Osmotic Pressure Gradient Effects on Water Diffusion in Porous Rock: Can They Pervert Permeability Tests?

Generation of a large network of hydraulic cracks is of key importance not only for the success of fracking of shale but also for the recent scheme of sequestration of CO2 in deep formations of basalt, peridotite and basalt with peridotite inclusions, which are mafic rocks that combine chemically with CO2. In numerical simulation of the development of fracture network, an important problem is the permeability of the porous rock. The objective of this paper is to calculate the effect of osmotic pressure gradients caused by gradients of concentration of the ions of Ca, Mg, Na, etc. on the effective permeability of rock. The basic differential equation are formulated and their explicit solution for appropriate initial and boundary conditions are obtained under certain plausible simplifications.