The Reciprocity Principle in Flow Through Heterogeneous Porous Media

Publisher Summary This chapter discusses the reciprocity principle flowing through heterogeneous porous media. Geohydrological investigations of ground formations in the southwest deltaic area of the Netherlands have shown that in a horizontal layered formation, consisting of two leaky aquifers, separated and confined by semipervious strata, the drawdown distribution of the piezometric head in the upper aquifer. As a result of draining the lower aquifer by means of a steady well, equals the drawdown distribution in the lower aquifer caused by pumping the upper aquifer with the same discharge. In this particular case, the phenomenon of reciprocity principle is proved mathematically, and the reciprocity of drawdown and discharge is valid as a general principle is discussed. The principle is drawdown of the piezometric head at an arbitrary point “A” in a heterogeneous anisotropic porous medium, caused by pumping with a discharge “Q” in another arbitrary point “B” at the time “t” after the beginning of the pumping is equal to the drawdown in “B” as a result of pumping in “A” with the same discharge “Q” and after the time “t.” This theorem is proved for steady flow.