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Separation of mixtures: fundamentals and technologies
4 Separation of mixtures: fundamentals and technologies F . Z E M A N , Royal Military College of Canada, Canada
Abstract: The modern city is a marvellous mixture bringing all manner of products, foods and people together. The end result of these activities is waste; waste that magically disappears with the flush of a toilet or placement of a bag on a curb. In this view, metropolises are waste aggregators and generators with all of the waste having to leave the city, by conservation of mass. It is in our interest to separate the benign components but this is rarely easy and never free. This chapter discusses several industrial separation processes and important metrics for their comprehension. Key words: separation process, mass balance, conservation mass, purity, recovery.
4.1
Introduction
Urban history is tied to waste management. Ever larger cities are producing ever greater quantities of waste, which require increasingly complex means to dispose of safely. Confronting this challenge is complicated by the fact is that cities are de facto waste mixing facilities. Literally millions of chemical compounds – some natural, some not – are brought into the city as part of the consumption pattern. These are mixed by citizens into three waste streams (atmospheric, aqueous and solid) and partially treated prior to release to the environment. Partial treatment implies that some are collected (e.g. waste put to the curb for collection) and some not (e.g. litter and fuel washed into neighboring bodies of water). Others, such as atmospheric emissions depend on the quality of the gas purification at the source but are released individually to the environment in a series of distributed point sources. Sewage treatment, on the other hand, is a large point source discharge that must be absorbed into the neighboring body of water. In short, resources are consumed and wastes are discharged, with some
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4.1 Flowsheet of a generic separation process; separating input F into two product streams P1 and P2; Q and W, respectively, denote energy input as heat and work, including electrical work; x denotes an array of mass fractions; T and p denote temperature and pressure respectively.
containing hazardous chemicals. To protect both public health and the environment, governments issue regulations that limit releases to the environment. Compliance may require technologies that separate recyclable compounds (e.g. water) from those posing a nuisance or a hazard (e.g. sewage and bacteria). This chapter presents fundamental concepts that guide the design of processes for separating substances.
4.1.1 Fundamental separation concepts Separation processes physically transform mixtures into products of differing compositions. They are ubiquitous in pollution control systems (Noble and Terry, 2004) and in the wider spectrum of chemical processing operations, from petroleum refining to the production of circuit boards and pharmaceuticals (Seader et al., 2011). They separate and purify by exploiting differences in physical and chemical properties such as boiling point, size and reactivity. The designer of a process must weigh the targeted degree of separation, i.e. the purity of the product, against the cost of the necessary equipment and energy required. Consider the generic separation process shown schematically in Fig. 4.1, which separates one input stream (the ‘feed’ with flowrate F) into two output streams (the ‘products’, with flowrates P1 and P2). The process represented by the box comprises a hypothetical system of separation and ancillary equipment. Separation processes come in a myriad of configurations; some more common ones are described in this chapter. Each process stream is characterized by its mass flowrate (not shown) and its ‘state’, which is defined by its temperature T, pressure p and composition
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(i.e. an array of component ‘mass fractions’ x, which must sum to one; in a stream formed by mixing 70 g of water, 20 g of NaCl and 10 g of KCl, xwater = 0.7, xNaCl = 0.2, xKCl = 0.1). A set of intensive variables (properties independent of total mass) such as the just-mentioned T, p and composition, determine all other state properties (such as density, corrosiveness and internal energy per unit mass). Extensive variables are proportional to total mass (e.g. volume = mass/density). Energy flows into and out of all systems as the thermal, kinetic and potential energy contents of the entering and exiting streams. Separating compounds usually requires additional energy input to reverse the spontaneous tendency of molecules to mix. This additional energy is transferred to the system either as heat (Q, e.g. the energy released by the condensation of steam in a heat exchanger) or work (W, e.g. electrically powered gas compression). Energy costs (e.g. those of steam and electricity) often dominate operating expenses. Operating and capital expenses determine a process’s economic viability. Null (1987) includes energy costs in an instructive discussion of process selection criteria. Referring to Fig. 4.1, the objective of most separation processes is to maximize the mass fraction of one component (let’s call it A) in one of the product streams. Significantly, in a simple single-stage process, it is typically not possible to produce a stream that is both rich in A and recovers (i.e. exits with) essentially all of the A that enters with the feed. The following sections explore the features of several separation processes.
4.2
Characterization of separation processes
4.2.1 Agents of separation Separation processes require equipment designed to exploit differences in specific molecular and particulate properties. For example, if the goal is to remove suspended solids from a liquid stream, pressure-driven filtration is likely to be the technology of choice. Figures 4.2, 4.3 and 4.4 depict five well-
4.2 Equilibrium-based separations: (a) distillation; (b) extraction.
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4.3 Rate-based separations: (a) membrane gas permeation; (b) liquid filtration (compressed gas pressurizes the feed liquid).
4.4 Adsorption/desorption, with two columns operated in tandem, cycling between adsorption and desorption.
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Table 4.1 Some well-established separation technologies, the exploited property differences and the drivers of separation Separation process
Physical property
Agent of separation
Figure
Distillation Extraction Membrane permeation Filtration
Boiling point Solubility Permeability
Heat A second solvent Non-porous membrane Porous membrane
4.2(a) 4.2(b) 4.3(a) 4.3(b)
Solid particles
4.4
Adsorption
Molecular and particulate size Affinity for a solid surface
established separation processes. Table 4.1 enumerates the physical properties they exploit and the essential factors that enable them to do it (i.e. the agents of separation).
4.2.2 Operating modes Once the appropriate separation process has been chosen, further consideration must be given to its mode of operation. Chemical processes generally operate in one of three ways – continuously, batch-wise or in semibatch mode. As the name implies, continuous operation involves a steady stream of inputs and outputs with periodic stoppages, either planned or accidental. Batch processes occur in discrete units. Reactants are loaded into a vessel, brought to a specified state (pressure, temperature, etc.) and allowed to react for a given period of time. Then, the process is stopped and the vessel emptied of product and another batch prepared. The third option happens when one piece of the process is ‘used up’, such as a filter medium. A common example would be the filter in a home water purification system where periodic replacement of one component (i.e. the filter) is necessary. Distillation (Fig. 4.2(a)), extraction (Fig. 4.2(b)) and membrane permeation (Fig. 4.3(a)) processes normally operate continuously with feed continually delivered and products continually recovered. The filtration process (Fig. 4.3(b)) operates batch-wise, with successive batches undergoing the same sequence of steps: an outlet valve closes, an inlet valve opens and a batch of feed enters; then the inlet valve shuts and the feed is processed; finally the outlet valve opens and products exit. The adsorption process depicted in Fig. 4.4 – in which a mixture of A and B (gases or liquids) is exposed to particles that selectively adsorb B and thereby purify A – operates in semi-batch mode. Paired vessels (‘columns’ I and II), each packed with the sorbent particles, cycle between adsorption and desorption phases. Three-way valves control the traffic. In phase 1, valves 1, 2 and 4 open, feed continuously enters column I, purified A exits, and B continues to adsorb until the particles’ capacities are exhausted; simultaneously, valves
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5, 6 and 3 open, purge fluid C enters column II, and the batch of B that had adsorbed in the previous cycle desorbs and exits with the purge stream. In phase 2, the valves reverse roles to direct A and B to column II and C to column I. Continuous processes are designed to operate in the steady state with flowrates and compositions varying from one location to another, but not with time. Batch processes are intrinsically non-steady-state operation with the same location undergoing considerable changes over the entire cycle. Continuous processes normally require less oversight. Batch processes are often manually controlled and therefore more labor intensive. Semi-batch processes, naturally, fall in between. From an operating perspective, once a continuous processes is operational, it is beneficial to keep things running smoothly, while batch processes have more flexibility although with lower production rates and typically higher costs.
4.2.3 Equilibrium vs. rate-based separations Another important concept to explore is the desired basis for the separation. In particular, separations based on equilibrium and rates are important. Equilibrium separations are based on differences that are stable, such as oil and water. Given time and the proper conditions, the oil will naturally separate from the water and the two can be physically separated. Rate-based processes consider the kinetic properties of the components, i.e. how fast things move or occur. Here, time is the controller with separations affected by allowing a specified amount of time to elapse rather than reaching equilibrium. In other words, equilibrium-based separations exploit differences between the compositions of two phases (i.e. a liquid and a gas, two immiscible liquids, a solid and a liquid, or a solid and a gas) that persist after their temperatures and pressures have equalized and their compositions have ceased to change. (Molecules continually cross fluid interfaces in both directions; at equilibrium, each component’s flows in the two directions equalize.) Distillation and extraction are two processes that use this mechanism (Wankat, 2011). In distillation, a mixture of liquids is separated in a vertical reactor (column) using a temperature gradient provided by a boiler at the base of the column. The column contains multiple trays that act as mixing sites for the liquid flowing down, towards the boiler, and the vapor flowing in the opposite direction. Differences between the compositions of liquid and vapor phases arise from volatility differences of the components being separated. When a liquid mixture is partially vaporized or a vapor mixture is partially liquefied, more volatile (i.e. likely to enter the gas phase owing to a lower boiling point) components tend to concentrate in the vapor phase and less volatile ones in the liquid phase. In extraction, differences between the
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compositions of partially miscible liquids (e.g. oil and water) reflect differences in distribution coefficients (ratios of component solubilities in two solvents). Gas permeation (Fig. 4.3(a)) and liquid filtration (Fig. 4.3(b)) are ratebased separations that exploit intrinsic differences in the rates at which components cross non-porous and porous membranes, respectively. The difference between a porous and non-porous membrane is the transport mechanism. In a porous membrane, a component of the mixture will travel through the spaces in the membrane to the other side. The membrane is chosen based on the size of those spaces in order to decide which components can pass. Non-porous membranes, on the other hand, absorb materials from the mixture and these compounds then diffuse towards the other side. The diffusion is a natural process driven by the concentration gradient across the membrane. It occurs through a series of random motions of the molecules. In both cases, porous and non-porous, the overall performance is measured in terms of permeability, i.e. the ability of a material to transmit fluids. Permeabilities in non-porous membranes are proportional to solubility (the capacity of a membrane material to absorb the component) and diffusivity (the mobility of dissolved component molecules). Permeabilities in porous membranes depend on the ratios of molecular or particulate dimensions to pore diameters. It is worth remembering that even if a component of a mixture is too large to pass through a membrane, it is still a rate-based separation, just that in this case the rate is zero. Adsorption, which refers to the adhesion of a compound to a solid surface (Fig. 4.4) may be either equilibrium or rate-based. When selectivity arises from differences among affinities for a particle’s surface, separation is equilibrium-based and the pores provide large internal surface areas. When selectivity derives from differences in component sizes, separation is ratebased and the pores serve as molecular sieves. In this way, smaller particles can be separated from a mixture by removing the larger particles to which they have adsorbed. All five separation processes require energy input: heat (the agent of separation) in distillation; mixing and pumping in extraction and filtration; compression or vacuum pumping in permeation and adsorption. The amount of energy required to effect the separation is of particular concern with respect to costs and, more recently, greenhouse gas emissions. Fundamentally, the energy is required as separation processes seek to reverse entropy. If the natural tendency is towards disorder, with pollutants spreading throughout the environment over time, then reversing it will necessarily require energy. The further the process proceeds (i.e. to higher purity), the more energy will be required. Often there is an economic limit,
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as is the case with separating carbon dioxide (CO2) from power plant exhaust gases, which is optimized at between 85 and 90% separation.
4.3
Balance equations
The design of separation processes always begins with material balance calculations. It is in this fundamental step that the scale of the various separation processes is identified and a complete list of components is evolved. Nothing disappears in separation processes and, as such, much care is needed to ensure that the final location of all the compounds is identified. It is as important to know where the minor fraction of the compound of interest finally resides as the amount in the product stream.
4.3.1 General balance equation One of the governing concepts in any separation process is the principle of mass/matter conservation, which states that the mass of an isolated system (i.e. one that is closed to all matter and energy) will remain constant over time. If we consider a city as the system then it is certain that mass can exit the city limits; however, we also import mass in the form of food, water and the air passing through. Furthermore, in today’s globalized world, cities are always both upstream and downstream of other cities. It is therefore very important to track all of the mass entering any specified limits, from an air filter up to the city limits. Balance equations (also called conservation) lie at the heart of this analysis and the design of chemical processes. Quite simply, they enforce the following truism: Accumulation ¼ Input Output þ Production Consumption ½4:1 The production and consumption terms are included to allow the consideration of chemical reactions, critical to most industrial processes and pollution mitigation schemes. In the simple case of removing suspended solids from wastewater, there is no reaction and the mass balance involves comparing the incoming mass with the two output streams (cleaner water and the separated mud). In the case of combustion, any fuel that exits the process (i.e. output) would be associated with leaks or incomplete combustion. Ideally the fuel would be completely combusted so therefore accumulation = output = production = zero and the input (feed rate) equals consumption (combustion rate). In order to complete the mass balance, the chemical reactions associated with combustion (i.e. the oxidation of fuel to carbon dioxide and water vapor) are needed to describe the products. Here, all possible reactions must be considered, including
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incomplete reactions (i.e. the production of carbon monoxide) and side reactions (i.e. the production of nitrous oxide compounds). There are several variations on the general mass balance equation. When the above terms are in units of quantity per time, equation 4.1 is a differential balance that applies at any instant of time. When they express quantity, equation 4.1 is an integral balance that is applicable over a specific time period. Production and consumption are each zero when equation 4.1 is applied to total mass, energy or the mass of a component that is neither formed nor consumed in a chemical reaction.
4.3.2 Mass balances The remainder of this chapter focuses on steady-state, non-reactive processes and, therefore, on relations among input and output flows and compositions. This simplification can be expanded to include production and consumption by applying the same methodology to relevant chemical reactions, the key being complete descriptions of all chemical reactions. The following text also contains some standard nomenclature used in chemical engineering, in particular the subscripts ‘i’ and ‘j’. In a system with many compounds it is useful to use a dual subscript system to keep track of the component (i) and location (j) of interest, especially when discussing mass fractions (x). So, the nomenclature x1,2 refers to the fraction of the compound labeled 1 found in stream 2. In the example below, the letter F refers to the feed stream for the simple case with only one feed. Should multiple feeds be involved, as in the natural gas combustion case (methane and air), numerical subscripts could be used for both. By now, the need for a legend and flow chart is clear. These are first steps that help the designer avoid confusion and mixing up of streams. When equation 4.1 is applied to the mass of component i in the process shown in Fig. 4.1, it assumes the form Fxi ¼ P1 xi1 þ P2 xi2
½4:2
This equation literally states that the fraction of compound i in the feed stream is equal to the fraction of i in each product stream multiplied by the mass of said stream. When it is applied to total mass, it becomes F ¼ P1 þ P2
½4:3
Note that there are as many independently enforceable mass balances as there are components. The proper application of the principle of mass conservation will therefore depend on identifying all of the relevant components and keeping track of their locations. The more precise the quantification of the mass balance, the more involved the required
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measurements. Given that all measuring equipment has detection limits, it is usually necessary to work with an accepted level of uncertainty. The exact level will likely depend on the cost of compliance with regulation and any legal requirements, such as the US Environmental Protection Agency’s Toxic Release Inventory, which for example is measured in millions of pounds annually but must meet guidelines of thousandths of milligrams per liter in the case of mercury. Determining the product flows and compositions that are possible when a mixture of A and B is separated involves mass balances and the identity X xi ¼ 1 ½4:4 i
Understanding equation 4.4 starts with the knowledge that the mass fraction x is dimensionless, meaning it is a fraction that can be expressed in units of kilograms of component per kilogram of mixture. It follows that the sum of the mass fraction of components in any one stream cannot exceed 1, i.e. there is no more mass than that contained in the stream. For example, let F = 100 mol/s and xAF = 0.7, which means that 70 mol/s of component A are entering the separation process contained in 100 mol/s of feed. As a reminder, one mole of a substance is a specified number of molecules known as Avogadro’s number. In addition, the compositions in the product streams are 95% A (xA1 = 0.95) in the first (P1) and 98% B (xB2 = 0.98) in the second (P2). In short, this describes a typical separation process wherein a mixed stream is separated into streams dominated by specific components of the feed. Equation 4.4 can be applied to this example by recognizing that if there are only two compounds and the mass fraction per stream is unity, the product stream 1 must contain 5% B (1 0.95) and P2 must contain 2% A (1 0.98). Mathematically speaking, specification of the product purities has exhausted our degrees of freedom: we are not free to also specify, say, the fraction of the feed that leaves as product 1. The reason for this is that flowrates P1 and P2 are constrained as follows to satisfy two mass balances, e.g., an A balance (equation 4.2) and a total mass balance (equation 4.3). Alternatively, the solution could have been found using a mass balance on compounds A and B, or B and total mass. 9 xA F ¼ xA1 P1 þ xA2 P2 = P1 ¼ 73:1; P2 ¼ 26:9 mol=s 0:7ð100Þ ¼ 0:95P1 þ 0:02P2 ; 100 ¼ P1 þ P2 Check (using the redundant B mass balance) 0:05ð73:1Þ þ 0:98ð26:9Þ ¼ 30 ¼ 0:3ð100Þ ¼ xB F ¼ ð1 xA ÞF Just as important as product purity is component recovery, ri, i.e. the
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fraction of entering component i that emerges in the i-rich product: rA ¼
P1 xA1 73:1ð0:95Þ ¼ 0:992 ¼ FxA 100ð0:7Þ
rB ¼
P2 xB2 26:9ð0:98Þ ¼ 0:879 ¼ FxB 100ð0:3Þ
Recovery of 99.2% of the entering A is likely to be satisfactory when A is valuable and its contamination with 5% B is acceptable. If B is valuable as well, losing 12.1% of it in the A-rich product may be unacceptable. On the other hand, if B has no value and is environmentally hazardous, discharging it in concentrated form is likely to be proscribed, potentially necessitating further processing. Producing high-purity products with high component recoveries is theoretically possible. Doing so in practice depends on an exploitable property difference and a process that will economically exploit it. Evaluating the options begins with preliminary process calculations. As an aside, the mass fraction can also be specified in terms of the number of molecules present; this would be in units of moles per second (mol/s) where one mole is 600 trillion quadrillion molecules (661023), the aforementioned Avogadro’s number.
4.4
Preliminary separation process calculations
In this section, two candidate processes for separating gases A, B and C (e.g. the sulfur dioxide, carbon dioxide and nitrogen in power plant exhaust) are examined.
4.4.1 Gas permeation In the simple membrane permeation device depicted in Fig. 4.3(a), the feed is delivered to the retentate compartment. A fraction permeates (dissolves in, diffuses across and desorbs from the membrane) and exits, via the permeate compartment, as the permeate product. The fraction that does not permeate becomes the retentate product. The membrane’s selectivity is a function of the component permeabilities (Koros and Chern, 1987). Permeability K is defined such that a component’s permeation rate N (mass/time) is the product of its K value, the membrane’s surface area (SM) and the difference between its partial pressures in the retentate and permeate compartments, i.e. across the membrane: Ni ¼ Ki SM ðpR xiR pP xiP Þ
i ¼ A; B; C
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The partial pressure difference is the driving force of permeation; pR and pP are the absolute pressures in the two compartments. Assuming ideal gas behavior, the partial pressure is the product of the absolute pressure and the mass fraction. The term partial pressure refers to the pressure that the component in question would exert if it alone occupied the volume in question. Consider a box filled with air at atmospheric pressure. If oxygen is approximately 21% of the gas in the box and the pressure is 1 atm (i.e. 101.3 kPa) then the partial pressure of oxygen is 0.21 atm. Generating a product enriched in A is possible when KA either exceeds or is less than KB and KC. In the former case, component A passes through the membrane more rapidly and the A-enriched stream is the permeate; in the latter case, components B and C readily pass through, leaving A in the retentate. To simplify the process calculations, we assume the following. . . .
Both compartments are well mixed, which implies that their contents are uniform and their compositions are identical to those of the associated product streams. Only a small fraction of the feed permeates. Therefore, the mass flow leaving in the retentate stream is almost equivalent to the feed (R ≈ F) and the mass fraction of all components is also similar (xiR ≈ xiF). The partial pressure on the permeate side of the membrane is much lower than anywhere else in the system (i.e. pR ≈ pF and pP<< pF).
These conditions represent the situation where the component of interest is a small fraction of the feed gas and a vacuum is used to remove any gas crossing the membrane as soon as it reaches the other side. These simplifications reduce equation 4.5 to Ni &Ki SM pF xiF
½4:6
Equation 4.6 states that the permeation rate (i.e. the rate at which the compound of interest crosses the membrane) is entirely driven by conditions in the feed gas. While the objective of material scientists is to produce membranes permeable to only one component, the reality is that all components will permeate at different rates. It follows that the composition of the permeate product stream under these assumptions is defined as X X Ni ¼pF SM Ki xiF i ¼ A; B; C ½4:7 P¼ i
i
and the mass fraction of each component in the permeate product can be
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4.5 Permeate composition vs. αBA; αCA = 0.2; equimolar feed.
calculated from ai xiF xPj ¼ xAF þ aBA xBF þ aCA xCF
i ¼ A; B; C; aiA
Ki ¼ KA
½4:8
in which the coefficients αBA and αCA refer to the membrane’s selectivities for B and C relative to A. This allows the engineer to calculate, for a given production of A, the relative amount of impurities B and C. To further elucidate these concepts, sample calculations were performed for an equimolar feed gas (xAF = xBF = xCF = 1/3) and αCA fixed at 0.2 (i.e. a membrane five times more permeable to A than to C). Figure 4.5 shows the calculated dependence of the permeate composition on αAB. As one might expect, when αBA = 0.1, the permeate is rich in A (xAP = 0.76); when αBA = 10, the permeate is rich in B (xBP = 0.89). The B-rich permeate is purer ðxi ¼ 1Þ than the A-rich permeate because with αCA = 0.2 and αBA = 10, the membrane is 50 times more permeable to B than to C. Recall that the calculations were for cases in which only a very small fraction of the feed stream permeates. Consequently, the component recoveries are negligible. When larger fractions of the feed permeate (because of a greater membrane area or a higher feed pressure), recoveries will be higher, purities lower. There is a tradeoff between recovery and purity because the gas in the retentate compartment is the source of the
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4.6 Single-stage absorption process; well-stirred vessel; L and G are liquid and gas molar flowrates; x and y are mole fraction arrays; T = 258C; p = 1 atm.
permeate. This tradeoff, which is common to single-stage processes, is again encountered in the next section.
4.4.2 Absorption Absorption, also known as scrubbing, is an equilibrium-based separation that exploits differences in the solubilities of gases in liquids (Kohl, 1987). In general, the process seeks to remove a component of a gas stream, e.g. sulfur compounds that cause acid rain (known as SOx), by transferring them from one phase to another. It differs from adsorption in that the components enter the bulk volume and do not just adhere to the surface. Figure 4.6 depicts a simple absorption process. A nozzle and mechanical agitation generate small gas bubbles and correspondingly large total interfacial areas, both of which promote gas/liquid equilibration and uniformity of phase compositions. Note that typically the mass fraction in the gas phase is denoted using the variable y, instead of x. Consider the selective removal of sulfur dioxide and carbon dioxide from a mixture containing 1 mol% SO2, 15 mol% CO2 and 84 mol% N2, via absorption in water at 258C and 1 atm. The results are predictable on the basis of equation 4.4, plus the following phase equilibrium relationships: xi;out ¼ ki yi;out kSO2 ¼ 2:56102 ; kCO2 ¼ 6:16104 ; kN2 ¼ 1:26105 ; kH2O ¼ 32Þ
½4:9
In equation 4.9, ki refers to Henry’s constant, which defines the ratio of the dissolved content of a gas in relation to the partial pressure in the gas phase above the liquid. Based on the values presented in equation 4.9, SO2 concentrations in water can be 100 times that of CO2 and 1000 times that of
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4.7 Recoveries of SO2 and CO2 (percentages of their removal from the feed gas) as functions of the ratio of the molar feed rates of liquid and gas.
N2. As a result, we would expect little N2 in solution despite the fact that it is almost 100 times more prevalent than SO2 in the gas phase. The curious result is that any gas can be scrubbed using distilled water, which contains no dissolved gases; however, it is usually more economical to find a more aggressive solvent. The concept of component mass balances can also be applied as follows: Gin yi;in þ Lin xi;in ¼ Gout yi;out þ Lout xi;out
½4:10
Equations 4.4, 4.9 and 4.10 comprise ten linear relationships among ten unknowns: the flowrates of the two product streams and four mole fractions for any two of SO2, CO2 and N2. The appendix outlines an easily implemented algorithm for solving them. The important concept is that all of the gases present will enter the liquid phase based on the governing laws and estimations of scrubbing efficiency must track all species. Figures 4.7 and 4.8 depict the dependence on the entering liquid to gas ratio (Lin/Gin) of the calculated SO2 and CO2 recoveries and mole fractions in the exiting liquid (little nitrogen is absorbed owing to the low Henry’s constant). As Lin/Gin increases, the SO2 and CO2 capture rates increase, asymptotically approaching 100%, while their concentrations in the exiting liquid approach zero. Conceptually, a higher L/G ratio means that each bubble of gas will have to traverse through more liquid to reach the exit,
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4.8 Mole fractions of SO2 and CO2 in the effluent vs. the ratio of inlet molar feed rates of liquid and gas.
thus providing more opportunity, as well as a steeper concentration gradient across the liquid. This is highlighted in Fig. 4.7 where the same percentage recovery of CO2 requires an increase in liquid flow proportional to the difference in Henry’s constant. The tradeoff between recovery and purity (admittedly a misnomer in reference to a liquid composed almost entirely of solvent water) is again a characteristic of a single-stage process.This is highlighted in Fig. 4.8 where the liquid to gas ratios needed for high recovery (in Fig. 4.7) result in low mass fractions in the liquid phase (xout) in a larger volume. The tradeoff is more acute should the liquid require treatment. In absorption, it is attributable to the equilibration of the product streams with one another. It is avoidable in counter-current, multi-stage separations.
4.5
Multi-stage separations
The performance limitations of single-stage processes may be overcome without excessive additional operating expenses if judicious design choices are made (Kelly, 1987). The gas permeation process discussed in Section 4.4.1 may be expanded as indicated in Fig. 4.9, by re-compressing and cooling the permeate and feeding it to a second membrane module. Permeate 2 will be purer than permeate 1 (yA2 > yA1,), but A’s recovery will be lower. This is a result of distributing the A recovered from the first stage across two streams making the high-purity fraction (P2 yA2) a smaller portion of that in the feed (FxAF). By the same token, nothing is to be gained by supplementing the single
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4.9 Two-stage gas permeation process.
4.10 Two-stage co-current absorption process. Properties of fluid streams other than the feeds are subscripted with the numbers of the stages of origin.
4.11 Two-stage counter current absorption process. Properties of fluid streams other than the feeds are subscripted with the numbers of the stages of origin.
absorption stage in Fig. 4.6 with a co-current second stage, as depicted in Fig. 4.10 (co-current implies that streams flow in the same direction). This is because the compositions of pre-equilibrated phases will not change when re-exposed to one another. By contrast, substantial dividends are to be derived by operating a twostage process counter currently, as in Fig. 4.11: yA2 will be lower than yA1 (because the gas fed to stage 2 will have been partially depleted of A in stage 1) and xA1 will exceed its value in the single-stage absorption process (Fig. 4.6), both without sacrifice of recovery. The significant advantage of counter current flow is that the concentration gradient (the driving force) is always
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at its maximum. Where the scrubbing solution enters the process, and the gas exits, the gas is depleted but as the solution is ‘empty’ there is still a driving force. Similarly at the other end, the solution is ‘full’ but the component concentration in the gas phase is at its highest, still providing a driving force. This can be compared to co-current flow where the concentrations approach equilibrium near the exit. The foregoing sections have touched the surface of separation processes. As one might imagine, the mechanisms that both drive them and limit their performance are generally more complex, as is noted in Section 4.7.
4.6
Filtration
Processes along the lines sketched in Fig. 4.3(b) are widely deployed both to filter (as in water purification) and to reduce volume (as in the concentration of fruit juice) (Chen et al., 2011). The concept is quite simple. The diameter of the filter’s pores, DP, must be small enough to prevent the passage of targeted molecules and/or particles. The filter, which is essentially a porous membrane, may be anything from a woven cloth that retains silt, clay and sand, to a polymeric film that enables the desalination of brackish water. Table 4.2 classifies filtration processes according to the minimum effective diameter of what is retained, DR, and lists typical values of Δp, the pressure differentials that will ensure acceptable filtration rates. Filtration rates vary directly with Δp and inversely with D2P . Consequently, pumping pressures with associated equipment costs and power consumption, are minimized by deploying a membrane with the largest DP that will provide the desired retention. Because the maximum allowable filter pore size DP increases with the diameter of the target particle or molecule (DR), and the required Δp decreases as DP increases, operating Δp values vary inversely with DR. Filtration can and does produce high-purity water with high recovery. However, the membranes require frequent cleaning to remove biofilms (of proliferating micro-organisms) and filter cakes (of retained particles), both of which are inimical to filtration. Furthermore, even when what is retained remains in solution, filtration is slowed by the tendency of retained solutes to concentrate at the membrane surface – a phenomenon referred to as concentration polarization (see Fig. 4.12). Solutes accumulate until their concentrations at the membrane surface (CSM) reach the point at which their rates of diffusion (random thermal motion that has the effect of transferring solutes to regions of lower concentration) away from the membrane surface offset their rates of convective transfer (solvent drag) to the surface. When CSM reaches a solute’s solubility limit, the solute precipitates, causing the growth of a gel layer analogous to a filter cake, with similarly adverse effects on filtration. A more subtle effect of concentration polarization is an increase in DP,
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Table 4.2 Filtration processes Size (m) Type Examples
Filtration process
1010–109 109–108 108–107 107–106 106–105 105–104 104–103 Ionic Molecular Macromolecular Cellular and microparticulate Metal ions Viruses Sand Sugar ______Proteins______ ____RO____
____Bacteria____ _____________Algae____________ ___Clays___ Silt
______NF______ _________MF________ __________UF__________ ____Conventional filtration____
Δp (atm) 3–70 5–15 2–10 0.5–2.0 0.1–2.0 Source: adapted from Chen et al., 2011. RO, reverse osmosis; NF, nanofiltration; UF, ultrafiltration; MF, microfiltration.
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4.12 Boundary layer region adjacent to filtration membrane, illustrating concentration polarization of retained solute.
4.13 Filtration rate V (volume/time) vs. transmembrane pressure differential; characteristic results with a feed of pure water and a solution of retained solute are shown.
the osmotic pressure differential across the membrane. Because filtration rates are proportional to Δp – DP, osmotic pressure retards filtration. The solid curve in Fig. 4.13 typifies filtration data: rather than increasing monotonically with Δp, as it does with a pure water feed, the filtration rate levels off because of increasing osmotic pressure.
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Conclusions and sources of further information
This chapter has covered the basics of separation processes and demonstrated that separation is possible, provided sufficient energy is expended. The separation process also produces two streams containing a mixture of components in the feed stream. Additionally, it is important to note that in none of the processes is mass destroyed. Separation involves exactly that – a separation that will allow the undesirable component to be concentrated and disposed of in a more secure manner. While they provide definite shortterm benefits, it is also true that lower emission or discharge limits can be offset by larger consumption. Simply put, reducing the emission of SOx compounds by a factor 100 from one facility is offset if 100 more facilities are built. The ratio is reduced further if the new facilities emit more than the original. This is being played out with globalization and the ‘offshoring’ of pollution. This chapter has provided an introduction to the concepts that guide the selection and design of separation processes. Readers seeking more depth and breadth are referred to the textbooks by Noble and Terry (2004), Wankat (2011) and Seader et al. (2011).
4.8
Acknowledgement
The author would like to acknowledge Dr J. Meldon for significant contributions to this chapter. His efforts in providing the fundamental underpinning, topic selection and all the figures are greatly appreciated.
4.9
References
Chen JP, Mou H, Wang LK, Matsuura T and Wei Y (2011) Membrane separation: basics and applications. In Wang LK, Chen JP, Hung Y-T and Shammas NK (eds). Membrane and Desalination Technologies. New York, Springer, pp. 271– 332. Kelly RM (1987) General processing considerations. In Rousseau RW (ed.). Handbook of Separation Process Technology. New York, Wiley, pp. 197–225. Kohl AL (1987) Absorption and stripping. In Rousseau RW (ed.). Handbook of Separation Process Technology. New York, Wiley, pp. 340–404. Koros WJ and Chern RT (1987) Separation of gaseous mixtures using polymeric membranes. In Rousseau RW (ed.). Handbook of Separation Process Technology. New York, Wiley, pp. 862–953. Noble RD and Terry PA (2004) Principles of Chemical Separations with Environmental Applications. Cambridge, UK, Cambridge University Press. Null HR (1987) Selection of a separation process. In Rousseau RW (ed.). Handbook of Separation Process Technology. New York, Wiley, pp. 982–995. Seader JD, Henley EJ and Roper DK (2011) Separation Process Principles, 3rd edn. New York, Wiley.
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Wankat PC (2011) Separation Process Engineering, 3rd edn. Upper Saddle River, NJ, Prentice Hall.
4.10
Appendix: Algorithm for solving equations 4.4, 4.9 and 4.10
The equations are of the following general form: Lxi þ Gyi
¼ Fzi
yi ¼ Ki xi
i ¼ 1; :::; c
c X
i ¼ 1; :::; c
ðA4:1Þ ðA4:2Þ
xi ¼ 1
ðA4:3Þ
i¼1 c X i¼1
yi ¼
c X
K i xi ¼ 1
ðA4:4Þ
i¼1
in which c is the number of components; L = Lout, G = Gout, x = xout, y = yout, F = Lin + Gin, Fzi = Linxin,i + Ginyin,i; Ki = 1/ki. Let f = Gin/F. It follows that Lin/F = 1 f. Division by F and insertion of equation A4.2 transforms equation A4.1 to: ð1 fÞxi þ fKi xi ¼ zi
and so
xi ¼
zi 1 f þ Ki xi
Insertion of equation A4.5 transforms equation A4.3 to: c X zi ¼ 1 1 f þ Ki fi i¼1
ðA4:5Þ
ðA4:6Þ
Equation A4.6 is equivalent to a cth degree polynomial in f, as may be verified by multiplying both sides of it by the product of the c denominators. Accordingly, there are c values of f that will satisfy equation A4.5, pairs of which may be complex conjugates. One real root, easily determined by trial and error, will lie in the physically possible interval of zero to one. The values of all other unknowns follow explicitly from f.
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Abstract: The modern city is a marvellous mixture bringing all manner of products, foods and people together. The end result of these activities is waste; waste that magically disappears with the flush of a toilet or placement of a bag on a curb. In this view, metropolises are waste aggregators and generators with all of the waste having to leave the city, by conservation of mass. It is in our interest to separate the benign components but this is rarely easy and never free. This chapter discusses several industrial separation processes and important metrics for their comprehension. Key words: separation process, mass balance, conservation mass, purity, recovery.
4.1
Introduction
Urban history is tied to waste management. Ever larger cities are producing ever greater quantities of waste, which require increasingly complex means to dispose of safely. Confronting this challenge is complicated by the fact is that cities are de facto waste mixing facilities. Literally millions of chemical compounds – some natural, some not – are brought into the city as part of the consumption pattern. These are mixed by citizens into three waste streams (atmospheric, aqueous and solid) and partially treated prior to release to the environment. Partial treatment implies that some are collected (e.g. waste put to the curb for collection) and some not (e.g. litter and fuel washed into neighboring bodies of water). Others, such as atmospheric emissions depend on the quality of the gas purification at the source but are released individually to the environment in a series of distributed point sources. Sewage treatment, on the other hand, is a large point source discharge that must be absorbed into the neighboring body of water. In short, resources are consumed and wastes are discharged, with some
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4.1 Flowsheet of a generic separation process; separating input F into two product streams P1 and P2; Q and W, respectively, denote energy input as heat and work, including electrical work; x denotes an array of mass fractions; T and p denote temperature and pressure respectively.
containing hazardous chemicals. To protect both public health and the environment, governments issue regulations that limit releases to the environment. Compliance may require technologies that separate recyclable compounds (e.g. water) from those posing a nuisance or a hazard (e.g. sewage and bacteria). This chapter presents fundamental concepts that guide the design of processes for separating substances.
4.1.1 Fundamental separation concepts Separation processes physically transform mixtures into products of differing compositions. They are ubiquitous in pollution control systems (Noble and Terry, 2004) and in the wider spectrum of chemical processing operations, from petroleum refining to the production of circuit boards and pharmaceuticals (Seader et al., 2011). They separate and purify by exploiting differences in physical and chemical properties such as boiling point, size and reactivity. The designer of a process must weigh the targeted degree of separation, i.e. the purity of the product, against the cost of the necessary equipment and energy required. Consider the generic separation process shown schematically in Fig. 4.1, which separates one input stream (the ‘feed’ with flowrate F) into two output streams (the ‘products’, with flowrates P1 and P2). The process represented by the box comprises a hypothetical system of separation and ancillary equipment. Separation processes come in a myriad of configurations; some more common ones are described in this chapter. Each process stream is characterized by its mass flowrate (not shown) and its ‘state’, which is defined by its temperature T, pressure p and composition
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(i.e. an array of component ‘mass fractions’ x, which must sum to one; in a stream formed by mixing 70 g of water, 20 g of NaCl and 10 g of KCl, xwater = 0.7, xNaCl = 0.2, xKCl = 0.1). A set of intensive variables (properties independent of total mass) such as the just-mentioned T, p and composition, determine all other state properties (such as density, corrosiveness and internal energy per unit mass). Extensive variables are proportional to total mass (e.g. volume = mass/density). Energy flows into and out of all systems as the thermal, kinetic and potential energy contents of the entering and exiting streams. Separating compounds usually requires additional energy input to reverse the spontaneous tendency of molecules to mix. This additional energy is transferred to the system either as heat (Q, e.g. the energy released by the condensation of steam in a heat exchanger) or work (W, e.g. electrically powered gas compression). Energy costs (e.g. those of steam and electricity) often dominate operating expenses. Operating and capital expenses determine a process’s economic viability. Null (1987) includes energy costs in an instructive discussion of process selection criteria. Referring to Fig. 4.1, the objective of most separation processes is to maximize the mass fraction of one component (let’s call it A) in one of the product streams. Significantly, in a simple single-stage process, it is typically not possible to produce a stream that is both rich in A and recovers (i.e. exits with) essentially all of the A that enters with the feed. The following sections explore the features of several separation processes.
4.2
Characterization of separation processes
4.2.1 Agents of separation Separation processes require equipment designed to exploit differences in specific molecular and particulate properties. For example, if the goal is to remove suspended solids from a liquid stream, pressure-driven filtration is likely to be the technology of choice. Figures 4.2, 4.3 and 4.4 depict five well-
4.2 Equilibrium-based separations: (a) distillation; (b) extraction.
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4.3 Rate-based separations: (a) membrane gas permeation; (b) liquid filtration (compressed gas pressurizes the feed liquid).
4.4 Adsorption/desorption, with two columns operated in tandem, cycling between adsorption and desorption.
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Table 4.1 Some well-established separation technologies, the exploited property differences and the drivers of separation Separation process
Physical property
Agent of separation
Figure
Distillation Extraction Membrane permeation Filtration
Boiling point Solubility Permeability
Heat A second solvent Non-porous membrane Porous membrane
4.2(a) 4.2(b) 4.3(a) 4.3(b)
Solid particles
4.4
Adsorption
Molecular and particulate size Affinity for a solid surface
established separation processes. Table 4.1 enumerates the physical properties they exploit and the essential factors that enable them to do it (i.e. the agents of separation).
4.2.2 Operating modes Once the appropriate separation process has been chosen, further consideration must be given to its mode of operation. Chemical processes generally operate in one of three ways – continuously, batch-wise or in semibatch mode. As the name implies, continuous operation involves a steady stream of inputs and outputs with periodic stoppages, either planned or accidental. Batch processes occur in discrete units. Reactants are loaded into a vessel, brought to a specified state (pressure, temperature, etc.) and allowed to react for a given period of time. Then, the process is stopped and the vessel emptied of product and another batch prepared. The third option happens when one piece of the process is ‘used up’, such as a filter medium. A common example would be the filter in a home water purification system where periodic replacement of one component (i.e. the filter) is necessary. Distillation (Fig. 4.2(a)), extraction (Fig. 4.2(b)) and membrane permeation (Fig. 4.3(a)) processes normally operate continuously with feed continually delivered and products continually recovered. The filtration process (Fig. 4.3(b)) operates batch-wise, with successive batches undergoing the same sequence of steps: an outlet valve closes, an inlet valve opens and a batch of feed enters; then the inlet valve shuts and the feed is processed; finally the outlet valve opens and products exit. The adsorption process depicted in Fig. 4.4 – in which a mixture of A and B (gases or liquids) is exposed to particles that selectively adsorb B and thereby purify A – operates in semi-batch mode. Paired vessels (‘columns’ I and II), each packed with the sorbent particles, cycle between adsorption and desorption phases. Three-way valves control the traffic. In phase 1, valves 1, 2 and 4 open, feed continuously enters column I, purified A exits, and B continues to adsorb until the particles’ capacities are exhausted; simultaneously, valves
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5, 6 and 3 open, purge fluid C enters column II, and the batch of B that had adsorbed in the previous cycle desorbs and exits with the purge stream. In phase 2, the valves reverse roles to direct A and B to column II and C to column I. Continuous processes are designed to operate in the steady state with flowrates and compositions varying from one location to another, but not with time. Batch processes are intrinsically non-steady-state operation with the same location undergoing considerable changes over the entire cycle. Continuous processes normally require less oversight. Batch processes are often manually controlled and therefore more labor intensive. Semi-batch processes, naturally, fall in between. From an operating perspective, once a continuous processes is operational, it is beneficial to keep things running smoothly, while batch processes have more flexibility although with lower production rates and typically higher costs.
4.2.3 Equilibrium vs. rate-based separations Another important concept to explore is the desired basis for the separation. In particular, separations based on equilibrium and rates are important. Equilibrium separations are based on differences that are stable, such as oil and water. Given time and the proper conditions, the oil will naturally separate from the water and the two can be physically separated. Rate-based processes consider the kinetic properties of the components, i.e. how fast things move or occur. Here, time is the controller with separations affected by allowing a specified amount of time to elapse rather than reaching equilibrium. In other words, equilibrium-based separations exploit differences between the compositions of two phases (i.e. a liquid and a gas, two immiscible liquids, a solid and a liquid, or a solid and a gas) that persist after their temperatures and pressures have equalized and their compositions have ceased to change. (Molecules continually cross fluid interfaces in both directions; at equilibrium, each component’s flows in the two directions equalize.) Distillation and extraction are two processes that use this mechanism (Wankat, 2011). In distillation, a mixture of liquids is separated in a vertical reactor (column) using a temperature gradient provided by a boiler at the base of the column. The column contains multiple trays that act as mixing sites for the liquid flowing down, towards the boiler, and the vapor flowing in the opposite direction. Differences between the compositions of liquid and vapor phases arise from volatility differences of the components being separated. When a liquid mixture is partially vaporized or a vapor mixture is partially liquefied, more volatile (i.e. likely to enter the gas phase owing to a lower boiling point) components tend to concentrate in the vapor phase and less volatile ones in the liquid phase. In extraction, differences between the
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compositions of partially miscible liquids (e.g. oil and water) reflect differences in distribution coefficients (ratios of component solubilities in two solvents). Gas permeation (Fig. 4.3(a)) and liquid filtration (Fig. 4.3(b)) are ratebased separations that exploit intrinsic differences in the rates at which components cross non-porous and porous membranes, respectively. The difference between a porous and non-porous membrane is the transport mechanism. In a porous membrane, a component of the mixture will travel through the spaces in the membrane to the other side. The membrane is chosen based on the size of those spaces in order to decide which components can pass. Non-porous membranes, on the other hand, absorb materials from the mixture and these compounds then diffuse towards the other side. The diffusion is a natural process driven by the concentration gradient across the membrane. It occurs through a series of random motions of the molecules. In both cases, porous and non-porous, the overall performance is measured in terms of permeability, i.e. the ability of a material to transmit fluids. Permeabilities in non-porous membranes are proportional to solubility (the capacity of a membrane material to absorb the component) and diffusivity (the mobility of dissolved component molecules). Permeabilities in porous membranes depend on the ratios of molecular or particulate dimensions to pore diameters. It is worth remembering that even if a component of a mixture is too large to pass through a membrane, it is still a rate-based separation, just that in this case the rate is zero. Adsorption, which refers to the adhesion of a compound to a solid surface (Fig. 4.4) may be either equilibrium or rate-based. When selectivity arises from differences among affinities for a particle’s surface, separation is equilibrium-based and the pores provide large internal surface areas. When selectivity derives from differences in component sizes, separation is ratebased and the pores serve as molecular sieves. In this way, smaller particles can be separated from a mixture by removing the larger particles to which they have adsorbed. All five separation processes require energy input: heat (the agent of separation) in distillation; mixing and pumping in extraction and filtration; compression or vacuum pumping in permeation and adsorption. The amount of energy required to effect the separation is of particular concern with respect to costs and, more recently, greenhouse gas emissions. Fundamentally, the energy is required as separation processes seek to reverse entropy. If the natural tendency is towards disorder, with pollutants spreading throughout the environment over time, then reversing it will necessarily require energy. The further the process proceeds (i.e. to higher purity), the more energy will be required. Often there is an economic limit,
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as is the case with separating carbon dioxide (CO2) from power plant exhaust gases, which is optimized at between 85 and 90% separation.
4.3
Balance equations
The design of separation processes always begins with material balance calculations. It is in this fundamental step that the scale of the various separation processes is identified and a complete list of components is evolved. Nothing disappears in separation processes and, as such, much care is needed to ensure that the final location of all the compounds is identified. It is as important to know where the minor fraction of the compound of interest finally resides as the amount in the product stream.
4.3.1 General balance equation One of the governing concepts in any separation process is the principle of mass/matter conservation, which states that the mass of an isolated system (i.e. one that is closed to all matter and energy) will remain constant over time. If we consider a city as the system then it is certain that mass can exit the city limits; however, we also import mass in the form of food, water and the air passing through. Furthermore, in today’s globalized world, cities are always both upstream and downstream of other cities. It is therefore very important to track all of the mass entering any specified limits, from an air filter up to the city limits. Balance equations (also called conservation) lie at the heart of this analysis and the design of chemical processes. Quite simply, they enforce the following truism: Accumulation ¼ Input Output þ Production Consumption ½4:1 The production and consumption terms are included to allow the consideration of chemical reactions, critical to most industrial processes and pollution mitigation schemes. In the simple case of removing suspended solids from wastewater, there is no reaction and the mass balance involves comparing the incoming mass with the two output streams (cleaner water and the separated mud). In the case of combustion, any fuel that exits the process (i.e. output) would be associated with leaks or incomplete combustion. Ideally the fuel would be completely combusted so therefore accumulation = output = production = zero and the input (feed rate) equals consumption (combustion rate). In order to complete the mass balance, the chemical reactions associated with combustion (i.e. the oxidation of fuel to carbon dioxide and water vapor) are needed to describe the products. Here, all possible reactions must be considered, including
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incomplete reactions (i.e. the production of carbon monoxide) and side reactions (i.e. the production of nitrous oxide compounds). There are several variations on the general mass balance equation. When the above terms are in units of quantity per time, equation 4.1 is a differential balance that applies at any instant of time. When they express quantity, equation 4.1 is an integral balance that is applicable over a specific time period. Production and consumption are each zero when equation 4.1 is applied to total mass, energy or the mass of a component that is neither formed nor consumed in a chemical reaction.
4.3.2 Mass balances The remainder of this chapter focuses on steady-state, non-reactive processes and, therefore, on relations among input and output flows and compositions. This simplification can be expanded to include production and consumption by applying the same methodology to relevant chemical reactions, the key being complete descriptions of all chemical reactions. The following text also contains some standard nomenclature used in chemical engineering, in particular the subscripts ‘i’ and ‘j’. In a system with many compounds it is useful to use a dual subscript system to keep track of the component (i) and location (j) of interest, especially when discussing mass fractions (x). So, the nomenclature x1,2 refers to the fraction of the compound labeled 1 found in stream 2. In the example below, the letter F refers to the feed stream for the simple case with only one feed. Should multiple feeds be involved, as in the natural gas combustion case (methane and air), numerical subscripts could be used for both. By now, the need for a legend and flow chart is clear. These are first steps that help the designer avoid confusion and mixing up of streams. When equation 4.1 is applied to the mass of component i in the process shown in Fig. 4.1, it assumes the form Fxi ¼ P1 xi1 þ P2 xi2
½4:2
This equation literally states that the fraction of compound i in the feed stream is equal to the fraction of i in each product stream multiplied by the mass of said stream. When it is applied to total mass, it becomes F ¼ P1 þ P2
½4:3
Note that there are as many independently enforceable mass balances as there are components. The proper application of the principle of mass conservation will therefore depend on identifying all of the relevant components and keeping track of their locations. The more precise the quantification of the mass balance, the more involved the required
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measurements. Given that all measuring equipment has detection limits, it is usually necessary to work with an accepted level of uncertainty. The exact level will likely depend on the cost of compliance with regulation and any legal requirements, such as the US Environmental Protection Agency’s Toxic Release Inventory, which for example is measured in millions of pounds annually but must meet guidelines of thousandths of milligrams per liter in the case of mercury. Determining the product flows and compositions that are possible when a mixture of A and B is separated involves mass balances and the identity X xi ¼ 1 ½4:4 i
Understanding equation 4.4 starts with the knowledge that the mass fraction x is dimensionless, meaning it is a fraction that can be expressed in units of kilograms of component per kilogram of mixture. It follows that the sum of the mass fraction of components in any one stream cannot exceed 1, i.e. there is no more mass than that contained in the stream. For example, let F = 100 mol/s and xAF = 0.7, which means that 70 mol/s of component A are entering the separation process contained in 100 mol/s of feed. As a reminder, one mole of a substance is a specified number of molecules known as Avogadro’s number. In addition, the compositions in the product streams are 95% A (xA1 = 0.95) in the first (P1) and 98% B (xB2 = 0.98) in the second (P2). In short, this describes a typical separation process wherein a mixed stream is separated into streams dominated by specific components of the feed. Equation 4.4 can be applied to this example by recognizing that if there are only two compounds and the mass fraction per stream is unity, the product stream 1 must contain 5% B (1 0.95) and P2 must contain 2% A (1 0.98). Mathematically speaking, specification of the product purities has exhausted our degrees of freedom: we are not free to also specify, say, the fraction of the feed that leaves as product 1. The reason for this is that flowrates P1 and P2 are constrained as follows to satisfy two mass balances, e.g., an A balance (equation 4.2) and a total mass balance (equation 4.3). Alternatively, the solution could have been found using a mass balance on compounds A and B, or B and total mass. 9 xA F ¼ xA1 P1 þ xA2 P2 = P1 ¼ 73:1; P2 ¼ 26:9 mol=s 0:7ð100Þ ¼ 0:95P1 þ 0:02P2 ; 100 ¼ P1 þ P2 Check (using the redundant B mass balance) 0:05ð73:1Þ þ 0:98ð26:9Þ ¼ 30 ¼ 0:3ð100Þ ¼ xB F ¼ ð1 xA ÞF Just as important as product purity is component recovery, ri, i.e. the
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fraction of entering component i that emerges in the i-rich product: rA ¼
P1 xA1 73:1ð0:95Þ ¼ 0:992 ¼ FxA 100ð0:7Þ
rB ¼
P2 xB2 26:9ð0:98Þ ¼ 0:879 ¼ FxB 100ð0:3Þ
Recovery of 99.2% of the entering A is likely to be satisfactory when A is valuable and its contamination with 5% B is acceptable. If B is valuable as well, losing 12.1% of it in the A-rich product may be unacceptable. On the other hand, if B has no value and is environmentally hazardous, discharging it in concentrated form is likely to be proscribed, potentially necessitating further processing. Producing high-purity products with high component recoveries is theoretically possible. Doing so in practice depends on an exploitable property difference and a process that will economically exploit it. Evaluating the options begins with preliminary process calculations. As an aside, the mass fraction can also be specified in terms of the number of molecules present; this would be in units of moles per second (mol/s) where one mole is 600 trillion quadrillion molecules (661023), the aforementioned Avogadro’s number.
4.4
Preliminary separation process calculations
In this section, two candidate processes for separating gases A, B and C (e.g. the sulfur dioxide, carbon dioxide and nitrogen in power plant exhaust) are examined.
4.4.1 Gas permeation In the simple membrane permeation device depicted in Fig. 4.3(a), the feed is delivered to the retentate compartment. A fraction permeates (dissolves in, diffuses across and desorbs from the membrane) and exits, via the permeate compartment, as the permeate product. The fraction that does not permeate becomes the retentate product. The membrane’s selectivity is a function of the component permeabilities (Koros and Chern, 1987). Permeability K is defined such that a component’s permeation rate N (mass/time) is the product of its K value, the membrane’s surface area (SM) and the difference between its partial pressures in the retentate and permeate compartments, i.e. across the membrane: Ni ¼ Ki SM ðpR xiR pP xiP Þ
i ¼ A; B; C
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The partial pressure difference is the driving force of permeation; pR and pP are the absolute pressures in the two compartments. Assuming ideal gas behavior, the partial pressure is the product of the absolute pressure and the mass fraction. The term partial pressure refers to the pressure that the component in question would exert if it alone occupied the volume in question. Consider a box filled with air at atmospheric pressure. If oxygen is approximately 21% of the gas in the box and the pressure is 1 atm (i.e. 101.3 kPa) then the partial pressure of oxygen is 0.21 atm. Generating a product enriched in A is possible when KA either exceeds or is less than KB and KC. In the former case, component A passes through the membrane more rapidly and the A-enriched stream is the permeate; in the latter case, components B and C readily pass through, leaving A in the retentate. To simplify the process calculations, we assume the following. . . .
Both compartments are well mixed, which implies that their contents are uniform and their compositions are identical to those of the associated product streams. Only a small fraction of the feed permeates. Therefore, the mass flow leaving in the retentate stream is almost equivalent to the feed (R ≈ F) and the mass fraction of all components is also similar (xiR ≈ xiF). The partial pressure on the permeate side of the membrane is much lower than anywhere else in the system (i.e. pR ≈ pF and pP<< pF).
These conditions represent the situation where the component of interest is a small fraction of the feed gas and a vacuum is used to remove any gas crossing the membrane as soon as it reaches the other side. These simplifications reduce equation 4.5 to Ni &Ki SM pF xiF
½4:6
Equation 4.6 states that the permeation rate (i.e. the rate at which the compound of interest crosses the membrane) is entirely driven by conditions in the feed gas. While the objective of material scientists is to produce membranes permeable to only one component, the reality is that all components will permeate at different rates. It follows that the composition of the permeate product stream under these assumptions is defined as X X Ni ¼pF SM Ki xiF i ¼ A; B; C ½4:7 P¼ i
i
and the mass fraction of each component in the permeate product can be
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4.5 Permeate composition vs. αBA; αCA = 0.2; equimolar feed.
calculated from ai xiF xPj ¼ xAF þ aBA xBF þ aCA xCF
i ¼ A; B; C; aiA
Ki ¼ KA
½4:8
in which the coefficients αBA and αCA refer to the membrane’s selectivities for B and C relative to A. This allows the engineer to calculate, for a given production of A, the relative amount of impurities B and C. To further elucidate these concepts, sample calculations were performed for an equimolar feed gas (xAF = xBF = xCF = 1/3) and αCA fixed at 0.2 (i.e. a membrane five times more permeable to A than to C). Figure 4.5 shows the calculated dependence of the permeate composition on αAB. As one might expect, when αBA = 0.1, the permeate is rich in A (xAP = 0.76); when αBA = 10, the permeate is rich in B (xBP = 0.89). The B-rich permeate is purer ðxi ¼ 1Þ than the A-rich permeate because with αCA = 0.2 and αBA = 10, the membrane is 50 times more permeable to B than to C. Recall that the calculations were for cases in which only a very small fraction of the feed stream permeates. Consequently, the component recoveries are negligible. When larger fractions of the feed permeate (because of a greater membrane area or a higher feed pressure), recoveries will be higher, purities lower. There is a tradeoff between recovery and purity because the gas in the retentate compartment is the source of the
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4.6 Single-stage absorption process; well-stirred vessel; L and G are liquid and gas molar flowrates; x and y are mole fraction arrays; T = 258C; p = 1 atm.
permeate. This tradeoff, which is common to single-stage processes, is again encountered in the next section.
4.4.2 Absorption Absorption, also known as scrubbing, is an equilibrium-based separation that exploits differences in the solubilities of gases in liquids (Kohl, 1987). In general, the process seeks to remove a component of a gas stream, e.g. sulfur compounds that cause acid rain (known as SOx), by transferring them from one phase to another. It differs from adsorption in that the components enter the bulk volume and do not just adhere to the surface. Figure 4.6 depicts a simple absorption process. A nozzle and mechanical agitation generate small gas bubbles and correspondingly large total interfacial areas, both of which promote gas/liquid equilibration and uniformity of phase compositions. Note that typically the mass fraction in the gas phase is denoted using the variable y, instead of x. Consider the selective removal of sulfur dioxide and carbon dioxide from a mixture containing 1 mol% SO2, 15 mol% CO2 and 84 mol% N2, via absorption in water at 258C and 1 atm. The results are predictable on the basis of equation 4.4, plus the following phase equilibrium relationships: xi;out ¼ ki yi;out kSO2 ¼ 2:56102 ; kCO2 ¼ 6:16104 ; kN2 ¼ 1:26105 ; kH2O ¼ 32Þ
½4:9
In equation 4.9, ki refers to Henry’s constant, which defines the ratio of the dissolved content of a gas in relation to the partial pressure in the gas phase above the liquid. Based on the values presented in equation 4.9, SO2 concentrations in water can be 100 times that of CO2 and 1000 times that of
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4.7 Recoveries of SO2 and CO2 (percentages of their removal from the feed gas) as functions of the ratio of the molar feed rates of liquid and gas.
N2. As a result, we would expect little N2 in solution despite the fact that it is almost 100 times more prevalent than SO2 in the gas phase. The curious result is that any gas can be scrubbed using distilled water, which contains no dissolved gases; however, it is usually more economical to find a more aggressive solvent. The concept of component mass balances can also be applied as follows: Gin yi;in þ Lin xi;in ¼ Gout yi;out þ Lout xi;out
½4:10
Equations 4.4, 4.9 and 4.10 comprise ten linear relationships among ten unknowns: the flowrates of the two product streams and four mole fractions for any two of SO2, CO2 and N2. The appendix outlines an easily implemented algorithm for solving them. The important concept is that all of the gases present will enter the liquid phase based on the governing laws and estimations of scrubbing efficiency must track all species. Figures 4.7 and 4.8 depict the dependence on the entering liquid to gas ratio (Lin/Gin) of the calculated SO2 and CO2 recoveries and mole fractions in the exiting liquid (little nitrogen is absorbed owing to the low Henry’s constant). As Lin/Gin increases, the SO2 and CO2 capture rates increase, asymptotically approaching 100%, while their concentrations in the exiting liquid approach zero. Conceptually, a higher L/G ratio means that each bubble of gas will have to traverse through more liquid to reach the exit,
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4.8 Mole fractions of SO2 and CO2 in the effluent vs. the ratio of inlet molar feed rates of liquid and gas.
thus providing more opportunity, as well as a steeper concentration gradient across the liquid. This is highlighted in Fig. 4.7 where the same percentage recovery of CO2 requires an increase in liquid flow proportional to the difference in Henry’s constant. The tradeoff between recovery and purity (admittedly a misnomer in reference to a liquid composed almost entirely of solvent water) is again a characteristic of a single-stage process.This is highlighted in Fig. 4.8 where the liquid to gas ratios needed for high recovery (in Fig. 4.7) result in low mass fractions in the liquid phase (xout) in a larger volume. The tradeoff is more acute should the liquid require treatment. In absorption, it is attributable to the equilibration of the product streams with one another. It is avoidable in counter-current, multi-stage separations.
4.5
Multi-stage separations
The performance limitations of single-stage processes may be overcome without excessive additional operating expenses if judicious design choices are made (Kelly, 1987). The gas permeation process discussed in Section 4.4.1 may be expanded as indicated in Fig. 4.9, by re-compressing and cooling the permeate and feeding it to a second membrane module. Permeate 2 will be purer than permeate 1 (yA2 > yA1,), but A’s recovery will be lower. This is a result of distributing the A recovered from the first stage across two streams making the high-purity fraction (P2 yA2) a smaller portion of that in the feed (FxAF). By the same token, nothing is to be gained by supplementing the single
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4.9 Two-stage gas permeation process.
4.10 Two-stage co-current absorption process. Properties of fluid streams other than the feeds are subscripted with the numbers of the stages of origin.
4.11 Two-stage counter current absorption process. Properties of fluid streams other than the feeds are subscripted with the numbers of the stages of origin.
absorption stage in Fig. 4.6 with a co-current second stage, as depicted in Fig. 4.10 (co-current implies that streams flow in the same direction). This is because the compositions of pre-equilibrated phases will not change when re-exposed to one another. By contrast, substantial dividends are to be derived by operating a twostage process counter currently, as in Fig. 4.11: yA2 will be lower than yA1 (because the gas fed to stage 2 will have been partially depleted of A in stage 1) and xA1 will exceed its value in the single-stage absorption process (Fig. 4.6), both without sacrifice of recovery. The significant advantage of counter current flow is that the concentration gradient (the driving force) is always
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at its maximum. Where the scrubbing solution enters the process, and the gas exits, the gas is depleted but as the solution is ‘empty’ there is still a driving force. Similarly at the other end, the solution is ‘full’ but the component concentration in the gas phase is at its highest, still providing a driving force. This can be compared to co-current flow where the concentrations approach equilibrium near the exit. The foregoing sections have touched the surface of separation processes. As one might imagine, the mechanisms that both drive them and limit their performance are generally more complex, as is noted in Section 4.7.
4.6
Filtration
Processes along the lines sketched in Fig. 4.3(b) are widely deployed both to filter (as in water purification) and to reduce volume (as in the concentration of fruit juice) (Chen et al., 2011). The concept is quite simple. The diameter of the filter’s pores, DP, must be small enough to prevent the passage of targeted molecules and/or particles. The filter, which is essentially a porous membrane, may be anything from a woven cloth that retains silt, clay and sand, to a polymeric film that enables the desalination of brackish water. Table 4.2 classifies filtration processes according to the minimum effective diameter of what is retained, DR, and lists typical values of Δp, the pressure differentials that will ensure acceptable filtration rates. Filtration rates vary directly with Δp and inversely with D2P . Consequently, pumping pressures with associated equipment costs and power consumption, are minimized by deploying a membrane with the largest DP that will provide the desired retention. Because the maximum allowable filter pore size DP increases with the diameter of the target particle or molecule (DR), and the required Δp decreases as DP increases, operating Δp values vary inversely with DR. Filtration can and does produce high-purity water with high recovery. However, the membranes require frequent cleaning to remove biofilms (of proliferating micro-organisms) and filter cakes (of retained particles), both of which are inimical to filtration. Furthermore, even when what is retained remains in solution, filtration is slowed by the tendency of retained solutes to concentrate at the membrane surface – a phenomenon referred to as concentration polarization (see Fig. 4.12). Solutes accumulate until their concentrations at the membrane surface (CSM) reach the point at which their rates of diffusion (random thermal motion that has the effect of transferring solutes to regions of lower concentration) away from the membrane surface offset their rates of convective transfer (solvent drag) to the surface. When CSM reaches a solute’s solubility limit, the solute precipitates, causing the growth of a gel layer analogous to a filter cake, with similarly adverse effects on filtration. A more subtle effect of concentration polarization is an increase in DP,
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Table 4.2 Filtration processes Size (m) Type Examples
Filtration process
1010–109 109–108 108–107 107–106 106–105 105–104 104–103 Ionic Molecular Macromolecular Cellular and microparticulate Metal ions Viruses Sand Sugar ______Proteins______ ____RO____
____Bacteria____ _____________Algae____________ ___Clays___ Silt
______NF______ _________MF________ __________UF__________ ____Conventional filtration____
Δp (atm) 3–70 5–15 2–10 0.5–2.0 0.1–2.0 Source: adapted from Chen et al., 2011. RO, reverse osmosis; NF, nanofiltration; UF, ultrafiltration; MF, microfiltration.
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4.12 Boundary layer region adjacent to filtration membrane, illustrating concentration polarization of retained solute.
4.13 Filtration rate V (volume/time) vs. transmembrane pressure differential; characteristic results with a feed of pure water and a solution of retained solute are shown.
the osmotic pressure differential across the membrane. Because filtration rates are proportional to Δp – DP, osmotic pressure retards filtration. The solid curve in Fig. 4.13 typifies filtration data: rather than increasing monotonically with Δp, as it does with a pure water feed, the filtration rate levels off because of increasing osmotic pressure.
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Conclusions and sources of further information
This chapter has covered the basics of separation processes and demonstrated that separation is possible, provided sufficient energy is expended. The separation process also produces two streams containing a mixture of components in the feed stream. Additionally, it is important to note that in none of the processes is mass destroyed. Separation involves exactly that – a separation that will allow the undesirable component to be concentrated and disposed of in a more secure manner. While they provide definite shortterm benefits, it is also true that lower emission or discharge limits can be offset by larger consumption. Simply put, reducing the emission of SOx compounds by a factor 100 from one facility is offset if 100 more facilities are built. The ratio is reduced further if the new facilities emit more than the original. This is being played out with globalization and the ‘offshoring’ of pollution. This chapter has provided an introduction to the concepts that guide the selection and design of separation processes. Readers seeking more depth and breadth are referred to the textbooks by Noble and Terry (2004), Wankat (2011) and Seader et al. (2011).
4.8
Acknowledgement
The author would like to acknowledge Dr J. Meldon for significant contributions to this chapter. His efforts in providing the fundamental underpinning, topic selection and all the figures are greatly appreciated.
4.9
References
Chen JP, Mou H, Wang LK, Matsuura T and Wei Y (2011) Membrane separation: basics and applications. In Wang LK, Chen JP, Hung Y-T and Shammas NK (eds). Membrane and Desalination Technologies. New York, Springer, pp. 271– 332. Kelly RM (1987) General processing considerations. In Rousseau RW (ed.). Handbook of Separation Process Technology. New York, Wiley, pp. 197–225. Kohl AL (1987) Absorption and stripping. In Rousseau RW (ed.). Handbook of Separation Process Technology. New York, Wiley, pp. 340–404. Koros WJ and Chern RT (1987) Separation of gaseous mixtures using polymeric membranes. In Rousseau RW (ed.). Handbook of Separation Process Technology. New York, Wiley, pp. 862–953. Noble RD and Terry PA (2004) Principles of Chemical Separations with Environmental Applications. Cambridge, UK, Cambridge University Press. Null HR (1987) Selection of a separation process. In Rousseau RW (ed.). Handbook of Separation Process Technology. New York, Wiley, pp. 982–995. Seader JD, Henley EJ and Roper DK (2011) Separation Process Principles, 3rd edn. New York, Wiley.
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Wankat PC (2011) Separation Process Engineering, 3rd edn. Upper Saddle River, NJ, Prentice Hall.
4.10
Appendix: Algorithm for solving equations 4.4, 4.9 and 4.10
The equations are of the following general form: Lxi þ Gyi
¼ Fzi
yi ¼ Ki xi
i ¼ 1; :::; c
c X
i ¼ 1; :::; c
ðA4:1Þ ðA4:2Þ
xi ¼ 1
ðA4:3Þ
i¼1 c X i¼1
yi ¼
c X
K i xi ¼ 1
ðA4:4Þ
i¼1
in which c is the number of components; L = Lout, G = Gout, x = xout, y = yout, F = Lin + Gin, Fzi = Linxin,i + Ginyin,i; Ki = 1/ki. Let f = Gin/F. It follows that Lin/F = 1 f. Division by F and insertion of equation A4.2 transforms equation A4.1 to: ð1 fÞxi þ fKi xi ¼ zi
and so
xi ¼
zi 1 f þ Ki xi
Insertion of equation A4.5 transforms equation A4.3 to: c X zi ¼ 1 1 f þ Ki fi i¼1
ðA4:5Þ
ðA4:6Þ
Equation A4.6 is equivalent to a cth degree polynomial in f, as may be verified by multiplying both sides of it by the product of the c denominators. Accordingly, there are c values of f that will satisfy equation A4.5, pairs of which may be complex conjugates. One real root, easily determined by trial and error, will lie in the physically possible interval of zero to one. The values of all other unknowns follow explicitly from f.
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