Water flooding is one of the most common methods during secondary recovery. The management of water injection can enhance the productivity of wells; whereas, the absence of proper supervision on injection can irreparably damage formations. Conventional approach to evaluate water flooding behavior is constructing a geological model, linking flow characteristics of the formation to the model, up-scaling it, and eventually running simulations so many times. The problem with this approach is that this method is computationally too expensive and time consuming. In addition, lots of data are required as an input. Therefore, there is a great interest to implement other physically based theories to quickly predict the performance of reservoirs when certain data are not available (e.g. during exploration phase). The percolation approach is one of these methods, which is based on the principal that a formation can be divided into two parts: permeable and impermeable medium. The percolation theory is a basic mathematical model for connectivity prediction in systems with complex geometries.
During water flooding, production and injection wells are normally drilled in a geometric configuration called flooding patterns. These well configurations enable us to attain an optimum production rate at the same time as to use the benefits of reservoir characteristics such as formation dip angle, faults, fractures, and permeability changes. The most common flooding patterns includes four-spot, five-spot, seven-spot, nine-spot, flat-linear pattern, and flat-fit pattern. The classic percolation approach uses two wells (i.e., injection and production wells) in a reservoir model. The effect of multiple wells in different configurations (i.e., injection well patterns) has not been investigated yet in the percolation literature. The main idea of this study is to implement an isotropic 2-D model within the framework of site percolation to determine the effect of water flooding patterns on percolation predictions. Square-shaped objects, representing formation sand bodies that contain hydrocarbon, are randomly distributed in the background of a formation by Monte Carlo simulations. The master curves of mean connectivity in a formation are then modeled by finite-size scaling laws for different injection patterns. All implemented codes are developed in C# language.
The results enable us to predict the connectivity of different water flooding patterns without any need for further detailed simulations. In addition, the percolation threshold as well as the connectivity exponent of different patterns is investigated in details. The implemented percolation-based model shows promising results that can be used when the conventional simulation-based approaches cannot be implemented due to uncertainty in input data.