Numerical Investigation of Wormhole Formation During Matrix Acidizingof Carbonate Rocks by Coupling Stokes-Brinkman Equation with ReactiveTransport Model Under Radial Flow Conditions

摘要

Matrix acidizing of carbonate formations has been widely used as a practical stimulation technique toimprove well performance near the wellbore.The principle of a matrix acidizing treatment is to createwormholes by the dissolution of carbonate rocks.The dissolution pattern can affect the efficiency of theacidizing based on the flow conditions.The actual acidizing treatments are performed by injecting acidicfluid into the formation through a wellbore resulting in a radial flow in the porous media.Consequently,amathematical model under radial flow conditions can accurately characterize mineral dissolution patterns,which provide valuable guidelines for designing of acidizing treatments.In this paper,we have developed a 3D mathematical model that couples the Stokes-Brinkman equationand reactive-transport equations under radial flow conditions,which has been utilized for modeling themineral dissolution processes during the acidizing treatment.We have developed and implemented anumerical procedure that solves the Stokes-Brinkman equation and the reactive transport equations bythe staggered grid finite difference method and the control volume finite difference method in cylindricalcoordinates,respectively,in a sequential fashion.Numerical validation and experiments have beenperformed using the proposed numerical solution procedure.Two dimensionless numbers,Damkohler number(Da)and Peclet number(Pe),are used in the simulationstudy to characterize the competitive coupling effects among the advection,diffusion,and chemicalreactions.We have performed the numerical experiments to investigate the type of dissolution correlated tothe variations of Da and Pe numbers based on the synthetic radial core-flooding scenarios.The numericalresults demonstrate that the proposed model is capable of describing the matrix acidizing treatments underradial flow conditions due to the advantage of the Stokes-Brinkman equation for flow in fractured porousmedia.The Da and Pe numbers are two crucial factors that can affect flow conditions,transport behavior ofsolute,and chemical reactions.Mineral dissolution patterns take different forms according to various Da andPe numbers and various alterations of rock properties are obtained accordingly.In addition,the emergenceof the wormhole structure during the injection of acid is discussed in this paper.This work presents a 3D mathematical model allowing us to simulate a matrix acidizing process atexact downhole environments.We present the numerical experiments and sensitivity studies of mineraldissolution in carbonate rocks to investigate the coupling effect of fluid flow and reactive transport processon the wormhole formation for a better matrix acidizing design in field operations.