Numerical Modelling Of Reactive Flow And Wormhole Formation In Carbonate Rocks

Acidizing is one type of treatment that is employed to increase the permeability around the wellbore.During this process,acid is injected into the rock under a pressure that is lower than the pressure that would cause the rock to fracture.The acid reacts with and dissolves some of the rock components,which can – in favorable cases – overcome some of the induced damage or just enhances the local permeability.In carbonate rocks,acidizing can not only reduce the damage,but it also can create conductive channels that extend some distance into the rock mass,known as wormholes,whose hydraulic conductivity is several orders of magnitude larger than that of the porous medium.The experimental observation has also shown that the amount of acid required to breakthrough is minimum when wormhole dissolution is formed.Therefore,simulating the reactive flow in carbonate medium and finding the optimum injection rate are of fundamental importance to reduce the acidization cost.Firstly,the current two-scale continuum model is improved and extend to the 3-D radial flow condition,and used to simulate reactive flow and wormhole formation in carbonate rocks.More specifically,a new method for generation of an initial porosity field is presented,unlike methods used in previous works,in which the porosity field is mesh dependent.A new structure-property relationship based on the fractal geometry theory is also presented to describe the evolution of local permeability,pore radius,and specific area with porosity variation.In numerical calculation,to improve the convergence rate,the heterogeneous medium in question is extended by adding a thin layer of homogeneous porous medium to its inlet.We compare the simulation results with the available experimental observations and find that they are qualitatively consistent with each other.Additionally,sensitivity analysis of the dissolution process with respect to acid injection rate and rock heterogeneity,including heterogeneity magnitude and correlation length,is presented.Then,a general numerical scheme for simulating reactive flow problem on unstructured grid is presented based on the finite volume method.The diffusion and convection terms involved in the reactive flow model are discretized by using the two points flux approximation(TPFA)and upwind scheme,respectively.The location of the centroid node inside each control volume is moved by using an optimization algorithm to make the connections with the surrounding cells as orthogonal as possible,which systematically improves the accuracy of the TPFA scheme.Additionally,in order to avoid the computational complexity resulting from the discretization of the non-linear term,the mass balance equation is only discretized in the spatial domain to get a set of ordinary differential equations(ODEs).These ODEs are coupled with the reaction equations and then solved using the numerical algorithm on ODEs.The efficiency and accuracy of the proposed method is studied by comparing the results obtained from the proposed numerical method with previous experimental and numerical results.These results indicate that compared with the previous methods,the proposed method predicts the wormhole structure more accurately.Finally,combining the two-scale continuum model and the discrete fracture network model,a continuum model is developed that calculates the reactive flow of acid in fractured carbonate rock with a complex fracture network.The locations of fractures in the model are explicitly defined and can capture complex geometric relationships.Numerical simulations of reactive flow in 2D fractured porous media,in cases with simple and complex fractures,under linear and radial flow conditions,are presented.In particular,a sensitivity analysis of the dissolution process with respect to the presence of fractures,fracture aperture,fracture distribution,and acid injection rate,is conducted.