A saturated reservoir or confined aquifer system responds to fluid withdrawal as a dynamic unit whose elemental volumes not only compress due to decrease in porosity but move horizontally and vertically in order for the system to remain contiguous.
Recent trends in the conceptual aspects of subsidence due to fluid withdrawal are toward developing a practical three-dimensional theory of reservoir movement. One approach to developing an adequate theory is to couple volume strain within a reservoir to calculated stress change. Transient displacement of reservoir material in a direction of interest is the sum of appropriate directional components of volume strain. It is not an integral sum of volume strain itself. To find directional components of strain in three dimensions requires so many parameters that, using this approach, a solution for matrix movement becomes intractable under most field conditions.
An alternative approach to developing a three-dimensional theory is proposed in this paper. It couples reservoir velocity fields in three dimensions to appropriate force fields. The generally neglected effect of the gravitational force field on transient movement of solids is included in the analysis. After calculating the transient velocity field of a saturated granular medium, it is conceptually possible to estimate the displacement of solids by integrating velocity over an appropriate interval of time.