Abstract
Previous workers have developed differential equations to describe oil displacement by water imbibition, but have not explicitly defined the relationship between recovery behavior for a single reservoir matrix block and its size. In the present work, imbibition theory is extended to show that the time required to recover a given fraction of the oil from a matrix block is proportional to the square of the distance between fractures. Using this relationship, recovery behavior for a large reservoir matrix block is predicted from an imbibition test on a small reservoir core sample. The prediction is then extended to analyze recovery behavior for fractured - matrix, water - drive reservoirs in which imbibition is the dominant oil-producing mechanism. Experimental data are presented to support the basic imbibition theory relating matrix block size, fluid viscosity level and permeability to recovery behavior.
Introduction
Imbibition has long been recognized as an important factor in recovering oil from water - wet, fractured-matrix reservoirs subjected to water flood or water drive. Recently, two approaches have been published which might be used to predict imbibition oil-recovery behavior for reservoir - sized matrix blocks. Graham and Richardson used a synthetic model to scale a single element of a fractured-matrix reservoir. Blair, on the other hand, used numerical techniques to solve the differential equations describing imbibition in linear and radial systems. This latter method requires auxiliary experimental data in the form of capillary pressure and relative permeability functions. These two approaches, i.e., synthetic models and numerical techniques, have been used to study a variety of reservoir fluid-flow problems. One purpose of this work is to present, with experimental verification, a third method for predicting imbibition oil recovery for large reservoir matrix blocks. This method uses scaled imbibition tests on small reservoir core samples to predict field performance. The imbibition tests are easier to perform than the capillary pressure and relative permeability tests required to apply the numerical method. Furthermore, when suitably preserved reservoir-rock samples are used, the properties of the laboratory system are the same as those of the field. This offers an important advantage over the use of synthetic models because there is usually some question as to how accurately reservoir-rock properties can be duplicated in such models. Based on the recovery behavior for a unit matrix block, an analysis is presented to predict oil recovery for a fractured, water-drive reservoir made up of many such unit blocks. In the analysis, it is assumed that the flow resistance and the volume of the reservoir fracture system are negligible compared with that of the porous matrix. These assumptions are generally consistent with observed characteristics of many fractured-matrix reservoirs, and have been employed in previous studies. It is further assumed that the effect of gravity on flow in the matrix blocks is negligible. On first thought, the latter assumption might appear to seriously limit application of the method. However, in a fractured reservoir, the effect of gravity on flow in a matrix block will be restricted by the height of the block. Furthermore, matrix permeabilities are often very low (10 md or less) in such reservoirs. This means that capillary or imbibition forces will be large, thus tending to minimize the relative importance of gravity. For these reasons, imbibition should be the dominant oil-recovery mechanism in many fractured-matrix, water-drive reservoirs. The predictive method presented in this report is applicable to such reservoirs.
SPEJ
P. 177^
Effect of viscosity on oil recovery by spontaneous imbibition from partially water-covered matrix blocks