Waterflood Performance of Heterogeneous Systems
Authors: Berruin Nouri A. , Morse Richard A. 
Published: December 2007

The waterflood performance of horizontal, randomly heterogeneous systems is investigated. Waterflood performance of a randomly (nonsystematically) stratified system approaches that of a uniform system with a flow capacity equal to that of the stratified system. Waterflood performance of a randomly heterogeneous system is found to be nearly rate insensitive.

Introduction
Since the introduction of the concept of the layered model for representing vertical permeability stratification, the reservoir engineer has been faced with the problem of adequately describing the layers that constitute the reservoir. To date, all published analytical methods for predicting waterflood performance for stratified reservoirs have ignored the actual spatial position of the layers in the reservoir and assumed a position of the layers in the reservoir and assumed a systematic permeability ordering of the reservoir layers with no crossflow between layers. Such an assumption was made so that a simplified analytical approach could be applied to an otherwise almost hopelessly complicated problem. problem. Recent reservoir engineering and geologic study has shown that wide variations of porosity, permeability, and capillary pressure characteristics may be expected within and between individual units of a reservoir system. Reservoir rock properties may have considerable (random) lateral variations whose effects on recovery performance cannot be determined precisely. Furthermore, performance cannot be determined precisely. Furthermore, a formation may have sections of complete vertical communication, while other parts may possess little or no vertical transparency. Hence, a reservoir may be identified as stratified, based on rock properties alone, by the most sophisticated statistical technique of reservoir classification, while the overall performance of the reservoir corresponds to that of a system in which rock properties are distributed randomly. In fact, a system properties are distributed randomly. In fact, a system may contain many randomly distributed discrete layers with varying rock properties, yet may include crossflow conditions. Under the influence of gravitational, capillary, and viscous forces, such a system most probably will behave like a homogeneous system. Also, one might expect that the waterflood performance of such a system would be slightly more favorable than an equivalent homogeneous system containing considerable gravity segregation. One might conclude that crossflow effects resulting from capillary, gravitational, and viscous forces must be accounted for when predicting the waterflood performance of stratified or homogeneous systems.It would seem intuitively that the recovery performance of waterflooding a heterogeneous system in performance of waterflooding a heterogeneous system in which rock properties are distributed randomly would approach that of an equivalent homogeneous system in which crossflow effects are negligible. Warren and Price showed that the most probable behavior of a Price showed that the most probable behavior of a heterogeneous system under single-fluid phase flow approached that of a homogeneous system having permeability equal to the geometric mean of the permeability equal to the geometric mean of the individual permeabilities. In this case, measured rock properties (mainly porosity and permeability) may be properties (mainly porosity and permeability) may be treated statistically as a sample from the total population (the reservoir); such properties then may be represented by probabilistic distributions.
JPT
P. 829