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As an essential carbonate reservoir parameter, porosity is closely related to rock properties. Digital rock physics (DRP) technology can help us to build forward models and find out the relationship between porosity and physical properties. In order to prepare models for the rock physical simulations of carbonate rocks, digital rock models with different porosities and fractures are needed. Based on a three-dimensional carbonate digital rock image obtained by X-ray microtomography ( μ -CT), we used erosion and dilation in mathematical morphology to modify the pores, and fractional Brownian motion model (FBM) to create fractures with different width and angles. The pores become larger after the erosion operation and become smaller after the dilation operation. Therefore, a series of models with different porosities are obtained. From the analysis of the rock models, we found out that the erosion operation is similar to the corrosion process in carbonate rocks. The dilation operation can be used to restore the matrix of the late stages. In both processes, the pore numbers decrease because of the pore surface area decreases. The porosity-permeability relation of the models is a power exponential function similar to the experimental results. The structuring element  B ’s radius can affect the operation results. The FBM fracturing method has been proved reliable in sandstones, and because it is based on mathematics, the usage of it can also be workable in carbonate rocks. We can also use the processes and workflows introduced in this paper in carbonate digital rocks reconstructed in other ways. The models we built in this research lay the foundation of the next step physical simulations.

Variable secondary porosity modeling of carbonate rocks based on μ -CT images