An Estimation Method of Water Drive Displacement Based on Formation Permeability Distribution and Inverse Problem Modeling

Abstract

Formation permeability distribution is important in the oil industry since it is a key tool in forecasting oil production performance, a matter of primary concern to oilfield operators. However, the direct problems of reservoir analysis are limited in practice by a lack of input parameters such as reservoir vertical heterogeneity. Therefore, inverse problem modeling is important to achieve reservoir vertical heterogeneity using production profiles, which are always known for existing reservoirs. In this way, what has occurred inside a reservoir can be understood by applying reservoir output in the reverse model. Because formation permeability can frequently be represented by a normal distribution and can describe heterogeneity and water production capability, an inverse problem of formation permeability was modeled to study reservoir vertical heterogeneity and reservoir production performance based on oil-water two-fluid flow theory and optimization problems. Moreover, through establishing an objective function, we obtained an optimal solution for water production rate. Finally, one case is simulated by this model and good results achieved, which are compatible with production and experimental data.

A Coupled Model of Two-Phase Fluid Flow and Heat Transfer to Transient Temperature Distribution and Seepage Characteristics for Water-Flooding Production Well with Multiple Pay Zones

“…Based on the BL displacement theory, the oil-water two-phase plane radial flow (non-piston-like displacement) mathematical model was established without considering the factors of gravity and capillary pressure [31]:…”

“…In Equation 3, the parameter m is given by a constant value; here, we let m = 0.8060. A special saturation "s wf " is defined as follows: as shown in Figure 4, based on the water cut curve (f w (s w )), selecting the point of irreducible water saturation (s wi ) as a fixed point and joining any other point on the curve, with a constructing function [31]:…”

“…In the pay zones, the initial water saturation was considered as a fixed value, which can be formulated as Equation (31). The water saturation of the inner boundary of the water drive reservoir changed with the production time, while the water saturation of the outer boundary was considered to be 100% at any production time because the outer boundary was the water supply edge, which was expressed as Equation 32.…”