Optimization of Spacing and Penetration Ratio for Infinite-Conductivity Fractures in Unconventional Reservoirs: A Section-Based Approach
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2017 Society of Petroleum Engineers. In this paper, we consider the development plan of shale gas or tight oil with multiple multistage fractured laterals in a large square drainage area that we call a "section" (usually 640 acres in the US). We propose a convenient section-based optimization of the fracture array with two integer variables, the number of columns (horizontal laterals) and rows (fractures created in a lateral), to provide some general statements regarding spacing of wells and fractures. The approach is dependent on a reliable and efficient productivity-index (PI) calculation for the boundary-dominated state (BDS). The dimensionless PI is obtained by solving a time-independent eigenvalue problem by use of the finite-element method (FEM) combined with the Richardson extrapolation. The results of the case study demonstrate two decisive factors: The dimensionless total fracture length, related to the total amount of proppant and fracturing fluid available for the section, and the feasible range of actual fracture half-lengths, related to current fracturing-technology limitations. Under the constraint of dimensionless total fracture length, increasing the number of columns (horizontal laterals) increases the total PI but with only diminishing returns, whereas the optimal fracture-penetration ratio decreases somewhat, but is still near unity. When adding the technological constraint of a limited range of fracture half-lengths that can be routinely and reliably created, only a few choices remain admissible, and the optimal decision can be easily made. These general statements for the ideal homogeneous and isotropic formation can serve as a reference in the more-detailed optimization works. In other words, we offer a first-pass method for decision making in early stages when detailed inputs are not yet available. The information derived from the section-based optimization method and the efficient and reliable algorithm for PI calculation should help the design of multistage fracturing in shale-gas or ultralow-permeability oil formations.
