Paper presented at the SPE European Formation Damage Conference, Noordwijk, The Netherlands, June 2011.
Application of Genetic Algorithms to the Optimization of Pressure Transient Analysis of Water Injectors using Type Curves
Abstract
Injection pressure fall-off (PFO) test analysis has proven to be a reliable vehicle for understanding and evaluating well performance. Recently the methodology has been extended to the understanding of injectors. This paper presents an optimization model for analysis and interpretation of PFO tests for fractured water injectors. An elliptical composite flow model mathematically represents the fractured injector well. The optimization scheme couples the mathematical model of the well with a Genetic Algorithm (GA) to reach the final solution. The pressure transients representing the behavior of an injector a closing fracture and the discontinuity in fluid mobility are best developed in elliptical coordinates. The methodology derives the dimension of the induced fractures, formation permeability, fracture conductivity and fracture face skin.
The current paper illustrates the solution methodology by showing the attained match for a West Africa offshore field case. The field case provides reasonable agreement for the fracture dimensions and characteristics as verified by other techniques.
Genetic Algorithms are one of the most common artificial intelligence techniques for optimization. The reported solution is obtained by applying a GA with a non-linear least square error function as an objective function. A special penalty function, mutation, crossover probabilities, and stopping criterion are used to obtain the global minimum of the objective function. The test data analysis is done through type curve matching of the pressure and its derivative by minimizing the objective function to help determine the parameters that provide the best match between the field data and the presented novel fractured injector type curves.