Economic and physical optimization of hydraulic fracturing

Abstract

Optimization has taken several different hues in all areas of engineering. Hydraulic fracturing, as applied to oil and gas wells, has had its share. In the past, and before the maturing of high-permeability fracturing and the tip screen out techniques, this well stimulation procedure was limited to low-permeability reservoirs and unrestricted fracturing. In such cases, the fracture length would be an appropriate design optimization variable against an economic criterion, e.g., the Net Present Value (NPV). This involved the balancing of incremental future revenue against the cost of execution. Also interesting would be parametric studies, allowing the variation of execution variables and the detection of differences in their respective design NPV. Such differences would be useful in decisions to measure a variable or stay within reasonable assumptions. The emergence of higher-permeability fracturing and the Unified Fracture Design (UFD) concept allowed two important notions. First, there is no difference between low and high-permeability reservoirs in terms of benefiting from fracturing. Just execution issues need to be resolved. Second, and more important, for any mass of proppant to be injected in any well, there exists only one fracture geometry that would maximize production. This geometry, consisting of length and propped width (with height as a parasitic variable) can be readily determined and, if placed, it will provide the maximum productivity index. All other combinations of length and width would result in lower productivity values. This is physical optimization.In this paper we combine the two: the economic and physical optimizations. For each proppant mass we first optimize the fracture physical performance, and then we apply the NPV criterion. We perform a series of parametric studies for a range of gas reservoirs and we use economic variables that differ in various parts of the world. We show how to determine the optimum fracture size. We then show how fracture treatments may be attractive in certain reservoirs in mature areas but not attractive elsewhere. We also show that for a diversified company, given the choice, few successful fractures in high-permeability reservoirs are far preferable to fracturing large numbers of wells in lower permeability fields, although the latter can be made economically attractive only through hydraulic fracturing.