Effluent Concentration Histories Research Articles

Stochastic and upscaled analytical modeling of fines migration in porous media induced by low-salinity water injection

Fines migration induced by injection of low-salinity water (LSW) into porous media can lead to severe pore plugging and consequent permeability reduction. The deep-bed filtration (DBF) theory is used to model the aforementioned phenomenon, which allows us to predict the effluent concentration history and the distribution profile of entrapped particles. However, the previous models fail to consider the movement of the waterflood front. In this study, we derive a stochastic model for fines migration during LSW flooding, in which the Rankine-Hugoniot condition is used to calculate the concentration of detached particles behind and ahead of the moving water front. A downscaling procedure is developed to determine the evolution of pore-size distribution from the exact solution of a large-scale equation system. To validate the proposed model, the obtained exact solutions are used to treat the laboratory data of LSW flooding in artificial soil-packed columns. The tuning results show that the proposed model yields a considerably higher value of the coefficient of determination, compared with the previous models, indicating that the new model can successfully capture the effect of the moving water front on fines migration and precisely match the effluent history of the detached particles.

Transport and retention of aqueous dispersions of superparamagnetic nanoparticles in sandstone

We evaluate the transport of surface-treated superparamagnetic iron-oxide nanoparticles in Boise-sandstone rocks by injecting aqueous dispersions of the particles into core plugs. Several different surface treatments yield stable dispersions of these particles, but provide very different transport characteristics. Effluent concentration histories are measured to obtain the particle retention in the rock. The results are used to optimize the particle surface coating so that the reservoir application requirements for the functional nanoparticles can be achieved. The application of interest here requires the nanoparticles to adsorb to oil/water interfaces.Our earlier experiments (Yu et al., 2010) showed that the paramagnetic nanoparticles stabilized with small negatively-charged citrate ligands have little retention in sedimentary rocks, but their preferred adsorption at the oil/water interfaces in rock pores was not achieved. A major improvement in surface coating optimization is achieved by creating a crosslinked polymer film that wraps around the nanoparticle so that it does not detach from the particle surface even under the harsh reservoir conditions. To fine-tune the coating to satisfy the reservoir application requirements, co-polymers and ter-polymers with different constituent monomers are employed. Nanoparticles stabilized with (poly-styrene sulfonate–alt-maleic acid) coating show a good adsorption tendency at the oil/water interfaces, while with very low adsorption at rock surface (~0.02mg/m2). The dispersion also has long-term stability even at high salinity (8wt% NaCl). Other polymers, such as (polyacrylic acid–r-butyl acrylate), (polyacrylic acid–b-styrene sulfonic acid), and (polyacrylic acid–r-butyl acrylate–b-styrene sulfonic acid), were also tested. The coating with the last polymer (PAA–PBA–PSS) provides a very low retention of particles in the rock, but only marginal preferred adsorption at oil/water interfaces.

Flow of dispersed particles through porous media — Deep bed filtration

Transport of dispersed particles in liquids through porous beds is widely recognized to occur in many industrial processes. The process of particle deposition from a colloidal suspension flowing through a porous medium is usually called deep bed filtration. The goal of the process can be either filtration of the particles by the granular media or, on the contrary, avoiding the particle filtration. Physical and chemical forces between suspended particles and grains of the media (collectors), particle size, fluid velocity and grain size play vital roles in the removal of particles from a suspension. Particle deposition can change the pore morphology and consequently the porosity of the porous medium and the local pressure gradient. This can cause permeability decline and therefore, loss of productivity or injectivity of wells. This article presents a comprehensive review of the literature related to deep bed filtration theories. Different mathematical models for evaluating both initial and transient stage of particle removal have been proposed during last decades. Trajectory analysis or convective diffusion equations have been used in microscopic modeling or so-called fundamental modeling to compute initial removal efficiency. Although these could predict the filter performance under favorable conditions but they underestimate the removal efficiency under unfavorable conditions. Hence, semi-empirical equations were developed for predicting removal efficiency under unfavorable conditions. Macroscopic or phenomenological modeling has been used to predict transient stage removal efficiency of deep bed filtration process. Predicting filter performance by this method requires the knowledge of functionality of filter coefficient. Filter coefficient can be obtained by using search optimization technique along with effluent concentration history. A review on different mathematical models for evaluating both initial and transient stage of particle removal process is presented.

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.

Parametric studies on the performance of cation exchange for the ammonium removal

Ion exchange performance to remove ammonium in drinking water was studied experimentally in batch and continuous operation systems under the various conditions. Data were collected using commercially available strongacid cationexchange resins of Na+ and H+ types. The performance was evaluated using equilibrium concentrations for the batch system or the effluent concentration histories for the continuous column system as a function of time or the solution volume passed through the experimental column until resins were exhausted. With high temperature or low initial feed concentration, ammonium removal characteristics of the batch system increase. At the solution concentrations of 0.5, 1.0, and 2.0 mg/L of NH4+-N and the temperatures of 15, 25, and 35 ‡C, the selectivity coefficients of resin were determined between 1.38 and 1.43 for Na+ type resin, and 3.22 and 3.47 for H+ type resin. The selectivity coefficient was correlated as a function of temperature using Kraus-Raridon equation. The breakthrough curves obtained from the continuous column operation give some results; i) with small column diameter or large column height, ii) with low initial feed concentration, iii) with low volumetric flow rate, or iv) with high solution temperature, the ammonium removal for the typical macroporous type resin increase. The results of this study could be scaled up and used as a design tool for the waterpurification systems of the drinking water treatment processes.

Effect of Deposition in Deep-Bed Filtration: Determination and Search of Rate Parameters

Particle deposition in deep-bed filters (porous media) is, by nature, an unsteady-state process and the extent of deposition plays an important role in determining filter performance. A general method of establishing the relationship between deposition rate and the extent of deposition from effluent concentration history of filters is presented. The efficacy of the method is examined and its utility demonstrated through its applications to certain experimental data.

Analysis of high-dispersion tracer tests in cores containing polymer gels

The analysis of a tracer experiment requires care when one of the fluid phases within the porous medium is immobile but miscible with the tracer carrier fluid. This situation gives rise to high levels of dispersion ( Pe<10) and interphase mass transfer. We show that applying the classical analytical expression for the tracer concentration in an infinite one-dimensional core introduces significant mass balance errors at low Peclet numbers, even though a good fit to the experimental data may be obtained. Next, we present a rapid test of whether mass transfer into the immobile phase is important. The test is based on the observation that theoretical effluent concentration histories from a finite core in the absence of interphase mass transfer span a well-defined and relatively limited area on a plot of concentration vs. time. If an experimental effluent history does not lie within this area, a mass transfer model must be applied. Finally, we show that at high mass transfer rates, the effluent history becomes insensitive to the volume fractions of the miscible fluid phases. Thus, it can be difficult to determine a unique set of fitting parameters for experiments in this regime. To avoid this difficulty, experiments designed to determine miscible, immobile phase volumes should be conducted at high flow rates (low residence times) or with slowly diffusing tracers.

A Continuous Stirred Tank Reactor Study on Chromic Acid Removal by Ion Exchange

ABSTRACT Dilute chromic acid removal by anion exchange was studied using a continuous stirred tank reactor (CSTR) system. A rate model based on film diffusion control was formulated for quantitative study on the chromate removal. For simplicity, the rate and mass balance equations were formulated for total Cr(VI) concentration. Equations were derived for the effluent concentration history as well as the time dependent Cr(VI) concentration in the resin. The derived equations for solid and liquid phase Cr(VI) concentration variations were tested and verified by the experimental results obtained. Effects of various operating conditions, such as resin size, feed concentration, and flow rate, were also discussed.

Development of a membrane-based vapor-phase bioreactor

A vapor-phase bioreactor has been developed utilizing porous metal membranes in a cylindrical design employing radial flow as opposed to traditional axial flow for the vapor stream. The system was evaluated for the biodegradation of p-xylene (p-xylene) from a water-saturated air stream by Pseudomonas putida ATCC 23973 immobilized onto sand. The biocatalyst was placed in the annular space between two cylindrical, porous stainless-steel membranes. Details of the reactor system are presented along with biological data verifying system performance. The feed flow rate and p-xylene concentration were varied between 60 and 130 cm(3)/min and 15-150 ppm, respectively. Continuous reactor operation was maintained for 80-200 h with removal efficiencies (based onp-xylene disappearance) between 80 and 95%. The effluent concentration histories were compared to determine the operating range of the bioreactor.

Polydispersed aerosol filtration in granular media

Granular filtration of polydispersed aerosols were studied experimentally. The objectives of the study were to investigate the effect of deposited particle size on the increase of the unit collector efficiency and to quantify the increase for predicting filter performance. An algorithm for determining the effluent concentration histories of polydispersed aerosol filtration was presented. Together with the correlations developed in this work, prediction of filter performance can be made readily. Good agreements between experiments and predictions based on the correlations established in this work were observed.

Analysis of the Transient Behavior of Deep-Bed Filtration

A model for clogged granular media which is presented and is based on the assumption that deposition leads to the presence of a deposit layer outside packing grains. The deposit layer is assumed to be nonuniform in thickness. The layer, however, is considered to be porous and therefore permits liquid flow through it. Conceptually, the model is an extension of the classical work of Happel and is a generalization of several sphere-in-cell models proposed by a number of investigators in recent years. With the presence of a porous deposit layer, liquid flows into the layer instead of being diverted away as in the case of a solid surface. As a result, deposition is enhanced. The extent of liquid flow into the deposit layer is a function of the layer thickness as well as its structure. The increase in deposition is expressed as the ratio of the instantaneous collection efficiency to the initial collection efficiency when the filter grains are free of deposited particles. The collection efficiency is calculated by assuming that the surface interactions between particle and filter grains are favorable and the dominant mechanism of collection is by interception, which is valid if the Brownian diffusion effect is insignificant. Predictions of effluent concentration histories based on this model were found in reasonably good agreement with experimental results.

Retention of toxic gases by modified carbon in fixed beds

A new model for the retention of toxic gas by modifed carbon in fixed-bed operations is presented. The retention of the toxic gas is assumed to be effected through two independent pathways: physical adsorption and chemical reaction between the toxic gas and carbon impregnants with the reaction taking place instantaneously. Reasonable agreement was obtained between experiments and predictions on breakthrough time and effluent concentration histories based on the model.

On the Estimation of Cation Exchange Parameters from Column Displacement Experiments

AbstractA procedure is presented for estimating cation exchange capacity (CEC) and exchange selectivity coefficients from miscible displacement experiments on undisturbed soil columns. The procedure provides an alternative to batch experiments and is applicable to scenarios involving either binary homovalent exchange or binary monodivalent exchange. Gapon's exchange equation is used in the latter case. Parameters are determined by nonlinear, least‐squares inversion of column effluent concentration histories. The procedure requires that hydraulic flux and total solution normality be kept constant. It is also assumed that ion exchange takes place instantaneously. When this assumption is violated, it is still possible to obtain a good description of the observed data, but the parameter estimates may be meaningless. The feasibility of estimating the dispersion coefficient in the advection‐dispersion equation along with the ion exchange parameters is evaluated. Results indicate that this is generally not possible for continuous injection experiments, but much better results are obtained for pulse injection experiments.

Simplified Models for Design of Fixed‐Bed Adsorption Systems

Fixed‐bed adsorber dynamics have been predicted successfully using the homogeneous surface diffusion model (HSDM) for over 100 adsorbate‐adsorbent systems which include a number of the possibly harmful organics that may be found in drinking water and wastewater. Solutions to the HSDM for fixed‐bed adsorber systems have been developed and can be used to: (1) Plan the scope of pilot‐scale studies by identifying least‐cost fixed‐bed adsorber operations; (2) interpret pilot‐scale test results; and (3) design full‐scale adsorbers if the HSDM can simulate pilot‐scale data. To facilitate the use of these solutions, the important model parameters and their effect on adsorber performance has been discussed; additionally, a detailed procedure for determining the effluent concentration history profile has been presented. Techniques to calculate the empty bed contact time of the mass transfer zone and the liquidand solid‐phase concentrations within the fixed bed have also been provided.

Design of Carbon Beds to Remove Humic Substances

The homogeneous surface diffusion model (HSDM) was found capable of simulating effluent concentration history profiles for a commercial humic acid, a peat fulvic acid (PFA), and a coagulated PFA. The model successfully simulated column data for four granular activated carbons (GAC), several empty bed contact times (EBCTs), two GAC mesh sizes, several infuent concentrations, and several hydraulic loadings. Accordingly, the HSDM was used to evaluate the impact of process design variables on cost and adsorber performance for the removal of these humic substances. Model calculations were carried out to evaluate the impact of EBCT and influent concentration on adsorber performance. It was found that for each doubling of EBCT in the range of 3.77–75.4 minutes the bed life of the carbon was more than doubled. For 50% reductions in influenct concentration, the bed life was about doubled for influent TOC concentrations ranging from 1–20 mg/L. By estimating the cost of treatment for various EBCTs, the most economical EBCT was determined for a single adsorber, for two adsorbers in-series, for two adsorbers in-parallel, and for three adsorbers in-parallel. Two adsorbers operated in-parallel were found to be more economical than a single adsorber, or two adsorbers operated in-series. The lowest cost operation was for three adsorbers operated in-parallel. Treatment costs for two adsorbers in-parallel were found to decrease with increasing treatment plant size, decreasing influent concentration, and decreasing GAC particle size.

Column Dynamics of Ternary Ion Exchange Part II: Solution Mass Transfer Controlling

The nonequilibrium theory for column dynamics of multicomponent ion exchange has been evaluated using the ternary system Ag-Na-H at a total solution concentration of 0.05 N (0.05 M) so that solution mass transfer controls the exchange. Ternary mass transfer coefficients have been related to binary values by both simple (constant) and improved (concentration-dependent) Fick's law models, as well as by simple and improved Nernst-Planck models. Binary coefficients of all four types were obtained directly from constant-pattern binary breakthroughs and the individual-component Nernst-Planck coefficients were derived from the binary coefficients. Using each of the four models, ternary effluent concentration histories (ECH) were predicted using the method of characteristics. All the models predicted effluent concentration histories that matched closely the experimental ones, indicating that either model may be used satisfactorily for prediction; the simple models are preferred to the improved ones since they contain fewer parameters.

Column Dynamics of Ternary Ion Exchange Part I: Diffusional and Mass Transfer Relations

The complete multicomponent ion-exchange diffusion equations based on irreversible thermodynamics and their approximations by the Nernst-Planck model or the Fick's law model are all put in the same algebraic form. Their differences occur only in the definition of the diffusion coefficients. Multicomponent diffusion coefficients. Multicomponent diffusion coefficients are related to those in binary systems by either the Nernst-Planck or Fick's law model. Using a linear driving force approximation for the flux equations, similar relationships are developed for estimating multicomponent (ternary) mass transfer coefficients based on the analysis of binary data. Hence from binary data and these relationships, multicomponent effluent concentration histories may be predicted numerically.