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Ahmed T.,Texas A&M University at Qatar | Nasrabadi H.,Texas A&M University at Qatar | Firoozabadi A.,Reservoir Engineering Research Institute RERI | Firoozabadi A.,Yale University
Energy and Fuels

CO 2 injection has been used to improve oil recovery for the last 4 decades. In recent years, CO 2 injection has become more attractive because of the dual effect: injection in the subsurface (1) allows for reduction of the CO 2 concentration in the atmosphere to reduce global warming and (2) improves the oil recovery. One of the screening criteria for CO 2 injection as an enhanced oil recovery method is based on the measurement of CO 2 minimum miscibility pressure (MMP) in a slim tube. The slim tube data are used for the purpose of field evaluation and for the tuning of the equations of state. The slim tube represents one-dimensional (1D) horizontal flow. When CO 2 dissolves in the oil, the density may increase. The effect of the density increase in high-permeability reservoirs when CO 2 is injected from the top has not been modeled in the past. The increase in density changes the flow path from 1D to two-dimensional (2D) and three-dimensional (3D) (downward flow). As a result of this density effect, the compositional path in a reservoir can be radically different from the flow path in a slim tube. In this work, we study the density effect from CO 2 dissolution in modeling of CO 2 injection. We account for the increase in oil density with CO 2 dissolution using the Peng-Robinson equation of state. The viscosity is modeled based on the Pedersen-Fredenslund viscosity correlation. We perform compositional simulation of CO 2 injection in a 2D vertical cross-section with the density effect. Our results show that the density increase from CO 2 dissolution may have a drastic effect on the CO 2 flow path and recovery performance. One conclusion from this work is that there is a need to have accurate density data for CO 2/oil mixtures at different CO 2 concentrations to model properly CO 2 injection studies. Our main conclusion is that the downward flow of the CO 2 and oil mixture may not be gravity-stable, despite the widespread assumption in the literature. © 2012 American Chemical Society. Source

Haugen K.B.,Yale University | Firoozabadi A.,Yale University | Sun L.,Reservoir Engineering Research Institute RERI
AIChE Journal

The combination of successive substitution and the Newton method provides a robust and efficient algorithm to solve the nonlinear isofugacity and mass balance equations for two-phase split computations. The two-phase Rachford-Rice equation may sometimes introduce complexity, but the Newton and bisection methods provide a robust solution algorithm. For three-phase split calculations, the literature shows that the computed three-phase region is smaller than measured data indicate. We suggest that an improved solution algorithm for the three-phase Rachford-Rice equations can address the problem. Our proposal is to use a two-dimensional bisection method to provide good initial guesses for the Newton algorithm used to solve the three-phase Rachford-Rice equations. In this work, we present examples of various degree of complexity to demonstrate powerful features of the combined bisection-Newton method in three-phase split calculations. To the best of our knowledge, the use of the bisection method in two variables has not been used to solve the three-phase Rachford-Rice equations in the past. © 2010 American Institute of Chemical Engineers (AIChE). Source

Bestehorn M.,TU Brandenburg | Firoozabadi A.,Reservoir Engineering Research Institute RERI | Firoozabadi A.,Yale University
Physics of Fluids

We study the dissolution of CO2 in saline aquifers. The long diffusion times can be accelerated by orders of magnitude from mass transfer that origins from convection. Convection occurs at a critical time via a phase transition from the horizontally homogeneous diffusion state. To start the instability, perturbations that break the horizontal translation symmetry are necessary. We start with the basic equations and the boundary conditions, examine the linearized equations around the diffusive time and z-dependent base state and compare different definitions of the critical time found in the literature. Taking a simple model we show the role of fluctuations for delayed instabilities if the control parameter is slowly swept through the bifurcation point. Apart from the critical time we use a "visible" time where convection is manifested in the vertical CO2 transport. We specify the perturbations with respect to their strength and length scale, and compute the critical times for various cases by numerical integration of the basic equations in two spatial dimensions. Fluctuating concentration at the upper boundary, fluctuating porosity as well fluctuating permeability are studied in detail. For the permeability fluctuation, the compressibility of the fluid becomes important and the velocity field cannot be derived from a stream function. Our work also includes non-isothermal conditions with a prescribed vertical geothermal gradient and space dependent thermal conductivity. Temperature fields for different standard configurations are computed numerically and serve as starting condition for density-driven convection. Based on our work, we conclude that the visible time is much larger than the critical time. The visible time is a strong function of strength and length scale of the perturbations. © 2012 American Institute of Physics. Source

Mikyska J.,Czech Technical University | Firoozabadi A.,Reservoir Engineering Research Institute RERI
Energy and Fuels

The Peng-Robinson (PR) and cubic-plus-association (CPA) equations of state are used to predict the phase behavior and solubility of CO2 and normal alkanes from C1 to nC10 in several bitumens. Both of the equations of state are investigated over wide ranges of temperature and pressure. The results show that the PR-EOS describes mixure of bitumens with CO2 and alkanes when there is no second liquid phase or when the asphaltene content in the second liquid phase is not high. The CPA-EOS describes the phase behavior of mixtures of bitumens and CO2 and alkanes in liquid-liquid states even when the asphaltene content of one of the phases is high. High asphaltene content results in significant association and cross-association where the CPA-EOS is a natural choice. In this work the only adjustable parameter in the CPA-EOS is the cross-association energy parameter, and we show that the solubility of CO2 and alkanes in bitumens is usually not sensitive to this parameter. However, in two-phase liquid-liquid and three-phase liquid-liquid-vapor states with one phase having a high concentration of asphaltenes, the results become sensitive to the cross-association energy parameter. © 2015 American Chemical Society. Source

Li Z.,Reservoir Engineering Research Institute RERI | Firoozabadi A.,Reservoir Engineering Research Institute RERI
Fluid Phase Equilibria

A key element of efficient and robust three-phase split calculation is the initialization of phase mole fractions. While the initial guess of equilibrium ratios is made from two-phase split calculation and two-phase stability testing, initializing phase fractions through solving three-phase Rachford-Rice equations can be a challenge especially close to the bicritical points and phase boundaries. In this research, we examine three different methods: the improved two-dimensional bisection method, the minimization method, and the direct Newton method. We present a large number of three-phase examples of various degrees of complexity to demonstrate both robustness and efficiency of all these methods. The direct Newton method combined with the starting guess of phase fractions from two-phase split calculation and two-phase stability testing is the most efficient approach. © 2012 Elsevier B.V. Source

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