Numerical treatment of two-phase flow in porous media including specific interfacial area

In this work, we present a numerical treatment for the model of two-phase flow in porous media including specific interfacial area. For numerical discretization we use the cell-centered finite difference (CCFD) method based on the shifting-matrices method which can reduce the time-consuming operations. A new iterative implicit algorithm has been developed to solve the problem under consideration. All advection and advection-like terms that appear in saturation equation and interfacial area equation are treated using upwind schemes. Selected simulation results such as p(c) - S-w - a(wn) surface, capillary pressure, saturation and specific interfacial area with various values of model parameters have been introduced. The simulation results show a good agreement with those in the literature using either pore network modeling or Darcy scale modeling

Numerical simulation of a nonlinear diffusion type equation in a two phase media with linear porosity and permeability model

Predicting and understanding the behavior of pressure is important in reservoir maintenance and evaluation. This work studies the behavior of fluid pressure in a reservoir by numerical simulation of the pressure diffusion type equation in a two phase media with a linear porosity and permeability model. Because the porosity and permeability are pressure dependent, the resulting diffusion type equation is nonlinear and is solved using a backward-forward finite difference method. The simulation code was ran using a constant porosity and permeability model and a linear porosity and permeability model. The results from the linear porosity and permeability model was compared to that of the constant porosity and permeability model. In both cases the pressure gradient was greatest at the wellbore and decreases as the radial distances away from the wellbore increases. The pressure in both cases also decreased with time. However, at each location and time the pressure drop was lower in the linear porosity and permeability model than with the constant porosity and permeability. The backward-forward finite difference method proved to be useful in solving numerically the nonlinear diffusion type equation. This work can be applied in the oil and gas industry to predict pressure behavior in reservoirs and make investment decisions, production and maintenance decision

Two-Phase Flow Effect on Carbonate Matrix Acidizing

Matrix acidizing treatments are commonly used to improve the productivity of oil and gas wells in carbonate reservoirs. For a given volume of acid injection, the optimal injection rate can achieve the deepest wormhole penetration. Normally, the optimal condition is obtained through laboratory core flooding experiments with acid fluid injection into water saturated cores. However, in field treatments, acid fluid injected into oil and gas saturated formations creates a two-phase flow region. Two-phase flow effect on optimal treatment condition needs to be evaluated. The research is conducted through experimental investigation and numerical modeling. In order to investigate two-phase flow effect in matrix acidizing, a systematic experimental study that covers a variety of back pressures, temperatures and injection rates is conducted. Computerized Tomography (CT) scan images are taken for each core sample after acid injection to evaluate the structures of the wormholes. With the experimental study, the effect of evolved CO₂ on wormhole propagation is examined. The test results show that at low injection rate, CO₂ present as a gaseous phase lowers wormhole propagation efficiency dramatically, and enlarged wormhole diameter is observed. This work verifies that two-phase flow affects the wormhole propagation. A numerical model is developed to simulate two-phase flow effect on wormhole propagation. The model uses 3-D numerical simulation with two-scale continuum model and finite volume method to characterize matrix acidizing process. The model can capture both gravity effect and two-phase flow effect on wormhole propagation. From this numerical model, we are able to estimate the properties that cannot be measured from lab experiment. With the numerical model, we study the effect of several key factors, such as injection rate, viscosity, and residue non-wetting phase saturation on wormhole efficiency. The results show that wormhole propagation in two-phase flow region is quite different to single-phase flow. The presence of an immiscible phase, such as gas or oil, before acid injection, can increase the wormholing efficiency. The higher the oil viscosity, the lower volume of acid needed for wormhole penetrating the core. A higher initial saturation of oil, also reduces the breakthrough pore volume. High residue oil saturation has a positive effect on wormholing efficiency. It is important to investigate the effects and calibrate the lab results before using them in oil and gas reservoirs

Two-Phase Flow Effect on Carbonate Matrix Acidizing

Matrix acidizing treatments are commonly used to improve the productivity of oil and gas wells in carbonate reservoirs. For a given volume of acid injection, the optimal injection rate can achieve the deepest wormhole penetration. Normally, the optimal condition is obtained through laboratory core flooding experiments with acid fluid injection into water saturated cores. However, in field treatments, acid fluid injected into oil and gas saturated formations creates a two-phase flow region. Two-phase flow effect on optimal treatment condition needs to be evaluated. The research is conducted through experimental investigation and numerical modeling. In order to investigate two-phase flow effect in matrix acidizing, a systematic experimental study that covers a variety of back pressures, temperatures and injection rates is conducted. Computerized Tomography (CT) scan images are taken for each core sample after acid injection to evaluate the structures of the wormholes. With the experimental study, the effect of evolved CO₂ on wormhole propagation is examined. The test results show that at low injection rate, CO₂ present as a gaseous phase lowers wormhole propagation efficiency dramatically, and enlarged wormhole diameter is observed. This work verifies that two-phase flow affects the wormhole propagation. A numerical model is developed to simulate two-phase flow effect on wormhole propagation. The model uses 3-D numerical simulation with two-scale continuum model and finite volume method to characterize matrix acidizing process. The model can capture both gravity effect and two-phase flow effect on wormhole propagation. From this numerical model, we are able to estimate the properties that cannot be measured from lab experiment. With the numerical model, we study the effect of several key factors, such as injection rate, viscosity, and residue non-wetting phase saturation on wormhole efficiency. The results show that wormhole propagation in two-phase flow region is quite different to single-phase flow. The presence of an immiscible phase, such as gas or oil, before acid injection, can increase the wormholing efficiency. The higher the oil viscosity, the lower volume of acid needed for wormhole penetrating the core. A higher initial saturation of oil, also reduces the breakthrough pore volume. High residue oil saturation has a positive effect on wormholing efficiency. It is important to investigate the effects and calibrate the lab results before using them in oil and gas reservoirs

Two-Phase Flow Effect on Carbonate Matrix Acidizing

Matrix acidizing treatments are commonly used to improve the productivity of oil and gas wells in carbonate reservoirs. For a given volume of acid injection, the optimal injection rate can achieve the deepest wormhole penetration. Normally, the optimal condition is obtained through laboratory core flooding experiments with acid fluid injection into water saturated cores. However, in field treatments, acid fluid injected into oil and gas saturated formations creates a two-phase flow region. Two-phase flow effect on optimal treatment condition needs to be evaluated. The research is conducted through experimental investigation and numerical modeling. In order to investigate two-phase flow effect in matrix acidizing, a systematic experimental study that covers a variety of back pressures, temperatures and injection rates is conducted. Computerized Tomography (CT) scan images are taken for each core sample after acid injection to evaluate the structures of the wormholes. With the experimental study, the effect of evolved CO₂ on wormhole propagation is examined. The test results show that at low injection rate, CO₂ present as a gaseous phase lowers wormhole propagation efficiency dramatically, and enlarged wormhole diameter is observed. This work verifies that two-phase flow affects the wormhole propagation. A numerical model is developed to simulate two-phase flow effect on wormhole propagation. The model uses 3-D numerical simulation with two-scale continuum model and finite volume method to characterize matrix acidizing process. The model can capture both gravity effect and two-phase flow effect on wormhole propagation. From this numerical model, we are able to estimate the properties that cannot be measured from lab experiment. With the numerical model, we study the effect of several key factors, such as injection rate, viscosity, and residue non-wetting phase saturation on wormhole efficiency. The results show that wormhole propagation in two-phase flow region is quite different to single-phase flow. The presence of an immiscible phase, such as gas or oil, before acid injection, can increase the wormholing efficiency. The higher the oil viscosity, the lower volume of acid needed for wormhole penetrating the core. A higher initial saturation of oil, also reduces the breakthrough pore volume. High residue oil saturation has a positive effect on wormholing efficiency. It is important to investigate the effects and calibrate the lab results before using them in oil and gas reservoirs