Suspensions In Porous Media Research Articles

Enhanced transport of K-nZVI by bentonite suspensions in porous media

Enhanced transport of K-nZVI by bentonite suspensions in porous media

Shape and surface property effects on displacement enhancement by nanoparticles

This work studies the mechanisms of shape and surface property effects on multiphase displacement enhancement by nanoparticle suspensions in porous media. Three representative nanoparticles with promising industry applications, namely silica nanoparticles, graphene oxide and hydroxylated carbon nanotubes have been considered comprehensively. The correspondence between particle shape and surface property, interfacial adsorption behaviors, and displacement patterns has been analyzed systematically. Significant differences in adsorption tendencies and consequences are revealed via adsorption characterizations with theoretical derivations and microscopic modeling. For liquid–liquid interfacial adsorption, sheet-like and fibrous shapes with amphiphilicity are more beneficial to adsorption and retention at interface, which promotes dynamic interfacial tension reduction and emulsion stabilization. For solid surface adsorption, spherical and fibrous shapes with hydrophilicity are more favorable for formation of nanoscale rough structures, which induces the development and maintenance of wetting films. Visualization and quantification of multiphase displacement in complex structures via microfluidic experiments enable us to evaluate the relative performances and unravel displacement enhancement modes. Hydroxylated carbon nanotubes exhibit optimal performance, followed by graphene oxide and then silica nanoparticles, with clear distinction in interfacial phenomena. Enhanced liquid–liquid interfacial adsorption behaviors result in the invasion into un-swept regions with sweeping efficiency enhancement, whereas enhanced solid surface adsorption behaviors drive the detachment of defending phase in the form of isolated ganglia.

Modeling transport and filtration of nanoparticle suspensions in porous media.

Recently membrane filters have gained in significance due to the need to provide protection against airborne pollution. A question of importance, and some controversy, is the efficiency of filters for small nanoparticles with diameters below 100nm as these are considered particularly dangerous due to possible penetration into the lungs. The efficiency is measured by the number of particles blocked by the pore structure after passing though the filter. To study the penetration into pores by nanoparticles suspended in a fluid, a stochastic transport theory based on an atomistic model is used to calculate particle density and flow within the pores, resulting pressure gradient, and filter efficiency. The importance of pore size relative to particle diameter and of the parameters of the pore wall interactions are investigated. The theory is applied to aerosols in fibrous filters and found to reproduce common trends in measurements. As particles enter the initially empty pores on relaxation to the steady state the small penetration measured at the onset of filtration increases faster in time the smaller the nanoparticle diameter. Control of pollution by filtration is achieved by strong repulsion of pore walls for particle diameters greater than twice the effective pore width. For smaller nanoparticles the steady-state efficiency decreases as the pore wall interactions weaken. Effective efficiency is increased when the suspended nanoparticles inside the pores combine into clusters of sizes greater than the filter channel width.

Insights into the Effects of Salinity on the Transport Behavior of Polymer-Enhanced Branched-Preformed Particle Gel Suspension in Porous Media

The branched-preformed particle gel (B-PPG) is a novel viscoelastic particle gel used for improving sweep efficiency and enhancing oil recovery in a heterogeneous mature reservoir. To improve the performance of B-PPG, partially hydrolyzed polyacrylamide (HPAM) is used to increase the viscosity and to prepare a homogeneous B-PPG suspension. Although some encouraging progress has been made in the application of polymer-enhanced B-PPG suspension, its transport behavior in porous media is still unclear, which is crucial for its application in enhanced oil recovery (EOR) in a heterogeneous reservoir. Due to the complex reservoir condition of different brine salinities, the physiochemical property of polymer-enhanced B-PPG suspension as well as its transport behavior in porous media can be affected, which may lead to unsatisfactory results. Understanding the effects of salinity on the transport behavior of polymer-enhanced B-PPG suspension in porous media is of vital importance in figuring out the flow behavior and improving the sweep efficiency in the mature reservoir. In this study, the effects of salinity on the swelling ratio, particle size, viscosity property, and suspension stability of B-PPG and polymer-enhanced B-PPG suspension were studied. Meanwhile, sand pack flow experiments were conducted to study the transport behavior of polymer-enhanced B-PPG suspension in porous media. The results show that when the brine salinity increases, the swelling ratio and particle size of B-PPG, as well as the viscosity and the suspension stability of polymer-enhanced B-PPG suspension all demonstrate a decreasing trend. In the range of 3550–10 651 mg·L–1, as the brine salinity increases, the resistance factor decreases and the transportation of polymer-enhanced B-PPG suspension in porous media becomes easier. In this case, the ratio of swollen B-PPG particle diameter to the pore throat diameter turns out to be the determining factor that governs the transport behavior. However, when the brine salinity is higher than 10 651 mg·L–1, with the increase of brine salinity, the resistance factor increases. As a result, the effects of viscosity and suspension stability of polymer-enhanced B-PPG suspension become more prominent.

Uncertainties associated with laboratory-based predictions of well index and formation damage

The filtration and the formation damage coefficients are the parameters in the mathematical models determining the degree of permeability decline during flow of colloidal suspensions in porous media. Measuring pressure in 3 points along the core allows simultaneous calculation of the filtration and the formation damage coefficients. We have calculated the combined standard uncertainties of the filtration and the formation damage coefficients. Application of the law of propagation of uncertainty to Darcy’s equation and the weighted least squares method to impedance index curves for the half- and the overall core resulted in the values of their slopes and intercepts, and the respective combined standard uncertainties. Combination of the values of these slopes into a transcendental equation and solving it analytically fully determined the filtration and formation damage coefficients with their relative combined standard uncertainties being significantly lower than those reported in the literature.

A Deep Bed Filtration Model of Two-Component Suspension in Dual-Zone Porous Medium

In the paper, a mathematical model for the filtration of two-component suspensions in a dual-zone porous medium is considered. The model consists of the mass balance equations, the kinetic equations for active and passive zones of porous medium for each component of the suspension and Darcy’s law. To solve the problem, a numerical algorithm for computer experimentation is developed on the basis of finite difference method. Based on numerical results, the main characteristics of suspension filtration in a porous medium are established. Influences of model parameters on transport and deposition of suspended particles of two-component suspension in porous media are analysed. It is shown that the polydispersity of suspension and multistage nature of the deposition kinetics can lead to various effects that are not characteristic for the transport of one-component suspensions with one-stage particle deposition kinetics. In particular, in distribution of the concentration of suspended particles in a moving fluid non-monotonic dynamics are obtained at individual points in the medium. It is shown that at the points of the medium near to the input section, the concentration of deposited particles can reach partial capacities in the passive zone.

Tricoupled hybrid lattice Boltzmann model for nonisothermal drying of colloidal suspensions in micropore structures

A tricoupled hybrid lattice Boltzmann model (LBM) is developed to simulate colloidal liquid evaporation and colloidal particle deposition during the nonisothermal drying of colloidal suspensions in micropore structures. An entropic multiple-relaxation-time multirange pseudopotential two-phase LBM for isothermal interfacial flow is first coupled to an extended temperature equation for simulating nonisothermal liquid drying. Then the coupled model is further coupled with a modified convection diffusion equation to consider the nonisothermal drying of colloidal suspensions. Two drying examples are considered. First, drying of colloidal suspensions in a two-pillar micropore structure is simulated in two dimensions (2D), and the final configuration of colloidal particles is compared with the experimental one. Good agreement is observed. Second, at the temperature of 343.15 K (70^{∘}C), drying of colloidal suspensions in a complex spiral-shaped micropore structure containing 220 pillars is simulated (also in 2D). The drying pattern follows the designed spiral shape due to capillary pumping, i.e., transport of the liquid from larger pores to smaller ones by capillary pressure difference. Since the colloidal particles are passively carried with liquid, they accumulate at the small menisci as drying proceeds. As liquid evaporates at the small menisci, colloidal particles are deposited, eventually forming solid structures between the pillars (primarily), and at the base of the pillars (secondarily). As a result, the particle deposition conforms to the spiral route. Qualitatively, the simulated liquid and particle configurations agree well with the experimental ones during the entire drying process. Quantitatively, the model demonstrates that the evaporation rate and the particle accumulation rate slowly decrease during drying, similar to what is seen in the experimental results, which is due to the reduction of the liquid-vapor interfacial area. In conclusion, the hybrid model shows the capability and accuracy for simulating nonisothermal drying of colloidal suspensions in a complex micropore structure both qualitatively and quantitatively, as it includes all the required physics and captures all the complex features observed experimentally. Such a tricoupled LBM has a high potential to become an efficient numerical tool for further investigation of real and complex engineering problems incorporating drying of colloidal suspensions in porous media.

Modeling the transport and retention of polydispersed colloidal suspensions in porous media

Colloid suspensions commonly exhibit a distribution of sizes, but most transport models only consider a single colloid size. A mathematical model was therefore developed to describe the advective and dispersive transport and first-order retention and release of a stable or aggregating polydispersed colloid suspension in porous media. The colloid size distribution was described using a unimodal or a bimodal lognormal probability density function (PDF), and Brownian aggregation was considered by making lognormal PDF parameters a function of time. Filtration theory was used to predict the retention rate coefficients for the various colloid sizes. The amount of retention for a stable polydispersed suspension was highly dependent on the colloid size distribution parameters, especially for a bimodal lognormal PDF. Increasing the distribution variance produced hyper-exponential retention profiles and an increase or a decrease in colloid retention depending on whether the medium colloid size was close to the optimum size for transport. Aggregation produced a similar decrease in the breakthrough concentrations with injection time as ripening, especially when the sticking efficiency was low. Aggregation effects were much more pronounced at higher input concentration levels, which also produced retention profiles that were increasingly hyper-exponential. Simulation results indicate that the colloid size distribution of stable and aggregating polydispersed suspensions always becomes more uniform and approaches the optimum transport size with increasing distance, suggesting that consideration of polydispersed suspensions is of primary importance near the injection surface.

A Study on Particle Suspension Flow and Permeability Impairment in Porous Media Using LBM–DEM–IMB Simulation Method

The paper studies the particle retention and permeability impairment in porous media. This problem results from the re-injection of produced groundwater during oil production into the oilfields in order to reduce environmental damage. The lattice Boltzmann method (LBM) is used to simulate the fluid flow. The discrete element method (DEM) is adopted to simulate the particle motion. The fluid–solid interactions are simulated using the immersed moving boundary method (IMB). Based on the coupling LBM–DEM–IMB method, the paper studies the effect of particle diameter, flow rate, particle volume fraction and injection amount on the particle retention and permeability impairment. Results indicate that larger particle diameter, lower flow rate, higher volume fraction and more particle injection lead to more severe permeability impairment. In order to further study the effect of particle suspensions on heterogeneous reservoirs, a two-channel model with different permeabilities is established. The simulations show that smaller particles tend to retain in the low permeable channel and its permeability impairment is more severe. On the contrary, larger particles can reduce the permeability of high permeable channel, but they can protect the permeability of low permeable channel due to the mechanism of membrane filtration. Therefore, the sweep efficiency and oil recovery of the heterogeneous reservoirs can be improved by re-injecting produced groundwater after reasonable pretreatment. The re-injection also reduces environmental damage resulting from the large amounts of produced water in petroleum engineering. This paper provides some references for general studies on the flow of particle suspension in porous media.

Simulation of deformable preformed particle gel propagation in porous media

Preformed particle gel (PPG) treatment is a proven cost‐effective method for improving oil recovery. Although PPG system has a suspension‐like property, it has different propagation rules from the rigid particle suspension in porous media because of its good deformation property. In this study, an advanced phenomenological model of PPG propagation in porous media is presented. The model includes both PPG plugging and restarting behaviors. Log‐normal and normal distribution functions have been introduced in this model to calculate the PPG plugging probability. Power‐law equation is used to calculate the PPG restarting rate. This method can represent the commensurate relation between PPG and throat size. Then, the equations are solved numerically, using an explicit finite‐difference formulation in conjunction with a fourth‐order Runge‐Kutta method. The results match favorably with several laboratory experiments. Finally, the propagation rules and sensitivity analysis of PPG size, permeability and injection rate to propagation rules, and permeability reduction are performed. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4628–4641, 2017

Water retention against drying with soft-particle suspensions in porous media.

Polymers suspended in granular packings have a significant impact on water retention, which is important for soil irrigation and the curing of building materials. Whereas the drying rate remains constant during a long period for pure water due to capillary flow providing liquid water to the evaporating surface, we show that it is not the case for a suspension made of soft polymeric particles called microgels: The drying rate decreases immediately and significantly. By measuring the spatial water saturation and concentration of suspended particles with magnetic resonance imaging, we can explain these original trends and model the process. In low-viscosity fluids, the accumulation of particles at the free surface induces a recession of the air-liquid interface. A simple model, assuming particle transport and accumulation below the sample free surface, is able to reproduce our observations without any fitting parameters. The high viscosity of the microgel suspension inhibits flow towards the free surface and a drying front appears. We show that water vapor diffusion over a defined and increasing length sets the drying rate. These results and model allow for better controlling the drying and water retention in granular porous materials.

Modeling Deep Bed Filtration Considering Limited Particle Retention

The classic deep bed filtration model (CDBFM) has been widely used for predicting transport and retention of particulate suspensions in porous media. In the CDBFM, the filtration coefficient function is assumed to be dependent of the retained particle concentration, and the boundary conditions are fixed at the porous media inlet cross section. However, if particle retention is limited, no more retention occurs (filtration coefficient equals zero) in regions where maximum retention (jamming limit) is reached. In this article, a model for deep bed filtration considering limited retention is proposed and analytical solutions are obtained. In cases where jamming limit is reached, the well-known CDBFM and the proposed model significantly differ from each other. Contrary to the CDBFM solutions, the obtained solutions show that concentrations along porous media are highly influenced by maximum retention front, which propagates with velocity independent of filtration coefficient.

Deep bed and cake filtration of two-size particle suspension in porous media

Abstract Formation of low permeable external filter cake during drilling and water injection has been widely reported in the literature. It may cause significant decrease in well index. The process is very sensitive to size distribution of injected particles. We propose a new mathematical model for cake formation with deep bed filtration for two-particle-size injection. The basic equations account for three stages: formation of cake from large particles with simultaneous deep bed filtration of small particles; small particle capture in the cake with formation of the internal cake inside the external cake; build-up of the uniform cake from the mixture of two-size particles. The analytical model is derived for three stages. Two regimes of the cake formation are identified, which correspond to the high and low concentrations of injected small particles. The laboratory coreflood with two-particle-size suspension injection with monitoring the rate and pressure drop along the core is performed. The matched mathematical model shows good agreement with the laboratory data.

Experimental investigation for colloid migration in porous media under particle-rock repulsion

Electrophoretic mobilities of carboxylate-modified latex microspheres and zeta potential of soda-lime glass beads were measured at zero ionic strength and high pH. Surface potential for latex microspheres was calculated using Ohshima’s theory for soft particles. Total potential of interaction between colloidal particles and engineered porous medium evaluated according to DLVO theory showed negligibly small secondary minimum, a high potential barrier, and a primary minimum. Such conditions favour particle-bead repulsion resulting in size exclusion being a major particle retaining mechanism. Normalised outlet concentration is inverse function of particle concentration. Concentration of captured particles reduced along the length of the column in downstream direction. An analytical model for deep bed filtration of suspension in porous media and straining under size exclusion capture mechanism is developed and validated by laboratory tests on suspension flow in engineered media. The model is successfully matched with the results from column experiments, predicting the suspended particle concentrations at the outlet.

Transport and straining of suspensions in porous media: Experimental and theoretical study

An analytical model for deep bed filtration of suspension in porous media and straining under size exclusion capture mechanism is developed and validated by laboratory tests on suspension flow in engineered media. The fraction of swept particles is introduced in the inlet boundary condition. The model is successfully matched with the results from column experiments, predicting the suspended particle concentrations at the outlet.

Particle Detachment Under Velocity Alternation During Suspension Transport in Porous Media

Flow of suspensions in porous media with particle capture and detachment under alternate flow rates is discussed. The mathematical model contains the maximum retention concentration function of flow velocity that governs the particle release and is used instead of equation for particle detachment kinetics from the classical filtration model. An analytical model for suspension injection with alternate rates was derived, and a coreflood by suspension with alternate rates was carried out. The modelling and laboratory data are in a good agreement, which validates the modified particle detachment model with the maximum retention function.

Theoretical Definition of Formation Damage Zone With Applications to Well Stimulation

Flow of particulate suspension in porous media with particle retention and consequent permeability reduction is discussed. Using analytical model for suspension injection via single well, the permeability damage zone size was defined and expressed by transcendental equation. Analysis of field data shows that usually the size of damaged zone does not extend more than 1 m beyond the injector. The definition of damage zone size is used for design of well stimulation via deposition removal.

A stochastic theory for deep bed filtration accounting for dispersion and size distributions

We develop a stochastic theory for filtration of suspensions in porous media. The theory takes into account particle and pore size distributions, as well as the random character of the particle motion, which is described in the framework of the theory of continuous-time random walks (CTRW). In the limit of the infinitely many small walk steps we derive a system of governing equations for the evolution of the particle and pore size distributions. We consider the case of concentrated suspensions, where plugging the pores by particles may change porosity and other parameters of the porous medium. A procedure for averaging of the derived system of equations is developed for polydisperse suspensions with several distinctive particle sizes. A numerical method for solution of the flow equations is proposed. Sample calculations are applied to compare the roles of the particle size distribution and of the particle flight dispersion on the deposition profiles. It is demonstrated that the temporal flight dispersion is the most likely mechanism forming the experimentally observed hyperexponential character of the deposition profiles.

Flow Characteristics of Microbubble Suspensions in Porous Media as an Oxygen Carrier

AbstractMicrobubble suspensions were generated as an oxygen carrier for aerobic biodegradation, and their flow characteristics in porous media were investigated. Commercial surfactants including sodium dodecyl sulfate (SDS), and dodecylethyldimethylammonium bromide (DEDAB), saponin (a natural surfactant), and collagen (a protein hydrolysate) were examined as base materials for generating microbubble suspensions. Among them, 2×CMC (critical micellar concentration) of SDS, DEDAB, and saponin developed microbubble suspensions with the highest gas hold‐up and half‐drainage time. Visualization of the flow patterns in sand showed that the microbubble suspensions were separated into a liquid and gas phase directly after injection, showing much faster movement of liquid phase flow. The gas front of the microbubble suspensions flowed in a plug‐flow manner, particularly in cases of SDS and DEDAB. The experimental results from both homogeneous and heterogeneous cells confirmed that the microbubble flow could overcome the heterogeneity in porous media. However, the plug‐flow characteristics and flow propagation of the microbubble suspensions to the low‐permeability zone was accompanied by a large pressure drop, which needs to be considered for future field application.

The inverse problem of determining the filtration function and permeability reduction in flow of water with particles in porous media

Deep bed filtration of particle suspensions in porous media occurs during water injection into oil reservoirs, drilling fluid invasion of reservoir production zones, fines migration in oil fields, industrial filtering, bacteria, viruses or contaminants transport in groundwater etc. The basic features of the process are particle capture by the porous medium and consequent permeability reduction. Models for deep bed filtration contain two quantities that represent rock and fluid properties: the filtration function, which is the fraction of particles captured per unit particle path length, and formation damage function, which is the ratio between reduced and initial permeabilities. These quantities cannot be measured directly in the laboratory or in the field; therefore, they must be calculated indirectly by solving inverse problems. The practical petroleum and environmental engineering purpose is to predict injectivity loss and particle penetration depth around wells. Reliable prediction requires precise knowledge of these two coefficients. In this work we determine these quantities from pressure drop and effluent concentration histories measured in one-dimensional laboratory experiments. The recovery method consists of optimizing deviation functionals in appropriate subdomains; if necessary, a Tikhonov regularization term is added to the functional. The filtration function is recovered by optimizing a non-linear functional with box constraints; this functional involves the effluent concentration history. The permeability reduction is recovered likewise, taking into account the filtration function already found, and the functional involves the pressure drop history. In both cases, the functionals are derived from least square formulations of the deviation between experimental data and quantities predicted by the model.