## 1 Background Study
Uniform flux assumption was also used in a study to evaluate the pressure behavior of a fractured horizontal well with the threshold pressure gradient consideration. In this study, the global flow or transient pressure progressed through the network of pressure indicating a constant rate or flux with changes in pressure only. The results obtained from the study were validated using a numerical method and the equation developed matched the response of a fractured well in Xinjiang Oil Field in China [4]. Thus, the assumption used in our study, which considered uniform flux assumption instead of infinite fracture conductivity, is well studied in the literature as well. A study conducted on a hydraulically fractured well created a model that was hybrid in nature and that modelled the well's pressure distribution numerically but analytically at the reservoir condition. The reason behind the numerical approach being used to compute the fracture performance close to the wells is because it can detail the properties of the fracture, such as the non-uniform shape of the fractures being considered. Another reason for the numerical modelling in the form of the flow into the wellbore was because the flow was non-conformant to [PERSON]'s flow, which actually created a non-Darcy flow. This non-Darcy flow created an additional pressure drop due to flow convergence around the wellbore, which actually necessitates the numerical model [1]. This model also predicted the performance of a hydraulically fractured well but resorted to a numerical approach for the performance in the vicinity of the wellbore. The drawback of this study was that a numerical approach was utilized, which is less accurate compared to the analytical approach used in our study. A method was developed to study the pressure transient analysis in fractured horizontal wells with fracture networks. In this work, line source function was used to create the model. The flow at the intersection between fractures was modelled using nodal analysis and diffusivity equation. Finally, the numerical inversion was conducted using Laplace Transformation. There were a few flow regimes that formed in this particular study, namely first bilinear flow, 'MF-HF' support, the second bilinear flow, formation linear flow, cross flow and pseudo-radial flow. This method has more consideration such as the inclusion of the fracture's intersection but still requires the numerical method to perform the inversion. Any inclusion of the numerical method results in less accuracy. On top of that, the equation that we built has a more general application whereby a single equation can cater for all flow regimes [5]. A study was conducted in an infinite slab reservoir by considering infinite and finite conductivity fractures by assuming uniform flux with a constant drawdown rate. The variables in this study were properties of fractures such as the half-length, conductivity and angles. An analytical solution was used to analyze pressure transient testing for the mid time stage while the early and late time stages were analyzed by using the semi-analytical model. This approach was very different from our equation, which actually catered for all of the time regions [6]. The equation built by us also showed some improvement during a study conducted in a horizontal well, which tested the performance of a single fracture and multiple fractures. In that study, the performance of both scenarios was tested using the numerical approach, which was later transformed in the Laplace space. The analytical approach always has a superiority over the numerical approach due to the accuracy presented. In our case, all of the flow regimes were evaluated using a single equation instead of having different equations designated for each flow regime or without resorting to the numerical approach [7]. A study was conducted modelling a hydraulic fracture in a tight formation such as a shale gas reservoir with pre-existing natural fractures.