R. Farajzadeh

Foam–oil interaction in porous media: Implications for foam assisted enhanced oil recovery

The efficiency of a foam displacement process in enhanced oil recovery (EOR) depends largely on the stability of foam films in the presence of oil. Experimental studies have demonstrated the detrimental impact of oil on foam stability. This paper reviews the mechanisms and theories (disjoining pressure, coalescence and drainage, entering and spreading of oil, oil emulsification, pinch-off, etc.) suggested in the literature to explain the impact of oil on foam stability in the bulk and porous media. Moreover, we describe the existing approaches to foam modeling in porous media and the ways these models describe the oil effect on foam propagation in porous media. Further, we present various ideas on an improvement of foam stability and longevity in the presence of oil. The outstanding questions regarding foam-oil interactions and modeling of these interactions are pointed out.

Enhanced Mass Transfer of CO2 into Water: Experiment and Modeling

Concern over global warming has increased interest in quantification of the dissolution of CO 2 in (sub-)-surface water. The mechanisms of the mass transfer of CO 2 in aquifers and of transfer to surface water have many common features. The advantage of experiments using bulk water is that the underlying assumptions to the quantify mass-transfer rate can be validated. Dissolution of CO 2 into water (or oil) increases the density of the liquid phase. This density change destabilizes the interface and enhances the transfer rate across the interface by natural convection. This paper describes a series of experiments performed in a cylindrical PVT-cell at a pressure range of p i = 10―50 bar, where a fixed volume of CO 2 gas was brought into contact with a column of distilled water. The transfer rate is inferred by following the gas pressure history. The results show that the mass-transfer rate across the interface is much faster than that predicted by Fickian diffusion and increases with increasing initial gas pressure. The theoretical interpretation of the observed effects is based on diffusion and natural convection phenomena. The CO 2 concentration at the interface is estimated from the gas pressure using Henrys solubility law, in which the coefficient varies with both pressure and temperature. Good agreement between the experiments and the theoretical results has been obtained.

Mass Transfer of CO2 Into Water and Surfactant Solutions

Abstract The mass transfer of CO2 into water and aqueous solutions of sodium dodecyl sulphate (SDS) is experimentally studied using a pressure, volume, temperature (PVT) cell at different initial pressures and a constant temperature (T = 25°C). It is observed that the transfer rate is initially much larger than expected from a diffusion process alone. The model equations describing the experiments are based on Ficks Law and Henrys Law. The experiments are interpreted in terms of two effective diffusion coefficients—one for the early-stages of the experiments and the other one for the later stages. The results show that at the early stages, the effective diffusion coefficients are one order of magnitude larger than the molecular diffusivity of CO2 in water. Nevertheless, in the later stages the extracted diffusion coefficients are close to literature values. It is asserted that at the early stages, density-driven natural convection enhances the mass transfer. A similar mass transfer enhancement was observed for the mass transfer between a gaseous CO2 rich phase with an oil (n-decane) phase. It is also found that at the experimental conditions studied addition of pure SDS does not have a significant effect on the mass transfer rate of CO2 in water.

Numerical Simulation of Natural Convection in Heterogeneous Porous media for CO2 Geological Storage

We report a modeling and numerical simulation study of density-driven natural convection during geological CO2 storage in heterogeneous formations. We consider an aquifer or depleted oilfield overlain by gaseous CO2, where the water density increases due to CO2 dissolution. The heterogeneity of the aquifer is represented by spatial variations of the permeability, generated using Sequential Gaussian Simulation method. The convective motion of the liquid with dissolved CO2 is investigated. Special attention is paid to instability characteristics of the CO2 concentration profiles, variation of mixing length, and average CO2 mass flux as a function of the heterogeneity characterized by the standard deviation and the correlation length of the log-normal permeability fields. The CO2 concentration profiles show different flow patterns of convective mixing such as gravity fingering, channeling, and dispersive based on the heterogeneity medium of the aquifer. The variation of mixing length with dimensionless time shows three separate regimes such as diffusion, convection, and second diffusion. The average CO2 mass flux at the top boundary decreases quickly at early times then it increases, reaching a constant value at later times for various heterogeneity parameters.

The effect of interface movement and viscosity variation on the stability of a diffusive interface between aqueous and gaseous CO2

Carbon dioxide injected in an aquifer rises quickly to the top of the reservoir and forms a gas cap from where it diffuses into the underlying water layer. Transfer of the CO2 to the aqueous phase below is enhanced due to the high density of the carbon dioxide containing aqueous phase. This paper investigates the behavior of the diffusive interface in an enclosed space in which initially the upper part is filled with pure carbon dioxide and the lower part with liquid. Our analysis differs from a conventional analysis as we take the movement of the diffusive interface due to mass transfer and the composition dependent viscosity in the aqueous phase into account. The same formalism can also be used to describe the situation when an oil layer is underlying the gas cap. Therefore we prefer to call the lower phase the liquid phase. In this paper we include these two effects into the stability analysis of a diffusive interface between CO2 and a liquid in the gravity field. We identify the relevant bifurcation parameter as q = eRa, where e is the width of the interface. This implies the (well known) scaling of the critical time ∼Ra−2 and wavelength ∼Ra−1(The critical time tc and critical wavelength kc are defined as follows: σ(k) ⩽ 0 ∀t ⩽ tc; equality only holds for t = tc and k = kc). Inclusion of the interface upward movement leads to earlier destabilization of the system. Increasing viscosity for increasing CO2 concentration stabilizes the system. The theoretical results are compared to bulk flow visual experiments using the Schlieren technique to follow finger development in aquifer sequestration of CO2. In the appendix, we include a detailed derivation of the dispersion relation σ(k) in the Hele-Shaw case [C. T. Tan and G. M. Homsy, Phys. Fluids 29, 3549–3556 (1986)]10.1063/1.865832 which is nowhere explicitly given.

An empirical theory for gravitationally unstable flow in porous media

In this paper, we follow a similar procedure as proposed by Koval (SPE J 3(2):145–154, 1963) to analytically model CO2 transfer between the overriding carbon dioxide layer and the brine layer below it. We show that a very thin diffusive layer on top separates the interface from a gravitationally unstable convective flow layer below it. Flow in the gravitationally unstable layer is described by the theory of Koval, a theory that is widely used and which describes miscible displacement as a pseudo two-phase flow problem. The pseudo two-phase flow problem provides the average concentration of CO2 in the brine as a function of distance. We find that downstream of the diffusive layer, the solution of the convective part of the model, is a rarefaction solution that starts at the saturation corresponding to the highest value of the fractional-flow function. The model uses two free parameters, viz., a dilution factor and a gravity fingering index. A comparison of the Koval model with the horizontally averaged concentrations obtained from 2-D numerical simulations provides a correlation for the two parameters with the Rayleigh number. The obtained scaling relations can be used in numerical simulators to account for the density-driven natural convection, which cannot be currently captured because the grid cells are typically orders of magnitude larger than the wavelength of the initial fingers. The method can be applied both for storage of greenhouse gases in aquifers and for EOR processes using carbon dioxide or other solvents.

Detailed Modeling of the Alkali Surfactant Polymer (ASP) Process by Coupling a Multi-purpose Reservoir Simulator to the Chemistry Package PHREEQC

Accurate modeling of an Alkali Surfactant Polymer (ASP) flood requires detailed representation of the geochemistry and, if natural acids are present, the saponification process. Geochemistry and saponification affect the propagation of the injected chemicals and the amount of generated natural soaps. These in turn determine the chemical phase behavior and hence the effectiveness of the ASP process. In this paper it is shown that by coupling the Shell in-house simulator MoReS with PHREEQC a robust and flexible tool has been developed to model ASP floods. PHREEQC is used as the chemical reaction engine, which determines the equilibrium state of the chemical processes modeled. MoReS models the impact of the chemicals on the flow properties, solves the flow equations and transports the chemicals. The validity of the approach is confirmed by benchmarking the results with the ASP module of the UTCHEM simulator (UT Austin). Moreover, ASP core floods have been matched with the new tool. The advantages of using PHREEQC as the chemical engine are its rich database of chemical species and its flexibility to change the chemical processes to be modeled. Therefore, the coupling procedure presented in this paper can also be extended to other chemical-EOR methods.

Filtration of micron-sized particles in granular media revealed by x-ray computed tomography

We investigate the deep-bed filtration of micron-sized hematite particles suspended in distilled water during flow in siliceous granular porous media, where particle retention is mostly due to surface (van der Waals and electrostatic) interactions. We show that x-ray computed tomography enables three-dimensional images of the filtration process to be generated. The one-dimensional filtrate concentration profiles obtained by averaging the images over sections perpendicular to the flow direction are rapidly decaying functions of the distance from the porous medium inlet and slide upward in the course of time, consistently with the filtration model presented by Herzig et al. [Ind. Eng. Chem. 62, 8 (1970)]. Finally, the filtration coefficient is found to decrease rapidly as a function of time: This indicates that the attractive interaction responsible for the retention of the hematite particles is strongly attenuated as the particles accumulate of the pore surfaces.

Effect of Gas Permeability and Solubility on Foam

We perform a study on the influence of gas permeability and solubility on the drainage and stability of foam stabilized with an anionic surfactant. Our study compares the foam stability for four pure gases and two gas mixtures while previous works only compared two pure gases. Drainage and foam-volume-decay rates are calculated from the experimental data and analysed. We find good agreement with existing theory as the foam stability is strongly influenced by the properties of the gas phase, in particular its solubility in the aqueous phase (measured by Henry’s solubility constant, ) and permeability (measured by foam-film permeability coefficient, ). The foam volume decreases considerably with increasing . Moreover, we observe that foams are more stable when a less soluble gas is added to a more soluble gas. Our analysis confirms theories linking drainage, stability, and coarsening rate. Finally, we introduce a new formulation for the foaming index that considers gas solubility and permeability.

Selecting the “Right” ASP Model by History Matching Core Flood Experiments

SUMMARY In order to design and analyze Alkaline Surfactant Polymer (ASP) pilots and to generate reliable ASP field forecasts a robust scalable modeling workflow for the ASP process is required. A starting point of such a workflow is to carry out ASP coreflood tests and history match those using numerical models. This allows validation of the models and generates a set of chemical flood parameters that can be used for field-scale simulation forecasts. It is well established that lowering of interfacial tension due to mixing of in-situ generated soap with injected surfactant and improved mobility control due to the polymer play a crucial role in the ASP process. Therefore, all models for the ASP process take into account these mechanisms in one way or the other. However, ASP models can differ in the detail in which (geo-)chemical reactions and the phase behavior are addressed. Inclusion of more details into the numerical model could result in better understanding and more accurate prediction, but it comes at a price, viz. it requires more measured input data and increases computational time. Thus, depending on the accuracy requirements, available experimental data and time the modeling of ASP flood can be performed using different simulation approaches. This paper describes several modeling approaches for ASP. We start with a brief description of these methods and their input requirements. Then we compare the ASP core flood simulation results demonstrating the advantages and disadvantages of presented approaches. Finally we give recommendations and guidelines on how and when the proposed models could be used.