Estimation of two-phase flow functions using NMR imaging data

Accurate estimates of relative permeability and capillary pressure functions (collectively referred as flow functions) are important for management of underground hydrocarbon and water resources. In this work simultaneous estimation of two-phase flow functions from dynamic displacement data on core samples is investigated. Saturation profile data is included in addition to traditional production and pressure drop data and new experimental designs are investigated to improve accuracy of flow function estimates.; NMR imaging is used to measure saturation profiles during two-phase flowing experiments on core samples. The estimation is posed as an inverse problem and the flow functions are estimated simultaneously from measured data. Including saturation data in addition to the conventional production and pressure drop data is shown to improve the accuracy of estimates of multiphase flow functions. Guidelines regarding better experimental designs are developed using covariance analysis and supported with experiments.; Multiphase flow through porous media belongs to a class of processes, called Distributed Parameter Systems (DPS), where the state variables vary in time and space. The properties to be estimated appear as parameters in a set of coupled partial differential equations. A general estimation methodology, particularly suited to large scale DPS estimation problems, is developed.; Nuclear Magnetic Resonance (NMR) can probe porous microstructure and provide a wealth of information about storage and transport of fluids in porous media. A critical step in analysis of NMR data is the modeling of NMR relaxation and estimation of model parameters. Relaxation in porous media is characterized by a continuous distribution of relaxation rates and can be represented by Fredholm Integral equation of the first kind, a well known ill-posed problem. A robust linear technique is developed to solve the integral equation. B-splines are used to represent the unknown distribution and regularization used to improve the conditioning of the estimation. A new methodology to recover pore size distribution from NMR T1 relaxation data and a new methodology to quantify NMR imaging data is developed.