The relationship between dry rock bulk modulus and porosity – An empirical study

There are various approaches to computing dry rock bulk modulus as a function of porosity and, from this, inferring velocity and density changes due to reservoir fluid change as a function of porosity. One such approach is the pore space stiffness method. A second approach is the critical porosity model (Mavko and Mukerji, 1995). Using the clean sandstones at different pressures from a dataset collected by Han (1986), and Han et al. (1986), we will evaluate the accuracy of each method. Based on the observations as a function of reservoir pressure, we will also predict an empirical relationship between pore space stiffness and pressure. INTRODUCTION Fluid replacement modeling is a procedure whereby the in-situ properties of a reservoir are replaced with alternate values from which seismic parameters such as Pwave velocity, S-wave velocity and density can be computed. The basic equations for P and S-wave velocity in the saturated, porous reservoir can be written as sat sat sat sat P K V ρ μ 3 _ + = , (1) sat sat sat S V ρ μ = _ , (2) where the subscript sat indicates the fluid-saturated case, VP is the P-wave velocity, VS is the S-wave velocity, ρ is the density, μ is the shear modulus, and K is the bulk modulus, or the inverse of compressibility. We will assume that the values given in equations (1) and (2) are the observed in-situ values. Our goal is to then compute new values representing alternate reservoir conditions. In equations (1) and (2), the saturated density can either be measured in-situ or computed from the equation φ φ φ φ o o g g w w m sat S ρ S ρ S ρ ) ( ρ ρ + + + − = 1 , (3) where the subscripts m, w, g and o indicate matrix, water, gas and oil, S is the fraction of saturation of each fluid component and φ is porosity. (Note that even if we measure the in-situ density values, equation (3) will be used in the fluid replacement modeling case). ________________________________________________________________________ 1 Hampson-Russell, A CGGVeritas Company, Calgary, Alberta, [email protected] 2 Hampson-Russell, A CGGVeritas Company, Houston, Texas, [email protected]