Determination of Nanoparticle Macrotransport Coefficients from Pore Scale Processes

Nanoparticle transport in porous media is modeled using a hierarchical set of differential equations corresponding to pore scale and macroscale. At the pore scale, movement and interaction of a single particle with a solid matrix is modeled using the advection–dispersion–sorption equation. A single nanoparticle entering the space encounters viscous, diffusion and surface forces. Surface forces (electrostatic and van der Waals forces) between nanoparticles and mineral grains appear as sorption propensity on solid matrix boundary condition. These local events are then transformed into a macroscale continuum by imposing periodic boundary conditions for contiguous unit cells representing porous media and using a scheme of moment analysis. At the macroscale, propagation and retention of particles are characterized by three position-independent coefficients: mean nanoparticle velocity vector \({\bar{\mathbf{U}}}^*\), macroscopic dispersion coefficient \({\bar{\mathbf{D}}}^*\), and mean nanoparticle retention rate constant \({\bar{K}}^*\). The modeling results are validated with a set of nanoparticle transport tests in porous microchips. We also present simulations of realistic porous media, where an actual image of sandstone samples is processed into binary tones. The representative unit cells are constructed from the resulting binary image by searching for areas within the sample with maximum similarities to the whole sample in terms of porosity and specific surface area, which are found to show strong correlations with the resulting \({\bar{\mathbf{U}}}^*\) and \({\bar{K}}^*\), respectively.     

Pore Scale and Macroscopic Displacement Mechanisms in Emulsion Flooding

The flow properties of complex fluids through porous media give rise to multiphase flow displacement mechanisms that operate at different scales, from pore-level to Darcy scale. Experiments have shown that injection of oil-in-water emulsions can be used as an effective enhanced-oil recovery (EOR) method, leading to substantial increase in the volume of oil recovered. Pore-scale flow visualization as well as core flooding results available in the literature have demonstrated that the enhanced recovery factor is regulated by the capillary number of the flow. However, the mechanisms by which additional oil is displaced during emulsion injection are still not clear. In this work, we carried out two different experiments to evaluate the effect of emulsion flooding both at pore and macro scales. Visualization of the flow through sand packed between transparent plexiglass parallel plates shows that emulsion flooding improves the pore-level displacement efficiency, leading to lower residual oil saturation. Oil recovery results during emulsion flooding in tertiary mode (after waterflooding) in parallel sandstone cores with very different absolute permeability values prove that emulsion flooding also leads to enhancement of conformance or volumetric sweep efficiency. Combined, the results presented here show that injection of emulsion offers multiscale mechanisms resulting from capillary-driven mobility control.     

Mechanisms Involved in Microbially Enhanced Oil Recovery

Microbial enhanced oil recovery (MEOR) represents a possible cost-effective tertiary oil recovery method. Although the idea of MEOR has been around for more than 75 years, even now little is known of the mechanisms involved. In this study, Draugen and Ekofisk enrichment cultures, along with Pseudomonas spp. were utilized to study the selected MEOR mechanisms. Substrates which could potentially stimulate the microorganisms were examined, and l-fructose, d-galacturonic acid, turnose, pyruvic acid and pyruvic acid methyl ester were found to be the best utilized by the Ekofisk fermentative enrichment culture. Modelling results indicated that a mechanism likely to be important for enhanced oil recovery is biofilm formation, as it required a lower in situ cell concentration compared with some of the other MEOR mechanisms. The bacterial cells themselves were found to play an important role in the formation of emulsions. Bulk coreflood and flow cell experiments were performed to examine MEOR mechanisms, and microbial growth was found to lead to possible alterations in wettability. This was observed as a change in wettability from oil wet (contact angle 154°) to water wet (0°) due to the formation of biofilms on the polycarbonate coupons.     

Microscopic Mechanisms of Oil Recovery By Near-Miscible Gas Injection

As gas flooding becomes a more viable means of enhanced oil recovery, it is important to identify and understand the pore-scale flow mechanisms, both for the development of improved gas flooding applications and for the predicting phase mobilisation under secondary and tertiary gas flooding. The purpose of this study was to visually investigate the pore-level mechanisms of oil recovery by near-miscible secondary and tertiary gas floods. High-pressure glass micromodels and model fluids representing a near-miscible fluid system were used for the flow experiments. A new pore-scale recovery mechanism was identified which significantly contributed to oil recovery through enhanced flow and cross-flow between the bypassed pores and the injected gas. This mechanism is strongly related to a very low gas/oil interfacial tension (IFT), perfect wetting conditions and simultaneous flow of gas and oil in the same pore, all of which occur as the gas/oil critical point is approached. The results of this study helps us to better understand the pore-scale mechanisms of oil recovery in very low-IFT (near-miscible) systems. In particular we show that in near-miscible gas floods, behind the main gas front, the recovery of the oil continues by cross-flow from the bypassed pores into the main flow stream and as a result almost all of the oil, which has been contacted by the gas, could be recovered. Our observations in high-pressure micromodel experiments have demonstrated that this mechanism can only occur in near-miscible processes (as opposed to immiscible and completely miscible processes), which makes oil displacement by near-miscible gas floods a very effective process.     

Microbial Enhanced Oil Recovery in Fractional-Wet Systems: A Pore-Scale Investigation

Microbial enhanced oil recovery (MEOR) is a technology that could potentially increase the tertiary recovery of oil from mature oil formations. However, the efficacy of this technology in fractional-wet systems is unknown, and the mechanisms involved in oil mobilization therefore need further investigation. Our MEOR strategy consists of the injection of ex situ produced metabolic byproducts produced by Bacillus mojavensis JF-2 (which lower interfacial tension (IFT) via biosurfactant production) into fractional-wet cores containing residual oil. Two different MEOR flooding solutions were tested; one solution contained both microbes and metabolic byproducts while the other contained only the metabolic byproducts. The columns were imaged with X-ray computed microtomography (CMT) after water flooding, and after MEOR, which allowed for the evaluation of the pore-scale processes taking place during MEOR. Results indicate that the larger residual oil blobs and residual oil held under relatively low capillary pressures were the main fractions recovered during MEOR. Residual oil saturation, interfacial curvatures, and oil blob sizes were measured from the CMT images and used to develop a conceptual model for MEOR in fractional-wet systems. Overall, results indicate that MEOR was effective at recovering oil from fractional-wet systems with reported additional oil recovered (AOR) values between 44 and 80%; the highest AOR values were observed in the most oil-wet system.     

Impact of Rock Heterogeneity on Interactions of Microbial-Enhanced Oil Recovery Processes

Residual oil saturation reduction and microbial plugging are two crucial factors in microbial-enhanced oil recovery (MEOR) processes. In our previous study, the residual saturation was defined as a nonlinear function of the trapping number, and an explicit relation between the residual oil saturation and the trapping number was incorporated into a fully coupled biological (B) and hydrological (H) finite element model. In this study, the BH model is extended to consider the impact of rock heterogeneity on microbial-enhanced oil recovery phenomena. Numerical simulations of core flooding experiments are performed to demonstrate the influences of different parameters controlling the onset of oil mobilization. X-ray CT core scans are used to construct numerical porosity-permeability distributions for input to the simulations. Results show clear fine-scale fingering processing, and that trapping phenomena have significant effects on residual oil saturation and oil recovery in heterogeneous porous media. Water contents and bacterial distributions for heterogeneous porous media are compared with those for homogenous porous media. The evolution of the trapping number distribution is directly simulated and visualized. It is shown that the oil recovery efficiency of EOR/MEOR will be lower in heterogeneous media than in homogeneous media, largely due to the difficulty in supplying surfactant to unswept low-permeability zones. However, MEOR also provides efficient plugging along high-permeability zones which acts to increase sweep efficiency in heterogeneous media. Thus, MEOR may potentially be more suited for highly heterogeneous media than conventional EOR.     

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.     

Modelling Low-Salinity Oil Recovery Mechanisms Using an Ion Dissociation Model

Experimental evidence shows that injecting low-salinity water during the oil recovery process can lead to an increase in the amount of oil recovered. Numerous mechanisms have been proposed to explain this effect, and, in recent years, two which have gained notable support are multicomponent ionic exchange (MIE) and pH increase. Both mechanisms involve ion exchange reactions within the thin film of water separating the oil in a reservoir from the clay minerals on the surface of the reservoir rock. Since the reactions occur on the molecular scale, an upscaled model is required in order to accurately determine the dominant mechanism using centimetre-scale experiments. In this paper, we develop the first stages of this upscaling process by modelling the pore-scale motion of an oil slug through a clay pore throat. We use a law-of-mass-action approach to model the exchange reactions occurring on the oil–water and clay–water interfaces in order to derive expressions for the surface charges as functions of the salinity. By balancing the disjoining pressure in the water film with the capillary pressure across the oil–water interface, we derive an expression for the salinity-dependent film thickness. We compare the two mechanisms by modifying an existing model for the velocity of an oil slug through a pore throat. Numerical results show that the velocity increases as the salinity decreases. The percentage increase is larger for the MIE mechanism, suggesting that MIE may be the dominant causal mechanism; however, this will vary depending on the particular clay and oil being studied.

     

A Practical Methodology to Screen Oil Recovery Processes Involving Spontaneous Imbibition

Transport in Porous Media - We present a general novel technique to monitor saturation changes on small rock samples of only 15 mm in diameter and 20 mm in length for the purpose...     

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.     

CO2 Injection in Geological Formations: Determining Macroscale Coefficients from Pore Scale Processes

Carbon dioxide (CO₂) injections in geological formations are usually performed for enhanced hydrocarbon recovery in oil and gas reservoirs and storage and sequestration in saline aquifers. Once CO₂ is injected into the formation, it propagates in the porous rock by dispersion and convection. Chemical reactions between brine ions and CO₂ molecules and consequent reactions with mineral grains are also important processes. The dynamics of CO₂ molecules in random porous media are modeled with a set of differential equations corresponding to pore scale and continuum macroscale. On the pore scale, convective–dispersive equation is solved considering reactions on the inner boundaries in a unit cell. A unit cell is the smallest portion of a porous media that can reproduce the porous media by repetition. Inner boundaries in a unit cell are the surfaces of the mineral grains. Dispersion process at the pore scale is transformed into continuum macroscale by adopting periodic boundary conditions for contiguous unit cells and applying Taylor-Aris dispersion theory known as macrotransport theory. Using this theory, the discrete porous system changes into a continuum system within which the propagation and interaction of CO₂ molecules with fluid and solid matrix of the porous media are characterized by three position-independent macroscopic coefficients: the mean velocity vector , dispersivity dyadic , and mean volumetric CO₂ depletion coefficient .     

Analytical Modeling for Gravity Segregation in Gas Improved Oil Recovery of Tilted Reservoirs

Stone’s model for gravity segregation in gas improved oil recovery (IOR) indicates the distance that injected gas and water travel together before the segregation being completed (length of complete segregation). This model is very useful for co-injection of water and gas into horizontal depleted reservoirs. A proof by Rossen and van Duijn showed that Stone’s model applies to steady-state gas–liquid flow, and also foam flow, in horizontal reservoirs as long as the standard assumptions of fractional flow theory (incompressible flow, Newtonian mobilities, local equilibrium) are applied. However, until now, there has been no analytical study on the length of segregation when co-injection of water and gas occurs in tilted reservoirs. In this article, in order to extent the validity of Stone’s model to tilted reservoirs, governing equations of fluids displacement based on fractional flow theory are solved by the method of characteristics, MOC. The results are then compared to Stone’s model and to the results of a three-dimensional finite-difference compositional reservoir simulator. This study shows that Stone’s model should be corrected for tilted reservoirs and that the presented math proof can model gravity segregation in gas IOR of tilted reservoirs, appropriately. The effect of co-injecting of water and gas into tilted reservoirs on recovery efficiency is also examined.     

Pore Scale Modeling of Rate Effects in Imbibition

We use pore scale network modeling to study the effects of flow rate and contact angle on imbibition relative permeabilities. The model accounts for flow in wetting layers that occupy roughness or crevices in the pore space. Viscous forces are accounted for by solving for the wetting phase pressure and assuming a fixed conductance in wetting layers. Three-dimensional simulations model granular media, whereas two-dimensional runs represent fracture flow.We identify five generic types of displacement pattern as we vary capillary number, contact angle, and initial wetting phase saturation: flat frontal advance, dendritic frontal advance, bond percolation, compact cluster growth, and ramified cluster growth. Using phase diagrams we quantify the range of physical properties under which each regime is observed. The work explains apparently inconsistent experimental measurements of relative permeability in granular media and fractures.     

A Pore Scale Study of Non-Newtonian Effect on Foam Propagation in Porous Media

CO₂ injection is one of the most promising techniques to enhance oil recovery. However, an unfavorable mobility ratio, reservoir heterogeneity and gravity segregation can reduce the macroscopic sweep efficiency. In situ foaming of injected CO₂ is the method that has the most potential for improving sweep efficiency based on controlling CO₂ mobility. This study investigates the foaming behavior of N,N,N′-trimethyl-N′-tallow-1,3-diaminopropane (DTTM) surfactant with CO₂ in a transparent porous microflow model with natural rock pore structures. It focuses on the effect of the salinity induced non-Newtonian behavior of DTTM solution on foam propagation. The performance of foams stabilized by 0.5 wt% DTTM solution over the viscosity range from 0.71 (at 5 wt% NaCl) to 41 cp (at 20 wt% NaCl) was compared with conventional polymer-enhanced foams whose liquid phase contained a commonly used foaming surfactant, C15–18 Internal Olefin Sulfonate (C15–18 IOS) and a hydrolyzed polyacrylamide. Such comparisons have also provided insight into the respective impacts of liquid phase viscosification by worm-like surfactant micelles and polymer on foam texture associated with its rheological characteristics. It was found that at low aqueous phase viscosity (injection liquid viscosity of 0.71 cp) the maximum achievable viscosity of DDTM foam was around 1000 cp, which was 80 times IOS stabilized foam. The interfacial tension of DTTM was higher than that of IOS, resulting coarser foam texture and higher individual lamella resistance. An increase in DTTM solution viscosity by a factor of 33 decreased foam generation and viscosity for gas injection. This was not observed for the simultaneous injection of gas and DTTM solution. Overall, the effect of liquid phase viscosity on transient foam behavior during gas injection is similar for both DTTM and IOS regardless of the difference in the nature of viscosifying agents (WLM vs 3330 s polymer). An increase in gas injection pressure without liquid injection delayed foam propagation and reduced the magnitude of foam viscosity. The results from this study indicated that DTTM surfactant is an important alternative to commercially available polymers that have been used to enhance foam performance in porous media. This particular surfactant type also overcomes several disadvantages of polymers such as limited temperature and salinity tolerance, shear degradation, and filtering in low permeability formations.

     

A Numerical Study of Instability Control for the Design of an Optimal Policy of Enhanced Oil Recovery by Tertiary Displacement Processes

In this paper, we consider the problem of control of hydrodynamic instability arising in the displacement processes during enhanced oil recovery by SP-flooding (Surfactant?CPolymer). In particular, we consider a flooding process involving displacement of a viscous fluid in porous media by a less viscous fluid containing polymer and surfactant over a finite length which in turn is displaced by a even less viscous fluid such as water. The maximum stabilization capacities of several monotonic and non-monotonic viscous profiles created by non-uniform polymer concentration are studied in the presence of interfacial tensions created by surfactants. The study has been carried out numerically to determine and characterize the most optimal viscous profiles of each family. Similarities in optimal monotonic viscous profiles of this constant-time injection policy and other injection policies by previous workers are noted. The presence of interfacial instability (due to viscosity jump) and layer instability (due to viscosity gradient) in appropriate proportions has been numerically demonstrated to be a necessary condition for monotonic as well as optimal non-monotonic profiles except in the limiting case of infinite time injection in which case maximum stabilization appears to result from pure layer instability. It has also been demonstrated numerically that the optimal non-monotonic viscous profiles can have better stabilization potential than the optimal monotonic profiles. Many other new features of this injection policy which have not been recognized before have been discussed.     

Mechanisms of Microscopic Displacement During Enhanced Oil Recovery in Mixed-Wet Rocks Revealed Using Direct Numerical Simulation

Transport in Porous Media - We demonstrate how to use numerical simulation models directly on micro-CT images to understand the impact of several enhanced oil recovery (EOR) methods on microscopic...     

Oil Recovery by Low Salinity Water Injection into a Reservoir: A New Study of Tertiary Oil Recovery Mechanism

Low salinity water injections for oil recovery have shown seemingly promising results in the case of clay-bearing sandstones saturated with asphaltic crude oil. Reported data showed that low salinity water injection could provide up to 20% pore volume (PV) of additional oil recovery for core samples and up to 25% PV for reservoirs in near wellbore regions, compared with brine injection at the same Darcy velocity. The question remains as to whether this additional recovery is also attainable in reservoirs. The answer requires a thorough understanding of oil recovery mechanism of low salinity water injections. Numerous hypotheses have been proposed to explain the increased oil recovery using low salinity water, including migration of detached mixed-wet clay particles with absorbed residual oil drops, wettability alteration toward increased water-wetness, and emulsion formation. However, many later reports showed that a higher oil recovery associated with low salinity water injection at the common laboratory flow velocity was neither necessarily accompanied by migration of clay particles, nor necessarily accompanied by emulsion. Moreover, increased water-wetness has been shown to cause the reduction of oil recovery. The present study is based on both experimental and theoretical analyses. Our study reveals that the increased oil recovery is only related to the reduction of water permeability due to physical plugging of the porous network by swelling clay aggregates or migrating clay particles and crystals. At a fixed apparent flow velocity, the value of negative pressure gradient along the flow path increases as the water permeability decreases. Some oil drops and blobs can be mobilized under the increased negative pressure gradient and contribute to the additional oil recovery. Based on the revealed mechanism, we conclude that low salinity water injection cannot be superior to brine injection in any clay-bearing sandstone reservoir at the maximum permitted injection pressure. Through our study of low salinity water injection, the theory of tertiary oil recovery has been notably improved.     

Influence of Microbial Growth on Hydraulic Properties of Pore Networks

From laboratory experiments it is known that bacterial biomass is able to influence the hydraulic properties of saturated porous media, an effect called bioclogging. To interpret the observations of these experiments and to predict possible bioclogging effects on the field scale it is necessary to use transport models, which are able to include bioclogging. For these models it is necessary to know the relation between the amount of biomass and the hydraulic conductivity of the porous medium. Usually these relations were determined using bundles of parallel pore channels and do not account for interconnections between the pores in more than one dimension. The present study uses two-dimensional pore network models to study the effects of bioclogging on the pore scale. Numerical simulations were done for two different scenarios of the growth of biomass in the pores. Scenario 1 assumes microbial growth in discrete colonies clogging particular pores completely. Scenario 2 assumes microbial growth as a biofilm growing on the wall of each pore. In both scenarios the hydraulic conductivity was reduced by at least two orders of magnitude, but for the colony scenario much less biomass was needed to get a maximal clogging effect and a better agreement with previously published experimental data could be found. For both scenarios it was shown that heterogeneous pore networks could be clogged with less biomass than more homogeneous ones.     

Pore Network Investigation of Trapped Gas and Foam Generation Mechanisms

Transport in Porous Media - The mobility of gas is greatly reduced when the injected gas is foamed. The reduction in gas mobility is attributed to the reduction in gas relative permeability and the...