## 1 Background Study
Unlike other approaches, the authors of the study relied on modelling the fractures from a close range instead of observing the model as a dual porosity model. The source function was solved analytically using the superposition principle, but flows from in between the fractures were modelled using the numerical approach rendering the works less accurate in comparison to the work we conducted, which completely relied on a single analytical equation from the beginning to the end [8]. Individual flow regimes were evaluated using different equations in a study conducted on pressure transient analysis of multi-fracture horizontal wells whereby at least four different flow regimes were expected to occur during the entire flow period, namely fracture radial, radial-linear, formation linear and pseudo-radial. In our study, all of the flow regimes to occur were modelled using a single analytical equation, which also showed a good match with the numerical study. The equation we created removes the hassle of turning to a new equation whenever a new flow regime comes in [9]. Instead of separating the radial flow from the fracture to the wellbore and the linear flow from the reservoir to the fracture, a new method called trilinear flow was established in a study to find an approximation for the analytic solution of finite-conductivity vertical fractures. However, this solution was only applicable for a short-time analysis, which definitely could not predict the pseudo-radial flow that appeared after the linear flow into the fractures. Unlike the trilinear approach, the equation we built can cater for all of the flow regimes regardless of the time span. The equation that we built is equally as accurate too since the equation built is an analytical equation [10]. A study was conducted to investigate the performance in terms of the productivity index and drainage area for a fractured horizontal well in a tight reservoir where the equation used was similar to well testing for a gas reservoir and the pseudo-pressure function. However, the drawback of this pseudo-function is that it is a semi-analytical model, which is subjected to a lack of accuracy that can contribute to false results for the overall analysis. The equation built by us is completely an analytical equation, which cannot be affected by the same fallacy. However, to compute such parameters, namely productivity index and drainage area, as there are no direct outputs from our equation there will be a need for some additional steps before arriving at the required outputs but with no reduction in accuracy [11]. A study was conducted to investigate the performance of hydraulic fracturing in a tight reservoir and shale gas reservoir. Despite both fields being known for being unconventional, the contrast in permeability between the two fields was still high in disparity whereby the tight reservoir has permeability in the range of millidarcy while the latter reservoir has permeability in the range of nanodarcy. The investigation was performed using a trilinear model, which could only provide an accurate estimation at the earlier time, as discussed before. The tendency of the authors of the study to resort to the trilinear method showed that there was not a better prediction simulator that was as good as the equation that we constructed, which gave us more stance to come up with such an equation [12]. A similar study was conducted to investigate the pressure transient response of a hydraulically fractured horizontal well with natural micro-fracture. In this study, Laplace Transformation, source function and superposition principle were used to generate a semi-analytical model that matched a numerical solution, thus, confirming the reliability of the model. Further works were performed by conducting sensitivity analysis, which indicated the sensitive parameters towards the pressure response. Upon verification of the model, the model was then used as a type curve to evaluate the performance of a well stimulation technique from a field called Jimusar Sag [13].