IPR of triple continuum reservoirs, analytical approach

The existence of vugs in naturally fractured carbonate reservoirs has been widely seen in oil and gas reservoirs. The multiphase flow is taking place in multimedia such as matrix, fractures and vugs. Hence, the standard famous Darcy law may not apply to describe the multiphase flow in such reservoirs. A new triple-continuum conceptual model has been developed by several investigators to help to understand multiphase flow behavior through vuggy fractured carbonate reservoirs. The most well-known conceptual model is the single permeability, triple porosity model. In this conceptual model, vuggy fractured rock is considered as a triple-continuum medium, consisting of (1) highly permeable fractures, (2) low-permeability rock matrix, and (3) various-sized vugs. The Inflow Performance Relationship (IPR) that describes the relation between the sand-face flowing pressure and well standard flow rate for such system can be generated either numerically or analytically. This study investigates the analytical approach of IPR of triple continuum reservoirs. The IPR is derived from the analytical solution of diffusivity equation. The objective of this study is to solve the fluid flow equations that govern the flow in triple continuum reservoir under semi-steady flow regime. Then, the productivity index is calculated and the effects of different reservoir parameters are investigated. Various sensitivity analysis was implemented to gain better understanding especially for the effect of inter-porosity and storativity. The generated IPR of the triple continuum reservoir is the same as the single continuum reservoir except that it is multiplied by E (error parameter = 0 E 1). The max value of E is one where the fractures are the only present continuum in the reservoir (single continuum).