Damköhler number-based research on dividing dissolution patterns in carbonate acidizing

Abstract

In general, the main dissolution patterns in carbonate acidizing include face dissolution, wormhole dissolution and uniform dissolution. Wormholes can also be divided into single, dominant wormhole, ramified wormhole and so on. The wormholes can establish advantageous channels for oil and gas in the reservoirs, increase the permeability of formations and achieve the ultimate goal of carbonate matrix acidizing. Considering the factors that affect carbonate acidizing, the flow rate of acid plays the key role in determining dissolution patterns. Many scholars have carried out the researches by means of numerical simulation or physical simulation experiment individually, but the reports which combine the two methods and define the flow rate boundary between different dissolution patterns in carbonate acidizing are rare. In this paper, the flow rate of acid was dimensionless on the basis of Damköhler number (Da), and the boundary of acid injection rate was confirmed by combining numerical simulation with physical simulation experiments. Among the various types of dissolution models, the two-scale continuum model comprehensively considers the convection, diffusion and acid-rock interfacial reaction and is capable of dynamically monitoring the acidizing region at different time steps. This paper, using the finite difference method, solved the typical two-scale continuum model. In order to extend the calculation of the range of Damköhler number, Steffensen's acceleration method was applied to the porosity variation equation. The previous conclusion that at higher injection rate the breakthrough pore volume of acid is in direct proportion to the one-third power of the average pore velocity was validated. Furthermore, the typical pressure fall-off curve was analyzed. Results show that the typical pressure drop curve changes from the power-law curve to the straight line, as the injection rate decreases. Based on the analysis of porosity field and concentration field, combined with physical simulation experiment, the change law of dissolution pattern with Da was analyzed, which clarify the injection rates boundary of dissolution pattern. The results show when Da is between 50 and 200, the core appears wormholes, when Da is between 1 and 50, the dissolution pattern is the transition stage from wormhole to uniform dissolution and when Da is between 200 and 500, the core dissolution pattern is the transition stage from wormhole to face dissolution. The Damköhler number and injection rates of different dissolution patterns can be used to guide the design of acidizing construction.