Abstract
Darcy model fails to accurately model flow in karst reservoirs because the flow profiles in free-flow regions such as vugs, fractures and caves do not conform to Darcy’s law. Flows in karsts are often modelled using the Brinkman model. Recently, the DMOPD approach was introduced to reduce the complexity of modelling single-phase flow in Karst aquifers. Modelling two-phase flow using the Brinkman’s equation requires either a method of tracking the front or introducing the saturation component in the Brinkman’s equation. Both of these methods introduce further complexity to an already complex problem. We propose an alternative approach called the two-phase Darcy’s Model with optimized permeability distribution (TP-DMOPD) to model pressure and saturation distributions in karst reservoirs. The method is a modification to the DMOPD approach. Under the TP-DMOPD model, the caves are initially divided into zones and the permeability of each zone is estimated. During this stage of the TP-DMOPD model, the fluid inside the reservoir is assumed to be in a single-phase. Once the permeability distribution is obtained, the two-phase Darcy model is used to simulate flow in the reservoir. The example applications tested showed that the TP-DMOPD approach was able to model two-phase flow in karst reservoirs.
Highlights
About 60% of the world’s oil reserves are located in fractured carbonate reservoirs (Akbar et al 2000)
We introduce the TP-Darcy model with optimized permeability distribution (DMOPD) model (TwoPhase Darcy’s Model with Optimized Permeability Distribution), in an attempt to the simulation of two-phase flows in karst reservoirs consisting of megakarstic features such as caves
For the producers located in the caves (P2–P5), we observe a faster breakthrough of the injected water when the reservoir is modelled using the TP-DMOPD model
Summary
About 60% of the world’s oil reserves are located in fractured carbonate reservoirs (Akbar et al 2000). The DMOPD approach works on the principle that the Darcy model can be made to mimic the velocity profile obtained using the Brinkman model by dividing the free-flow region into zones and assigning different values of permeability to each zone The distribution is such that the central zone has the maximum value of permeability and this gradually decreases as one moves towards the walls of the caves. We introduce the TP-DMOPD model (TwoPhase Darcy’s Model with Optimized Permeability Distribution), in an attempt to the simulation of two-phase flows in karst reservoirs consisting of megakarstic features such as caves. Under this method, the permeability in the caves is estimated while assuming that a single-phase fluid is flowing in the reservoir. Results indicated that the Darcy model predicted a later breakthrough of water at the producers when compared to the TP-DMOPD model
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