Pore-Scale Flow in Surfactant Flooding

Recovery of oil from the blocks of an initially oil-wet, naturally fractured, reservoir as a result of counter-current flow following introduction of aqueous wettability-altering surfactant into the fracture system is considered, as an example of a practical process in which phenomena acting at the single pore-scale are vital to the economic displacement of oil at the macroscopic scale. A Darcy model for the process is set up, and solutions computed illustrating the recovery rate controlling role of the bulk diffusion of surfactant. A central ingredient of this model is the capillary pressure relation, linking the local values of the pressure difference between the oleic and aqueous phases, the aqueous saturation and the surfactant concentration. Using ideas from single capillary models of oil displacement from oil-wet tubes by wettability-altering surfactant, we speculate that the use of a capillary pressure function, with dependences as assumed, may not adequately represent the Darcy scale consequences of processes acting at the single pore-scale. Multi-scale simulation, resolving both sub-pore and multi-pore flow processes may be necessary to resolve this point. Some general comments are made concerning the issues faced when modelling complex displacement processes in porous media starting from the pore-scale and working upwards.     

Simulation and transport phenomena of a ternary two-phase flow

A chemical flood model for a three-component (petroleum, water, injected chemical) two-phase (aqueous, oleic) system is presented. It is ruled by a system of nonlinear partial differential equations: the continuity equation for the transport of each of its components and Darcy's equation for the two-phase flow. The transport mechanisms considered are ultralow interfacial tension, capillary pressure, dispersion, adsorption, and partition of the components between the fluid phases (including solubilization and swelling).The mathematical model is numerically solved in the one-dimensional case by finite differences using an explicit and direct iterative procedure for the discretization of the conservation equations. Numerical results are compared with Yortsos and Fokas' exact solution for the linear waterflood case including capillary pressure effects and with Larson's model for surfactant flooding. The effects of the above-mentioned transport mechanisms on concentration profiles and on oil recovery are also analyzed.     

Imbibition of Anionic Surfactant Solution into Oil-Wet Capillary Tubes

The displacement of oil by anionic surfactant solutions in oil-wet horizontal capillary tubes is studied. The position of the oil–water interface is recorded with time. The surfactant solution used is a mixture of several different surfactants and co-solvents tailored to produce ultra-low interfacial tension (IFT) for the specific oil used in the study. The surfactant solution results in ultra-low IFT at optimum salinity and room temperature. Several experimental parameters including the capillary tube radius and surfactant solution viscosity are varied to study their effect on the interface speed. Two different models are used to predict the oil–water interface position with time. In the first model, it is assumed that the IFT is constant and ultra-low throughout the experiments. The second model involves change of wettability and IFT by adsorption of surfactant molecules to the oil–water interface and the solid surface. Comparing the predictions to the experimental results, it is observed that the second model provides a better match, especially for smaller capillary tubes. The model is then used to predict the imbibition rate for very small capillary tubes, which have equivalent permeability close to oil reservoirs. The results show that the oil displacement rate is limited by the rate of diffusion of surfactants to the interface.     

The Physical Origin of Interfacial Coupling in Two-Phase Flow through Porous Media

Recently developed transport equations for two-phase flow through porous media usually have a second term that has been included to account properly for interfacial coupling between the two flowing phases. The source and magnitude of such coupling is not well understood. In this study, a partition concept has been introduced into Kalaydjian's transport equations to construct modified transport equations that enable a better understanding of the role of interfacial coupling in two-phase flow through natural porous media. Using these equations, it is demonstrated that, in natural porous media, the physical origin of interfacial coupling is the capillarity of the porous medium, and not interfacial momentum transfer, as is usually assumed. The new equations are also used to show that, under conditions of steady-state flow, the magnitude of mobilities measured in a countercurrent flow experiment is the same as that measured in a cocurrent flow experiment, contrary to what has been reported previously. Moreover, the new equations are used to explicate the mechanism by which a saturation front steepens in an unstabilized displacement, and to show that the rate at which a wetting fluid is imbibed into a porous medium is controlled by the capillary coupling parameter, . Finally, it is argued that the capillary coupling parameter, , is dependent, at least in part, on porosity. Because a clear understanding of the role played by interfacial coupling is important to an improved understanding of two-phase flow through porous media, the new transport equations should prove to be effective tools for the study of such flow.     

Analysis of capillary interaction and oil recovery under ultrasonic waves

Although, the effects of ultrasonic irradiation on multiphase flow through porous media have been studied in the past few decades, the physics of the acoustic interaction between fluid and rock is not yet well understood. Various mechanisms may be responsible for enhancing the flow of oil through porous media in the presence of an acoustic field. Capillary related mechanisms are peristaltic transport due to mechanical deformation of the pore walls, reduction of capillary forces due to the destruction of surface films generated across pore boundaries, coalescence of oil drops due to Bjerknes forces, oscillation and excitation of capillary trapped oil drops, forces generated by cavitating bubbles, and sonocapillary effects. Insight into the physical principles governing the mobilization of oil by ultrasonic waves is vital for developing and implementing novel techniques of oil extraction. This paper aims at identifying and analyzing the influence of high-frequency, high-intensity ultrasonic radiation on capillary imbibition. Laboratory experiments were performed using cylindrical Berea sandstone and Indiana limestone samples with all sides (quasi-co-current imbibition), and only one side (counter-current imbibition) contacting with the aqueous phase. The oil saturated cores were placed in an ultrasonic bath, and brought into contact with the aqueous phase. The recovery rate due to capillary imbibition was monitored against time. Air–water, mineral oil–brine, mineral oil–surfactant solution and mineral oil-polymer solution experiments were run each exploring a separate physical process governing acoustic stimulation. Water–air imbibition tests isolate the effect of ultrasound on wettability, capillarity and density, while oil–brine imbibition experiments help outline the ultrasonic effect on viscosity and interfacial interaction between oil, rock and aqueous phase. We find that ultrasonic irradiation enhances capillary imbibition recovery of oil for various fluid pairs, and that such process is dependent on the interfacial tension and density of the fluids. Although more evidence is needed, some runs hint that wettability was not altered substantially under ultrasound. Preliminary analysis of the imbibition recoveries also suggests that ultrasound enhances surfactant solubility and reduce surfactant adsorption onto the rock matrix. Additionally, counter-current experiments involving kerosene and brine in epoxy coated Berea sandstone showed a dramatic decline in recovery. Therefore, the effectiveness of any ultrasonic application may strongly depend on the nature of interaction type, i.e., co- or counter-current flow. A modified form of an exponential model was employed to fit the recovery curves in an attempt to quantify the factors causing the incremental recovery by ultrasonic waves for different fluid pairs and rock types.     

A Non-isothermal Pore Network Drying Model with Gravity Effect

The concept of immiscible displacement as an invasion percolation (IP) process driven by heat and mass transfer is used in a pore network model for convective drying of capillary porous media. The coupling between heat and mass transfer occurs at the liquid–gas interface through temperature-dependent equilibrium vapor pressure and surface tension as well as the phase change enthalpy (in evaporation and condensation). The interfacial effects due to capillary forces and gravity are combined in an invasion potential; viscous forces are neglected. Simulation results show stabilized invasion patterns and finite drying front width by the influence of gravity.     

Roles of interfacial dynamics in the interaction behaviours between deformable oil droplets

Drainage and deformation of the intervening film can arguably represent the dynamic nature of colliding soft matters. The development of an interaction force analysis between soft interfaces helps to probe the drop deformation and the interfacial properties. Based on the SRYL model, the fluid flow inside the droplet and the convection-diffusion of the surfactant at the oil-water interface is coupled to model the distribution of a non-ionic surfactant (Span80) during drop deformation using AFM. This study quantifies the in situ interfacial concentration with a trace amount of surfactant at the interface and indicates its effect on the interaction forces between two immersed oil droplets in an aqueous solution.     

A sequential numerical chemical compositional simulator

Chemical flooding in the petroleum industry has a larger scale of oil recovery efficiency than water flooding. On the other hand, it is far more technical, costly, and risky. Numerical reservoir simulation can be employed to conduct mechanism study, feasibility evaluation, pilot plan optimization, and performance prediction for chemical flooding to improve recovery efficiency and reduce operational costs. In this article, we study numerical simulation of chemical flooding such as alkaline, surfactant, polymer, and foam (ASP+foam) flooding. The main displacement mechanisms in this type of flooding are interfacial tension lowering, capillary desaturation, chemical synergetic effects, and mobility control. The model of chemical flooding involves such physicochemical phenomena as dispersion, diffusion, adsorption, chemical reactions, and in situ generation of surfactant from acidic crude oil. The numerical simulator is based on a sequential solution approach that solves both pressure and compositions implicitly, and is applied to three experiments, a chemical flow without mass transfer between phases, a laboratory sandstone core, and an ASP+foam displacement problem with mass transfer, and to a real oilfield. A comparison with UTCHEM is also performed. These applications and comparison indicate that this numerical simulator is practical, efficient, and accurate for simulating complex chemical flooding processes.      

Numerical Simulation of Diagenetic Alteration and Its Effect on Residual Gas in Tight Gas Sandstones

In this study, we numerically cemented a segmented X-ray microtomography image of a sandstone to understand changes to pore space connectivity, capillary control on gas, and water distributions, and ultimately production behavior in tight gas sandstone reservoirs. Level set method-based progressive quasi-static algorithm (a state-of-the-art direct simulation of capillarity-dominated fluid displacement) was used to find the gas/water configurations during drainage and imbibition cycles. Further, we account for gas?Cwater interfacial tension changes using 1D burial history model based on available geologic data. We have found the displacement simulation method robust, and that diagenetic changes impart a significantly larger effect on gas trapping compared with interfacial tension changes.     

Radial viscous fingering patterns in Hele-Shaw cells

Viscous fingering experiments were performed by injecting a liquid to radially displace a much more viscous liquid in a Hele-Shaw cell consisting of two parallel closely-spaced glass plates. Both smooth and etched plates were used to study the influence of plate roughness on the fingering mechanism. Effect of flow rate and interfacial tension was also demonstrated. The results show that symmetric dendritic finger patterns can form in the presence of anisotropy provided by an etched square network, for both miscible and immiscible fingers. Chaotic finger patterns can form both in a cell with smooth surfaces and in one having a network of randomly oriented channels etched on one plate. Due to interfacial tension, the immiscible finger patterns are less ramified than their miscible counterparts, are more sensitive to the flow rate and become compact as the flow rate decreases. Possible applications of two-phase displacement studies in Hele-Shaw cells are discussed, which include two-phase flow in porous media and acid fracturing of oil reservoirs.     

Modeling and Simulation of Microbial Enhanced Oil Recovery Including Interfacial Area

The focus of this paper is the derivation of a nonstandard model for microbial enhanced oil recovery (MEOR) that includes the interfacial area (IFA) between oil and water. We consider the continuity equations for water and oil, a balance equation for the oil–water interfacial area, and advective–dispersive transport equations for bacteria, nutrients, and biosurfactants. Surfactants lower the interfacial tension (IFT), which improves oil recovery. Therefore, the parametrizations of the IFT reduction and residual oil saturation are included as a function of the surfactant concentration in the model. We consider for the first time in context of MEOR, the role of IFA in enhanced oil recovery. The motivation to include the IFA is to model the hysteresis in the capillary pressure–saturation relationship in a physically based manner, to include the effects of observed bacteria migration toward the oil–water interface and the production of biosurfactants at the oil–water interface. A comprehensive 2D implementation based on two-point flux approximation and backward Euler is proposed. An efficient and robust linearization scheme is used to solve the nonlinear systems at each time step. Illustrative numerical simulations are presented. The differences in the oil recovery profiles obtained with and without IFA are discussed. The presented model can also be used to design new experiments toward a better understanding and eventually optimization of MEOR.     

Multiphase flow with a simplified model for oil entrapment

A computationally simple procedure is described to model effects of oil entrapment on three-phase permeability-saturation-capillary pressure relations. The model requires knowledge of airwater saturation-capillary pressure relations, which are assumed to be nonhysteretic and are characterized by Van Genuchten's parametric model; scaling factors equal to the ratio of water surface tension to oil surface tension and to oil-water interfacial tension; and the maximum oil (also referred to as nonwetting liquid in a three-phase medium) saturation which would occur following water flooding of oil saturated soil. Trapped nonwetting liquid saturation is predicted as a function of present oil-water and air-oil capillary pressures and minimum historical water saturation since the occurrence of oil at a given location using an empirically-based algorithm. Oil relative permeability is predicted as a simple function of apparent water saturation (sum of actual water saturation and trapped oil saturation) and free oil saturation (difference between total oil and trapped oil saturation), and water relative permeability is treated as a unique function of actual water saturation. The proposed method was implemented in a two-dimensional finite-element simulator for three-phase flow and component transport, MOFAT. The fluid entrapment model requires minimal additional computational effort and computer storage and is numerically robust. The applicability of the model is illustrated by a number of hypothetical one- and two-dimensional simulations involving infiltration and redistribution with changes in water-table elevations. Results of the simulations indicate that the fraction of a hydrocarbon spill that becomes trapped under given boundary conditions increases as a nonlinear function of the maximum trapped nonwetting liquid saturation. Dense organic liquid plumes may exhibit more pronounced effects of entrapment due to the more dynamic nature of flow, even under static water table conditions. Disregarding nonwetting fluid entrapment may lead to significant errors in predictions of immiscible plume migration.     

Positive Effect of Flow Velocity on Gas–Condensate Relative Permeability: Network Modelling and Comparison with Experimental Results

Positive velocity dependency of relative permeability of gas–condensate systems, which has been observed in many different core experiments, is now well acknowledged. The above behaviour, which is due to two-phase flow coupling in condensing systems at low interfacial tension (IFT) conditions, was simulated using a 3D pore network model. The steady-dynamic bond network model developed for this purpose was also equipped with a novel anchoring technique, which was based on the equivalent hydraulic length concept adopted from fluid flow through pipes. The available rock data on the co-ordination number, capillary pressure, absolute permeability, porosity and one set of measured relative permeability curves were utilised to anchor the capillary, volumetric and flow characteristics of the constructed network model to those properties of the real core sample. Then the model was used to predict the effective permeability values at other IFT and velocity levels. There is a reasonable quantitative agreement between the predicted and measured relative permeability values affected by the coupling rate effect.     

Experimental evaluation of Marangoni stress and surfactant concentration at interface of contaminated single spherical drop using spatiotemporal filter velocimetry

Spatiotemporal filter velocimetry (SFV) was extended to Lagrangian measurements with boundary-fitted measurement areas, and was applied to flows about single spherical drops of glycerol-water solution falling in stagnant silicon oil under clean and contaminated conditions to examine its applicability to the estimation of the Marangoni stress and surfactant concentration at a moving interface. Effects of bulk concentration of surfactant on the velocity field, the Marangoni stress and the surface concentration of surfactant were discussed from the measured data. As a result, we confirmed that accurate velocity distribution in the vicinity of the interface measured by SFV enables us to evaluate interfacial velocity and interfacial shear stresses and to estimate the Marangoni stress, interfacial tension and surfactant concentration at the interface with the assumption of negligible surface viscosity. The flow inside the drop and the interfacial velocity become weak due to the Marangoni stress caused by the gradient of surfactant concentration at the interface as the bulk concentration of surfactant increases. These results demonstrate that SFV is of great use in experimental analysis of adsorption and desorption kinetics at a moving interface.     

1D Simulations for Microbial Enhanced Oil Recovery with Metabolite Partitioning

We have developed a mathematical model describing the process of microbial enhanced oil recovery (MEOR). The one-dimensional isothermal model comprises displacement of oil by water containing bacteria and substrate for their feeding. The bacterial products are both bacteria and metabolites. In the context of MEOR modeling, a novel approach is partitioning of metabolites between the oil and the water phases. The partitioning is determined by a distribution coefficient. The transfer part of the metabolite to oil phase is equivalent to its ”disappearance,” so that the total effect from of metabolite in the water phase is reduced. The metabolite produced is surfactant reducing oil–water interfacial tension, which results in oil mobilization. The reduction of interfacial tension is implemented through relative permeability curve modifications primarily by lowering residual oil saturation. The characteristics for the water phase saturation profiles and the oil recovery curves are elucidated. However, the effect from the surfactant is not necessarily restricted to influence only interfacial tension, but it can also be an approach for changing, e.g., wettability. The distribution coefficient determines the time lag, until residual oil mobilization is initialized. It has also been found that the final recovery depends on the distance from the inlet before the surfactant effect takes place. The surfactant effect position is sensitive to changes in maximum growth rate, and injection concentrations of bacteria and substrate, thus determining the final recovery. Different methods for incorporating surfactant-induced reduction of interfacial tension into models are investigated. We have suggested one method, where several parameters can be estimated in order to obtain a better fit with experimental data. For all the methods, the incremental recovery is very similar, only coming from small differences in water phase saturation profiles. Overall, a significant incremental oil recovery can be achieved, when the sensitive parameters in the context of MEOR are carefully dealt with.     

On the interfacial roughness scale in turbulent stratified two-phase flow: 3D lattice Boltzmann numerical simulations with forced turbulence and surfactant

Numerical 3D simulations of turbulent, stratified two-phase shear flow with a surfactant laden interface were used to test and develop a phenomenological interfacial roughness scale model where the energy required to deform the interface (buoyancy, interfacial tension, and viscous work) is proportional to the turbulent kinetic energy adjacent to the interface.The turbulence was forced in the upper and lower liquids in the simulations, to emulate the interfacial dynamics without requiring (prohibitively) large simulation domains and Reynolds numbers. The addition of surfactant lead to an increased roughness scale (for the same turbulent kinetic energy) due to the introduction of interfacial dilatational elasticity that suppressed horizontal motion parallel to the interface, and enhanced the vertical motion.The phenomenological roughness scale model was not fully developed for dilatational elasticity in this work, but we proposed a source term that represents surfactant induced pressure fluctuations near the interface. This source term should be developed further to account for the relation between surfactant density fluctuations and turbulence adjacent to the interface. We foresee that the roughness scale model can be used as a basis for more general interfacial closure relations in Reynolds averaged turbulence models, where also mobile surfactant is accounted for.     

Pore-Scale Network Modeling of Three-Phase Flow Based on Thermodynamically Consistent Threshold Capillary Pressures. I. Cusp Formation and Collapse

We present a pore-scale network model of two- and three-phase flow in disordered porous media. The model reads three-dimensional pore networks representing the pore space in different porous materials. It simulates wide range of two- and three-phase pore-scale displacements in porous media with mixed-wet wettability. The networks are composed of pores and throats with circular and angular cross sections. The model allows the presence of multiple phases in each angular pore. It uses Helmholtz free energy balance and Mayer–Stowe–Princen (MSP) method to compute threshold capillary pressures for two- and three-phase displacements (fluid configuration changes) based on pore wettability, pore geometry, interfacial tension, and initial pore fluid occupancy. In particular, it generates thermodynamically consistent threshold capillary pressures for wetting and spreading fluid layers resulting from different displacement events. Threshold capillary pressure equations are presented for various possible fluid configuration changes. By solving the equations for the most favorable displacements, we show how threshold capillary pressures and final fluid configurations may vary with wettability, shape factor, and the maximum capillary pressure reached during preceding displacement processes. A new cusp pore fluid configuration is introduced to handle the connectivity of the intermediate wetting phase at low saturations and to improve model’s predictive capabilities. Based on energy balance and geometric equations, we show that, for instance, a gas-to-oil piston-like displacement in an angular pore can result in a pore fluid configuration with no oil, with oil layers, or with oil cusps. Oil layers can then collapse to form cusps. Cusps can shrink and disappear leaving no oil behind. Different displacement mechanisms for layer and cusp formation and collapse based on the MSP analysis are implemented in the model. We introduce four different layer collapse rules. A selected collapse rule may generate different corner configuration depending on fluid occupancies of the neighboring elements and capillary pressures. A new methodology based on the MSP method is introduced to handle newly created gas/water interfaces that eliminates inconsistencies in relation between capillary pressures and pore fluid occupancies. Minimization of Helmholtz free energy for each relevant displacement enables the model to accurately determine the most favorable displacement, and hence, improve its predictive capabilities for relative permeabilities, capillary pressures, and residual saturations. The results indicate that absence of oil cusps and the previously used geometric criterion for the collapse of oil layers could yield lower residual oil saturations than the experimentally measured values in two- and three-phase systems.     

Direct numerical simulation of surfactant-stabilized emulsions

A 3D lattice Boltzmann model for two-phase flow with amphiphilic surfactant was used to investigate the evolution of emulsion morphology and shear stress in starting shear flow. The interfacial contributions were analyzed for low and high volume fractions and varying surfactant activity. A transient viscoelastic contribution to the emulsion rheology under constant strain rate conditions was attributed to the interfacial stress. For droplet volume fractions below 0.3 and an average capillary number of about 0.25, highly elliptical droplets formed. Consistent with affine deformation models, gradual elongation of the droplets increased the shear stress at early times and reduced it at later times. Lower interfacial tension with increased surfactant activity counterbalanced the effect of increased interfacial area, and the net shear stress did not change significantly. For higher volume fractions, co-continuous phases with a complex topology were formed. The surfactant decreased the interfacial shear stress due mainly to advection of surfactant to higher curvature areas. Our results are in qualitative agreement with experimental data for polymer blends in terms of transient interfacial stresses and limited enhancement of the emulsion viscosity at larger volume fractions where the phases are co-continuous.