This paper presents a mathematical integration process through which all of the important useful information and data related to stimulated rock are properly extracted and embedded so that the total effects of the hydraulic fracturing stimulation are properly presented by the microseismic data detected and collected during the hydraulic fracturing process. A multistage hydraulic fracturing strategy is often used to help maximize the stimulated reservoir volume (SRV). The current analysis is based on chaining the stage results one-by-one. At each stage, the three-dimensional (3D) SRV is constructed based on its observed microseismic events using an enhanced convex hull approach. This algorithm offers both a mathematical approximation of 3D volume and a 3D visualization of the SRV geophysical shape(s). More detailed geometric characteristics are further calculated from the ellipsoid that best fits the constructed SRV, which relies on the acquired microseismic events. The characteristics include length, width, height, and orientation's azimuth of the stimulated rock. Moreover, it forms the basis for calculating the overall SRV using the stage-by-stage approach.

In the advanced phase, this algorithm offers characteristics related to the interaction between multiple stages. The accurate 3D geophysical geometry of the overlapping volume between multiple stages is extracted and is calculated, and the percentage of overlapping volume over the SRV is estimated at each stage. These volume overlapping quantities reveal the potential communication between these stages, indicating the efficiency of hydraulic fracturing efforts and implying the loss of treatment fluid. This algorithm provides the field engineers with several useful aspects: an essential, reliable, and direct compound tool to dynamically visualize the stimulated reservoir geometry and treatment field evolution; a real-time evaluation of the efficiency of a hydraulic fracturing treatment; and parameters to help increase the production of a stimulated reservoir.

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