The major goal to propose the semi-analytical method is to model/simulate hydraulic fracturing process based on closed form solution of a Theory of Elasticity problem. The analysis results for a Single-Fracture case is going to be compared to well-known resolved problem to show the performance of the proposed method. However, for the case of Multi-Fracture, some findings and outcomes are being addressed. Unlike well-known methods such as PKN or KGD, which rely on some simplifying assumptions (such as the elliptical cross-section of the fractures) our proposed method attempts to model and simulate the process numerically in 3D form which is more realistic and versatile. Several numerical methods have been proposed by 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 Elasticity Problem to reduce the volume of numerical integrations and produce satisfactory results in much less amount of time. The formulation computes displacements and displacement derivatives. After computer codes were designed and developed to implement the proposed semi-analytical Method, which is a simplified form of Boundary Element Method (BEM), the results are compared to a benchmark example previously published in research papers both numerically and graphically. The computer code is capable to analyze pressurized penny-shaped fractures and compute displacement and displacement derivative fields. By acquiring these values in generated grid nodes in the domain, Cauchy strains and stresses can be obtained. By all the stress components at grid nodes, principal stress values and directions, and therefore, maximum shear stress and direction can be computed. After that, the computer code has to be verified and validated by comparison of results and well-known resolved examples. The examples are, but not limited to, Okada problems published in 1985 and 1992. The other Problem is pressurized Penny-Shaped horizontal fracture which is called Fialko Model. The comparisons show the validity of the proposed method. The boundary element formulation in this method is an exact solution and generates exact values for displacements, displacement derivatives and stress fields and does not need numerical integration. However, since hydraulic fractures of any shape and geometry are being discretized by proposed Boundary Element, the final outputs will be approximated results. This method, which is going to be shown, is much faster than other numerical methods.

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