Thesis (M.S.)--West Virginia University, 2000. / Title from document title page. Document formatted into pages; contains xi, 94 p. : ill. (some col.), maps. Includes abstract. Includes bibliographical references (p. 63-64).

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (M.S.)--West Virginia University, 2007. / Title from document title page. Document formatted into pages; contains xii, 136 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 75-76).

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 248-254). Available also in a digital version from Dissertation Abstracts.

Gas injection, the fastest growing tertiary oil recovery technique, holds the promise of significant recoveries from those depleted oil reservoirs around the world which fall into a pressure range of (50-200) bar mainly. However, its application with the usual techniques is restricted by the need for various surface facilities such as enormous gas supply and storage. The only surface facility that downhole gasification of hydrocarbons (DHG) requires, on the other hand, is a portable electricity generator. DHG consists in producing inert gases, H2, CO, CO2 and CH4 through the steam reforming reaction of a part of the produced oil in a gasifier-reformer reactor positioned alongside the producer well in the reservoir. The gases, mainly H2 -the most effective displacing gas among produced gases- are injected into a gas cap above the oil formation, to increase oil recovery through a gas displacement drive mechanism. So far, DHG has only been tested under laboratory conditions using methane, pentane/reservoir gas and naphtha/reservoir gas as feedstock at conditions of reservoir pressure up to 130 bar. The studies varied reaction temperature, steam to carbon (S/C) ratio, catalyst types and catalyst loading in the gasifier-reformer reactor of a small pilot scale rig. These experimental studies demonstrated that pressure is one of the main factors influencing the effectiveness of the DHG process. From this starting point, the present investigation was directed at extending the pressure range up to 160 bar in the gasifier-reformer reactor using a naphtha fraction as feedstock in order to investigate whether the conversion and H2 concentration in produced dry gas can be maintained at acceptable levels under conditions of high pressure. To this end, experimental studies were carried out within the laboratory using the existing DHG rig on the small pilot scale, which was successfully commissioned and revamped for the purposes of this study. Initially, the investigation focused on exploring operating conditions, namely, steam to carbon (S/C) ratio, length of the gasifier-reformer reactor tube/ catalyst loading and the relative performance of two different catalysts. Subsequently, experiments on shutdown/start up cycles followed by variation of temperature were performed to simulate the effect of sudden electrical disruptions that usually occur in field operations. Experimental results using naphtha at pressure from 80 to 160 bar at 650 ºC, S/C= 6 achieved total feedstock conversion, no coke deposits and, most importantly, high H2 concentration in the produced dry gas (56-63 vol. % plus other gases). The best result was obtained with a crushed HiFUEL R110 catalyst (40-60 wt. % of NiO/CaO.Al2O3) and a reactor tube length of 72 cm, but the results with a C11-PR catalyst (40 wt. % of NiO/MgO.Al2O3) and a reactor tube length of 30 cm were similarly favourable. These results were supported by results of a numerical DHG model which indicated total feedstock conversion and values of H2 around 67 vol. % (using n-heptane as model surrogate). The results suggest that the DHG process is technically feasible at the pressure values studied, perhaps up to 200 bar where there are many hundreds of depleted, light oil reservoirs, especially in North America and other parts of the world below that pressure value.

We consider the structural and physical properties of complex model morphologies and microstructures obtained by Xray-CT imaging. The Minkowski functionals, a family of statistical measures based on the Euler-Poincar&eacute characteristic of n-dimensional space, are shown to be sensitive measures of the morphology of disordered structures. Analytic results for the Boolean model are given and used to devise a reconstruction scheme, which allows one to accurately reconstruct a complex Boolean structure given at any phase fraction for all other phase fractions. The percolation thresholds of either phase are obtained with good accuracy. From the reconstructions one can subsequently predict property curves for the material across all phase fractions from a single 3D image. We illustrate this for transport and mechanical properties of complex Boolean systems and for experimental sandstone samples. By extending the Minkowski functionals to parallel surfaces using operations from mathematical morphology, a powerful discrimination of structure is obtained. Further the sensitivity of the Minkowski functionals under experimental conditions is analysed. Accurate calculations of conductive and elastic properties directly from tomographic images are achieved by estimating and minimising several sources of numerical error. Simulations of electrical conductivity and linear elastic properties on microtomographic images of Fontainebleau sandstone are in excellent agreement with experimental measurements over a wide range of porosity. The results show the feasibility of combining digitised images with transport and elasticity calculations to accurately predict physical properties of individual material morphologies. We show that measurements of properties based on microtomographic images are more accurate than those based on conventional theories for disordered materials. We study the elastic behaviour of model clean and cemented sandstones. Results are in excellent agreement with available experimental data, and are compared to conventional theoretical and empirical laws. A new predictive empirical method is given for predicting the elastic moduli of sandstone morphologies. The method gives an excellent match to numerical and experimental data.

It has long been known that any activity that results in changes in subsurface pressure, such as hydrocarbon production or waste or water reinjection, also causes underground deformations and movement, which can be described in terms of volumetric changes. Such deformations induce surface movement, which has a significant environmental impact. Induced surface deformations are measurable as vertical displacements; horizontal displacements; and tilts, which are the gradient of the surface deformation. The initial component of this study is a numerical model developed in C++ to predict and calculate surface deformations based on assumed subsurface volumetric changes occurring in a reservoir. The model is based on the unidirectional expansion technique using equations from Okada’s theory of dislocations (Okada, 1985). A second numerical model calculates subsurface volumetric changes based on surface deformation measurements, commonly referred to as solving for the inverse case. The inverse case is an ill-posed problem because the input is comprised of measured values that contain error. A regularization technique was therefore developed to help solve the ill-posed problem. A variety of surface deformation data sets were analyzed in order to determine the surface deformation input data that would produce the best solution and the optimum reconstruction of the initial subsurface volumetric changes. Tilt measurements, although very small, were found to be much better input than vertical displacement data for finding the inverse solution. Even in an ideal case with 0 % error, tilts result in a smaller RMSE (about 12 % smaller in the case studied) and thus a better resolution. In realistic cases with error, adding only 0.55 % of the maximum random error in the surface displacement data affects the back-calculated results to a significant extent: the RMSE increased by more than 13 times in the case studied. However, in an identical case using tilt measurements as input, adding 20 % of the maximum surface tilt value as random error increased the RMSE by 7 times, and remodelling the initial distribution of the volumetric changes in the subsurface was still possible. The required area of observation can also be reduced if tilt measurements are used. The optimal input includes tilt measurements in both directions: dz/dx and dz/dy. iv With respect to the number of observation points chosen, when tilts are used with an error of 0 %, very good resolution is obtainable using only 0.4 % of the unknowns as the number of benchmarks. For example, using only 10 observation points for a reservoir with 2500 elements, or unknowns resulted in an acceptable reconstruction. With respect to the sensitivity of the inverse solution to the depth of the reservoir and to the geometry of the observation grid, the deeper the reservoir, the more ill-posed the problem. The geometry of the benchmarks also has a significant effect on the solution of the inverse problem.

It has long been known that any activity that results in changes in subsurface pressure, such as hydrocarbon production or waste or water reinjection, also causes underground deformations and movement, which can be described in terms of volumetric changes. Such deformations induce surface movement, which has a significant environmental impact. Induced surface deformations are measurable as vertical displacements; horizontal displacements; and tilts, which are the gradient of the surface deformation. The initial component of this study is a numerical model developed in C++ to predict and calculate surface deformations based on assumed subsurface volumetric changes occurring in a reservoir. The model is based on the unidirectional expansion technique using equations from Okada’s theory of dislocations (Okada, 1985). A second numerical model calculates subsurface volumetric changes based on surface deformation measurements, commonly referred to as solving for the inverse case. The inverse case is an ill-posed problem because the input is comprised of measured values that contain error. A regularization technique was therefore developed to help solve the ill-posed problem. A variety of surface deformation data sets were analyzed in order to determine the surface deformation input data that would produce the best solution and the optimum reconstruction of the initial subsurface volumetric changes. Tilt measurements, although very small, were found to be much better input than vertical displacement data for finding the inverse solution. Even in an ideal case with 0 % error, tilts result in a smaller RMSE (about 12 % smaller in the case studied) and thus a better resolution. In realistic cases with error, adding only 0.55 % of the maximum random error in the surface displacement data affects the back-calculated results to a significant extent: the RMSE increased by more than 13 times in the case studied. However, in an identical case using tilt measurements as input, adding 20 % of the maximum surface tilt value as random error increased the RMSE by 7 times, and remodelling the initial distribution of the volumetric changes in the subsurface was still possible. The required area of observation can also be reduced if tilt measurements are used. The optimal input includes tilt measurements in both directions: dz/dx and dz/dy. iv With respect to the number of observation points chosen, when tilts are used with an error of 0 %, very good resolution is obtainable using only 0.4 % of the unknowns as the number of benchmarks. For example, using only 10 observation points for a reservoir with 2500 elements, or unknowns resulted in an acceptable reconstruction. With respect to the sensitivity of the inverse solution to the depth of the reservoir and to the geometry of the observation grid, the deeper the reservoir, the more ill-posed the problem. The geometry of the benchmarks also has a significant effect on the solution of the inverse problem.

With the recent development of smart-well technology, the reservoir community now faces the challenge of developing robust and efficient techniques for reservoir characterization by means of data inversion. Unfortunately, classical history-matching methodologies do not possess computational efficiency and robustness needed to assimilate data measured almost in real time. Therefore, the reservoir community has started to explore techniques previously applied in other disciplines. Such is the case of the representer method, a variational data assimilation technique that was first applied in physical oceanography. The representer method is an efficient technique for solving linear inverse problems when a finite number of measurements are available. To the best of our knowledge, a general representer-based methodology for nonlinear inverse problems has not been fully developed. We fill this gap by presenting a novel implementation of the representer method applied to the nonlinear inverse problem of identifying petrophysical properties in reservoir models. Given production data from wells and prior knowledge of the petrophysical properties, the goal of our formulation is to find improved parameters so that the reservoir model prediction fits the data within some error given a priori. We first define an abstract framework for parameter identification in nonlinear reservoir models. Then, we propose an iterative representer-based scheme (IRBS) to find a solution of the inverse problem. Sufficient conditions for convergence of the proposed algorithm are established. We apply the IRBS to the estimation of absolute permeability in single-phase Darcy flow through porous media. Additionally, we study an extension of the IRBS with Karhunen-Loeve (IRBS-KL) expansions to address the identification of petrophysical properties subject to linear geological constraints. The IRBS-KL approach is compared with a standard variational technique for history matching. Furthermore, we apply the IRBS-KL to the identification of porosity, absolute and relative permeabilities given production data from an oil-water reservoir. The general derivation of the IRBS-KL is provided for a reservoir whose dynamics are modeled by slightly compressible immiscible displacement of two-phase flow through porous media. Finally, we present an ad-hoc sequential implementation of the IRBS-KL and compare its performance with the ensemble Kalman filter. / text

The data assimilation process of adjusting variables in a reservoir simulation model to honor observations of field data is known as history matching and has been extensively studied for few decades. However, limited success has been achieved due to the high complexity of the problem and the large computational effort required by the practical applications. An automatic history matching module based on the ensemble Kalman filter is developed and validated in this dissertation. The ensemble Kalman filter has three steps: initial sampling, forecasting through a reservoir simulator, and assimilation. The initial random sampling is improved by the singular value decomposition, which properly selects the ensemble members with less dependence. In this way, the same level of accuracy is achieved through a smaller ensemble size. Four different schemes for the assimilation step are investigated and direct inverse and square root approaches are recommended. A modified ensemble Kalman filter algorithm, which addresses the preference to the ensemble members through a nonequally weighting factor, is proposed. This weighted ensemble Kalman filter generates better production matches and recovery forecasting than those from the conventional ensemble Kalman filter. The proposed method also has faster convergence at the early time period of history matching. Another variant, the singular evolutive interpolated Kalman filter, is also applied. The resampling step in this method appears to improve the filter stability and help the filter to deliver rapid convergence both in model and data domains. This method and the ensemble Kalman filter are effective for history matching and forecasting uncertainty quantification. The independence of the ensemble members during the forecasting step allows the benefit of high-performance computing for the ensemble Kalman filter implementation during automatic history matching. Two-level computation is adopted; distributing ensemble members simultaneously while simulating each member in a parallel style. Such computation yields a significant speedup. The developed module is integrated with reservoir simulators UTCHEM, GEM and ECLIPSE, and has been implemented in the framework Integrated Reservoir Simulation Platform (IRSP). The successful applications to two and three-dimensional cases using blackoil and compositional reservoir cases demonstrate the efficiency of the developed automatic history matching module.