Modeling and Analysis of Carbonate Matrix Acidizing Using a New Two-Scale Continuum Model

Summary Matrix acidizing is a common technique for carbonate reservoir stimulation. In this work, a new two-scale continuum model is developed to study the 2D acidizing process. The Navier-Stokes-Darcy equation is used instead of the Darcy’s-law equation to describe fluid flow. The continuity equation is also modified to consider the mass-exchange term between fluid and solid phases. The comparison results show that neglecting the solid-matrix-dissolution source term results in overestimation of pore volume (PV) to breakthrough (PVBT). The Darcy’s-law equation does not well-capture physical behaviors of fluid phase with low acid-injection velocity compared with the Navier-Stokes-Darcy equation. On the basis of this model, we discuss different processes influencing matrix acidizing, including convection, diffusion, and reaction, and different models, including classical and new two-scale continuum models. Besides, a comprehensive parametric study is also conducted to study the effect of parameters with respect to acid and rock physical parameters on the matrix-acidizing process. The typical dissolution patterns and optimal acid-injection rate presented in experimental studies can be well-observed by the new two-scale continuum model. Increasing the acid-injection concentration has a limited effect on the amount of acid mass but substantially reduces the amount of solute required. The acidizing curve is very sensitive to the dispersity coefficient, acid-surface-reaction rate, and porosity/permeability relationship.

The Effect of the Vadasz Number on the Onset of Thermal Convection in Rotating Bidispersive Porous Media

The onset of thermal convection in uniformly rotating bidispersive horizontal porous layer, uniformly heated from below, is analyzed. A generalized Darcy equation for the macro-phase is considered to take the Vadasz number into account. It is proved that the presence of the Vadasz number can give rise to oscillatory motion at the loss of stability of thermal conduction solution.

Propagation of Reaction Front in Porous Media with Natural Convection

This paper examines the influence of convective instability on the reaction front propagation in porous media. The model includes heat and concentration equations and motion equations under Boussinesq approximation. The non-stationary Darcy equation is adopted and the fluid is supposed to be incompressible. Numerical results are performed via the dispersion relation. The simulations show that the propogating reaction front loses stability as Vadasz number increase, it shows also more stability is gained when Zeldovich number increased.

PENURUNAN PERSAMAAN DARCY DARI PERSAMAAN NAVIER-STOKES UNTUK RESERVOIR ALIRAN LINIER DAN RADIAL

<p><em>Calculation of hydrocarbon flow in the form of oil or gas in Petroleum Engineering is used the Darcy equation. Deriving the Navier Stokes equation produces a general equation that cannot be used for special conditions, for example linear or radial flow because the formulation is different. In this paper, the Darcy equation obtained through experimental evidence is derived from the Navier Stokes equation with several assumptions and simplifications . The calculation in this paper uses a numerical solution, which uses Fortran language, as one approach. Then by using field data, the Darcy equation is used in calculating the flow rate and the velocity of linear fluid in the reservoir. And also the calculation of the pressure from the well to the outermost point of the reservoir with radial fluid flow, so that the pressure gradient data can be obtained from the well to the outermost point of the reservoir.</em><em></em></p>