Mathematical Analysis of Oil Displacement by Water in Heterogeneous Reservoirs

Abstract

Prediction of reservoir performance during water displacement process is a routine procedure for homogeneous reservoirs but complicated in heterogeneous reservoirs. The Stiles method has consequently been used over time in the industry for such reservoirs. This method, however, is evidently time consuming and tedious as the varying permeability values are reordered and lumped. This paper applies the Welge procedure to a stratified reservoir without reordering or lumping of permeability with the aim to ensure improved productivity by more proper planning, more efficient use of resources and determination of the economic viability of the project. This paper also seeks to formulate a procedure that can judiciously handle even larger sets of permeability values to produce more accurate result A fractional flow equation was derived for any number of layers to generate a single fractional flow curve (FFC). Injection inflow into a layer was determined using the layer capacities and this facilitated calculation of times to breakthrough and times to attain a particular saturation after breakthrough. A formula was then derived to determine the oil produced at any instant. A software was designed for the entire procedure to ensure faster and more accurate predictions. Results showed that heterogeneities had no effect on the microscopic displacement and thus the fractional flow curve remained unchanged whether the reservoir was heterogeneous or not. Heterogeneities affected only the total flow in the distinct layers and thus times to attain specified average water saturations. The results of oil recovery obtained were compared to those obtained using the Stiles method to demonstrate that this method is faster without loss of accuracy.

Water displacement characteristics at the high water-cut stage based on microscopic experiments and simulations

“…16,17 Nwaka and Isehunwa performed a mathematical analysis of oil displacement by water in heterogeneous reservoirs. 18 Zhao and Jiang studied on the classification and formation mechanism of microscopic remaining oil in high water-cut stage based on machine learning. 19 Pore-scale simulations have been essential tools to obtain a better understanding of development mechanisms.…”