The major goal to propose the semi-analytical method is to model/simulate hydraulic fracturing processbased on closed form solution of a Theory of Elasticity problem. The analysis results for a Single-Fracturecase is going to be compared to well-known resolved problem to show the performance of the proposedmethod. However, for the case of Multi-Fracture, some findings and outcomes are being addressed. Unlikewell-known methods such as PKN or KGD, which rely on some simplifying assumptions (such as theelliptical cross-section of the fractures) our proposed method attempts to model and simulate the processnumerically in 3D form which is more realistic and versatile. Several numerical methods have been proposedby industry scholars such as BEM and FEM which comprise very complicated numerical integrations and,hence, involve computational resources dramatically. Our proposed method utilizes a closed form ElasticityProblem to reduce the volume of numerical integrations and produce satisfactory results in much less amountof time. The formulation computes displacements and displacement derivatives. After computer codes weredesigned and developed to implement the proposed semi-analytical Method, which is a simplified form ofBoundary Element Method (BEM), the results are compared to a benchmark example previously publishedin research papers both numerically and graphically. The computer code is capable to analyze pressurizedpenny-shaped fractures and compute displacement and displacement derivative fields. By acquiring thesevalues in generated grid nodes in the domain, Cauchy strains and stresses can be obtained. By all the stresscomponents at grid nodes, principal stress values and directions, and therefore, maximum shear stress anddirection can be computed. After that, the computer code has to be verified and validated by comparison ofresults and well-known resolved examples. The examples are, but not limited to, Okada problems publishedin 1985 and 1992. The other Problem is pressurized Penny-Shaped horizontal fracture which is called FialkoModel. The comparisons show the validity of the proposed method. The boundary element formulationin this method is an exact solution and generates exact values for displacements, displacement derivativesand stress fields and does not need numerical integration. However, since hydraulic fractures of any shapeand geometry are being discretized by proposed Boundary Element, the final outputs will be approximatedresults. This method, which is going to be shown, is much faster than other numerical methods.
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