A new mathematical model considering adsorption and desorption process for productivity prediction of volume fractured horizontal wells in shale gas reservoirs

摘要

It has proved that seepage flow of shale gas reservoirs is much more complicated compared to most conventional reservoirs due to massive multistage, multi-cluster hydraulic fracturing stimulations. It becomes crucially essential to develop new methods to better stimulate such a complex system, further understand the recovery mechanisms, and perfect optimization development plans of shale gas reservoirs. The published three linear flow models simplified the complex process and got very good results. However, desorption and adsorption mechanism, which is the key mechanism of shale gas reservoirs, was ignored. Consequently, in this paper, a numerical model considering desorption and adsorption process was established and solved under the polar coordinates and the Laplace space respectively to predict productivity of volume fractured horizontal wells in shale gas reservoirs. Single well productivity formula and bottom hole pressure formula of shale gas reservoirs were developed. In addition, based on the new established numerical model and its analytical solution, productivity of a volume fractured horizontal wells in a shale gas reservoir of Western China were calculated and compared with both the actual production data and results predicted by Eclipse simulator. Results showed that the predicted results are in good agreement with the field test. Although the simplifications resulted in errors to some extend, the improved trilinear model can also be recommended for the production prediction of the fractured horizontal wells in shale gas reservoirs. It is concluded that computational convenience of the trilinear-flow solution makes it a practical alternative to more rigorous but computationally intensive and time-consuming solutions.