Research On The Effects Of Pore Structure On The Elastic Wave Properties In Carbonate Rocks

Carbonate rocks have extremely complicated pore system,and show significant heterogeneity.Because the porosity cannot effectively reflect the degree of compaction in carbonate rocks,conventional methods for pore pressure prediction don't suit to carbonate reservoirs.Calculations based on effective medium theory(EMT)indicate that scatterings in the porosity-velocity crossplot due to the influence of pore structure can result in significant deviations in the pore pressure predictions by conventional methods.At the same porosity,the soft cracks with lower pore aspect ratio lead to abnormal low velocities and pore pressure overestimation which results in lost circulation and reservoir damage.However,the stiff moldic-pores and vugs with higher pore aspect ratio lead to abnormal high velocities and pore pressure underestimation which results in well kick and even blowout.Therefore,besides the porosity,the velocity model of carbonates should also include the effects of pore structure in order to gain more reliable pore pressure prediction results.Aiming to quantitatively investigate the effects of pore structure on the elastic wave propagation in carbonate rocks,this paper systematically carried out experimental and numerical modeling studies.In the experiments,a physical model was firstly developed through numerous trials to model the rock with multiple pore structures.The consolidated mixture of carbonate rock cuttings and epoxy was used as the matrix,and interparticle pores were formed among the carbonate rock cuttings.During the process of making the physical model,predesigned materials with different shapes,sizes and volume were randomly added into the cuttings-epoxy mixture to simulate secondary pores,which helps to quantitatively control the parameters of secondary pores.Seventy two samples with different pore structures were designed based on the control variate principle and prepared by the above method.The P-and S-wave velocities of each sample were measured.The experiment results showed that the effects of primary pores on carbonate velocities can be well described by conventional empirical velocity-porosity relations used for sandstones.The effects of secondary pores on carbonate velocities should consider more detailed factors except secondary porosity,such as the pore aspect ratio(AR),and pore size.Our experiment results indicated that samples with larger AR and(or)larger secondary pore size have higher velocities.Based on the measurements,a general velocity model was developed for carbonate rocks considering the effects of both primary and secondary pores when the ratio of wave length to pore size(?/d)was larger than 10(i.e.the long wavelength condition).According to our experiment examination of EMT models for rocks with multiple pore structures,it is better to use self-consistent model when the secondary pore size is relatively small.The Kuster-Toksoz formulations and differential effective medium model are satisfactory choices when the secondary pore size is relatively large.In the numerical modeling,based on the similarity principle and pore structure information,2-D geometrical models of porous media are developed and provide a pore-scale modeling method for elastic wave properties of porous rocks with finite element method.Experimental results verified the numerical modeling,and the method was shown to be reliable.Using this pore scale modeling method,the effects of pore structure on the velocities and the scattering attenuation of carbonate rocks are analyzed.The modeling results indicate that the P-wave velocity increases as a power function as the pore aspect ratio increases.P-wave velocity of carbonate rocks is dispersive depending on ?/d.Such scale dependent dispersion is more evident for carbonate rocks with higher porosity,lower AR,and/or lower P-wave impedance of pore fluids.These modeling results are consistent with the former experiment observations.The pore distribution,pore size,AR,and pore density are important factors influencing the scattering attenuation in carbonate rocks.At long wavelength,the scattering attenuation coefficient increases as a power function as the pore density increases,and it increases exponentially with an increase in aspect ratio.In order to investigate the combined effects of pore structure and pore fluids on the elastic properties and velocities of saturated carbonates with complex pore structure,eight synthetic carbonate cores containing either void cracks or vuggy pores are prepared.The P-and S-wave velocities of eight synthetic cores at dry,brine,and kerosene saturated conditions are measured,respectively.The experiment results indicate that cores with cracks show shear stiffening after brine-saturation mainly because of the viscous coupling effects,and have abnormal high velocities.Cores with vuggy pores show shear weakening after brine-saturation due to the reduction in free surface energy,and have abnormal low velocities.When the cores are kerosene-saturated,they show shear stiffening regardless of secondary pore types,and have abnormal high velocities.But cores with cracks display stronger shear stiffening effects than cores with vuggy pores at kerosene saturation because of more active viscous coupling.The dynamic moduli changes with saturation increase as the secondary porosity increases.Gassmann's equation underestimates the velocities at shear stiffening and overestimates the velocities at shear weakening.The velocity deviation between Gassmann's prediction and experiments increases as the increase of shear modulus change.