## 2 Methodology  
A workflow is presented for the long-term prediction of flowrate and bottomhole flowing pressure. The workflow integrates reservoir simulation and well test analysis for better performance prediction of a hydraulically fractured tight formation. The following five steps discuss the workflow. * Estimate fracture half-length and permeability through well testing analysis. In cases 1: where the half slope or quarter slope is not captured in a log-log plot, it can be estimated using negative skin. * Construct a grid in the direction of the main stress. A fracture is growing in the 2: opposite direction to the main stress, which is the perpendicular direction of the minimum stress direction. Hence, the common grid size follows the main stress direction. Meanwhile, fine gridding is required in direction perpendicular to the main stress direction. In practice, the longer side could be the general half-length size obtained in step 1. The short side could be around 40 ft or less. * To reduce the simulation time, apply dual porosity for the fractured cells only. * Match the simulation model to pressure behavior obtained during well testing: For 4: infinite conductivity fracture model, the matching parameter of the simulation model is fracture porosity. On the other hand, for finite conductivity fracture model, the matching parameters are fracture permeability and fracture porosity of the simulation model. * Predict performance using the well test matched simulation model. * In order to demonstrate the proposed approach, a synthetic reservoir model with fine grid blocks and an aerial grid size of \(5\times 5\) ft is constructed using commercial numerical reservoir modeling and simulation software. Some of the important information used to construct the model is generated based on information from several wells found in Northern India. The data used to construct the reference sector model are presented in Table 1. This case is selected to represent a real case model of shale gas formation with a hydraulic fracture. Figure 1 displays the fine grid reservoir model and a vertical well with a hydraulic fracture. Using the same property, two other coarse grid reservoir models, namely coarse grid model 1 and coarse grid model 2, with an aerial dimension of 100 \(\times\) 10 ft and 100 \(\times\) 40 ft, respectively, are constructed as shown in Figure 2. The respective data are also presented in Table 1, along with the reference sector model. In order to minimize the simulation run time, only a sector model of the reference synthetic model is used. This is possible by first identifying the drainage area without a boundary effect. A dual-porosity model is used for the fractured area only. In the simulation model, the sigma factor controls the flow between the matrix and the fracture. In the fine grid, the single porosity can be applied to draw a fracture directly; however, in a coarse grid, it is better to use dual porosity in the fracture. \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **Reference Sector Model** & **Coarse Model 1** & **Coarse Model 2** \\ \hline Area ft2 & 3000 \(\times\) 3000 & 10,000 \(\times\) 5000 & 10,000 \(\times\) 5000 \\ Pay thickness (ft) & 90 & 90 & 90 \\ Grid size (DX, DY, DZ, ft) & 5, 5, 30 & 100, 10, 30 & 100, 40, 30 \\ Grid number (X \(\times\) Y) & 600 \(\times\) 600 & 100 \(\times\) 500 & 100 \(\times\) 125 \\ Total grids & 1,080,000 & 150,000 & 37,500 \\ Horizontal permeability & 0.5 mD & 0.5 mD & 0.5 mD \\ Vertical permeability & 0.05 mD & 0.05 mD & 0.05 mD \\ Fracture permeability & 50,000 mD & 50,000 mD & 50,000 mD \\ Matrix porosity & 0.15 & 0.15 & 0.15 \\ Fracture porosity & 0.01 & 0.02 & 0.0025 \\ Sigma & 0.24 & 0.24 & 0.24 \\ Running time & 2382.35 s & 253.16 s & 36.15 s \\ Reference pressure & 3000 Psi & 3000 Psi & 3000 Psi \\ B\({}_{0}\) at 3000 psi & 1.3 & 1.3 & 1.3 \\ Oil viscosity at 3000 psi & 0.3 & 0.3 & 0.3 \\ Compressibility at 3000 psi & \(2.5\times e^{-5}\) & \(2.5\times e^{-5}\) & \(2.5\times e^{-5}\) \\ \hline \hline \end{tabular}
\end{table}