A Computational Navier-Stokes Fluid-Dynamics-Simulation Study of Wormhole Propagation in Carbonate-Matrix Acidizing and Analysis of Factors Influencing the Dissolution Process

Abstract

Summary This study demonstrates the application of an alternative numerical-simulation approach to effectively describe the flow field in a two-scale carbonate-matrix-acidizing model. The modified model accurately captures the dissolution regimes that occur during carbonate-matrix acidizing. Sensitivity tests were performed on the model to compare the output with experimental observations and previous two-scale models in the literature. A nonlinear reaction-kinetics model for alternative acidizing fluids is also introduced. In this work, the fluid-field flow is described by the Navier-Stokes momentum approach instead of Darcy's law or the Darcy-Brinkman approach used in previous two-scale models. The present model is implemented by means of a commercial computational-fluid-dynamics (CFD) package to solve the momentum, mass-conservation, and species-transport equations in Darcy scale. The software is combined with functions and routines written in the C programming language to solve the porosity-evolution equation, update the pore-scale parameters at every timestep in the simulation, and couple the Darcy and pore scales. The output from the model simulations is consistent with experimental observations, and the results from the sensitivity tests performed are in agreement with previously developed two-scale models with the Darcy approach. The simulations at very-high injection rates with this model require less computational time than models developed with the Darcy approach. The results from this model show that the optimal injection rate obtained in laboratory coreflood experiments cannot be directly translated for field applications because of the effect of flow geometry and medium dimensions on the wormholing process. The influence of the reaction order on the optimal injection rate and pore volumes (PVs) of acid required to reach breakthrough is also demonstrated by simulations run to test the applicability of the model for acids with nonlinear kinetics in reaction with calcite. The new model is computationally less expensive than previous models with the Darcy-Brinkman approach, and simulations at very-high injection rates with this model require less computational time than Darcy-based models. Furthermore, the possibility of extending the two-scale model for acid/calcite reactions with more-complex chemistry is shown by means of the introduction of nonlinear kinetics in the reaction equation.

A Newton’s Second Law Abided Darcy-Brinkman-Forchheimer Framework in Matrix Acidization Simulation

“…From Figure 10, it can be seen that the acid-efficiency curve in this work matches the corresponding curve in Fig. 8 of [17] well when the range of the injected velocity is from 4.17 × 10 −7 m/s to 1.67 × 10 −4 m/s. When the injected velocity is 1.67 × 10 −7 m/s, its corresponding PVBT is 6.62, which is not reasonable.…”

“…It is emphasized that the 3D simulation results of the improved DBF framework are given for the first time in this work. The improved DBF framework can simulate similar numerical results with the works [42] and [17], which demonstrates its reliability.…”

“…It is observed that Equation (17) includes the variable that is a function of porosity from Equation (8) and (9), (18) which means that is in fact a function of porosity and the velocity. Thus, Equation (17) can substitute in Equation (13), and then a new equation with porosity being the unknown can be derived.…”

“…For Equation 22, (19), (8), (12), and (23), every variable is imposed at the centre of the cube. For Equation (17), except the variable u, the other variables are imposed at the centre of the cube. However, ‖ ‖ should also be imposed at the centre of the cube.…”

“…The grid has 180 cells in the x-direction and 72 cells in the y-direction, which is the same size as that of [17]. Since the work [17] declares their grid is fine enough to describe matrix acidization, our grid is also capable to do that.…”