Stochastic modeling of the variation of velocity and permeability as a function of effective pressure using the Bed-of-Nails asperity-deformation model
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The mechanical and transport properties of porous and cracked media, such as velocity and permeability, are sensitive to the effects of effective pressure, which itself is a function of the confining pressure and the pore-fluid pressure. The dependence of permeability and velocity on effective pressure has previously been modeled using the Bed-of-Nails asperity-deformation model. The main objective of this research was to explore the sensitivity of the Bed-of-Nails and effective-pressure models to random, Gaussian errors, by using an inverse approach. To achieve this, numerical modeling of pre-existing velocity and permeability experimental data sets was done. Extrapolation to 600 MPa was performed using an epidosite data set of compressional velocity as a function of confining pressure, only using measurements in the range 0-100 MPa. The results showed that, given sufficient data and considering random error only, extrapolation can be done with a level of error of less than 1.5%. Model error can also be significant in this type of exercise because it can give rise to systematic misfit, although in this case it was shown that the effects of model error were not considerable. Modeling the variation of compressional velocities as a function of confining and pore-fluid pressures in a deep-sea chalk showed that the best-fitting asperity-deformation model is sensitive to the effective-pressure model. Measurements of permeability in a Navajo-sandstone specimen as a function of confining pressure were numerically modeled, and the results showed that measurements made at low pressures, specifically near Pe = 0, are very important to constrain the model. The same result was found in the case of permeability as a function of confining and pore-fluid pressure in a Wilcox-shale where the lack of measurements near Pe = 0 caused the error in the model parameters to be overestimated. This occurs because the rate of change of permeability as a function of effective pressure is very high at low pressures. The lack of sufficient data near Pe = 0 overestimates the curvature matrix and, therefore, the errors in the model parameters.
Genova Barazarte, Ezequiel (2007). Stochastic modeling of the variation of velocity and permeability as a function of effective pressure using the Bed-of-Nails asperity-deformation model. Master's thesis, Texas A&M University. Available electronically from