J. Hazard. Mat. 165, 944-949. Apiratikul R., Pavasant P., 2008. Batch and column studies of biosorption of heavy metals by Caulerpa lentillifera. Bioresour.
Chapter 3 Fixed-bed adsorption studies
Adriana S. FRANCA 1 and Leandro S. OLIVEIRA 1
1
Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
Introduction The removal of toxic pollutants from aqueous waste streams is currently one of the most important environmental issues being investigated. A great number of industries, such as textile, paper and pulp, printing, iron-steel, coke, petroleum, pesticide, paint, solvent, pharmaceutics, wood preserving chemicals, consume large volumes of water and organic based chemicals and, as a result, generate effluents with large quantities of undesired pollutants that must be removed to acceptable levels before discharge into natural water streams. Currently, the primary concern has always been with the presence of heavy metals due to their high toxicity and impact on human health and environment. Recently, an increasing interest has also been focused on the presence of dyes in waste streams due to their refractory biodegradation and toxic nature, which affects the photosynthetic activity in aquatic life and the subsequent food chain. Other types of problems related to the presence of pollutants in water streams are the eutrophication and deterioration of water bodies caused by excessive phosphate in water, which is usually present in industrial processes effluents, and the high toxicity impaired by phenolic compounds. Adsorption has gained increasing popularity in recent years as a unit operation for removing pollutants from effluents, because, aside from the fact that it produces a high quality treated effluent that can meet stringent environmental emission standards (Sze et al., 2008), it is also recognized to be superior to other techniques for water re-use in terms of initial cost, flexibility and simplicity of design, ease of operation and insensitivity to toxic pollutants (Uddin et al., 2009). Adsorption also does not require the addition of chemical compounds in the process and does not result in the formation of harmful substances (Ahmad
Chapter 3
and Hameed, 2010). Hence, adsorption is by far the most studied technique for the prospective removal of pollutants from wastewater in recent years. The most commonly employed adsorbent for the removal of pollutants from aqueous solutions is the activated carbon, both in laboratory and industrial scales. Although activated carbons present extraordinary capacity for the removal of pollutants, their main disadvantage is their inherently high cost, which requires them to be regenerated for re-use, which further increases the cost of wastewater treatment. Thus, there has been an intensive search for alternative adsorbents, which are of inexpensive materials and do not require any expensive additional pretreatment step, in order to render the adsorptive removal of pollutants from wastewaters more economically viable. This has resulted in the development and successful use of a variety of adsorbents based on solid wastes (Bhatnagar and Sillanpää, 2010, 2009; Oliveira and Franca, 2008). In small-scale laboratory studies, the most common method employed to evaluate the feasibility of removing one or more pollutants from aqueous solutions is the batch adsorption test in which the adsorbent and the adsorbate solution are placed in a flask and kept under agitation for a specific period of time. Adsorption equilibrium isotherms and adsorption kinetics are usually the targeted data in batch tests. The information obtained from adsorption isotherms and contact time studies in a batch system is useful in determining the effectiveness of the adsorbent-adsorbate system and it is generally used for the preliminary screening of an adsorbent before running more expensive tests. However, adsorption isotherms are not sufficient to give all the accurate scale-up data required when designing large-scale effluent treatment systems which employ adsorption columns. The lack of correspondence between batch and column data occurs because (i) adsorption in fixed-bed columns does not necessarily operate under equilibrium conditions since the contact time is not sufficiently long for the attainment of equilibrium, (ii) granular adsorbents rarely become totally exhausted in commercial processes, and (iii) chemical or biological changes occurring in the adsorbent cannot be predicted by the isotherms (Gupta et al., 2000). Besides, other operational problems such as uneven flow pattern (channeling) in the column, recycling and regeneration cannot be studied in batch experiments. Therefore, continuous adsorption studies are required to collect the experimental data for the design of adsorption columns and for subsequent scale-up from pilot plant to industrial scale operation. The most relevant information to be determined in laboratory experiments and to be used in the design of large-scale fixed-bed systems is the breakthrough curve or the shape of the adsorption wave front within the column, which determines the operating life-span of the bed and its regeneration time. The amount of solute adsorbed has a determinant impact on the effective use of the column, but the operating time will also play a major role in the column performance for it will determine the throughput of the process. The dynamic behavior of a fixed-bed adsorption column and the characteristic breakthrough curve of the adsorption phenomena can be more easily studied through mathematical models. The prediction of breakthrough behavior has been addressed in the literature by the use of two distinct types of mathematical models (Wu et al., 2005): (i) simplified semi-empirical models that are based on an approximated theory of dynamic adsorption and empirical knowledge; and (ii) sets of partial differential equations that accurately describe the adsorption process in fixed beds. It should be emphasized at this point that the literature pertaining fixed-bed adsorptive removal of wastewater pollutants is quite abundant and it is not the purpose of this chapter to cover the extensive information they present, but rather highlight and critically analyze the information that directly contributes 80
Fixed-bed adsorption studies
to the clear understanding of the current status and the future perspectives of fixed-bed adsorption studies for the removal of pollutants from wastewaters. Therefore, this review is structured into two parts, i.e., a discussion of the fundamental concepts and calculations involved in fixed-bed adsorption followed by an overview of fixed-bed adsorption studies with specific applications in pollutant removal. Determination and prediction of breakthrough curves Industrial adsorption processes are in many cases associated with adsorption in a column. Adsorbent particles are packed in a column and a fluid that contains one or more adsorbates flows through the bed. Adsorption takes place from the inlet of the column and proceeds to the exit. In the course of adsorption, a saturated zone is formed near the inlet of the column and a region with decreasing concentration is observed throughout the column (Suzuki, 1990). Adsorption will take place in Figure 1. Schematic representation of the mass transfer zone (adsorption front) this region, the so called “mass movement through the column. transfer zone”, represented schematically in Figure 1. When the volume of the fluid begins to flow through the C Saturation point column, the mass transfer zone varies from 0% of the inlet concentration (corresponding to the adsorbate-free adsorC bent) to 100% of the inlet concentration (corresponding to total saturation of the Breakthrough Breakthroughpoint point adsorbent). From a practical C point of view, the saturation t t t Time time, ts, is established when the adsorbate concentration in the Figure 2. Schematic representation of a breakthrough curve. effluent reaches 90-95% of the inlet concentration, at which the adsorbent is considered to be essentially exhausted (Calero et al., 2009). If adsorbate concentrations in the effluent stream are measured continuously, the dynamic behavior of the column can be described in terms of the concentration-time profile, also known as the “breakthrough curve” (see Figure 2). The breakthrough point or breakthrough time is chosen arbitrarily at some low effluent concentration. Effluent Concentration
i
50
r
r
50
s
81
Chapter 3
The breakthrough curve can also be expressed in terms of a normalized concentration, usually defined as the ratio between the adsorbate concentrations in the fluid at the outlet and inlet of the column (C/Ci), as a function of time (t) or volume of the effluent (Vef , mL), for a fixed value of bed height. The volume of the effluent can be calculated by Eq. (1) where ttotal is the total time (min) necessary for the adsorption front to establish itself and move down the length of the adsorbentfilled column, and Q corresponds to the volumetric flow rate through the column (mL min-1). The adsorption front corresponds to the portion of the curve between the breakthrough and saturation points, and is assumed to have a constant length or depth, δ. The time required for movement of the adsorption front along the column is given by Eq. (2) where Vb represents the volume of the effluent (mL) at breakthrough time.
Vef = Q × ttotal
(1)
tδ =
Vvf – Vb Q
(2)
Given that the adsorption front moves at a constant rate, the time and depth ratios are equal and the relation is given by Eq (3) where z is the bed depth and tf is the time required for initial formation of the adsorption front. The fractional capacity of the adsorbent in the adsorption front at break point is given by Eq. (4). The area under the breakthrough curve represents the total mass of adsorbate that was removed (mtotal) for a specific inlet concentration and flow rate. It can be calculated using Eq. (5) where C is the adsorbate concentration in the fluid phase (mg mL-1). δ tδ (3) = z ttotal – tf
f =1– mtotal =
Q 1000
tf tδ t=ttotal
∫ t=0
(4) Cdt
(5)
The adsorbate removal efficiency (%R) can be evaluated using Eq. (6). The adsorption capacity, qe (mg of adsorbate per g of adsorbent) and the equilibrium concentration, Ce (mg L-1), can then be determined using Eqs. 7 and 8 where m corresponds to the mass of adsorbent (g) within the column. The service or breakthrough time, tr, is established when the adsorbate (pollutant) concentration in the liquid phase (effluent) reaches a determined value, generally related to the permitted disposal limit for that specific pollutant, that makes possible to determine the effluent volume treated (Calero et al., 2009). 1000mtotal %R = × 100 (6) Ci Qttotal 82
qe =
mtotal m
(7)
Fixed-bed adsorption studies
Ce =
Ci Qttotal / 1000 – mtotal Vef
(8)
For design purposes, two major parameters are of interest in fixed bed adsorption: (i) the total volume of effluent passed per unit cross section at the breakpoint, and (ii) the nature of the breakthrough curve (Gupta et al., 2000). The development of a model that describes the breakthrough curve is difficult in most cases, since the adsorbate concentration in the fluid, which moves across the adsorbent, changes continuously and, thus, the process does not operate at steady state. In order to provide an accurate description of adsorption dynamics such model should be comprised of (i) conservation equations representing the mass and heat transfer phenomena involved, (ii) one or more equations representing the mechanisms that control adsorption rate, and (iii) an isotherm equation representing equilibrium behavior. Given that the fundamental equations that describe adsorption in a fixed-bed column depend on the mechanism responsible for the process (mass transfer from the fluid to the surface of the solid, diffusion and/or reaction on the surface of the solid), these must include mass balances for the sorbed solute between the solid and the fluid and the rate of the process, among other factors. The material balance for each component of interest (adsorba te) for a control volume defined in either the fluid or solid phase can be written as: mass rate of component change
=
mass flux of component in
–
mass flux of component out
mass rate of ± of component adsortion/desorption
The flux of a component in or out of the control volume can include bulk flow, dispersive flow and molecular diffusion (Weber Jr. and Smith, 1987). The resulting differential equations representing the variation of adsorbate concentration in both the fluid and solid phases can be represented by Eqs. (9) and (10) where C and q correspond to adsorbate concentrations (mg L-1) in the effluent and in the solid, respectively, εb represents the bed porosity, Uo is the superficial velocity (cm min−1) and Dl and Ds represent the liquid and solid diffusion coefficients, respectively. δC δC δ 2C δq εb + Uo (9) – D1 + (1 – εb ) = 0 2 δt δz δz δt
δq Ds δ 2 δC – 2 r = 0 δt δr r δr
(10)
By use of an appropriate equation of state, the conservation equations can be also adapted for a gas feed (Crittenden and Thomas, 1998). An evaluation of Eq. (9) shows that the first term of the equation represents the accumulation of adsorbate in the fluid phase. The second term represents the convective flow within the bed and, taking a more rigorous approach, the velocity term should be placed inside the derivative. Nevertheless, changes in bulk fluid velocity across the mass transfer zone are negligible for systems comprised of a dilute solution of a specific adsorbate in an inert carrier fluid, which is the case for the majority of studies applied to pollutant removal. However, if the adsorbate is present at high concentrations, the fluid velocity will decrease along the bed and the variation of velocity should be retained inside the derivative term in the model (Crittenden and Thomas, 1998). The third term in Eq. (9) represents the axial dispersion within the bed. It can be 83
Chapter 3
omitted if plug flow is assumed, that being the case in most of the studies given that it is undesirable to have radially dispersed flow in an adsorption bed. Nonetheless, if axial dispersion is significant, that term should be taken into consideration and the flow is usually referred to as dispersed plug flow. The fourth and last term depicted in Eq. (9) represents the rate of adsorption, and is written in general form as in Eq. (11) where the adsorption rate, rad (mg L−1 min−1), depends on the mechanism responsible for adsorption. This mechanism may be controlled by mass transfer from the bulk solution to the surface of the adsorbent. Alternatively, it may be controlled by diffusion and reaction within the adsorbent particles. So, a mathematical description of adsorption rate must be added to these transport equations. The adsorption isotherm equation is the fourth and final key equation for the mathematical modeling of a fixed bed adsorption process. δq (1 – εb) = rad (11) δt The equations derived to model the system with theoretical rigor are differential in nature and usually require numerical methods to solve. In general, complete time-dependent analytical solutions to differential equation based models of the proposed rate mechanisms are not available. Because of this, various simple mathematical models have been developed to predict the dynamic behavior of the column and allow some kinetic coefficients to be estimated. However, many of these models do not take into account mass transfer and are, therefore, less rigorous than other theoretical models. They will be presented firstly in the following paragraphs, followed by the more complex models based on mass transfer theory. Bohart and Adams model (BDST) The fundamental equations describing the relationship between adsorbate concentration and time in a flowing system were established by Bohart and Adams (1920) for the adsorption of chlorine on charcoal. In the literature, it is referred to as either Adams-Bohart or Bohart-Adams model. Although it was originally applied to a gas-solid system, it has been extensively employed for liquid/ solid systems to describe pollutant adsorption in fixed bed columns, including dyes (Han et al., 2009, 2008; Batzias et al., 2009; Batzias and Sidiras, 2007; Hamdaoui, 2006), heavy metals (Calero et al., 2009; Mondal, 2009; Kiran and Kaushik, 2008; Malkoc et al., 2006; Goel et al., 2005; Sağ and Aktay, 2001) and phenols (Aksu and Gonen, 2004; Wolborska, 1989). This model, which is equivalent to the logistic or S-shaped curve (Oulman, 1980), assumes that the adsorption rate is proportional to both the residual capacity of the solid and the concentration of the adsorbing species. It is better suited to describe the initial part of the breakthrough curve (Calero et al., 2009; Piscitelle et al., 1998). It can be described by Eq. (12) where k AB is the kinetic constant (L mg−1 min−1). The analytical solution of the previous equation together with the mass balance (Eq. 9) and neglecting axial dispersion is given by Eq. (13) (Chu, 2010; Bohart and Adams, 1920) where ρp represents the apparent adsorbent density (g cm-3) and v is the interstitial velocity (cm s-1). δq = kABC(qe – q) (12) δt
84
Fixed-bed adsorption studies
C exp(α) z k ρ q z 1 – εb = , α = kABCi t – , β = AB p e Ci exp(α) + exp(β) + 1 Uo ν εb
(13)
This model is commonly employed with the following simplifications: (i) the sum of exponential terms, exp(α)+exp(β), is usually larger than 1, so the “1” is neglected, and (ii) the z/Uo term in α is neglected in comparison to t, given that the time needed for the adsorbate to exit the column is much larger than the time needed for the solution to flow from the inlet to the outlet. Also, the expression ρpqe(1-εb) is equivalent to the sorption capacity per unit volume of the bed, No, and εbν corresponds to the superficial velocity, Uo. After taking the natural logarithm the resulting equation can be written according Eq. (14) where Ci and C are the inlet and effluent adsorbate concentrations (mg L−1), respectively, z represents the bed depth (cm) and t is the time (min). Based on this equation, values describing the characteristic operational parameters of the column can be determined from a plot of ln (Ci /C -1) against t at a given bed height and flow rate. The Bohart-Adams model in its linear form is also known as Bed Depth Service Time or simply BDST (Walker and Weatherly, 1997), given the direct relationship between these parameters, z and t (Hutchins, 1973). Setting t=0 and solving Eq. (14) for z yields Eq. (15) where z0 corresponds to the minimum bed depth to be provided for an effluent of maximum desired concentration C. Eq. (14) can be re-written according Eq. (16) where a = kAB N0 z/U0 and b = kABCi . This equation corresponds to the “logistic curve”, an S-shaped curve symmetrical around its midpoint at t = a/b, C = Ci/2. One of the limitations of applying this simple logistic function is that it requires symmetry, which is not the case of many breakthrough curves, given the nature of the adsorption systems under study. A recent study indicates that the BDST model was not appropriate for describing non-symmetric breakthrough curves obtained for copper biosorption on seaweed biomass immobilized in polymeric beads, controlled by internal diffusion (Chu and Hashim, 2007). The basic assumptions that the intraparticle diffusion and external mass resistance are negligible, and that adsorption kinetics is controlled by the surface chemical reaction between the solute and the adsorbent, are rare in real systems. The model is also not accurate in predicting the effects of changes in breakthrough concentration (Ko et al., 2000). Nevertheless, besides its inherent limitations, the BDST model has been regarded as the simplest approach in fixed bed analysis enabling the most rapid prediction of adsorbent performance (Ayoob et al., 2007; McKay and Bino, 1990). C z ln i – 1 = kAB N0 – kAB Ci t (14) U0 C
z0 =
U0 C ln i – 1 kAB N0 C
(15)
C 1 = Ci 1 + e a–bt
(16)
Clark model Clark (1987) developed a mathematical model to overcome the symmetry problem of simple logistic function, by incorporating the parameter n of the Freundlich adsorption isotherm. It is based on 85
Chapter 3
the combination of the mass transfer concept and Freundlich isotherm, and the resulting equation can be represented by Eq. (17) where n corresponds to the inverse of the slope of the Freundlich isotherm. A recent study by Han et al. (2009) found that the Clark model was more adequate for the description of breakthrough curves obtained for methylene blue adsorption by tree leaf powder in comparison to Bohart-Adams, which was only suitable for the initial portion of the breakthrough curve. On the other hand, in a study by Hamdaoui (2009) regarding the removal of copper by Purolite C100-MB cation exchange resin, a better description of the breakthrough curve with BohartAdams model in comparison to Clark’s was obtained. 1/ n–1 Cin–1 C= (17) 1 + e a–bt Thomas model Thomas model (Thomas, 1944) is one of the most general and widely employed in association to biosorption in fixed bed columns (Calero et al., 2009; Zhang et al., 2009; Han et al., 2007; Aksu and Gonen, 2004). It assumes Langmuir kinetics of adsorption–desorption and no axial dispersion. Its major limitations are associated to the fact that it is based on second order reversible reaction kinetics and also on the consideration that adsorption is controlled by the mass transfer at the interface and not limited by the chemical reaction. It is commonly presented in the literature by the expression described in Eq. (18) or in its linearized form (Eq. (19)) where kTH is the Thomas rate constant (mL min-1 mg-1) and q0 corresponds to the maximum concentration of the solute in the solid phase or maximum adsorption capacity (mg g-1). A comparison between Eqs. (14) and (19) indicates that this is equivalent to the BDST model, with U0 = Q/S and N0 zS = q0 m(S corresponds to the bed cross-section area). C 1 = (18) Ci 1 + exp[(kTH / Q)(q0m – CiVef)]
ln
Ci k qm – 1 = TH 0 – kTHCi t Q C
(19)
According to Chu (2010), Eq. (19) has been erroneously labeled as the Thomas model in the literature. The actual Thomas model assumes that adsorption can be described by a pseudo second-order reaction rate expression (Eqs. (20) and (21)) where K = kT1 / kT2 , k T1 corresponds to the second-order forward rate constant and kT2 is the first-order reverse rate constant. The previous equation is also known as the Langmuir kinetic equation, given that at equilibrium (δq / δt = 0) it will result in the well known Langmuir isotherm equation. The main difference between the BDST and Thomas models is related to the form of isotherm. While the former assumes a rectangular isotherm, the later assumes a Langmuir one. However, if K LC >> 1, the Langmuir isotherm approaches the rectangular one and both models become equivalent. The reader is referred to the article by Chu (2010) for further discussions on the differences and similarities between these two models and their derivations.
86
Fixed-bed adsorption studies
δq = kT1C(q0 – q) – kT2 q δt
(20 )
δq q = kT1 C(q0 – q) – δt K
(21)
Yoon and Nelson model The following model, mathematically similar to the previous one (see equation 18), was proposed by Yoon and Nelson (1984) for description of adsorption of gases onto activated coal. It is based on the assumption that the probability of adsorption for each adsorbate molecule decreases at a rate proportional to both the adsorbate adsorption and adsorbate breakthrough probabilities. It can be represented by Eq. (22) where kYN is the Yoon and Nelson’s proportionality constant (min−1) and t50 corresponds to the amount of time required for attaining 50% of the initial adsorbate concentration (min). This model does not require any detailed data regarding the characteristics of adsorbate and adsorbent, and the physical properties of adsorption bed (Aksu and Gonen, 2004). The product between kYN and t50 is constant for a specific adsorbate and adsorbent, and also independent of both the inflow adsorbate concentration and the flow rate (Yoon and Nelson, 1984; Tsai et al., 2000). If this model provides an accurate description of the experimental data, a plot of C/(Ci-C) versus time will provide a straight line of slope 1/ kYN and intercept t50 . According to this model, the amount of adsorbate being removed in a fixed bed corresponds to half the amount entering the column for a time of 2 x t50 . Thus, for a specific bed, Eq. (23) can be written. According to the previous equation, the maximum adsorption capacity varies as a function of inlet adsorbate concentration, flow rate, adsorbent mass and 50% breakthrough time (Sivakumar and Palanisamy, 2009). C 1 = (22) Ci 1 + exp[kYN (t50 – t)]
q0 =
mtotal Ci /2[Q × 2t50] C Qt = = i 50 1000m m 1000m
(23)
Wolborska model This model was proposed for the description of adsorption dynamics using mass transfer equations for diffusion mechanisms in the range of the low-concentration breakthrough curve (Wolborska, 1989). It can be described by the Eqs. (24) and (25) where Cs is the adsorbate concentration at the interface between the adsorbent and the fluid phase (mg L−1), D is the axial mass diffusion coefficient (cm2 min−1), ν is the velocity of the migration front (cm min−1) and βa is the kinetic coefficient of the external mass transfer (min−1). δq δq =–ν = βa(C – CS) (24) δt δz
87
Chapter 3
δC δC δq δ 2C + Uo + =D (25) δt δz δt δz2 Considering Cs
