# Browsing by Subject "Multiphase flow--Mathematical models"

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Item Algorithms for numerical modeling and inversion of multi-phase fluid flow and electromagnetic measurements(2005) Alpak, Faruk Omer; Torres-Verdín, Carlos; Sepehrnoori, Kamy, 1951-Show more The focus of this dissertation is the estimation of petrophysical properties of rock formations based on the combined use of electromagnetic and fluid-flow measurements. Traditionally, borehole electromagnetic measurements are interpreted independently in terms of spatial variations of electrical resistivity. The estimated spatial variations of electrical resistivity are subsequently interpreted in terms of variations of fluid saturation and porosity. Such a strategy can lead to erroneous conclusions concerning the petrophysical evaluation of rocks because the spatial distribution of electrical resistivity is often governed by the interplay between salt concentration, absolute permeability, relative permeability, and capillary pressure. To date, no consistent effort has been advanced to use the physics of multi-phase fluid flow as the leading phenomenon in the interpretation of borehole electromagnetic measurements. This dissertation develops several efficient nonlinear inversion algorithms that quantitatively combine borehole electromagnetic and fluid-flow phenomena. These inversion algorithms also provide a measure of uncertainty and non-uniqueness in the presence of noisy and imperfect measurements. The combined use of electromagnetic and fluid-flow measurements drastically reduces non-uniqueness and uncertainty of the estimated petrophysical parameters and, therefore, increases the accuracy of the estimates. Specific problems considered in this dissertation are the estimation of spatial distributions of porosity, permeability, and fluid saturation, as well as the estimation of relative permeability and capillary pressure. Joint and independent nonlinear inversions are performed for large-scale petrophysical properties from in-situ permanent sensor data and near-borehole scale petrophysical variables of rock formations from wireline formation tester and electromagnetic induction logging measurements. For cases where fluid-flow related measurements are absent, the coupled dual-physics inversion strategy allows quantitative interpretation of electromagnetic measurements consistent with the physics of fluid flow. It is conclusively shown that the simultaneous use of fluid-flow and electromagnetic data sets reduces non-uniqueness in the inverted petrophysical model.Show more Item A coupled geomechanics and reservoir flow model on parallel computers(2004) Gai, Xiuli, 1970-; Wheeler, Mary F. (Mary Fanett)Show more Land subsidence due to the exploitation of groundwater and hydro- carbon fluids has triggered extensive studies in coupled fluid flow and ge- omechanics simulations. However, numerical modeling of coupled processes imposes great computational challenges. Coupled analysis for large scale full- field applications with millions of unknowns has been, historically, considered extremely complex and unfeasible. The purpose of this dissertation is to in- vestigate accurate and efficient numerical techniques for coupled multiphase flow and geomechanics simulations on parallel computers. We emphasize the iterative coupling approach in extending conven- tional fluid-flow modeling to coupled fluid-flow and geomechanics modeling. To overcome the slow convergence—a major drawback of this method—we propose new preconditioning schemes to achieve a faster convergence rate. Efficient and parallel scalable linear solvers are developed to reduce the com- putational overhead induced by the solution of discrete elasticity equations. Special communications techniques are implemented to optimize parallel effi- ciency. In this dissertation we first derive the mathematical model for multi- phase flowin a deformable porous medium. We then present a new formulation of the iterative coupling scheme and prove the optimality of two physics-based preconditioners that are traditionally used in the petroleum industry. Practi- cal strategies and new preconditioners are proposed to improve the numerical performance of the iteratively coupled approach. In addition, we develop two types of preconditioners for solving the linear elasticity system, namely, multi- level domain decomposition preconditioners using a super-coarsening multigrid algorithm and displacement decomposition preconditioners. Parallel imple- mentation issues are also addressed. Numerical examples are presented to demonstrate the robustness, efficiency and parallel scalability of the proposed linear solution techniques.Show more Item A coupled wellbore/reservoir simulator to model multiphase flow and temperature distribution(2007-12) Pourafshary, Peyman, 1979-; Sepehrnoori, Kamy, 1951-; Podio, A. L.Show more Hydrocarbon reserves are generally produced through wells drilled into reservoir pay zones. During production, gas liberation from the oil phase occurs due to pressure decline in the wellbore. Thus, we expect multiphase flow in some sections of the wellbore. As a multi-phase/multi-component gas-oil mixture flows from the reservoir to the surface, pressure, temperature, composition, and liquid holdup distributions are interrelated. Modeling these multiphase flow parameters is important to design production strategies such as artificial lift procedures. A wellbore fluid flow model can also be used for pressure transient test analysis and interpretation. Considering heat exchange in the wellbore is important to compute fluid flow parameters accurately. Modeling multiphase fluid flow in the wellbore becomes more complicated due to heat transfer between the wellbore fluids and the surrounding formations. Due to mass, momentum, and energy exchange between the wellbore and the reservoir, the wellbore model should be coupled with a numerical reservoir model to simulate fluid flow accurately. This model should be non-isothermal to consider the effect of temperature. Our research shows that, in some cases, ignoring compositional effects may lead to errors in pressure profile prediction for the wellbore. Nearly all multiphase wellbore simulations are currently performed using the "black oil" approach. The primary objective of this study was to develop a non-isothermal wellbore simulator to model transient fluid flow and temperature and couple the model to a reservoir simulator called General Purpose Adaptive Simulator (GPAS). The coupled wellbore/reservoir simulator can be applied to steady state problems, such as production from, or injection to a reservoir as well as during transient phenomena such as well tests to accurately model wellbore effects. Fluid flow in the wellbore may be modeled either using the blackoil approach or the compositional approach, as required by the complexity of the fluids. The simulation results of the new model were compared with field data for pressure gradients and temperature distribution obtained from wireline conveyed pressure recorder and acoustic fluid level measurements for a gas/oil producer well during a buildup test. The model results are in good agreement with the field data. Our simulator gave us further insights into the wellbore dynamics that occur during transient problems such as phase segregation and counter-current multiphase flow. We show that neglecting these multiphase flow dynamics would lead to unreliable results in well testing analysis.Show more Item History matching by simultaneous calibration of flow functions(2007) Barrera, Alvaro Enrique, 1974-; Srinivasan, SanjayShow more Reliable predictions of reservoir flow response corresponding to various recovery schemes require a realistic geological model of heterogeneity and an understanding of its relationship with the flow properties. This dissertation presents results on the implementation of a novel approach for the integration of dynamic data into reservoir models that combines stochastic techniques for simultaneous calibration of geological models and multiphase flow functions associated with porelevel spatial representations of porous media. In this probabilistic approach, a stochastic simulator is used to model the spatial distribution of a discrete number of rock types identified by rock/connectivity indexes (CIs). Each CI corresponds to a particular pore network structure with a characteristic connectivity. Primary drainage and imbibition displacement processes are modeled on the 3-D pore networks to generate multiphase flow functions corresponding to networks with different CIs. During history matching, the stochastic simulator perturbs the spatial distribution of the CIs to match the simulated pressures and flow rates to historic data, while preserving the geological model of heterogeneity. This goal is accomplished by applying a probabilistic approach for gradual deformation of spatial distribution of rock types characterized by different CIs. Perturbation of the CIs in turn results in the update of all the flow functions including the effective permeability, porosity of the rock, the relative permeabilities and capillary pressure. The convergence rate of the proposed method is comparable to other current techniques with the distinction of enabling consistent updates to all the flow functions. The resultant models are geologically consistent in terms of all the flow functions, and consequently, predictions obtained using these models are likely to be more accurate. To compare and contrast this comprehensive approach to reservoir modeling against other approaches that rely on modeling and perturbing only the permeability field, a realistic case study is presented with implementation of both approaches. Comparison is made with the history-matched model obtained only by perturbing permeability. It is argued that reliable predictions of future production can only be made when the entire suite of flow functions is consistent with the real reservoir.Show more