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Shahraeeni E.,ETH Zurich | Shahraeeni E.,Reservoir Engineering Research Institute | Lehmann P.,ETH Zurich | Or D.,ETH Zurich
Water Resources Research | Year: 2012

Prediction of drying rates from porous media remains a challenge due to complex interactions between ambient conditions and porous medium properties. Evaporation from a gradually drying porous surface across air boundary layer exhibits nonlinear behavior due to enhanced diffusive fluxes from increasingly isolated active pores. These nonlinear interactions were quantified by modeling evaporation from surfaces composed of individual pores considering surface water content dynamics and internal transport within the medium. Wind tunnel experiments show that in contrast with nearly constant evaporation rates obtained at low atmospheric demand (typically <5 mm/d), evaporation fluxes under high atmospheric demand (high air velocities) exhibit a continuous decrease with surface drying even in the absence of internal capillary flow limitations. The isolated pore evaporation model captures surface drying dynamics for a range of atmospheric demands associated with air velocity and boundary layer thickness. As a surface dries under low atmospheric demand (low air speed, thick boundary layer), the remaining active pores become gradually isolated with a conforming vapor concentration field becoming increasingly three-dimensional thereby enhancing evaporative flux per pore. Such enhancement may fully compensate for reduced evaporative surface area leading to observed constant evaporation rate under low demand. For high evaporative demand, limitations to vapor field configuration within thin boundary layer limit flux compensation efficiency and leads to decreasing evaporative flux with surface drying irrespective of internal supply capacity. The model provides new insights into the intrinsic links between surface properties and atmospheric conditions in determining a range of evaporative dynamics for similar surface wetness conditions. © 2012 American Geophysical Union.

Myint P.C.,Yale University | Myint P.C.,Lawrence Livermore National Laboratory | Firoozabadi A.,Yale University | Firoozabadi A.,Reservoir Engineering Research Institute
Physics of Fluids | Year: 2013

The density increase from carbon dioxide (CO2) dissolution in water or hydrocarbons creates buoyancy-driven instabilities that may lead to the onset of convection. The convection is important for both CO2 sequestration in deep saline aquifers and CO2 improved oil recovery from hydrocarbon reservoirs. We perform linear stability analyses to study the effect of fluid compressibility and interface movement on the onset of buoyancy-driven convection in porous media. Compressibility relates to a non-zero divergence of the velocity field. The interface between the CO2 phase and the aqueous or hydrocarbon phase moves with time as a result of the volume change that occurs upon CO2 dissolution. Previous stability analyses have neglected these two aspects by assuming that the aqueous or hydrocarbon phase is incompressible and that the interface remains fixed in position. The stability analyses are used to compute two key quantities: (1) the critical time and (2) the critical wavenumber. Our results indicate that compressibility has a negligible effect on the critical time and the critical wavenumber in CO2-water mixtures. We use thermodynamics to derive an expression which shows that the two opposing physical processes which contribute to the divergence are comparable in magnitude and largely cancel each other. This result explains why compressibility does not significantly affect the onset, and it also demonstrates the link between compressibility and the volume change that causes movement of the interface. Compared to when the interface is fixed in position, a moving interface in CO2-water mixtures may reduce the critical time by up to around 10%, which can be significant in low permeability formations. The decrease in the critical time due to interface movement may be much more pronounced in hydrocarbons than in water. This could have important implications for CO2 improved oil recovery. © 2013 AIP Publishing LLC.

Moortgat J.,Reservoir Engineering Research Institute | Firoozabadi A.,Reservoir Engineering Research Institute
Journal of Computational Physics | Year: 2013

Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a compositional numerical simulator for three-phase flow in fractured media has not appeared in the literature, to the best of our knowledge. In this work, we present a three-phase fully compositional simulator for fractured media, based on higher-order finite element methods. To achieve computational efficiency, we invoke the cross-flow equilibrium (CFE) concept between discrete fractures and a small neighborhood in the matrix blocks. We adopt the mixed hybrid finite element (MHFE) method to approximate convective Darcy fluxes and the pressure equation. This approach is the most natural choice for flow in fractured media. The mass balance equations are discretized by the discontinuous Galerkin (DG) method, which is perhaps the most efficient approach to capture physical discontinuities in phase properties at the matrix-fracture interfaces and at phase boundaries. In this work, we account for gravity and Fickian diffusion. The modeling of capillary effects is discussed in a separate paper. We present the mathematical framework, using the implicit-pressure-explicit-composition (IMPEC) scheme, which facilitates rigorous thermodynamic stability analyses and the computation of phase behavior effects to account for transfer of species between the phases. A deceptively simple CFL condition is implemented to improve numerical stability and accuracy. We provide six numerical examples at both small and larger scales and in two and three dimensions, to demonstrate powerful features of the formulation. © 2013 Elsevier Inc.

Moortgat J.,Reservoir Engineering Research Institute | Li Z.,Reservoir Engineering Research Institute | Firoozabadi A.,Reservoir Engineering Research Institute
Water Resources Research | Year: 2012

Most simulators for subsurface flow of water, gas, and oil phases use empirical correlations, such as Henry's law, for the CO2 composition in the aqueous phase, and equations of state (EOS) that do not represent the polar interactions between CO2 and water. Widely used simulators are also based on lowest-order finite difference methods and suffer from numerical dispersion and grid sensitivity. They may not capture the viscous and gravitational fingering that can negatively affect hydrocarbon (HC) recovery, or aid carbon sequestration in aquifers. We present a three-phase compositional model based on higher-order finite element methods and incorporate rigorous and efficient three-phase-split computations for either three HC phases or water-oil-gas systems. For HC phases, we use the Peng-Robinson EOS. We allow solubility of CO2 in water and adopt a new cubic-plus-association (CPA) EOS, which accounts for cross association between H2O and CO2 molecules, and association between H2O molecules. The CPA-EOS is highly accurate over a broad range of pressures and temperatures. The main novelty of this work is the formulation of a reservoir simulator with new EOS-based unique three-phase-split computations, which satisfy both the equalities of fugacities in all three phases and the global minimum of Gibbs free energy. We provide five examples that demonstrate twice the convergence rate of our method compared with a finite difference approach, and compare with experimental data and other simulators. The examples consider gravitational fingering during CO2 sequestration in aquifers, viscous fingering in water-alternating-gas injection, and full compositional modeling of three HC phases. © 2012. American Geophysical Union. All Rights Reserved.

Cheng P.,Yale University | Bestehorn M.,TU Brandenburg | Firoozabadi A.,Yale University | Firoozabadi A.,Reservoir Engineering Research Institute
Water Resources Research | Year: 2012

Solubility trapping of carbon dioxide (CO2) in deep saline aquifers is considered one of the most effective methods for carbon sequestration. Dissolution of CO2 into the brine may create gravitational instabilities that lead to the onset of convection, which greatly enhances the storage efficiency and reduces the possibilities of leakage. Convection appears in the form of downward traveling fingers of relatively dense, CO2-dissolved fluid. Many natural aquifer formations display considerable permeability anisotropy, where the horizontal permeability k h may be several times greater than the vertical permeability k z. It has been previously found that increasing kh for a fixed kz reduces the critical time tc at which onset occurs and the critical wavelength λc with which the fingers initially form. We extend earlier work by showing how and why this occurs. Our results reveal new insights about λc. We have studied the behavior for times greater than tc using high-resolution numerical simulations. We show that the enhanced dissolution from convection can become significant much earlier in anisotropic media. Furthermore, the effects of anisotropy may be sustained for a long period of time. Our results suggest that permeability anisotropy can allow a wider range of aquifer formations to be considered for effective sequestration. © 2012. American Geophysical Union.

Jimenez-Angeles F.,Reservoir Engineering Research Institute | Firoozabadi A.,Reservoir Engineering Research Institute | Firoozabadi A.,Yale University
Journal of Physical Chemistry C | Year: 2014

Methane hydrates are crystalline structures composed of cages of hydrogen-bonded water molecules in which methane molecules are trapped. The nucleation mechanisms of crystallization are not fully resolved, as they cannot be accessed experimentally. For methane hydrates most of the reported simulations on the phenomena capture some of the basic elements of the full structure. In few reports, formation of crystalline structures is reached by imposing very high pressure, or dynamic changes of temperature, or a pre-existing hydrate structure. In a series of nanoscale molecular dynamics simulations of supersaturated water-methane mixtures, we find that the order of the crystalline structure increases by decreasing subcooling. Crystalline structures I and II form and coexist at moderate temperatures. Crystallization initiates from the spontaneous formation of an amorphous cluster wherein structures I, II, and other ordered defects emerge. We observe the transient coexistence of sI and sII in agreement with experiments. Our simulations are carried out at high methane supersaturation. This condition dramatically reduces the nucleation time and allows simulating nucleation at moderate subcooling. Moderate temperatures drive hydrates to more ordered structures. © 2014 American Chemical Society.

Moortgat J.,Reservoir Engineering Research Institute | Firoozabadi A.,Reservoir Engineering Research Institute | Firoozabadi A.,Yale University
Advances in Water Resources | Year: 2010

We present advances in compositional modeling of two-phase multi-component flow through highly complex porous media. Higher-order methods are used to approximate both mass transport and the velocity and pressure fields. We employ the Mixed Hybrid Finite Element (MHFE) method to simultaneously solve, to the same order, the pressure equation and Darcy's law for the velocity. The species balance equation is approximated by the discontinuous Galerkin (DG) approach, combined with a slope limiter. In this work we present an improved DG scheme where phase splitting is analyzed at all element vertices in the two-phase regions, rather than only as element averages. This approximation is higher-order than the commonly employed finite volume method and earlier DG approximations. The method reduces numerical dispersion, allowing for an accurate capture of shock fronts and lower dependence on mesh quality and orientation. Further new features are the extension to unstructured grids and support for arbitrary permeability tensors (allowing for both scalar heterogeneity, and shear anisotropy). The most important advancement in this work is the self-consistent modeling of two-phase multi-component Fickian diffusion. We present several numerical examples to illustrate the powerful features of our combined MHFE-dg method with respect to lower-order calculations, ranging from simple two component fluids to more challenging real problems regarding CO2 injection into a vertical domain saturated with a multi-component petroleum fluid. © 2010 Elsevier Ltd.

Sun M.,Reservoir Engineering Research Institute | Firoozabadi A.,Reservoir Engineering Research Institute | Firoozabadi A.,Yale University
Journal of Colloid and Interface Science | Year: 2013

Anti-agglomeration is a promising solution for gas hydrate risks in deepsea hydrocarbon flowlines and oil leak captures. Currently ineffectiveness at high water to oil ratios limits such applications. We present experimental results of a new surfactant in rocking cell tests, which show high efficiency at a full range of water to oil ratios; there is no need for presence of the oil phase. We find that our surfactant at a very low concentration (0.2. wt.% of water) keeps the hydrate particles in anti-agglomeration state. We propose a mechanism different from the established water-in-oil emulsion theory in the literature that the process is effective without the oil phase. There is no need to emulsify the water phase in the oil phase for hydrate anti-agglomeration; with oil-in-water emulsion and without emulsion hydrate anti-agglomeration is presented in our research. We expect our work to pave the way for broad applications in offshore natural gas production and seabed oil capture with very small quantities of an eco-friendly surfactant. © 2013 Elsevier Inc.

Lukanov B.,Reservoir Engineering Research Institute | Firoozabadi A.,Yale University
Langmuir | Year: 2014

The self-assembly of amphiphilic molecules is a key process in numerous biological and chemical systems. When salts are present, the formation and properties of molecular aggregates can be altered dramatically by the specific types of ions in the electrolyte solution. We present a molecular thermodynamic model for the micellization of ionic surfactants that incorporates quantum dispersion forces to account for specific ion effects explicitly through ionic polarizabilities and sizes. We assume that counterions are distributed in the diffuse region according to a modified Poisson-Boltzmann equation and can reach all the way to the micelle surface of charge. Stern layers of steric exclusion or distances of closest approach are not imposed externally; these are accounted for through the counterion radial distribution profiles due to the incorporation of dispersion potentials, resulting in a simple and straightforward treatment. There are no adjustable or fitted parameters in the model, which allows for a priori quantitative prediction of surfactant aggregation behavior based only on the initial composition of the system and the surfactant molecular structure. The theory is validated by accurately predicting the critical micelle concentration (CMC) for the well-studied sodium dodecyl sulfate (SDS) surfactant and its alkaline-counterion derivatives in mono- and divalent salts, as well as the molecular structure parameters of SDS micelles such as aggregation numbers and micelle surface potential. © 2014 American Chemical Society.

Moortgat J.,Reservoir Engineering Research Institute | Sun S.,King Abdullah University of Science and Technology | Firoozabadi A.,Reservoir Engineering Research Institute | Firoozabadi A.,Yale University
Water Resources Research | Year: 2011

A wide range of applications in subsurface flow involve water, a nonaqueous phase liquid (NAPL) or oil, and a gas phase, such as air or CO2. The numerical simulation of such processes is computationally challenging and requires accurate compositional modeling of three-phase flow in porous media. In this work, we simulate for the first time three-phase compositional flow using higher-order finite element methods. Gravity poses complications in modeling multiphase processes because it drives countercurrent flow among phases. To resolve this issue, we propose a new method for the upwinding of three-phase mobilities. Numerical examples, related to enhanced oil recovery and carbon sequestration, are presented to illustrate the capabilities of the proposed algorithm. We pay special attention to challenges associated with gravitational instabilities and take into account compressibility and various phase behavior effects, including swelling, viscosity changes, and vaporization. We find that the proposed higher-order method can capture sharp solution discontinuities, yielding accurate predictions of phase boundaries arising in computational three-phase flow. This work sets the stage for a broad extension of the higher-order methods for numerical simulation of three-phase flow for complex geometries and processes. Copyright 2011 by the American Geophysical Union.

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