Waterflood Pattern Optimization Using Genetic Algorithms with Multi-tank Material Balance
Authors: Zangl G. , Hermann R. 
Published: December 2007

Abstract
Waterflood operation is the most widely used secondary recovery method. Large reservoirs containing thousands of wells are operated under waterflood conditions to increase the ultimate recovery. Due to lack of resources and appropriate tools, waterflood optimization is often done on trial and error bases. In advanced cases, a numerical reservoir simulator is used for this task. Nevertheless, both it is very rarely acknowledged, that through the given variation of well injection volumes and the resulting variation of total fluid produced and the watercut of the producing wells, additional information can be gained.
This paper presents an approach, where the strength of the relationship between injection and production wells is determined from time dependent production data including only very basic geological information. A data-driven optimization routine - a genetic algorithm - is used to identify the interference strength in form of a matrix. This interference matrix is transformed to fit into a multi-tank material balance model. Each tank represents the control volume of a well. By adjusting the interference matrix, the average tank pressure calculated from the material balance is matched against the measured pressures. The ratio of the interference values, which has been derived by the genetic algorithm, is preserved during the history matching process. The resulting parameter - interference and average tank pressure - can be used for a detailed analysis of the waterflood performance of each individual pattern.
As a result, the injection volumes of each well can be allocated to the surrounding production wells. Irregular injection allocation and preferred flow paths can be detected and injection rates adjusted to account for this fact. The recovery factor can be used to rank the pattern for the most remaining recoverable reserves, so that only the high value patterns are optimized. The calculated pressure can be used to check the pressure maintenance program. The average pressure of the reservoir should be evenly distributed to avoid unwanted effects like gas dissolution. This distribution can be proven and optimized by the material balance model.

Introduction
An optimal water injection policy maximizes oil recovery per barrel of injected water while minimizing formation damage and maintaining reservoir pressure. Optimal water injection especially into low permeability or fractured oil reservoirs is problematic because of highly nonlinear and complex reservoir dynamics.
Likewise, current first principle models of fluid movement in these rock systems are insufficient to design, operate, and predict the performance of large-scale waterfloods. Historically, the conflict between prudent reservoir management and meeting field injection-production targets has resulted in reservoir and well damage, injectant recirculation and irreversibly lost oil production.
Wide varieties of injection-production well arrangements have been applied in waterflooding. The largely portion of these arrangements are repeating injection-production well patterns, like five-spot, seven-spot and nine-spot.
These waterflood patterns have been introduced to increase the areal sweep efficiency. The largest gain of such a waterflood pattern comes definitely from the displacement of oil by water. In the ideal case, this displacement takes place in form of a homogenous front. Depending on the mobility ratio of oil and water, this front starts to generate fingers resulting in bypasses oil. After the waterfront breaks through at the producer, high watercut and low oil production characterizes the production behavior of this producer. Water injection can be optimized for production wells before water breakthrough by understanding the frontal displacement. The more homogenous the waterfront can move, the better the sweep efficiency will be. The velocity of the frontal movement depends on the amount of water injected in the wells surrounding the producer and the amount of total fluid that is produced from the well in the center of the water injectors. A lot of literature has been published to analyze the frontal displacement.