Abstract
Experimental data demonstrate that physical properties of porous rocks change under pressure. In this paper an assumption is made and proved that under pressure the changes of physical properties such as porosity, density, permeability, resistivity and velocity of elastic waves are controlled to a large extent by the pore compressibility of rocks. It is also shown that the pore compressibility of rocks can be determined, within the range of pressures from 0 to 20,000 psi, by knowing the maximum pore compressibility and the magnitude of the pressure. Mathematical equations were developed which permit one to define changes in physical properties of porous rocks under pressure. These equations were verified by experimental data obtained from the study of sandstones.
Introduction
In studying the behavior of porous rocks under pressure in the field of petroleum technology, the most interesting aspect is the observation of those properties which characterize the rocks as possible reservoirs for example, porosity, permeability, resistivity, density and be velocity of elastic waves. The literature dealing with this problem mainly contains data concerning the study of only one or at most two of these parameters, but not of the group as a whole. An attempt is made in this paper to find general equations involving each of these parameters, which will permit the study of the behavior of rocks under pressure. All experimental data used here were obtained from the investigation of consolidated sandstones.
EXPERIMENTAL
In addition to the use of published experimental data, an experiment was carried out which studied the main physical properties of sandstones under pressure. Two homogeneous quartz sandstones were chosen for this purpose:the Torpedo sandstone bona Kansas, andthe Medina sandstone from Ohio.
The porosity of the Torpedo sandstone was 20.2 per cent, and that of the Medina 8.7 per cent. Permeabilities were 45 md and less than 1 md, respectively. Each sandstone contained about 5 per cent clay minerals, consisting mostly of kaolinite and chlorite, which were distributed quite evenly throughout the samples. One cylindrical sample 2 in. in diameter and 5 in. in length was cut from each sandstone and then saturated in a vacuum with a 3N solution of NaCl. This high concentration was used in order to obtain true formation factors and to decrease the swelling of the clay minerals. The methods of mounting the samples and measuring the changes in porosity and resistivity were practically the same as those described by Fatt and Mann. Changes of resistivity under pressure were studied for sandstones with 100 per cent water saturation, and for sandstones with the irreducible water saturation. The irreducible saturation was obtained by enclosing the saturated rock samples in relatively fine silicate powder so as to remove the water by capillary action. This procedure is described by Orkin and Kuchinski. Changes of permeability with pressure were determined at room temperature using nitrogen as the flowing medium.
In studying the effects of pressure, one series of measurements was made using an internal pore pressure Pi equal to the atmospheric pressure, while the overburden pressure P. ranged from 0 to 20,000 psi. A second series of measurements was used over the same range of overburden pressure, but with an internal pore pressure of 1,800 psi When the results were compared on the basis of net overburden pressure (P, - 0.85 Pi ), there was practically no difference for these two sandstones. The origin of the factor 0.85 in the expression for net overburden pressure is given by Brandt, Fatt and Geertsma.
SPEJ
P. 360^
Study of pore pressure variation during liquefaction using two constitutive models for sand