The influence of fracture surface morphology on nonuniform etching in limestone acid fracturing

The success of acid fracturing in tight limestone reservoirs relies on the formation of nonuniform etching on the fracture wall. However, almost all acid fracturing models neglect the effect of fracture surface morphology on nonuniform etching. In this study, a three-dimensional acid fracturing mathematical model is developed to quantify and analyze the influence of rough fracture surface morphology on nonuniform etching for the first time by defining a morphology coefficient to describe the degree of local and overall morphological undulations of the fracture surface from a three-dimensional scale. The model uses the moving mesh partial differential equation (MMPDE) method to describe the flow field and spatial variation in the fracture as the fracture surface is continuously dissolved with the acid during acid fracturing, and the MMPDE moving mesh is coupled with the flow field, mass transfer, acid-rock reaction and fracture width variation. Based on the model, the effects of flow pattern, morphology coefficient, initial fracture width and fracture type on the nonuniform etching are studied. The simulation results demonstrate that the rough fracture surface can disturb the flow field and make the acid distribution more turbulent, which is conducive to the formation of nonuniform etching on the fracture surface. This phenomenon of flow rate differentiation can enhance the acid transfer distance. The local etching degree of the fracture surface decreases with the increase of the morphology coefficient of the area, and the strongly etching areas will appear around it. When the morphology coefficient of the local fracture area is larger than 1.2218, the area can appear obvious strongly etching areas and weakly etching areas after acid etching. The larger the initial fracture width is, the smaller the degree of nonuniform etching on the fracture surface. The prediction model constructed based on multiple linear regression was highly accurate (R2 = 0.9268) for the standard deviation of facture width (StdWidth) after acid etching. The critical value of StdWidth is recommended to be 0.6 as the criterion for judging the nonuniform etching ability. When the nonuniformity of the fracture surface is greater than this value, it is considered that the nonuniform etching ability is strong. In addition, the fracture with shear damage can produce relative sliding distance, which makes the fracture morphology on both sides of the fracture surface unevenly distributed and thus disturbs the flow field, which enhances the degree of nonuniform etching on the fracture surface. As the sliding distance increase, the magnitude of this enhancement also increases gradually. This study proposes a new three-dimensional characterization method for rough fracture surface morphology, solves the issue of mismatching flow field due to dynamic change in fracture width during acid fracturing.