Browsing by Subject "Reservoir description and engineering"

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    Perturbation methods for rapid modeling and inversion of single-phase pressure diffusion measurements
    (2017-08-11) Escobar Gomez, Juan Diego; Torres-Verdín, Carlos; Sepehrnoori, Kamy; Balhoff, Matthew; Heidari, Zoya; Alpak, Faruk O
    Numerical simulation enables improved quantitative understanding of pressure diffusion phenomena in spatially complex reservoirs. Despite recent computational advances, traditional numerical simulation algorithms still pose significant challenges in flexibility and computer performance, especially concerning the solution of time-domain problems that require multiple implementations of a forward model. In this dissertation I develop a time-domain perturbation theory suitable for modeling anisotropic and heterogeneous single-phase flow systems. Although theoretically valid for any spatially-dependent rock/fluid property, the study emphasizes arbitrary spatial variations of tensorial permeability. The efficiency of integral-equation solutions is invoked by coupling perturbation theory and the superposition principle to accurately model arbitrary transient flow regimes, boundary conditions, and rockproperty distributions. Developed algorithms require a maximum of two numerical simulations to construct flow-history-dependent Permeability Sensitivity Functions (PSF) for the entire spatial-temporal domain. Rapid Forward Modeling (RFM) of pressure transients is implemented via perturbed-type solutions by weighing the sensitivity functions with spatial permeability perturbations. Regardless of the gradient-based technique, Rapid Inverse Modeling (RIM) of hydraulic measurements is also approached by efficiently adapting the sensitivity functions to calculate the entries of the associated Jacobian matrix. Research findings confirm the flexibility and reliability of perturbation methods after successful validation with numerical reservoir simulators in both cylindrical and Cartesian coordinates. Multidimensional synthetic studies modeling hydraulic-testing tools and multi-well conditions were examined for diverse anisotropic, heterogeneitydominated fluid-flow regimes. With perturbations of more than one order of magnitude in background permeability, it was found that perturbed-type solutions can be obtained in approximately three orders of magnitude less CPU time compared to conventional finitedifference methods, with relative errors in pressure as low as < 7%. Additionally, the use of sensitivity functions for (1) selecting the subset of measurements input to the estimation of spatial distributions of permeability and (2) reducing the sequential calculation of Jacobian matrices invoked by nonlinear, gradient-based inversion, provide a stable and efficient alternative for the quantitative interpretation of single-phase transient pressure measurements.