Browsing by Subject "Porous media"
Now showing 1 - 11 of 11
Results Per Page
Sort Options
Item Analysis of nonlinear Darcy-Forchheimer flows in porous media(Texas Tech University, 2009-08) Cakmak, Adem; Aulisa, Eugenio; Ibragimov, Akif; Kirby, Robert C.; Rengasamy, RaghunathanThis thesis is focused on certain theoretical aspects of nonlinear non-Darcy flows in porous media, and their application in reservoir and hydraulic engineering. The goal of this work is to develop a mathematically rigorous framework to study the dynamical processes associated to all three classical nonlinear Forchheimer laws for slightly compressible fluids. In our approach each anisotropic Forchheimer equation is replaced by a constitutive equation which relates the velocity vector field with the pressure gradient in a non-linear way. This allows reducing the original system of equations to one degenerate parabolic equation for the pressure only. It is shown that under some hydrodynamic and thermodynamic constraints there exists stable equilibrium: pseudo-steady state regime for the Forchheimer flows in porous media, which serves as a global attractor for wide classes of the flows yielding an alternative time independent computation of productivity index/diffusive capacity of a well.Item Artificial Leaf for Biofuel Production and Harvesting: Transport Phenomena and Energy Conversion(2013-08) Murphy, Thomas Eugene; Berberoglu, HalilMicroalgae cultivation has received much research attention in recent decades due to its high photosynthetic productivity and ability to produce biofuel feedstocks as well as high value compounds for the health food, cosmetics, and agriculture markets. Microalgae are conventionally grown in open pond raceways or closed photobioreactors. Due to the high water contents of these cultivation systems, they require large energy inputs for pumping and mixing the dilute culture, as well as concentrating and dewatering the resultant biomass. The energy required to operate these systems is generally greater than the energy contained in the resultant biomass, which precludes their use in sustainable biofuel production. To address this challenge, we designed a novel photobioreactor inspired by higher plants. In this synthetic leaf system, a modified transpiration mechanism is used which delivers water and nutrients to photosynthetic cells that grow as a biofilm on a porous, wicking substrate. Nutrient medium flow through the reactor is driven by evaporation, thereby eliminating the need for a pump. This dissertation outlines the design, construction, operation, and modeling of such a synthetic leaf system for energy positive biofuel production. First, a scaled down synthetic leaf reactor was operated alongside a conventional stirred tank photobioreactor. It was demonstrated that the synthetic leaf system required only 4% the working water volume as the conventional reactor, and showed growth rates as high as four times that of the conventional reactor. However, inefficiencies in the synthetic leaf system were identified and attributed to light and nutrient limitation of growth in the biofilm. To address these issues, a modeling study was performed with the aim of balancing the fluxes of photons and nutrients in the synthetic leaf environment. The vascular nutrient medium transport system was also modeled, enabling calculation of nutrient delivery rates as a function of environmental parameters and material properties of the porous membrane. These models were validated using an experimental setup in which the nutrient delivery rate, growth rate, and photosynthetic yield were measured for single synthetic leaves. The synthetic leaf system was shown to be competitive with existing technologies in terms of biomass productivity, while requiring zero energy for nutrient and gas delivery to the microorganisms. Future studies should focus on utilizing the synthetic leaf system for passive harvesting of secreted products in addition to passive nutrient delivery.Item Experimental analysis of electrostatic and hydrodynamic forces affecting nanoparticle retention in porous media(2012-05) Murphy, Michael Joseph, 1986-; Bryant, Steven L.; Huh, ChunThere have been significant advances in the research of nanoparticle technologies for formation evaluation and reservoir engineering operations. The target applications require a variety of different retention characteristics ranging from nanoparticles that adsorb near the wellbore to nanoparticles that can travel significant distances within the porous medium with little or no retention on the grain substrate. A detailed understanding of the underlying mechanisms that cause nanoparticle retention is necessary to design these applications. In this thesis, experiments were conducted to quantify nanoparticle retention in unconsolidated columns packed with crushed Boise sandstone and kaolinite clay. Experimental parameters such as flow rate, injected concentration and sandpack composition were varied in a controlled fashion to test hypotheses concerning retention mechanisms and enable development and validation of a mathematical model of nanoparticle transport. Results indicate nanoparticle retention, defined as the concentration of nanoparticles remaining attached to grains in the porous medium after a volume of nanoparticle dispersion is injected through the medium and then displaced with brine, is a function of injected fluid velocity with higher injected velocities leading to lower retention. In many cases nanoparticle retention increased nonlinearly with increasing concentration of nanoparticles in the injected dispersion. Nanoparticle retention concentration was found to exhibit an upper bound beyond which no further adsorption from the nanoparticle dispersion to the grain substrate occurred. Kaolinite clay was shown to exhibit lower retention concentration [mg/m2] than Boise sandstone suggesting DLVO interactions do not significantly influence nanoparticle retention in high salinity dynamic flow environments.Item 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.Item Head Loss Through Fibrous Debris Bed with Different Types of Perforated Strainers(2014-05-03) Abdulsattar, Suhaeb SSafety related issues in Nuclear Power Plants (NPPs) have always been of concern, especially those issues that are related to Light Water Reactors (LWRs) and their Design Basis Accidents (DBA). One of the ongoing issues that has been extensively studied is the Generic Safety Issue GSI-191, which is dedicated to study and resolve the issues that arise after a Loss-Of-Coolant-Accident (LOCA). Fibrous debris produced during the blow-down phase of Loss-of-Coolant Accidents is transported into the sump and becomes an important cause of head loss through the sump strainer, affecting the Emergency Core Cooling System (ECCS) performance. This study was dedicated to measure the pressure drop across randomly accumulated debris bed on the sump strainer along with measuring the debris bed thickness. Two different types of strainers were installed vertically, one at a time, in a horizontal flow loop and the debris bed thickness was measured during the bed build up process and after reaching steady state. Fifteen tests were conducted to determine the head loss difference between the two strainers and to study the characteristics of the debris bed accumulated on each strainer. The results from this experimental study were compared based on the approaching velocity, debris bed thickness, and strainer type. A realistic permeability model for the NUKON fiber glass insulation material was suggested, to be utilized in related applications, the suggested head loss model was compared to other head loss models developed in previous studies. The permeability model was developed from experimental data acquired from approaching velocities in the viscous region. There was no significant head loss difference between the two strainers for the minimum and intermediate range. Based on the experimental data, the head loss difference between the two strainers for the maximum range was about four times higher than the calculated head loss. The flow rate measurement uncertainty was main reason for the difference in the maximum range. There is a probability that the debris bypass could be different between the two strainers, thus, a debris bypass study is required to further investigate this difference.Item Mechanistic study of menisci motion within homogeneously and heterogeneously wet porous media(2009-08) Motealleh, Siyavash; Bryant, Steven L.Oil reservoirs and soil can be homogeneously wet (water-wet, oil-wet, neutralwet) or heterogeneously wet (mixed wet or fractionally wet). The goal of this research is to model the detailed configuration of wetting and non-wetting phases within homogeneously and heterogeneously wet porous media. We use a dense random pack of equal spheres as a model porous medium. The geometry of the sphere pack is complex but it is known. In homogeneously wet porous media we quantify the effect of low saturations of the wetting phase on the non-wetting phase relative permeability by solving analytically the geometry of the wetting phase. At low saturations (at or near the drainage endpoint) the wetting phase exists largely in the form of pendular rings held at grain contacts. Pore throats correspond to the constriction between groups of three grains, each pair of which can be in contact. Thus the existence of these pendular rings decreases the void area available for the flowing non-wetting phase. Consequently, the existence of the pendular rings decreases the permeability of non-wetting phase. Our model explains the significant permeability reduction of the non-wetting phase with a small change in the wetting phase in a low permeability porous medium. To model heterogeneously wet porous medium, we assume that the porous medium is fractionally wet where each grain is either oil-wet or water-wet. These waterwet or oil-wet grains are distributed randomly within the porous medium. We calculate analytically the stable fluid configuration in individual pores and throats of a fractionally wet medium. The calculation is made tractable by idealizing the configurations as locally spherical (menisci) or toroidal (pendular rings.) Because the calculation of the interface position is entirely local and grain-based, it provides a single, generalized, geometric basis for computing pore-filling events during drainage as well as imbibition. This generality is essential for modeling displacements in fractionally wet media. Pore filling occurs when an interface becomes unstable in a pore throat (analogous to the Haines condition for drainage in a uniformly wet throat), when two or more interfaces come into contact and merge to form a single interface (analogous to the Melrose condition for imbibition in uniformly wet medium), or when a meniscus in a throat touches a nearby grain (a new stability criterion). The concept of tracking the fluid/fluid interfaces on each grain means that a traditional pore network is not used in the model. The calculation of phase saturation or other quantities that are conveniently computed in a network can be done with any approach for defining pore bodies and throats. The fluid/fluid interfaces are mapped from the grain-based model to the network as needed. Consequently, the model is robust as there is no difference in the model between drainage and imbibition, as all criteria are accounted for both increasing and decreasing capillary pressure.Item Modeling and simulation for the evaluation of the productivity index in stratified reservoir-well systems(2010-12) Gunatilake, Janitha; Aulisa, Eugenio; Ibragimov, Akif; Toda, Magdalena D.Our research is mainly focused on modeling the "Productivity Index" of a two-layered reservoir well system with linear Darcy flow. In particular, we consider two systems. For the first system, the permeability of the top layer is relatively small and is approaching to 0. The permeability of the top layer is exactly equal to 0 in the second system. For the Pseudo Steady State regime, we want the Productivity index of the former case to be convergent to the latter case. From the governing equations of the fluid flow in porous media, we develop a theoretical model for the system. Since we do not get the required convergence with the existing definition of the Productivity Index, we introduce a new definition to the Productivity Index taking porosity of the porous media into account. With this new definition, it was conjectured that under certain restrictions to the porosity, the first system converges to the second system. This conjecture was validated by the simulation results.Item Modeling of nanoparticle transport in porous media(2012-08) Zhang, Tiantian; Bryant, Steven L.; Huh, Chun; Delshad, Mojdeh; Prodanovic, Masa; Johnston, Keith P.The unique properties of engineered nanoparticles have many potential applications in oil reservoirs, e.g., as emulsion stabilizers for enhanced oil recovery, or as nano-sensors for reservoir characterization. Long-distance propagation (>100 m) is a prerequisite for many of these applications. With diameters between 10 to 100 nanometers, nanoparticles can easily pass through typical pore throats in reservoirs, but physicochemical interaction between nanoparticles and pore walls may still lead to significant retention. A model that accounts for the key mechanisms of nanoparticle transport and retention is essential for design purposes. In this dissertation, interactions are analyzed between nanoparticles and solid surface for their effects on nanoparticle deposition during transport with single-phase flow. The analysis suggests that the DLVO theory cannot explain the low retention concentration of nanoparticles during transport in saturated porous media. Moreover, the hydrodynamic forces are not strong enough for nanoparticle removal from rough surface. Based on different filtration mechanisms, various continuum transport models are formulated and used to simulate our nanoparticle transport experiments through water-saturated sandpacks and consolidated cores. Every model is tested on an extensive set of experimental data collected by Yu (2012) and Murphy (2012). The data enable a rigorous validation of a model. For a set of experiments injecting the same kind of nanoparticle, the deposition rate coefficients in the model are obtained by history matching of one effluent concentration history. With simple assumptions, the same coefficients are used by the model to predict the effluent histories of other experiments when experimental conditions are varied. Compared to experimental results, colloid filtration model fails to predict normalized effluent concentrations that approach unity, and the kinetic Langmuir model is inconsistent with non-zero nanoparticle retention after postflush. The two-step model, two-rate model and two-site model all have both reversible and irreversible adsorptions and can generate effluent histories similar to experimental data. However, the two-step model built based on interaction energy curve fails to fit the experimental effluent histories with delay in the leading edge but no delay in the trailing edge. The two-rate model with constant retardation factor shows a big failure in capturing the dependence of nanoparticle breakthrough delay on flow velocity and injection concentration. With independent reversible and irreversible adsorption sites the two-site model has capability to capture most features of nanoparticle transport in water-saturated porous media. For a given kind of nanoparticles, it can fit one experimental effluent history and predict others successfully with varied experimental conditions. Some deviations exist between model prediction and experimental data with pump stop and very low injection concentration (0.1 wt%). More detailed analysis of nanoparticle adsorption capacity in water-saturated sandpacks reveals that the measured irreversible adsorption capacity is always less than 35% of monolayer packing density. Generally, its value increases with higher injection concentration and lower flow velocities. Reinjection experiments suggest that the irreversible adsorption capacity has fixed value with constant injection rate and dispersion concentration, but it becomes larger if reinjection occurs with larger concentration or smaller flow rate.Item 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.Item Peaceman's numerical productivity index for non-linear flows in porous media(2009-08) Chang, Dahwei; Aulisa, Eugenio; Toda, Magdalena D.; Howle, Victoria E.From Darcy’s law to Darcy-Forchheimer equation, there have being a lot efforts finding solutions for flows in porous media. Peaceman used a system of well blocks to replace the well bore in finding numerical solutions for linear flows. Our work uses a single well block to find the pressure distribution throughout the well for non-linear flows. In the process we found a block invariant which can be used to build the pressure distribution formula. From it, we can find the productivity index, one of the important factors in petroleum engineering. Theoretical derivation and numerical data are also presented in this report.Item Sensitivity of AVA reflectivity to fluid hydrocarbon properties in porous media(2007-05) Bain, Kevin Alan, 1977-; Tatham, R.H. (Robert H.), 1943-The sensitivity of transmission and reflection coefficients to varying physical parameters of a hydrocarbon fluid is examined. In particular, earlier work on generalized fluid properties is extended to consider realistic hydrocarbon properties at in-situ conditions. I also expand previous studies of P-P reflectivity, including Biot theory fluid effects, to include P-Sv mode-converted reflections. The goal is to understand how the reflection coefficients change as individual fluid parameters, such as density or viscosity, are varied, which fluid parameters have the greatest affect on the transmission and reflection coefficients, and what actual hydrocarbon and reservoir properties are involved. There is no sensitivity to a fluid or hydrocarbon parameter if the transmission and reflection coefficients do not change as that parameter is varied. The sensitivity analysis is further refined by calculating partial derivates of the reflection coefficients with respect to fluid viscosity. Special attention is given to viscosity because viscosity may act as a proxy for permeability as well as partial gas-saturation in common reservoir sands. To this end I am able to quantitatively describe the degree of gas-saturation and its influence on reflection coefficients. This might provide a technique to lessen the uncertainty encountered in the fizz-gas risk phenomenon. In the gas-oil interfaces, I find that the changes in the P-P reflectivity to be as much as 1.3% for a decrease in oil viscosity corresponding to a change from 1 to 99% gassaturation. In the oil-brine interfaces, the changes in the P-P reflectivity are estimated to be a maximum of 2.6% for a decrease in oil viscosity corresponding to a change from 1 to 99% gas-saturation. Changes in P-SV reflectivity are negligible (<1%) for both models at typical seismic frequencies (~100 Hz).