## 3 Result and Discussion  
Figure 3 displays the simulated result of a pressure build-up test of the reference model. As presented in the previous section, this case is selected as a reference to represent a real reservoir. Well tests in exploration wells and new wells are often made in a sequence where a drawdown test precedes a build-up test. The build-up test is analytically interpreted by using well-established pressure transient analysis techniques found in many textbooks and the literature. The interpretation can be drawn using methods such as Horner analysis and Miller-Dyes-Hutchinson (MDH) analysis [22]. The detailed description of the equations for pressure transient analysis can be referred to from any well test analysis textbooks. The Horner analysis assumes infinite acting flow at shut-in, which is a short production period. The MDH analysis is based on the opposite assumption that the stable production period before shut-in is very long, and thus pressure changes that originate from the production can be ignored compared to the pressure changes due to a shut-in. The log-log plot analysis is also presented in Figure 4.  
From this analysis, the formation permeability and fracture half-length are estimated to be 0.5 md and 450 ft, respectively. Next, the two coarse grid models presented in Figure 2 are constructed by upscaling the reference model. The grid size along the main stress direction is set to 100 ft, and the size in the perpendicular direction is set to 10 ft and 40 ft for coarse model one and coarse model two, respectively. Dual porosity is set up only for the fractured plane cells. A simulation is run by applying the same constant flowrate tuning to the models. By using the parameters in Table 1, the pressure behaviors are very close to each other. The pressure results are presented in Figure 5. Here, we simulated an infinite conductivity case (the finite conductivity case can be simulated without difficulty changing fracture permeability). A half-slope straight line on a log-log plot in Figure 4 shows infinite conductivity fracture characteristics [12]. After the linear flow period, the infinite acting radial flow behavior occurs. This model--the infinite conductivity fractured model in well testing interpretation--is based on a fracture plane with zero thickness and total penetration. In the early time (1/2 slope straight line on log-log plot), the pressure drop is based on the area of the fracture plane (thickness \(\times\) fracture half-length) and formation permeability. Therefore, by taking the inverse of this pressure drop, the formation permeability and fracture half-length could be estimated. As mentioned before, even if the \(\frac{1}{2}\) slope is not recognized, the half-length can still be evaluated using negative skin. Figure 2: Coarse and coarser gridding for production performance comparison, (**a**) Coarse model 1 (**b**) Coarse model 2, (**c**) Reference sector model. Figure 4: Analysis of build-up test of the reference model in the log–log plot. Figure 3: Analysis of simulation result of the synthetic hydraulic fractured model in Cartesian Plot. In Figure 6, the early time (9 h) pressure behavior in the reservoir is a little bit different because of the shape of the fracture, even though the bottomhole pressure behavior is very similar, as shown in Figure 5. However, the pressure behavior in the reservoir is very similar at a later time (240 h), as shown in Figures 7 and 8. Those cases will go to a radial flow if there is no boundary effect. Finally, as shown in Figure 9, coarse models one and two could accurately represent the reference case with a considerably coarsened grid size with only 1.5% of the simulation time. After performing the model setup, the prediction could be performed in a single well as well as in a full field case. Figure 5: Bottom hole pressure of the Base Case, Coarse Case, and Reference for a constant flow rate. Figure 6: Pressure map in early time for **(a)** Base Case, **(b)** Coarse Case, and **(c)** Reference.