Theoretical Study On Multiscale Modeling Of Two-phase Flow Based On Discrete Fracture-vug Network Model

Fractured vuggy carbonate reservoir has been received much attention recently becauseof its significant contribution to the oil and gas reserves and production. Usually, fracturedvuggy carbonate reservoir has complex pore structures and contains not only matrix andfractures but also the vugs that are irregular in shape and vary in diameter from millimeters tometers. Modeling fluid flow through fractured vuggy porous media is a challenging problemdue to the presence of vugs which are connected via fracture networks at multiple scales. Themain challenge is the co-existence of porous and free-flow in such reservoirs. The existingmodels are not suitable to model the fluid flow in fractured vuggy carbonate reservoirs. Thus,developing a corresponding fluid flow model and its numerical simulation method is urgent.In this dissertation, we proposed a novel fluid flow model, i.e., discrete fracture-vug networkmodel, to model the realistic fluid flow in fractured vuggy carbonate reservoirs. This newmodel consists of three systems: rock matrix system, fractures system, and vugs system. Thefractures and vugs are embedded in porous rock, and the isolated vugs could be connected viadiscrete fracture network. The flow in porous rock and fractures follows Darcy’s law, and thevugs system is free fluid region. Firstly, a basic model for coupling two-phase free flow withporous flow is developed. It is valid on the representative elementary volume (REV) scale andaccounts for mass and momentum transfer across the fluid-porous interface. The developmentis based on a two-step upscaling approach, in which the volume averaging method is applied.In the first step, a set of general non-local average forms is derived from the pore-scaledescriptions. They are valid in the entire domain since any length-scale constraint has notbeen introduced. After introducing specific length-scale constraints, these non-local averageforms can be simplified and reduced to the models which are classically used in the free-flowregion and porous medium, respectively. In the second step, a set of jump conditions at thefluid-porous interface is developed by introducing the concept of surface-excess quantity. It isshown that the complex interface phenomena within the phases on the pore scale, and theeffects of the fluid-porous interface can be incorporated into the model in a consistent manner.The comparisons between analytical solutions and Beavers-Joseph experimental data indicate that the new fits are more in line with the experimental data than the previous studies. Then,the Galerkin finite element method has been used to model the fluid flow in the porous regionbased on the discrete fracture model. For the free-flow region, the upstream Petrov-Galerkinfinite element method has been applied to discretize the average two-fluid model based onoperator splitting method. And then an alternate solution scheme is used to couple such tworegions. At last, an efficient numerical model has been developed for immiscible two-phaseflow in fractured karst reservoirs based on the idea of equivalent continuum representation,which is suitable to the field-scale reservoir simulation. Based on the discrete fracture-vugmodel and homogenization theory, the equivalent absolute permeability tensors for each gridblocks are calculated. Then an analytical procedure to obtain a pseudo relative permeabilitycurves for a grid block containing fractures and cavities has been successfully implemented.Next, a full-tensor simulator has been designed based on a hybrid numerical method(combining mixed finite element method and finite volume method). Some numericalexamples have been used to validate the method. Summing up, an efficient fluid flow modeland its modeling theory have been developed in this dissertation, which can be applied to thefractured vuggy carbonate reservoirs.