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The present study provides a comprehensive set of new analytical expressions to help understand and quantify well interference due to competition for flow space between the hydraulic fractures of parent and child wells. Determination of the optimum fracture spacing is a key factor to improve the economic performance of unconventional oil and gas resources developed with multi-well pads. Analytical and numerical model results are combined in our study to identify, analyze, and visualize the streamline patterns near hydraulic fractures, using physical parameters that control the flow process, such as matrix permeability, hydraulic fracture dimensions and assuming infinite fracture conductivity. The algorithms provided can quantify the effect of changes in fracture spacing on the production performance of both parent and child wells. All results are based on benchmarked analytical methods which allow for fast computation, making use of Excel-based spreadsheets and Matlab-coded scripts. Such practical tools can support petroleum engineers in the planning of field development operations. The theory is presented with examples of its practical application using field data from parent and child wells in the Eagle Ford shale (Brazos County, East Texas). Based on our improved understanding of the mechanism and intensity of production interference, the fracture spacing (this study) and inter-well spacing (companion study) of multi-fractured horizontal laterals can be optimized to effectively stimulate the reservoir volume to increase the overall recovery factor and improve the economic performance of unconventional oil and gas properties.

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A long overdue distinction between so-called variant and invariant complex potentials is proposed here for the first time. Invariant complex potentials describe physical flows where a switch of the real and imaginary parts of the function will still describe the same type of physical flow (but only rotated by π/2). Such invariants can be formulated with Euler’s formula to depict the same flow for any arbitrary orientation with respect to the coordinate system used. In contrast, variant complex potentials, when swapping their real and imaginary parts, will result in two fundamentally different physical flows. Next, we show that the contour integrals of the real and imaginary part of simple variant and invariant complex potentials generally do not generate any discernable branch cut problems. However, complex potentials due to the multiple superpositions of simple flows, even when invariant, may involve many options for selecting the branch cut locations. Examples of such branch cut choices are given for so-called areal doublets and areal dipoles, which are powerful tools to describe the streamlines and pressure fields for flow in porous media with enhanced permeability flow channels. After a discussion of the branch cut solutions, applications to a series of synthetic and field examples with enhanced permeability flow channels are given with examples of the streamline and pressure field solutions.