A mathematical model for drainage and desorption area analysis during shale gas production

Abstract For shale gas production, more attention is paid to production decline analysis, pressure transient analysis, and flow mechanism in nano-scale matrix. A few studies were carried out to analyze the depth of drainage and desorption in shale gas reservoir. When simulating shale gas production performance, especially in the case of multi-stage fractured horizontal wells (MFHW), the understanding of depth of drainage can analyze the critical time of interference and its intensity, and the desorption area is also a key factor to calculate production contributed from adsorbed gas. In these regards, this study presents a semi-analytical solution with dynamic gas compressibility to predict drainage and desorption area for long term. An analytical simplification solution is obtained to predict for early production, which is accurate enough. Using the method of continuous succession of steady states, the approximation solution is in good agreement with the results of Fast-Matching Method (FMM). The results show that the seepage area of each fracture expands much faster in stimulated reservoir volume (SRV) than that in unstimulated area with an elliptic shape. Desorption area also expands fast in SRV but is limited in SRV due to ultra-tight properties in unstimulated area. It is also proved that critical desorption pressure (CDP) delays desorption which plays a significant role in area expansion. This approach turns out to be simple and efficient when applied to practical projects.