A Novel Method to Predict S-Wave Velocity of Carbonate Based on Variable Matrix and Equivalent Porous Medium Model

Taking the carbonate of the Majiagou Formation in the Ordos Basin as an example, this paper introduces a method for predicting the S-wave velocity of carbonate based on rock physics modeling. By analyzing the samples in the study area, we can find that the carbonate reservoirs in the study area have the following characteristics: (1) The lithology of the Majiagou Formation in the Ordos Basin is relatively complex, mainly composed of dolomite, lime dolomite, dolomitic limestone, gypsum, and gypsum-bearing dolomite. The pore types include intergranular pores formed by dolomitization, intergranular dissolution pores formed by dissolution, and fractures. (2) Due to the diverse types and complex distribution of rock-forming minerals, there are always some rock samples whose matrix modulus is beyond the upper or lower limits. Those were calculated using the Voigt–Reuss–Hill (VRH) average method. (3) The pore structure of carbonate is very complex due to diagenesis. Based on the influence of pore shape characteristics on rock elastic parameters, pore shapes are divided into three types using the pore aspect ratio. Among them, the aspect ratio of intergranular pores is the largest, while that of the fracture pores is the smallest, and the aspect ratio of intergranular dissolved pores falls between the two. Therefore, the accuracy of predicting S-wave velocity in this area based on traditional rock physics modeling methods is low. In this paper, we will introduce a new model that is aimed at improving the traditional rock physics model. The first improvement is based on a variable matrix modulus, which can be used for matrix modeling to mitigate the influence of uneven mineral distribution. The second enhancement involves quantitatively characterizing the impact of different pore aspect ratios on the S-wave velocity of carbonate rocks, using a porous differential equivalent medium (DEM) model.