E. Kazatchenko

Prediction of the s-wave velocity in carbonate formation using joint inversion of conventional well logs

In this paper, we propose a technique for the prediction of s-wave velocity in carbonate formations with different types of secondary porosity using conventional logs (p-wave slowness, micro-resistivity, total porosity and density). The technique consists of the determination of the pore microstructure parameters (matrix and secondary porosities, shapes of the secondary pores) using the joint petrophysical inversion of well logs and simulation of the s-wave log for the medium with obtained characteristics. In the inversion procedure, the calculation of the theoretical logs is based on the model of a double-porosity medium that consists of a homogeneous isotropic matrix with a primary pore system and secondary pores approximated by spheroidal inclusions placed in the matrix. Selecting the aspect ratio of inclusions we have simulated different types of secondary porosity such as vugs (close to spherical inclusions), vugs connected by channels (prolate spheroids) and cracks (flattened spheroids). We have applied the self-consistent method (the effective medium approximation) to simulate physical properties including the s-wave slowness from the double-porosity model. The technique has been verified using a theoretical model and experimental data from the South Zone of Mexico. The results of this technique application have demonstrated a good agreement between measured and reconstructed s-wave logs in carbonate formations.

Computation of continuum percolation threshold for pore systems composed of vugs and fractures

Abstract In this research, we study the connectivity of a network composed of pores with different shapes including combinations of vugs and fractures. For this purpose, we have developed a numerical simulation technique to determine the dependence of continuum percolation threshold on the pore-shape distribution for isotropic porous 2D and 3D networks composed by elliptical and spheroidal elements respectively. This technique is based on the following new algorithms: (1) analytical estimation of overlapping between inclusions; (2) partial discretization schemes (elements of a discrete pixel base with one continuous dimension) for numerical calculation of connected-cluster porosity; and (3) determining the percolation-threshold porosity by using Monte Carlo simulations for different relative pore sizes. By approximating the pore shapes by ellipses (2D) and spheroids (3D) and varying their aspect ratios, we can model different types of pores from vugs (spheres) to fractures (oblate spheroids) and channels (prolate spheroids). We have calculated the critical percolation porosity for the following models: (1) a network consisting of elements with constant shapes; (2) a network composed of elements with the uniform logarithmic distribution of aspect ratios; and (3) a network containing elements of two different shapes. To validate the simulation technique, we have compared the modeling results for the first model with a threshold-aspect ratio relationship published previously. Based on the modeling results we have found simple and explicit equations for 2D and 3D models to determine the percolation threshold for pore networks with the bimodal distribution of shapes. The equations use only the element concentrations and percolation-threshold values for each elements shape.

Application of petrophysical inversion of well logs for pore-system characterization of South Florida aquifer

Summary We applied and demonstrated the feasibility of a petrophysical inversion technique to reconstruct the secondary pore-space microstructure in carbonate doubleporosity aquifers. This technique consists of the joint inversion of acoustic (P- and S-wave velocities) and electromagnetic (conductivity) well logs using a unified pore-space model and self-consistent effective media approximation for theoretical calculating the elastic moduli and electrical conductivity. We have inverted experimental well log data from a South Florida aquifer in the western Hillsboro Basin of Palm Beach County, Florida. The inversion results allowed us to find the detail vertical distribution of the primary and secondary porosities in the carbonate aquifer formation.