Browsing by Subject "Multiphase Fluid Flow"

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Chemical and Thermochemical Wave Behavior in Multiphase Fluid Flow Through Permeable Media: Wave-Wave Interactions
(1988-05) Dria, Myra Ann; Lake, Larry W.; Schechter, Robert S.
The flow of reactive fluids through permeable media creates regions of constant composition for purely reactive flow. These regions are separated by waves, which mark the change in composition from one region to the next. We develop a theory which elucidates the interactions of these chemical waves with those formed from other flowing phenomena. We consider the following interactions: 1.) the intersection of precipitation/dissolution waves with other precipitation/dissolution waves formed from the sequential injection of fluid of a different composition, from a change in the direction of fluid flow, or from finite changes in the initial composition of the rock; 2.) the interactions of precipitation/dissolution waves with ion exchange waves; 3.) the interaction of thermal waves with chemical precipitation/dissolution waves, considering coupled and uncoupled thermal/chemical effects. Waves of a nature not previously found under constant (Riemann) boundary conditions are formed. Through the nondimensionalization of the chemical-energy balance, we define six dimensionless parameters, and investigate the relative effects of these parameters on temperature and composition. One dimensionless number can indicate when heat effects are important. The interaction of a thermal wave with precipitation/dissolution waves for nonadiabatic cases results in the formation of stationary waves and precipitation/dissolution waves with varying velocity. We assume a MarxLangenheim formulation sufficiently describes the movement of a thermal wave with thermal losses to the under- and overburden. A sequence may develop which contains mineral entities different from either the low or high temperature mineral sequence. We also show important effects of one additional dimensionless number obtained from restating the traditional Marx-Langenheim equation. The location of this thermal wave with respect to the precipitation/dissolution waves has a profound influence on the resulting fluid composition, mineral sequence, and the manner in which these compositions propagate within the permeable media. We further elucidate the nature of the Riemann problem for precipitation/dissolution reactions. Multiple discontinuities are regions of zero width in purely convective flow but appear with nonzero width in convective-dispersive flow. We show two cases which indicate the nonuniversality of the direction-dependent solution technique.
An Investigation of Countercurrent Imbibition Recovery in Naturally Fractured Reservoirs With Experimental Analysis and Analytical Modeling
(1997-12) Cil, Murat; Miller, Mark A; Reis, John C
Naturally fractured reservoirs occur worldwide containing potentially economic and strategic fluids such as gas, oil and water. Modeling of naturally fractured reservoirs has advanced considerably because of the desire to increase the recovery from naturally fractured oil reservoirs and to exploit the vast storage capacity of naturally fractured formations for underground disposal of nuclear wastes. Countercurrent expulsion of oil from matrix blocks to the surrounding fractures by capillary imbibition of water is one of the more important fluid flow mechanisms in naturally fractured reservoirs. Transfer functions are essential for dual porosity simulators to characterize the countercurrent fluid flow between matrix blocks and surrounding fractures. The primary objectives of this study are: 1) to conduct experimental studies with single matrix blocks to better understand the general characteristics of countercurrent imbibition, and 2) to develop a comprehensive analytical matrix/fracture transfer function. New experimental methods for cleaning laboratory cores, establishing initial water saturation in odd shaped rocks and obtaining a transparent epoxy seal on core pieces to observe imbibition fronts have been developed to examine the general characteristics of countercurrent imbibition in single matrix blocks. A new analytical model (matrix/fracture transfer function) capable of modeling 1D, 2D and 3D countercurrent imbibition flow inside single matrix blocks has been derived. Imbibition characteristics are identified by analyzing the results of experimental data. The examined characteristics are: 1) types of imbibition and recovery trends, 2) flux and transition time, 3) imbibition front and average saturation, 4) effect of core size and shape, 5) effect of temperature, 6) effect of initial water saturation, 7) reproducibility, and 8) long term recovery. Based on the identified characteristics, solution proce~ures are developed to use with the new analytical model for recovery predictions. Results indicate that some imbibition parameters stay the same regardless of the geometry of the matrix block and imbibition type. The concept of an equivalent dimensionless distance is shown to reduce the number solution steps by combining the two periods of countercurrent imbibition under one set of equations. This greatly simplifies the analyses of countercurrent imbibition recovery with the new model. An apparent relative permeability concept shows that relative permeabilities are independent of temperature, and the change of imbibition with temperature is primarily due to the change of fluid viscosity and interfacial tension. The results in this study can easily be incorporated into a dual porosity simulator for multiphase fluid flow in naturally fractured reservoirs.
Least-Squares Finite Element Method For Hydrocarbon Transport In Porous Media
(1997-08) Biswas, Deepankar; Carey, Graham F.; Sepehrnoori, Kamy
Mathematical models for the transport of constituent components of a multicomponent system in a porous medium play an important part in petroleum reservoir analysis and production. The success of such models is dependent on (1) how well the relevant physical and chemical processes controlling subsurface transport is represented by mathematical equations and their parameters and (2) how accurately and efficiently the equations are approximated with numerical methods. The existing models of multicomponent transport employ two basic sets of equations. The transport of solutes is described by a set of partial differential equations (mass conservation) with the corresponding constitutive relationships and the phase behavior is described by algebraic expressions. This study proposes a new least-squares mixed finite element method (LSFEM) for approximating multiphase flow equations and coupled multicomponent transport equations. The problem is first recast as a system of first-order partial-differential equations. Then a least-squares residual functional is constructed. The least-squares problem is then posed as a mixed finite-element model. This implies that a Co basis can be used. Also, the least-squares formulation leads to a symmetric algebraic system. Since derivatives of the field vi variables enter explicitly in the system, greater accuracy in the computed fluxes will be realized by this mixed method compared to the standard (non-mixed) Galerkin method. The accuracy and performance of the least-squares FEM for transport problems is studied. The effect of varying Peclet number on the accuracy and stability of the solutions is also investigated. Numerical dissipation and other properties of the scheme are examined. The method is verified for model problems by comparisons with analytic solutions and results in the literature. A thermodiffusion model is developed for areal compositional variations in hydrocarbon reservoirs from the fundamental equations of change in a multicomponent system. Under conditions of the stationary state and utilizing concepts of non-equilibrium thermodynamics to compute the fluxes, this model is solved using the least-squares finite-element method. Its usefulness and applicability are demonstrated by means of comparison to observed variations in a real gas field. Finally, given a system of equations describing transport, the computational cost of numerical simulation is dependent on the domain size and the resolution required to minimize numerical errors. However, the local resolution required for accurate solutions can vary over space and time as regions with rapid changes of concentration gradients propagate through the solution domain. Thus, such problems are suited for adaptive numerical strategies that seek to determine where increased numerical resolution is required and then provide more accurate approximations in those regions. Adaptive strategies based on the element residual as an error indicator in conjunction with unstructured remeshing are developed and tested for representative problems of subsurface transport.
Modeling the Electrical Submersible Jet Pump Producing High Gas-Liquid-Ratio Petroleum Wells
(1998-12) Moreira de Carvalho, Paulo; Sepehrnoori, Kamy; Podio, Augusto L.
The objective of this work is to present the concept of the Electrical Submersible Jet Pump (ESJP). It is a ne\v artificial-lift method for application in the petroleum production industry. This proposed artificial-lift method uses an electrical submersible multistage centrifugal pump in combination with a jet pump installed in the wellbore along the tubing string. Such a method is proposed to allow production of high gas-liquid-ratio petroleum wells using the existing electrical submersible pump technology. While applicable to any petroleum well, the driving force and main motivation for the development of this new technology is deep off shore petroleum production. In this work, also presented is a numerical model developed to simulate the operation of the system. In such a model, the system is analyzed as three coupled subsystems: the electrical submersible pump (ESP), the low gas-liquid-ratio (GLR) multiphase flow in the tubing string, and finally the flow inside the jet pump (JP). Both individual models used for the ESP performance and the multiphase flow inside the tubing string are available in the literature. In this dissertation is presented the modeling of the multiphase flow of fluids inside the liquid-jet gas pump (LJGP), which was developed based on the simultaneous solution of the mass, momentum, and energy conservation equations. A scaled model of the jet pump was manufactured of transparent material in order to allow visualization of the flow inside the jet pump throat and diffuser. A series of video recording were made of the multiphase flow inside the jet pump for some basic tests, which are available in a companion CDROM. Also, an extensive experimental work was developed in the test well at the production laboratory. A prototype of the system was installed and tested for various operating conditions. The results are presented in the dissertation body.