Abstract
Numerical simulation techniques were used to investigate the effects of common core heterogeneities upon apparent waterflood relative-permeability results. Effects of parallel and series stratification, distributed high and low permeability lenses, and vugs were considered. permeability lenses, and vugs were considered. Well distributed heterogeneities have little effect on waterflood results, but as the heterogeneities become channel-like, their influence on flooding behavior becomes pronounced. Waterflooding tests at different injection rates are suggested as the best means of assessing whether heterogeneities are important. Techniques for testing stratified or lensed cores are recommended.
Introduction
Since best results from waterflood tests performed on core plugs are obtained with homogeneous cores, plugs selected for testing are chosen for their plugs selected for testing are chosen for their apparent uniformity. We know, however, that uniform appearance can be misleading. For example, flushing concentrated hydrochloric acid through an apparently homogeneous core plug often produces "wormholes" in higher permeability regions. Also, we sometimes find that all core plugs from a region of interest have obvious heterogeneities, so any flooding tests must be run on nonhomogeneous core plugs. plugs. Nevertheless, relative permeabilities, as obtained routinely from core waterflood data, are calculated using the assumption that the core is a homogeneous porous medium. While it is obvious that porous medium. While it is obvious that heterogeneties mill affect these apparent relative permeabilities, there appear to be no experimental permeabilities, there appear to be no experimental results reported in the literature to indicate just how serious the problem is. Accordingly, a computer simulation study of core waterfloods was conducted to systematically examine the effects of different sizes and types of core heterogeneities on flood results. The study was performed by numerical simulation using two-dimensional, two-phase difference equation approximations to describe the immiscible water-oil displacement. For each simulation the permeability and porosity distribution of the heterogeneous core to be studied was specified; fluid flow characteristics of the system, including a single set of input relative-permeabilities curves, were stipulated The system was set in capillary pressure equilibrium at the reducible water saturation. Then a waterflood simulation was performed. From the resulting fluid production and pressure-drop data a set of production and pressure-drop data a set of relative-permeability curves was calculated using the standard computational procedure applicable to homogeneous cores. In this paper these calculated relative-permeability curves are denoted as "waterflood" curves to distinguish them from the specified input curves. The waterflood relative-permeability curves should closely match the input curves for homogeneous systems. Since the same set of input relative-permeability curves was used for all rock sections, deviations of the waterflood from the input relative-permeability curves gave an indication of the effects of heterogeneities. When the system was heterogeneous and there was good agreement between waterflood and input relative-permeability curves, then the heterogeneities did not strongly influence the flow behavior and the system responded homogeneously.
MATHEMATICAL MODEL AND METHOD
The waterflood simulations were carried out using two-dimensional, two-phase difference equation approximations to the incompressible-flow differential equations:*
.....................(1)
....................(2)
SPEJ
P. 381
A Nonempirical Relative Permeability Model for Hydrate-Bearing Sediments
