## 5 Results and Analysis  
### Type Curves and Flow Regimes  
The bottom-hole pseudo-pressure of a vertical fractured well with multiple hydraulic fractures in stress-sensitive gas reservoirs was calculated by the proposed model. Type curves for the bottom-hole pseudo-pressure were plotted and the characteristics of the bottom-hole pseudo-pressure behavior was analyzed. The established model in this work was suitable for multiple hydraulic fractures with arbitrary fracture number, arbitrary fracture length, and arbitrary fracture orientation. In order to investigate the effect of the hydraulic-fracture distribution on the pseudo-pressure response, without loss of generality, we mainly focused on the vertical fractured well with four fracture wings which is shown in Figure 6. The first and second fracture wings were assumed to have the equal length \((X_{\mathrm{f}})\), and the third and fourth fracture wings were set to be the equal length \((Y_{\mathrm{f}})\). Figure 7 shows the type curves for the bottom-hole pseudo-pressure of a vertical fractured well with multiple hydraulic fractures in stress-sensitive gas reservoirs. The type curves for the bottom-hole pseudo-pressure consist of the pseudo-pressure curve \((x-\mathrm{axis}:t_{\mathrm{D}}/C_{\mathrm{D}},y-\mathrm{axis}:\)\(\psi_{\mathrm{wD}})\) and the pseudo-pressure derivative curve \((x-\mathrm{axis}:\)\(t_{\mathrm{D}}/C_{\mathrm{D}},y-\mathrm{axis}:\)\(\psi_{\mathrm{wD}}^{\prime}\cdot t_{\mathrm{D}}/C_{\mathrm{D}})\). It is observed that there are seven possible flow regions in the type curves as follows:  
Figure 5: Comparisons of bottom-hole pseudo-pressure and bottom-hole pressure between our simulation results and the test data [44]. (**a**) bottom-hole pseudo -pressure, (**b**) bottom-hole pressure(1) Wellbore storage period (WSP): The produced gas comes from the storage gas in the wellbore, and the gas in the reservoir has not flowed into the wellbore. Both the pseudo-pressure curve and the pseudo-pressure derivative curve exhibit as straight lines with the slope being one. (2) Transitional flow after wellbore storage period (TFAWSP): the gas in the reservoir begins to flow into the wellbore. This flow period is controlled by both the wellbore storage and skin near the wellbore. The pseudo-pressure derivative curve appears as a \"hump\". (3) Bilinear flow period (BFP): Linear flows take place within the hydraulic fractures and perpendicular to the hydraulic-facture surfaces in the reservoir simultaneously. The pseudo-pressure derivative curve exhibits as a straight line with the slope being 1/4. (4) Transitional flow after bilinear flow period (TFABFP): The duration of this flow period is dependent on the difference of the hydraulic-fracture lengths. The shorter the hydraulic-fracture length is, the earlier the BFP ends. Therefore, this flow period will occur when the BFP of the shorter hydraulic fracture ends and the longer hydraulic fracture still lies in the BFP. The pseudo-pressure derivative curve appears as a straight line with the slope in the range of 1/4-1/2. (5) Linear flow period (LFP): When the BFP of each hydraulic fracture ends, the LFP will appear. In this period, the linear flow perpendicular to the hydraulic-facture surfaces in the reservoir dominates in the area near the wellbore. The pseudo-pressure derivative curve appears as a straight line with the slope being 1/2. Figure 6: Schematic of a vertical fractured well with four fracture wings. (6) Transitional flow after linear flow period (TFALFP): When the pressure wave continues to travel in the reservoir, the interference between the pressure waves from different hydraulic fractures will take place, which makes the slope of the pseudo-pressure derivative curve be greater than \(1/2\). It should be noted that the stress sensitivity begins to obviously affect the type curves in this period. As the magnitude of the \(\gamma_{\text{D}}\) increases, the pseudo-pressure and its derivative curves are shifted up.