Comparison of Single, Double, and Triple Linear Flow Models for Shale Gas/Oil Reservoirs

There have been many attempts to use mathematical method in order to characterize shale gas/oil reservoirs with multi-transverse hydraulic fractures horizontal well. Many authors have tried to come up with a suitable and practical mathematical model. To analyze the production data of a shale reservoir correctly, an understanding and choosing the proper mathematical model is required. Therefore, three models (the homogeneous linear flow model, the transient linear dual porosity model, and the fully transient linear triple porosity model) will be studied and compared to provide correct interpretation guidelines for these models. The analytical solutions and interpretation guidelines are developed in this work to interpret the production data of shale reservoirs effectively. Verification and derivation of asymptotic and associated equations from the Laplace space for dual porosity and triple porosity models are performed in order to generate analysis equations. Theories and practical applications of the three models (the homogeneous linear flow model, the dual porosity model, and the triple porosity model) are presented. A simplified triple porosity model with practical analytical solutions is proposed in order to reduce its complexity. This research provides the interpretation guidelines with various analysis equations for different flow periods or different physical properties. From theoretical and field examples of interpretation, the possible errors are presented. Finally, the three models are compared in a production analysis with the assumption of infinite conductivity of hydraulic fractures