Petroleum Engineering Seminar

Naturally-fractured carbonate karst reservoirs are characterized by various-sized solution caves that are connected via fracture networks at multiple scales. While the flow through the porous regions can be modeled by Darcy’s law, Stokes equation has to be used to describe the flow through the void spaces. This presents a major challenge in modeling the fluid flow through such formations because of the co-existence of porous and free-flow regions on multiple scales. Stokes-Brinkman equation was proposed as a fine scale model for flow through carbonate karst reservoirs. This equation is a unified description to multi-physics and multi-scale flow behavior. It is the first time that this equation is used to model the flow through carbonate karst reservoirs though it was first developed in 1940s. We show that the Stokes-Brinkman equation exceeds the traditional coupled Darcy-Stokes approach in modeling capacities without loss of accuracy. The numerical treatment of Stokes-Brinkman equation is not trivial though it is much more convenient comparing to the coupled Darcy-Stokes equations. A mixed finite element code was developed to solve the Stokes-Brinkman equation on unstructured grid. A series of numerical experiments are performed to test the proposed model on typical fracture-caves configurations. The Stokes-Brinkman equation is then used as a fine-scale flow model in the scale-up analysis of naturally fractured carbonate karst formations. An efficient numerical scheme is developed to deal with the large computational expense and the computational stability issues due to significant scale difference between fractures and formation blocks. It is shown that the scale-up results based on Stokes-Brinkman model agree well with fine-scale solutions. The proposed Stokes-Brinkman model flexibly adapts to the different flow physics in naturally-fractured carbonate karst reservoirs in a simple and effective way. It extends the modeling and predicting capability in efficient development of this important type of reservoir.

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