Carbonate rocks have a complex pore structure, show strong heterogeneity, and have a wide range of velocities that lead to more complicated velocity-porosity relationships compared with sandstones. We designed and prepared 72 carbonate synthetic cores with known pore structures according to the control variate principle. We measured the P- and S-wave velocities of these cores by an ultrasonic pulse transmission method, analyzed the effects of the pore aspect ratio (AR) and pore size d on velocities, and compared the experimental results with predictions of effective medium theories (EMTs). The matrix of our synthetic cores was consolidated mixture of carbonate cuttings and epoxy. We randomly imbedded predesigned penny-shaped silicone disks or expandable polystyrene balls into the matrix during the core preparation process to simulate secondary pores. The experimental results indicated that Han’s empirical linear velocity-porosity relation was a good prediction for cores with only interparticle pores. Secondary pores played an important role in the velocity variation of carbonates. Cores with a larger AR had faster velocities. Different ARs could lead to velocity variations as high as 1227m/s at a given porosity. When the wavelengths λ were larger than the pore size, cores with larger secondary pores found higher velocities under the same pore shape, pore fluid, and porosity condition. Different pore sizes could contribute to nearly 15% velocity variation at a given porosity. The comparison between our measurements and EMT predictions indicated that for carbonate rocks with a complicated pore structure, the self-consistent model gave more reliable predictions when the secondary pore size was relatively small (λ/d>10) and Kuster and Toksoz formulations as well as the differential effective medium model gave more satisfactory results when the secondary pore size was relatively large (λ/d=58, or even smaller).

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