Browsing by Subject "Multiphase flow"

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Comprehensive modeling of flow assurance : scales, hydrates, and asphaltenes
(2022-08-10) Coelho, Fernando Martins C.; Sepehrnoori, Kamy, 1951-; Ezekoye, Ofodike A.; Bahadur, Vaibhav; Lu, Yingda; Wang, Yaguo
In the oil and gas industry, “flow assurance” incorporates the efforts to prevent inadvertent disruptions to the hydrocarbon flow from the wells to processing facilities. It is a reference to the study of both organic and inorganic deposits that may hinder production. Such deposits are mainly formed by scale, hydrate, asphaltene, and wax. This dissertation enhances the modeling of flow-assurance issues within a single platform—UTWELL, a wellbore simulator developed at The University of Texas at Austin. Scales result from mineral precipitation due to changes in pressure and temperature along the water flow, inherent to any gas/oil production. This research focuses on how water evaporation and CO₂ affect scaling tendencies in an oil well. The results demonstrate that evaporation is only relevant for very a small amount of water in the system, characteristic of the early stages of production. Additionally, the model shows that gas lift can increase mineral precipitation depending on the CO₂ content from the injected gas. Hydrates are ice-like solids formed under high-pressure and low-temperature conditions that are commonly found in an oilfield. Hydrate formation can be inhibited either by dissolved ions (electrolytes) in the produced water or by deliberate injection of chemicals. This research develops a hydrate-check model to verify formation conditions along the flow. The integration with a geochemical package (PHREEQC) provides the tools to consider electrolyte inhibition, and a newly included equation of state (CPA) assesses the inhibition effect from added glycols (and alcohols). The model predicts that when gas-water ratio (GWR) exceeds 10⁵ scf/STB, water condensation reduces electrolyte inhibition significantly. On asphaltenes, this research also discusses two prediction methods: a consolidated model from Li and Firoozabadi (2010), using a simplified version of the cubic-plus-association equation of state (CPA EoS); and a newly proposed version of a solid model, based on the Peng-Robinson EoS. It is shown that, if provided with adequate onset data, the solid model can match results from the CPA model quite successfully, while requiring only half the computational time. However, the solid model cannot adjust to composition changes in the same manner as CPA. Therefore, its adoption seems more suitable for wellbore simulation than in the reservoir, where fluid mixing is widespread.
Construction and validation of microfluidic platforms for investigation of multiphase flow and nanofluids in porous media
(2018-06-27) Xu, Ke, Ph. D.; Balhoff, Matthew T.; Huh, Chun; Mohanty, Kishore K; Bonnecaze, Roger T; Daigle, Hugh
Flow and transport in porous media is the fundamental physical process in many important applications such as hydrocarbon recovery, carbon dioxide subsurface sequestration, treatment of non-aqueous liquid pollutions in soil systems, and flooding control for fuel cell systems. Clear description, correct modeling and precise prediction of flow in porous media are of great significance. Although many single-phase and multiphase systems can be characterized using macroscopic models such as Darcy’s law (or the multiphase form of it), other complex flow systems, such as emulsion flow, nanoparticle suspension flow, etc., require a more detailed description. For those complex cases, revealing the pore-scale physics is necessary for larger-scale modeling and predictions. Microfluidics provide a simple way to visualize micron-scale flow behavior with excellent controllability, thus helping to clarify the fundamental pore-scale flow mechanisms and is, therefore, useful for studying flow and transport in porous media. In this work, several special micromodel designs from the single-pore level to pore-network level on microchips were made in order to capture realistic pore-scale flow mechanisms while keeping the system simplified enough for easy quantification. At the single-pore level, the trapping and mobilization of a non-wetting oil droplet at a pore-throat structure are investigated on an ideal pore-throat microfluidic geometry. A simple physical model is derived and the effects of bare nanoparticle aqueous suspension in mobilizing oil is further studied. A dual-permeability microchannel is used to study the emulsion flow in natural fracture system and a synergistic effect between nanoparticles and non-ionic surfactant is investigated to stabilize the emulsion and to potentially improve sweep efficiency. At the pore-network-pore level, a 2.5-D porous micromodel is fabricated to introduce essential 3-D feature in traditional 2-D porous micromodel. On this advanced 2.5-D micromodel, multiple complex fluid systems, including spontaneous imbibition, unstable water drainage, ultra-low IFT flooding, bubble evolution under Ostwald ripening, nanofluid flooding, etc., have been studied, with new physics revealed and modeled. A novel EOR method using nanoparticle treated oil (NPTO) is proposed and validated.
Coupled geomechanics and multiphase flow modeling in naturally and hydraulically fractured reservoirs
(2022-05-05) Pei, Yanli; Sepehrnoori, Kamy, 1951-; Chin, Lee; Delshad, Mojdeh; Marcondes, Francisco; Olson, Jon
Fluid injection and production in highly fractured unconventional reservoirs could induce complex stress reorientation and redistribution. The strong stress sensitivity of fractured formations may also lead to non-negligible fracture opening or closure under the reservoir loading or unloading process. Hence, a coupled flow and geomechanics model is in high demand to assist with stress prediction and production forecast in unconventional reservoirs. In this dissertation, an enhanced geomechanics model is developed for fractured reservoirs and integrated with the in-house compositional reservoir simulator – UTCOMP for coupled flow and geomechanics modeling. The multiphase flow model is solved using the finite volume method (FVM) with an embedded discrete fracture model (EDFM) to represent flow through complex fractures. Based on static fracture assumption, the finite element method (FEM) is applied to solve the geomechanics model by incorporating fracture effects on rock deformation through pore pressure changes. An iterative coupling procedure is implemented between fluid flow and geomechanics, and the 3D coupled model is applied to predict spatiotemporal stress evolution in single-layer and multilayer unconventional reservoirs. To consider dynamic fracture properties, the geomechanics model is further enhanced by the extended finite element method (XFEM) with a modified linear elastic proppant model. The fracture surface is under the coeffects of pore pressure and proppant particles, and various enrichment functions are introduced to reproduce the discontinuous fields over fracture paths. The enhanced geomechanics model is validated against classical Sneddon and Elliot’s problem and presents a first-order spatial convergence rate. Numerical studies indicate that modeling fracture closure is necessary for poorly propped, highly stressed, or fast depleted reservoirs, and fracture opening can be significant under high permeability and low stiffness conditions. The coupled flow and geomechanics model is finally combined with a displacement discontinuity method (DDM) hydraulic fracture model to establish an integrated reservoir-geomechanics-fracture model for the end-to-end optimization of secondary stimulations. It is applied to Permian Basin and Sichuan Basin tight formations to optimize parent-child well spacing at different infill times. The integrated model provides hands-on guidelines for refracturing and infill drilling in multilayer unconventional reservoirs and can be easily adapted to other basins under their unique data
Development of a coupled wellbore-reservoir compositional simulator for damage prediction and remediation
(2013-08) Shirdel, Mahdy; Sepehrnoori, Kamy, 1951-
During the production and transportation of oil and gas, flow assurance issues may occur due to the solid deposits that are formed and carried by the flowing fluid. Solid deposition may cause serious damage and possible failure to production equipment in the flow lines. The major flow assurance problems that are faced in the fields are concerned with asphaltene, wax and scale deposition, as well as hydrate formations. Hydrates, wax and asphaltene deposition are mostly addressed in deep-water environments, where fluid flows through a long path with a wide range of pressure and temperature variations (Hydrates are generated at high pressure and low temperature conditions). In fact, a large change in the thermodynamic condition of the fluid yields phase instability and triggers solid deposit formations. In contrast, scales are formed in aqueous phase when some incompatible ions are mixed. Among the different flow assurance issues in hydrocarbon reservoirs, asphaltenes are the most complicated one. In fact, the difference in the nature of these molecules with respect to other hydrocarbon components makes this distinction. Asphaltene molecules are the heaviest and the most polar compounds in the crude oils, being insoluble in light n-alkenes and readily soluble in aromatic solvents. Asphaltene is attached to similarly structured molecules, resins, to become stable in the crude oils. Changing the crude oil composition and increasing the light component fractions destabilize asphaltene molecules. For instance, in some field situations, CO₂ flooding for the purpose of enhanced oil recovery destabilizes asphaltene. Other potential parameters that promote asphaltene precipitation in the crude oil streams are significant pressure and temperature variation. In fact, in such situations the entrainment of solid particulates in the flowing fluid and deposition on different zones of the flow line yields serious operational challenges and an overall decrease in production efficiency. The loss of productivity leads to a large number of costly remediation work during a well life cycle. In some cases up to $5 Million per year is the estimated cost of removing the blockage plus the production losses during downtimes. Furthermore, some of the oil and gas fields may be left abandoned prematurely, because of the significance of the damage which may cause loss about $100 Million. In this dissertation, we developed a robust wellbore model which is coupled to our in-house developed compositional reservoir model (UTCOMP). The coupled wellbore/reservoir simulator can address flow restrictions in the wellbore as well as the near-wellbore area. This simulator can be a tool not only to diagnose the potential flow assurance problems in the developments of new fields, but also as a tool to study and design an optimum solution for the reservoir development with different types of flow assurance problems. In addition, the predictive capability of this simulator can prescribe a production schedule for the wells that can never survive from flow assurance problems. In our wellbore simulator, different numerical methods such as, semi-implicit, nearly implicit, and fully implicit schemes along with blackoil and Equation-of-State compositional models are considered. The Equation-of-State is used as state relations for updating the properties and the equilibrium calculation among all the phases (oil, gas, wax, asphaltene). To handle the aqueous phase reaction for possible scales formation in the wellbore a geochemical software package (PHREEQC) is coupled to our simulator as well. The governing equations for the wellbore/reservoir model comprise mass conservation of each phase and each component, momentum conservation of liquid, and gas phase, energy conservation of mixture of fluids and fugacity equations between three phases and wax or asphaltene. The governing equations are solved using finite difference discretization methods. Our simulation results show that scale deposition is mostly initiated from the bottom of the wellbore and near-wellbore where it can extend to the upper part of the well, asphaltene deposition can start in the middle of the well and the wax deposition begins in the colder part of the well near the wellhead. In addition, our simulation studies show that asphaltene deposition is significantly affected by CO₂ and the location of deposition is changed to the lower part of the well in the presence of CO₂. Finally, we applied the developed model for the mechanical remediation and prevention procedures and our simulation results reveal that there is a possibility to reduce the asphaltene deposition in the wellbore by adjusting the well operation condition.
Development of a Moving Grid Point Method for the Solution of Multicomponent, Multiphase Flow Problems in One Dimension
(1984-08) Goggin, David Jon; Pope, Gary A.; Lake, Larry W.
The theory for a single component moving point finite difference method is extended for multicomponent, multi phase porous media flow problems in one dimension. The modified technique is applied for the solution of a three component, two phase solvent flood problem and a more complex co2 flood case. several versions of the multicomponent moving grid method are tested to illustrate the numerical improvements obtained for various spatial differencing and point velocity schemes. The method of characteristics is developed for the analytic solution of the partial differential equations commonly used to describe three component flow in porous media. The numerical results are compared to the solutions obtained along characteristics.
Energy production and CO₂ storage through multiphase flow experiments in hydrate systems
(2023-12) Murphy, Zachary Walter; Flemings, Peter Barry, 1960-; DiCarlo, David Anthony, 1969-; Waite, William; Cardenas, Meinhard B; Breecker, Daniel; You, Kehua
Gas hydrate is a solid ice-like compound composed of water and gas. In porous media at low temperatures, high pressures, and with sufficient gas, hydrate will form. Hydrate will occupy a fraction of the pore space, which greatly impacts the petrophysical and geomechanical properties of the system. This study investigates the morphology of gas hydrate within porous media and its impact on multiphase fluid flow behavior in these systems. To explore these impacts, I develop a method for forming hydrates in porous media and then perform systematic flow experiments on the hydrate-bearing samples. I first perform two-phase (water and hydrate) and three-phase (gas, water, and hydrate) relative permeability experiments. Through these experiments, I show that in hydrate systems water will always be the wetting phase and gas and hydrate will be the non-wetting phases. I then present a modeling framework for relative permeability in the presence of hydrate that is based on the porous media's characteristics and thermodynamically preferred pore occupancy, unlike most previous models that have fixed pore and tube geometry assumptions. By using the pore occupancy and treating hydrate as a fluid phase, the relative permeability of hydrate-bearing systems can be predicted from measurements of hydrate-free sediment. Lastly, I explore the potential of CH₄ hydrate reservoirs for simultaneous energy production and CO₂ storage. Using a sand-packed 7.6-meter tube saturated with CH₄ hydrate and water, I inject flue gas (CO₂+CH₄) and observe the dissociation of CH₄ hydrate and subsequent formation of CO₂ hydrate. Chromatographic analysis of the effluent gas unveils the formation of distinct compositional zones during this reactive transport process. These experiments illuminate a solidification and dissociation process where hydrate replacement is composed of a complex series of steps that is driven by the combination of fluid flow and thermodynamics. This dissertation advances the understanding of multiphase flow dynamics that are critical to the lifecycle of hydrate systems on both geologic and production timescales. It offers enhanced modeling of multiphase fluid flow and carbon exchange within hydrate systems, which are relevant to other geologic systems like permafrost.
Experimental study of convective dissolution of carbon dioxide in porous media
(2014-12) Liang, Yu, active 21st century; DiCarlo, David Anthony, 1969-
Geological carbon dioxide (CO₂) capture and storage in geological formations has the potential to reduce anthropogenic emissions. The viability of technology depends on the long-term security of the geological CO₂ storage. Dissolution of CO₂ into the brine, resulting in stable stratification, has been identified as the key to long-term storage security. The dissolution rate determined by convection in the brine is driven by the increase of brine density with CO₂ saturation. Here we present a new analog laboratory experiment system to characterize convective dissolution in homogeneous porous medium. By understanding the relationship between dissolution and the Rayleigh number in homogeneous porous media, we can evaluate if convective dissolution occurs in the field and, in turn, to estimate the security of geological CO₂ storage fields. The large experimental assembly will allow us to quantify the relationship between convective dynamics and the Rayleigh number of the system, which could be essential to trapping process at Bravo Dome. A series of pictures with high resolution are taken to show the existence and movement of fingers of analog fluid. Also, these pictures are processed, clearly showed the concentration of analog fluid, which is essential to analyze the convective dissolution in detail. We measured the reduction in the convective flux due to hydraulic dispersion effect compared to that in homogeneous media, to determine if convective dissolution is an important trapping process at Bravo Dome.
Grain-scale mechanisms of particle retention in saturated and unsaturated granular materials
(2010-12) Rodriguez-Pin, Elena; Bryant, Steven L.; Balhoff, Matthew; DiCarlo, David; Huh, Chun; Lloyd, Douglas R.
The phenomenon of particle retention in granular materials has a wide range of implications. For agricultural operations, these particles can be contaminants transported through the ground that can eventually reach to aquifers, consequently contaminating the water. In oil reservoirs, these particles can be clays that get detached from the rock and migrate with the flow after a change of pressure, plugging the reservoir with the consequent reduction in permeability. These particles can also be traceable nanoparticles, introduced in the reservoir with the purpose of identifying bypassed oil. For all these reasons it is important to understand the mechanisms that contribute to the transport and retention of these particles. In this dissertation the retention of micro and nano size particles was investigated. In saturated model sediments (sphere packs), we analyzed the retention of particles by the mechanism of straining (size exclusion). The analysis focused on experiments reported in the literature in which particles smaller than the smallest pore throats were retained in the sediment. The analysis yields a mechanistic explanation of these observations, by indentifying the retention sites as gaps between pairs of sediment grains. A predictive model was developed that yields a relationship between the straining rate constant and particle size in agreement with the experimental observations. In unsaturated granular materials, the relative contributions of grain surfaces, interfacial areas and contact lines between phases to the retention of colloidal size particles were investigated. An important part of this analysis was the identification and calculation of the length of the contact lines between phases. This estimation of contact line lengths in porous media is the first of its kind. The algorithm developed to compute contact line length yielded values consistent with observations from beads pack and real rocks, which were obtained independently from analysis of high resolution images. Additionally, the predictions of interfacial areas in granular materials were consistent with an established thermodynamic theory of multiphase flow in porous media. Since there is a close relationship between interfacial areas and contact lines this supports the accuracy of the contact line length estimations. Predictions of contact line length and interfacial area in model sediments, combined with experimental values of retention of colloidal size particles in columns of glass beads suggested that it is plausible for interfacial area and contact line to contribute in the same proportion to the retention of particles. The mechanism of retention of surface treated nanoparticles in sedimentary rocks was also investigated, where it was found that retention is reversible and dominated by attractive van der Waals forces between the particles and the rock’s grain surfaces. The intricate combination of factors that affect retention makes the clear identification of the mechanism responsible for trapping a complex task. The work presented in this dissertation provides significant insight into the retention mechanisms in relevant scenarios.
Implementation of full permeability tensor representation in a dual porosity reservoir simulator
(2001-08) Li, Bowei; Miller, Mark A.; Sepehrnoori, Kamy, 1951-
Transport and flow phenomena in porous media and fractured rock arise in many fields of science and engineering, including petroleum and groundwater engineering. Over the past few decades, there are two classes of models that have been developed for describing flow and transport phenomena in porous media and fractured rock. They are the continuum and discrete models. Continuum models include single porosity and dual porosity models. The latter is popularly applied in simulating flow in naturally fractured systems. Discrete feature models explicitly recognize the fracture system’s geometrical properties, such as orientation and intensity. But shortcomings have been experienced for such discrete models in that large computational efforts are required for a realistic treatment of a heavily fractured system. Such a large fractured system may contain millions of fracture features. The huge demand of computational resources may seriously undermine the application of discrete models for such systems. Moreover, the discrete feature model is more difficult vii to use for multiphase flow and complex recovery mechanisms for oil recovery process. The dual porosity model, a subclass of the continuum model, is a favorable approach to study flow in naturally fractured systems. In the dual porosity approach, it is assumed that the fissured porous media can be represented by two colocated continua called the matrix and the fracture system. High conductivity but low storativity typically characterizes the fracture system, whereas the matrix is usually characterized as low conductivity but high storativity. The matrix generally acts as a source that transfers its mass to the surrounding fractures; then fluid is transported to production wells. There are two main reasons for the acceptance of dual porosity model. The first reason is its ability to handle the length scale inconsistency between matrix and fractures. It is impractical to simulate a fractured system by a single porosity approach if a matrix block is gridded to the fracture’s length scale. But the dual porosity approach may divide the physical problem into two interactive problems. Therefore the dual porosity model captures the length scales of the physical problem, and is much easier to handle computationally. The second advantage of the dual porosity model is its capacity to address complex local phenomena at the matrix boundary surrounded by fractures. Conventional dual porosity models generally use a diagonal permeability tensor to formulate and discretize the flow equations for the fracture system. However, such practice does not always adequately reflect the characteristics of natural fractures characterized by heterogeneity and anisotropy ascribed to the fracture’s varied orientation, apertures, and intensity. Therefore, conventional dual porosity models may overlook the naturally fractured system’s directionality and heterogeneity. This study is designed to develop a novel approach to model fluid flow in natural fractured systems with a dual porosity approach. In the study, a full viii permeability tensor representation of fracture flow is implemented in the UTCHEM dual porosity chemical flood simulator. The full permeability tensor feature in the fracture system adequately captures the system’s characteristics, i.e., directionality and heterogeneity. At the same time, the powerful dual porosity concept is inherited. The capability of modeling the local complex physical phenomena is maintained in the simulator. The implementation has been verified through studying waterflooding in a cylindrical reservoir, and waterflooding in a spherical reservoir. As an application of the implementation, a study on a naturally fractured system was conducted. Simulation results were compared with that generated by the Fracman simulator (Golder Associates, 2000) a discrete feature model. Another application is waterflooding through a fractured system using dual porosity approach. A conclusion can be drawn from all these studies that for a heterogeneous and anisotropic system, full permeability tensor representation of flow is necessary to accurately simulate flow in such system.
Iteratively coupled reservoir simulation for multiphase flow in porous media
(2008-05) Lu, Bo, 1979-; Wheeler, Mary F. (Mary Fanett)
Fully implicit and IMPES are two primary reservoir simulation schemes that are currently used widely. However, neither of them is sufficiently accurate or ef- ficient, given the increasing size and degree of complexity of highly heterogeneous reservoirs. In this dissertation, an iterative coupling approach is proposed and developed to solve multiphase flow problems targeting the efficient, robust and accurate simulation of the hydrocarbon recovery process. In the iterative coupling approach, the pressure equation is solved implicitly, followed by the saturation equation, which is solved semi-implicitly. These two stages are iteratively coupled at the end of each time step by evaluating material balance, both locally and globally, to check the convergence of each iteration. Additional iterations are conducted, if necessary; otherwise the simulation proceeds to the next time step. Several numerical techniques are incorporated to speed up the program convergence and cut down the number of iterations per time step, thus greatly improving iterative model performance. The iterative air-water model, the oil-water model, and the black oil model are all developed in this work. Several numerical examples have been tested using the iterative approach, the fully implicit method, and the IMPES method. Results show that with the iterative method, about 20%-40% of simulation time is saved when compared to the fully implicit method with similar accuracy. As compared to the IMPES method, the iterative method shows better stability, allowing larger time steps in simulation. The iterative method also produces better mass balance than IMPES over the same time. The iterative method is developed for parallel implementation, and several test cases have been run on parallel clusters with large numbers of processors. Good parallel scalability enables the iterative method to solve large problems with millions of elements and highly heterogeneous reservoir properties. Linear solvers take the greatest portion of CPU time in reservoir simulations. This dissertation investigates advanced linear solvers for high performance computers (HPC) for reservoir simulation. Their performance is compared and discussed.
Lattice-Boltzmann modeling of multiphase flow through rough heterogeneously wet fractures
(2018-09-05) Estrada Santos, Javier Andres; Prodanović, Maša
Fractures are widely present in the subsurface, often representing primary channels for fluid flow in low permeability rocks. While fracture surfaces are composed by different minerals and are rough by nature, mathematical models to predict flow properties rarely take in account these heterogeneities. Therefore, the pore-scale mechanisms of flow through fractures are not well understood. Because characterizing multiphase flow phenomena in these geometries has received limited attention, this thesis aims to address this issue, by studying the effect of surface roughness and heterogeneous wettability in immiscible displacement through single fractures. Since analytical solutions are restricted to simple domains and obtaining data from laboratory experiments is unpractical, a 3D direct simulation approach via the lattice Boltzmann method was selected. This was chosen based on its rigorous kinetic derivation, its ability to simulate immiscible displacement, and its versatile boundary conditions. To study the effects of surface heterogeneities, synthetic domains exhibiting geometrical mineral arrangements, and self-affine fractures were created to carry out drainage and imbibition simulations with different input parameters. The relationships of different wetting/non-wetting patterns and surface roughness, with interfacial areas, capillary pressure, and residual fluid saturation were quantified. It has been shown that there is an effective heterogeneous feature size related to the fracture dimensions that modifies the capillary pressure behavior, and the shape of an invasive fluid front. We further found that for increasingly rough surfaces, there is a linear relation between the residual non-wetting saturation and capillary pressure with the aperture distribution. Thus, the shape, mineral size ratio, and surface roughness can have a significant effect on flow behavior. The results of this work can be used to better inform field simulations, by providing physically-accurate input parameters to characterize fracture network models, enhanced flow rate predictions for naturally fractured reservoirs can be obtained.
Modeling flow and geomechanics in fractured reservoirs
(2021-08-13) Jammoul, Mohamad; Wheeler, Mary F. (Mary Fanett); Arbogast, Todd; Balhoff, Matthew; Foster, John; Sharma, Mukul
Subsurface problems are inherently challenging because they involve multiple physical processes interacting with each other. Numerical models tend to break down the system into smaller problems that are easier to solve and that could be coupled within one framework. Fractured reservoirs are especially difficult to model due to the variety of physical processes that act at different scales. These processes include (1) fracture propagation, (2) flow through fractures and through the matrix, (3) hydrocarbon phase behavior, and (4) poroelastic deformations. Modeling the interaction between these processes plays an integral role in designing many energy and environmental applications. The primary objective of this work is to construct a holistic framework that can model flow and geomechanics in fractured reservoirs using computationally efficient algorithms. The framework can handle complex multiphysics problems including: multiphase flow, mechanical deformations, the capability to stimulate new fractures or activate existing ones, and the ability to seamlessly switch between propagation and production scenarios within the same simulation study. The approach includes coupling the in-house reservoir simulator (IPARS) with a phase-field fracture propagation model. In addition to hydraulic fracturing problems, the framework can model flow and geomechanics on fixed fracture networks with dynamic aperture variations. It can also simulate multiphase flow through natural fractures using general semi-structured grids. Two numerical schemes are introduced to improve the efficiency of computations. A multirate approach is proposed to enhance the performance of the L-scheme for decoupling the phase-field and displacement equations. A domain decomposition scheme is also presented to perform space-time refinement for flow through fractured reservoirs. Local time stepping and spatial mesh refinement can be used in the vicinity of the fractures while taking large grids cells with coarse time steps everywhere else in the reservoir. This motivates space and time adaptive mesh refinement in reservoir simulations.
Multiphase flow properties of sealing caprocks for CO₂ geological storage
(2018-06-25) Guiltinan, Eric Joseph; Cardenas, Meinhard Bayani, 1977-; Espinoza, David N.; Bennett, Philip C; Werth, Charles J; Flemings, Peter B
At the pore-scale, intermolecular forces are responsible for wetting, solubility, phase separation, and interfacial tension. These forces along with the pore structure, in porous media, and aperture distributions, in fractures, govern the physics of multiphase fluid flow and result in continuum scale parameters such as residual saturation and relative permeability. However, these forces are often overlooked and poorly understood. In this dissertation we explore how the pore-scale contributes to multiphase flow with an emphasis on geologic CO₂ sequestration and caprock integrity. First, we explore the wettability of organic shales, a likely caprock, for CO₂ storage. We provide the first reservoir condition brine/supercritical CO₂ contact angle measurements on an organic shale and find the organic shale to be water wet with little effect of organic content and thermal maturity. This means that capillary forces can hold back large CO₂ columns in these caprocks. Second, we investigate how pore structure controls the breakthrough pressure of mudstones through the use of resedimentation experiments combined with mercury intrusion porosimetry. We offer novel insights into the relationship between the coarse grained percolating network and the fine grained void ratio and show that the breakthrough pressure is related to the fine grained void ratio through a power-law. Third, we incorporate intermolecular forces into a numerical model to explore how heterogeneous wetting distributions contribute to the flow of CO₂ in fractures. We discover that the heterogeneous wetting contributes to residual saturation in fractures by providing opportunities for the predominately non-wetting CO₂ to surround the wetting phase. The wetting distribution also contributes to breakthrough time and the evolution of unsteady relative permeability. These results provide fundamental insight into how pore scale forces control continuum scale multiphase flow.
Numerical analysis of multiphase flows in porous media on non-rectangular geometry
(2017-12-06) Tao, Zhen; Arbogast, Todd James, 1957-; Wheeler, Mary F; Ghattas, Omar; Demkowicz, Leszek F; Hesse, Marc A
Fluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work, we investigate the behavior and numerical treatment of multiphase flow in porous media. To be more specific, we take the sequestration of CO₂ in geological media as an example. Mathematical modeling and numerical study of carbon sequestration helps to predict both short and long-term behavior of CO₂ storage in geological media, which can be a benefit in many ways. This work aims at developing accurate and efficient numerical treatment for problems in porous media on non-rectangular geometries. Numerical treatment of Darcy flow and transport have been developed for many years on rectangular and simplical meshes. However, extra effort is required to extend them to general non-rectangular meshes. In this dissertation work, for flow simulation, we develop new H(div)- conforming mixed finite elements (AT and AT [superscript red] ) which are accurate on cuboidal hexahedra. We also develop the new direct serendipity finite element (DS [subscript r] ), which is H¹ -conforming and accurate on quadrilaterals and a special family of hexahedra called truncated cubes. The use of the direct serendipity finite element reduces the number of degrees of freedom significantly and therefore accelerates numerical simulations. For transport, we use the newly developed direct serendipity elements in an enriched Galerkin method (EG), which is locally conservative. The entropy viscosity stabilization is applied to eliminate spurious oscillations. We test the EG-DS [subscript r] method on problems with diffusion, transport, and coupled flow and transport. Finally, we study two-phase flow in heterogeneous porous media with capillary pressure. We work on a new formulation of the problem and force the continuity of the capillary flux with a modification to conquer the degeneracy. The numerical simulation of two-phase flow is conducted on non-rectangular grids and uses the new elements.
On some problems in the simulation of flow and transport through porous media
(2009-08) Thomas, Sunil George; Wheeler, Mary F. (Mary Fanett)
The dynamic solution of multiphase flow through porous media is of special interest to several fields of science and engineering, such as petroleum, geology and geophysics, bio-medical, civil and environmental, chemical engineering and many other disciplines. A natural application is the modeling of the flow of two immiscible fluids (phases) in a reservoir. Others, that are broadly based and considered in this work include the hydrodynamic dispersion (as in reactive transport) of a solute or tracer chemical through a fluid phase. Reservoir properties like permeability and porosity greatly influence the flow of these phases. Often, these vary across several orders of magnitude and can be discontinuous functions. Furthermore, they are generally not known to a desired level of accuracy or detail and special inverse problems need to be solved in order to obtain their estimates. Based on the physics dominating a given sub-region of the porous medium, numerical solutions to such flow problems may require different discretization schemes or different governing equations in adjacent regions. The need to couple solutions to such schemes gives rise to challenging domain decomposition problems. Finally, on an application level, present day environment concerns have resulted in a widespread increase in CO₂capture and storage experiments across the globe. This presents a huge modeling challenge for the future. This research work is divided into sections that aim to study various inter-connected problems that are of significance in sub-surface porous media applications. The first section studies an application of mortar (as well as nonmortar, i.e., enhanced velocity) mixed finite element methods (MMFEM and EV-MFEM) to problems in porous media flow. The mortar spaces are first used to develop a multiscale approach for parabolic problems in porous media applications. The implementation of the mortar mixed method is presented for two-phase immiscible flow and some a priori error estimates are then derived for the case of slightly compressible single-phase Darcy flow. Following this, the problem of modeling flow coupled to reactive transport is studied. Applications of such problems include modeling bio-remediation of oil spills and other subsurface hazardous wastes, angiogenesis in the transition of tumors from a dormant to a malignant state, contaminant transport in groundwater flow and acid injection around well bores to increase the permeability of the surrounding rock. Several numerical results are presented that demonstrate the efficiency of the method when compared to traditional approaches. The section following this examines (non-mortar) enhanced velocity finite element methods for solving multiphase flow coupled to species transport on non-matching multiblock grids. The results from this section indicate that this is the recommended method of choice for such problems. Next, a mortar finite element method is formulated and implemented that extends the scope of the classical mortar mixed finite element method developed by Arbogast et al [12] for elliptic problems and Girault et al [62] for coupling different numerical discretization schemes. Some significant areas of application include the coupling of pore-scale network models with the classical continuum models for steady single-phase Darcy flow as well as the coupling of different numerical methods such as discontinuous Galerkin and mixed finite element methods in different sub-domains for the case of single phase flow [21, 109]. These hold promise for applications where a high level of detail and accuracy is desired in one part of the domain (often associated with very small length scales as in pore-scale network models) and a much lower level of detail at other parts of the domain (at much larger length scales). Examples include modeling of the flow around well bores or through faulted reservoirs. The next section presents a parallel stochastic approximation method [68, 76] applied to inverse modeling and gives several promising results that address the problem of uncertainty associated with the parameters governing multiphase flow partial differential equations. For example, medium properties such as absolute permeability and porosity greatly influence the flow behavior, but are rarely known to even a reasonable level of accuracy and are very often upscaled to large areas or volumes based on seismic measurements at discrete points. The results in this section show that by using a few measurements of the primary unknowns in multiphase flow such as fluid pressures and concentrations as well as well-log data, one can define an objective function of the medium properties to be determined, which is then minimized to determine the properties using (as in this case) a stochastic analog of Newton’s method. The last section is devoted to a significant and current application area. It presents a parallel and efficient iteratively coupled implicit pressure, explicit concentration formulation (IMPEC) [52–54] for non-isothermal compositional flow problems. The goal is to perform predictive modeling simulations for CO₂sequestration experiments. While the sections presented in this work cover a broad range of topics they are actually tied to each other and serve to achieve the unifying, ultimate goal of developing a complete and robust reservoir simulator. The major results of this work, particularly in the application of MMFEM and EV-MFEM to multiphysics couplings of multiphase flow and transport as well as in the modeling of EOS non-isothermal compositional flow applied to CO₂sequestration, suggest that multiblock/multimodel methods applied in a robust parallel computational framework is invaluable when attempting to solve problems as described in Chapter 7. As an example, one may consider a closed loop control system for managing oil production or CO₂sequestration experiments in huge formations (the “instrumented oil field”). Most of the computationally costly activity occurs around a few wells. Thus one has to be able to seamlessly connect the above components while running many forward simulations on parallel clusters in a multiblock and multimodel setting where most domains employ an isothermal single-phase flow model except a few around well bores that employ, say, a non-isothermal compositional model. Simultaneously, cheap and efficient stochastic methods as in Chapter 8, may be used to generate history matches of well and/or sensor-measured solution data, to arrive at better estimates of the medium properties on the fly. This is obviously beyond the scope of the current work but represents the over-arching goal of this research.
Phase behavior and the interaction of multiple gas molecules in hydrate-dominated geological flow processes
(2018-06-14) Darnell, Kristopher Nickolas; Flemings, Peter Barry, 1960-; DiCarlo, David; Hesse, Marc; Mohrig, David; Daigle, Hugh
Hydrate is a non-stoichiometric, ice-like solid compound of water and gas molecules that forms at low temperatures and high pressures. The stability of a particular hydrate is affected by the molecular composition of the environment in which it forms. For example, salt causes freezing point depression of hydrate much like it does for ice. In addition, a gas molecule, such as methane, that ordinarily forms hydrate at one pressure-temperature condition, may not form hydrate if the gas is mixed with another molecule, such as nitrogen, that requires increased pressure or decreased temperature to form hydrate. Here, I develop a modeling framework that incorporates the phase stability of gas mixtures to understand the coupling of equilibrium thermodynamics and fluid flow that governs hydrate-dominated geological flow processes. I first present a benchmark study that utilizes standard hydrate models to demonstrate the complex phase stability that occurs when salt and only methane are considered. The results show the impact that three-phase equilibrium, or the co-existence of a gas phase, a liquid water phase, and a hydrate phase, has on the evolution of hydrate systems. I then develop compositional phase diagrams for systems composed of water, methane, carbon dioxide, and nitrogen that elucidate how multiple hydrate-forming components interact to alter the composition of hydrate, completely de-stabilize hydrate, or create three-phase equilibrium conditions. I finally incorporate these compositional phase diagrams into a mathematical framework that describes multi-phase fluid flow that I use to simulate a subsurface injection strategy designed to simultaneously sequester carbon dioxide as hydrate and produce methane gas. The modeling framework illuminates the processes that govern the dynamic behavior of multiple hydrate-forming components. Simulations of subsurface injection demonstrate behaviors that support field and laboratory observations and clarify how composition impacts internal reservoir dynamics. The modeling framework developed here is general and flexible, so it can be modified to model additional components or to include additional physics. In particular, the modeling framework presented here is well-suited to simulate the buoyant ascent of thermogenic gas mixtures through marine sediments or the out-gassing of hydrate layers within the interior of icy planetary bodies like Enceladus.
Pipe fractional flow theory : principles and applications
(2014-01-14) Nagoo, Anand Subhash; Sharma, Mukul M.; Bonnecaze, Roger T; Edgar, Thomas F; Rochelle, Gary T; Lake, Larry W
The contribution of this research is a simple, analytical mathematical modeling framework that connects multiphase pipe flow phenomena and satisfactorily reproduces key multiphase pipe flow experimental findings and field observations, from older classic data to modern ones. The proposed unified formulation presents, for the first time, a reliably accurate analytical solution for averaged (1D) multiphase pipe flow over a wide range of applications. The two new fundamental insights provided by this research are that: (a) macroscopic single-phase pipe flow fluid mechanics concepts can be generalized to multiphase pipe flow, and (b): viewing and analyzing multiphase pipe flow in general terms of averaged relative flow (or fractional flow) can lead to a unified understanding of its resultant (global) behavior. The first insight stems from our finding that the universal relationship that exists between pressure and velocity in single-phase flow can also be found equivalently between pressure and relative velocity in multiphase flow. This eliminates the need for a-priori flow pattern determination in calculating multiphase flow pressure gradients. The second insight signifies that, in general, averaged multiphase flow problems can be sufficiently modeled by knowing only the averaged volume fractions. This proves that flow patterns are merely the visual, spatial manifestations of the in-situ velocity and volume fraction distributions (the quantities that govern the transport processes of the flow), which are neatly captured in the averaged sense as different fractional flow paths in our proposed fractional flow graphs. Due to their simplicity, these new insights provide for a deeper understanding of flow phenomena and a broader capability to produce quantitative answers in response to what-if questions. Since these insights do not draw from any precedent in the prior literature, a science-oriented, comprehensive validation of our core analytical principles was performed. Model validation was performed against a diverse range of vapor-liquid, liquid-liquid, fluid-solid and vapor-liquid-liquid applications (over 74,000 experimental measurements from over 110 different labs and over 6,000 field measurements). Additionally, our analytical theory was benchmarked against other modeling methods and current industry codes with identical (unbiased), named published data. The validation and benchmarking results affirm the central finding of this research – that simple, suitably-averaged analytical models can yield an improved understanding and significantly better accuracy than that obtained with extremely complex, tunable models. It is proven that the numerous, continuously interacting (local) flow microphysics effects in a multiphase flow can be (implicitly) accounted for by just a few properly validated (global) closure models that capture their net (resultant) behavior. In essence, it is the claim of this research that there is an underlying simplicity and connectedness in this subject if looking at the resultant macroscopic (averaged) behaviors of the flow. The observed coherencies of the macroscopic, self-organizing physical structures that define the subject are equivalently present in the macroscopic mathematical descriptions of these systems, i.e., the flow-pattern-implicit, averaged-equations mixture models that describe the collective behavior of the flowing mixture.
Pipe fractional flow through branched conduits
(2015-08) Stewart, Jeffrey Robert; Sharma, Mukul M.; Nagoo, Anand S
In the field of multiphase flow, the so-called phase splitting problem is a recurrent topic of discussion. In a branching conduit, it is of practical importance to know a priori how the phases split. Over the years, a variety of models have been developed to predict this and describe the physics involved. Despite this wealth of knowledge, little connection has been made between this question and fluid flow in networks. How phases split is determined by the system of equations solved, and no physics is incorporated to determine the phase split. To address this issue, a novel formulation of a multiphase network has been devised and validated against data and existing solutions, as well as compared to existing software. Additionally, current phase-splitting models have been discussed and compared. A new phase-splitting model based on a conservation-of-momentum approach is discussed and compared to branched-flow data. In building and validating this new model, a database of branched-flow experiments containing over 5000 data points from multiple laboratories has been gathered and systematized. This model has been incorporated into the existing network model to serve as additional equations when boundary conditions are unknown, and also to validate solutions found by the solver to ensure it is feasible. From this study, it was found that some current network solvers commercially available can arrive at inaccurate solutions. Moreover, such solvers can use an unorthodox approach to solve network problems and does not explicitly solve for Kirchhoff's laws. This issue is compounded by solution non-uniqueness--especially in networks with a high degree of looping. It is shown here that convergence is largely dependent on the initial guess. The phase splitting equation developed shows the degree of phase splitting at a junction varies primarily with branch configuration, pressure, void fraction, and flow rate. Current phase-splitting equations tend to exaggerate the phase split at a branch. In order to obtain the most exaggerated phase split, a vertical side-branch orientation should be used with a high mass takeoff.
Pore scale modeling of multiphase flow in heterogeneously wet media
(2018-10-09) Verma, Rahul (Ph. D. in petroleum engineering); Prodanovic, Masa; Bryant, Steven; DiCarlo, David; Mohanty, Kishore; Schembre-McCabe, Josephina
Pore scale simulation has recently become an important tool for understanding multiphase flow behavior in porous materials. It enables detailed mechanistic studies of upscaled flow parameters such as capillary-pressure saturation curves, residual saturation of each phase, and relative permeability. However, direct modeling of multiphase flow given the complex solid surfaces in a porous medium is a non-trivial problem. In this work, we develop a new quasi-static, variational level set formulation capable of handling trapped phases as well as wettability. We extend our previous work [1, 2] for simple geometries, and develop a new parallelized code enabling application of the method in larger geometries. We compare our model results against several experimental and semi-analytical datasets. The model is first applied to both homogeneous and heterogeneously wet rhomboidal pores, and compared against semi-analytical solutions derived by Mason and Morrow [3]. Subsequently, we focus on a quasi-2D micromodel study of fluid-fluid displacement for different wettabilities, which is quantified using the displacement efficiency and fractal dimension of the displacement patterns [4]. We then study classic experiments by Haines [5] and Leverett [6] for measuring the capillary pressure and relative permeability curves in sphere packs and sandpacks, respectively. We match trends in trapping in sandpacks during drainage/imbibition experiments by Pentland et al. [7], and also compare it against predictions by several other pore-scale models. Finally, we confirm the pore-scale hypothesis suggested by DiCarlo et al. [8] for explaining experimental observations of three-phase relative permeability of the intermediate-wet phase in sandpack experiments. For these three-phase experiments, we propose an approximation based on finding phases trapped between constant curvature surfaces, using two-phase simulations. We demonstrate the versatility of our methods by applying it to these disparate experimental datasets, and suggest future applications of our work.