A filtration model for the flow of dilute,stable emulsions in porous media—I. Theory

Flow of dilute, stable emulsions in porous media is important in several oil recovery processes. Because underground media have relatively low permeabilities, the emulsion drop sizes may overlap the pore sizes. Hence, strong interaction occurs between the emulsion droplets and pore constrictions, and local flow redistribution occurs within the porous medium. To predict quantitatively how emulsions are transported in underground media, a theoretical model is required which correctly accounts for the interactions between the flowing droplets and the pore walls.In Part I of this work, we present a simplified filtration model describing the flow of stable, dilute emulsions in unconsolidated porous media. In the model, emulsion drops are captured in pores by straining and interception and, thus, reduce the overall permeability. Transient flow behaviour is characterized by there parameters: a filter coefficient, a flow-redistribution parameter and a flow-restriction parameter. The filter coefficient controls the sharpness of the emulsion front, the flow-redistribution parameter dictates the steady-state retention, as well as the flow redistribution phenomenon, and the flow-restriction parameters describes the effectiveness of retained drops in reducing permeability.Critical comparison is made between the new filtration theory and the current continuum—viscous and retardation models for emulsion flow in porous media. Only the filtration picture is able to explain all the experimental observations. Quantitative comparison between the filtration flow theory and experiment is presented in Part II.     

Dispersion in flow through porous media—II. Two-phase flow

In this paper we extend our previous study (Sahimi et al., 1986, Chem. Engng Sci.41, 2103–2122) of dispersion processes in porous media occupied by two fluid phases. We report results of Monte Carlo investigations of dispersion in two-phase flow through disordered porous media represented by square and simple cubic networks of pores of random radii. The percolation theory of Heiba et al. (1982, SPE 11015, 57th Annual Fall Meeting of the Soc. Petrol. Engrs) is used to determine the statistical distribution of phases in the porespace. One of the phases is assumed to be strongly wetting on the porewall in the presence of the other phase. A pore size distribution is chosen which yields through the percolation theory of Heiba et al. network relative permeabilities that are in agreement with the available experimental data.As in one-phase flow dispersion is diffusive in the cases simulated, i.e. it can be described by the convective-diffusion equation. Longitudinal dispersivity in a given phase rises greatly as the saturation of that phase approaches residual (i.e. its percolation threshold); transverse dispersivity also increases, but more slowly. As residual saturation of a phase is neared, the backbone of the subnetwork occupied by the phase becomes increasingly tortuous, with local mazes spotted along it that are highly effective dispersers. Dispersivities are found to be phase, saturation and saturation history dependent.Some limited Monte Carlo experiments with a residence time representation of the effects of deadend paths within a phase or reversible adsorption on the pore walls demonstrate that the approach developed can be extended to study the influence of such delay mechanisms on the dispersion process.     

The aerobic and peroxide-induced coupling of aqueous thiols—II. Reaction mechanisms,model analysis,and a comparison of the model and experimental results

Kinetic results of the preceeding paper are used to formulate the most probable reaction mechanisms for the peroxide-induced and aerobic coupling of aqueous thiols. Parameters in the proposed mechanisms are evaluated for n-propylthiol using the results of independent measurements. A remarkably good agreement is achieved between the model and experimental results.The peroxide reaction, which is not affected by either copper ion or radical scavengers, is shown to be a nucleophilic substitution (S_N 2) reaction which proceeds by a two-step mechanism as follows: RS⁻ + H₂O₂

RSOH + OH⁻ rate-determining RS⁻ + RSOH → RSSR + OH⁻ In the reaction the thiolate anion acts as the nucleophile while hydrogen peroxide and the transient sulfenic acid, RSOH, function as electrophiles.The most plausible mechanism for the copper-catalyzed, aerobic coupling reaction is as follows: Cu⁺ (RSSR)₂⁺ + RS⁻

(RSSR)Cu⁺ (RS⁻) + RSSR (RSSR)Cu⁺ (RS⁻) + RS⁻

(RSSR)Cu⁺ (RS⁻)₂⁻ (RSSR)Cu⁺ (RS⁻)₂⁻ + O₂

Cu⁺(RSSR)₂⁺ + HO₂⁻ rate-determining RS⁻ + H₂O₂

RSOH + OH⁻ rate-determining RS⁻ + RSOH → RSSR + OH⁻ For the n-propylthiol substrate, the pertinent parameters in the mechanism are 1n (K₁) = −11,000 K/T + 33.6, where K₁ is dimensionless, 1n (K₂) = 4270 K/T −10.5, where K₂ is in 1/mol, 1n (k₂) = 30.0 − 5260 K/T, and 1n (k₂) = 26.8 − 6190 K/T, where k₁ and k₂ are in 1/(mol min).     

Multiplicity features of porous catalytic pellets—III. Uniqueness criteria for the lumped thermal model

Exact uniqueness criteria are presented for a porous catalytic pellet in which a p-th order exothermic reaction occurs using a lumped thermal model, which accounts for intraparticle concentration gradients and assumes that the pellet temperature is uniform but different from that of the surrounding fluid. In addition, we determine the boundaries of the parameter regions in which five solutions exist in either cylindrical or spherical pellets.     

A CFD model for gas uniform distribution in turbulent flow for the production of titanium pigment in chloride process☆

The fluid dynamic behavior of feeding gas (TiCl4) in an annular channel affects the combination of O2 and TiCl4 in an oxidation reactor, a key piece of equipment in titanium pigment production. The numerical procedure was validated by a 3-dimensional gas flow in the annular channel. Applying the validated model, the flow character-istics of TiCl4 in the oxidation reactor with a tangential inlet were simulated and characterized. The flow distribu-tion with five rectifying rings of different structure was simulated and analyzed. The results showed that the rectifying ring improved the distribution uniformity of the pressure and outlet velocity. Compared to the original case without a rectifying ring, the non-uniformity of the pressure and outlet velocity could be reduced by up to 91%and 69%respectively. The rectifying ring #5, which can be instal ed and adjusted easily, is more effective in realizing even distribution. In addition, instal ation of the rectifying ring effectively reduced the circulating flow in an annular channel as well as the total energy loss.     

A cylindrical photoreactor irradiated from the bottom—II. Models for the local volumetric rate of energy absorption with polychromatic radiation and their evaluation

This study of the radiation field generated in a cylindrical photoreactor irradiated from the bottom presents the theoretical foundations of a method for the experimental verification of three different radiation models. The expressions representing the local volumetric rate of energy absorption (LVREA) were formulated and applied to the prediction of the rate of an actinometric reaction. This reaction takes place inside a microreactor operated in a batch recycling system with polychromatic radiation.The values obtained portray the same behaviour as that of the energy densities calculated previously (Part I), thus becoming a valid, accurate method for the experimental measurement of the absolute values of the radiation field that are sought after (volumetric rate of energy absorption).The proposed approach is able to produce quasi-point values of the absolute values of the VREA at the microreactor as an excellent approximation to the absolute values of the LVREA (local measurements).The present work also points out the qualitative and quantitative discrepancies of the results predicted by the line models when compared with those of the extense source model with volumetric emission.     

Unified model for the prediction of consecutive solid–liquid filtration and expression at the constant pressure

Unified nonlinear model is proposed for the prediction of consecutive solid–liquid filtration and expression at the constant pressure. This model is based on the Darcy–Terzaghi filtration-consolidation equations modified to consider power-law pressure dependence of the specific cake resistance, and transforming Darcy law to the linear form. The model considers nonuniform structure of compressible filter cakes obtained by filtration and following expression. The profiles of local compressive pressure and local cake characteristics are simulated and compared for different moderately and highly compressible filter cakes (H.K. kaolin, CaCO₃, silica, activated sludge) based on the analytical and numerical solutions of the model. It is shown that the behavior of solid–liquid expression depends from the initial structure of compressed materials. Consolidation ratio U of the filter cakes with initially nonuniform structure formed by filtration differs from that of semi-solid materials with initially uniform structure. Different methods of determination of consolidation coefficient are analyzed and compared for nonuniformly structured filter cakes.     

Measurement and analysis of particle—particle interaction in a cocurrent flow of particles in a dilute gas—solid system

The experimental apparatus of Arastoopour et al.[3] was modified to measure pressure drop and solid velocities for cocurrent flow of particles in a pneumatic conveying line. The data were translated into particle—particle interaction expression using a force balance over the particles. The particle interaction is a combination of collision and drag force in a particles low relative velocity region. A correlation for particle—particle interaction with relative velocity between the particles of 0.3–4.6 m/s has been developed. The correlation describes our experimental data within the 10% deviation.     

A new method for the investigation of fluid-fluid mass transfer—II. Mass transfer in liquid-liquid systems

A new dynamic electrochemical method for the determination of liquid-liquid mass-transfer coefficients in a stirred cell and in a mixer cell is described. Current transients are recorded for different flow conditions and evaluated applying a non-linear regression analysis. The resulting mass-transfer coefficients correlate linearly with the stirring rate but the mean values over a long time period are considerably low. The extent of the investigated initial time dependence of the mass-transfer coefficient decreases with increasing electrolyte concentration.     

May the Knudsen equation be legitimately,or at least usefully,applied to dilute adsorbable gas flow in mesoporous media?

The question of applicability of Knudsen's equation to dilute adsorbable gas flow in mesoporous media was the subject of a recent debate between Ruthven et al. (2009), Ruthven (2010) and Bhatia and Nicholson, 2010, Bhatia and Nicholson, 2011. Here, we present a critique of the said debate and introduce new information of critical importance, which has nevertheless been disregarded by both sides thereof. It is pointed out that von Smolukowski's derivation leaves no doubt that Knudsen's equation is meant to apply to the limiting case of zero gas adsorption. In practice, this limit may be expected to be approached at high temperature/low gas adsorbability but the crux of the matter is (i) choice of the right transport parameter (in this case the “reduced permeability”) to provide a useful criterion of approach to the Knudsen limit and (ii) thorough study of the course followed by the said parameter in its approach to the said limit. In this light, we begin our review of the aforesaid new information with conventional surface flow theory, which can deal satisfactorily with higher and moderate, but not with the case of weak, adsorption (because the reduced permeability does not converge smoothly to the Knudsen limit). Even so, we show that it can provide a good answer to a significant question raised in the aforesaid debate. We continue with the more advanced (but still analytical) surface flow approach of Nicholson and Petropoulos (1973), which has provided a plausible physical mechanism for the experimentally observed passage of the reduced permeability through a minimum with rising temperature, in the weak adsorption region. It is shown here that the said experimental data constitute the first observations (including the “fine structure”) of what we have called “apparent or quasiKnudsen” (to avoid confusion with proper Knudsen) flow behavior, which is the central theme of the debate in question. We then pass onto a discussion on the confirmation of the above interpretation of quasiKnudsen-flow “fine structure”, as well as the identification of conditions favorable to the appearance of such flow in practice, afforded by the results of ab initio evaluation of dilute adsorbable gas flow, under suitable adsorption potentials, in model pores (and model pore networks) by and Petropoulos (1981, 1985) and Petropoulos and Petrou (1991).     

Hydrodynamic model of the vibro-spouted bed—II. Derivation of pressure from vibratory action

The particle velocity and the pressure distribution (derived from the vibratory action) in vibro-spouted beds (Rátkai, Gy., 1976, Powder Technol.15, 187–192) were discussed in Part I of this series. In Part II the dependence of the pressure which generates the particle flow, on the variables of the periodical motion is shown, taking into account the momentum transfer between the vibrated plate and the bed. The value of the pressure depends fundamentally on the velocity which characterizes the collisions occurring between the bed and the vibrated bottom. A detailed discussion showed that, in turn, the motion momentum transfer occurs only within a part of the period. The dependence of this effective part of the period on the frequency and the amplitude is discussed. A momentum transfer coefficient was introduced and it is shown that the momentum transfer into the bed is limited even under idealized circumstances, i.e. motion in vacuum.     

Estimation of dynamic change in gasification rate of chars—II. Overlapped grain model

Structure model of solids which considers the change in degree of overlapping of grains with progress of the solid consumption reaction on the surface of the grain was presented. The proposed model can describe the dynamic change in surface area which first increases to the maximum and then decreases during char gasification using only the initial porosity and the initial surface area. The proposed model together with the previous models was compared with the experimentally observed dynamic change in surface area during gasification. This model can explain the experimental result (Adschiri and Furusawa, 1987) that the maximum surface area was obtained at the porosity of around 0.5.     

A model for a countercurrent gas—solid—solid trickle flow reactor for equilibrium reactions. The methanol synthesis

The theoretical background for a novel, countercurrent gas—solid—solid trickle flow reactor for equilibrium gas reactions is presented. A one-dimensional, steady-state reactor model is developed. The influence of the various process parameters on the reactor performance is discussed. The physical and chemical data used apply to the case of low-pressure methanol synthesis from CO and H₂ with an amorphous silica—alumina as the product adsorbent. Complete reactant conversion is attainable in a single-pass operation, so that a recycle loop for the non-converted reactants is superfluous.In the following article the installation and experiments for which this theory was developed will be described.     

Thermal evaluation of the use of porous ceramic plates on ventilated façades—part II: Thermal behavior

The effects of porous ceramic plates on the thermal behavior of ventilated façades were evaluated, and the results are presented herein. Thermal behavior in a ventilated façade of specimens containing 40 wt% of lime mud and a firing temperature of 1100°C was evaluated and compared with a commercial porcelain ceramic tile, which was the reference material. An experimental apparatus was designed to evaluate the thermal performance of the studied ventilated façades. The results revealed that the ventilated façade composed of the studied porous ceramic tiles produced a greater reduction in temperature between the external environmental and the interior of a box representing a building (ΔT5) of 65.7°C, compared with the façade composed of the commercial porcelain ceramic tiles (ΔT5 = 56.0°C) and even the traditional façade (ΔT5 = 49.1°C). Thus, porous ceramic tiles based on byproducts are promising candidates for ventilated façade systems.     

Kinetics and thermodynamics of intercalation of bromine in graphite—II. Theory

A theory that describes the diffusion of an intercalate within graphite in a multiphase situation is presented. The theory was applied to the intercalation of bromine in graphite. Single-phase diffusion represents the intercalation of bromine in graphite as well as multiphase diffusion due to the dominance of the final stage.     

SustainPro—A tool for systematic process analysis,generation and evaluation of sustainable design alternatives

Chemical processes are continuously facing challenges from the demands of the global market related to economics, environment and social issues. This paper presents the development of a software tool (SustainPro) and its application to chemical processes operating in batch or continuous modes. The software tool is based on the implementation of an extended systematic methodology for sustainable process design (Carvalho et al., 2008, Carvalho et al., 2009). Using process information/data such as the process flowsheet, the associated mass/energy balance data and the cost data, SustainPro guides the user through the necessary steps according to work-flow of the implemented methodology. At the end the design alternatives, are evaluated using environmental impact assessment tools and safety indices. The extended features of the methodology incorporate life cycle assessment analysis and economic analysis. The application and the main features of SustainPro are illustrated through a case study of β-galactosidase production.     

Bio-polymers for improving liquid flow in pipelines—A review and future work opportunities

Several decades following Tom's discoveries on polymeric drag reducing agents (DRA) continue to see research efforts to produce robust and shear-stable DRA. Most efforts revolve around established artificial polymers, but questions have been raised recently about their environmental impact and safety. As such, a large number of researchers are looking into natural materials especially bio-polymers as substitutes. Several bio-polymers are found to exhibit drag reducing capabilities in aqueous media. All these factors suggest that bio-polymers would make a suitable alternative to artificial DRAs. This paper aims to present several works to-date on bio-polymer DRAs, and expose new possibilities.