition of the aij's.
The constraints are obtained from the limiting case in which the rate at which pc, pf(1), and pf(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
|pf(1) = pf(2).||(18)|