Nonlinear Behavior of Elastic Porous Media

Published in Petroleum Transactions, AIME, Volume 216, 1959, pages 179–187. Abstract A theoretical and experimental analysis is given of the change in volume of a porous medium due to changes in external and internal pressures. The results enable one to deduce directly the effect of large increments in stresses. It is shown that the three-dimensional representation of the volume of a nonlinear porous system is a cylindrical ruled surface, the generating lines of which have a slope according to the solid rock compressibility. Analytical expression for such a surface is very simple. It follows that the bulk and pore compressibilities depend only on the difference between pore fluid and external hydrostatic pressure, i.e., the effective rock frame pressure. From measurements on a number of sandstones as well as limestones it can be concluded that for practical values of this effective frame pressure the pore compressibility falls in the range between the compressibility of water and that of undersaturated crude oil. In general, pore compressibility is found to be higher the lower the porosity. For a particular limestone reservoir pore compressibility and porosity could be related by means of a simple empirical formula. Results from the described study find a direct application in material balance calculations and in problems of liquid flow through porous media. Since the elastic constants of the rock bulk material enter into equations for velocity of acoustic waves, the results are also of importance for calculating rates of wave propagation in these media. It is shown for sandstones with 15 to 30 per cent porosity that laboratory measured porosities may differ from those under reservoir conditions by about 1 per cent of their value. The difference for low porosity limestones can be of the order of 10 per cent. The subsidence caused by elastic deformation of reservoir rock is shown to be very small. Introduction General formulas relating pore and bulk volume to external and internal pressure can be derived, as has been shown by Biot, Gassmann and Geertsma. Their theories describe the differential change in volume caused by a variation in pore fluid tension and external hydrostatic tension.