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.
Introduction
Water-injection wells are frequently fractured either intentionally or unintentionally. For instance, in low-permeability formations or when low-quality water is injected, fracturing may be used in an attempt to increase well injectivity. Unintentional fracturing of water-injection wells may result when cold water is injected into a relatively hot reservoir. The cooling of the reservoir rock can reduce the rock stress such that the injection pressure exceeds the reduced formation strength and fracturing occurs. A considerable amount of research in the field of waterflood-induced fracturing has been carried out in recent years, which has resulted in the analytical description of fracture propagation from a single well in an infinite reservoir. Injection fall-Off (IFO) test analysis offers a cheap way to infer the dimensions of induced fractures from well tests.
An important first step towards the analysis of a fall-off test for closing waterflood-induced fractures was made by Hagoort in his thesis (1). Application of a simple rock mechanical model for the fracture enabled him to relate fracture closure to early-time fluid flow. He presented an analytical expression for the theoretical pressure response which is valid as long as formation fluid flow is still linear and perpendicular to the fracture and before the fracture has completely closed.
Koning (2) presented an extension of Hagoort's (1) model to account for different fracture geometries, transition from early time linear flow to late time pseudo-radial flow, pressure response during and after closure and the effect of an elliptical discontinuity in fluid mobility. He solved the fully transient diffusivity equation in two dimensions, and incorporating the fracture closure-induced flow via convolution techniques.
Van den Hoek (3) rebuilt Koning (2) model from scratch and subsequently extended it with a number of features that are essential for the interpretation of fall-off test on fractured water injectors. His extension relates to fractures with a finite (possibly changing) conductivity and to fracture face skin.
