A Demonstration of The Effect of "Dead-End" Volume On Pressure Transients in Porous Media

Abstract

Abstract Study of a model which contains "dead-end" pore volume indicates that pressure transients are influenced by the amount of dead-end pore volume and by the resistance of the flow path between the dead-end pore volume and the main flow channels. A semi-empirical method is demonstrated that makes possible measurement of the volume in the dead-end pores and the total pore volume. The difference between these two volumes is the volume of the flow channels. An indication of the flow resistance between the dead-end pore space and the main flow channels is also obtained. Introduction In some engineering calculations the distribution of pore volume in a petroleum reservoir need not be known. For example, a material balance calculation treats a reservoir as an oil-filled tank. In other calculations the distribution of pore volume appears implicitly through use of the porosity and the relative permeability and capillary pressure characteristics. It is the purpose of this paper to point out that under certain conditions the exact distribution of pore volume must be known in order to interpret correctly transient flow behavior. Eqs. 1 and 2 for a one-dimensional system require that, at any point x and at any time t, the average velocity vector be in the x direction. Furthermore, at any x and t there can be only one value of P. Also, all of the fluid leaving an element dx must have been stored in that element since t=0 as a result of the compressibility of the fluid or must have come in from the adjacent downstream element. In other words, no fluid can be generated in dx. These conditions are fulfilled for a homogeneous, isotropic porous medium. In fractured rock the over-all permeability of the system may be greater than that of the material making up the blocks. The blocks may then be sources. A vuggy limestone can be treated in a very similar manner. If there is a low permeability layer on the vug surface, the fluid in the vug may not be able to leave at a rate sufficient to make the pressure in the vug equal to that in the rock immediately around the vug. The vug then becomes a source and the system obeys Eq. 3 or Eq. 4.