SIMULATION OF PRESSURE SWING ADSORPTION IN FUEL ETHANOL PRODUCTION PROCESS

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1 SIMULATION OF PRESSURE SWING ADSORPTION IN FUEL ETHANOL PRODUCTION PROCESS Innovation Driven Solutions Focused

2 Available online at Computers and Chemical Engineering 32 (2008) Simulation of pressure swing adsorption in fuel ethanol production process Marian Simo a,, Christopher J. Brown b, Vladimir Hlavacek a a Department of Chemical and Biological Engineering, University at Buffalo, Buffalo, NY 14260, USA b Thermal Kinetics Systems, 667 Tifft Street, Buffalo, NY 14220, USA Received 7 February 2007; received in revised form 23 July 2007; accepted 31 July 2007 Available online 6 August 2007 Abstract Fermentation derived ethanol is gaining wide popularity as a car fuel additive. A major challenge in the production of ethanol is the high energy cost associated with the separation of ethanol from the large excess of water. Distillation is usually the method of choice; however, water cannot be completely removed due to the presence of the azeotrope. The pressure swing adsorption (PSA) process is attractive for the final separation since it requires little energy input and is capable of producing a very pure product. The goal of this work was to perform a thorough analysis of the PSA process and find process improvements with the aid of mathematical modeling. A general purpose package for the simulation of a cyclic PSA process was developed. The system of partial differential equations was solved via method of lines using a stiff equation integration package. Parameters for the model are based on the data from an operating plant as well as data from the literature. For the ethanol production technology our model provides a fundamental understanding of the dynamics of the cyclic process and effects of some operating parameters Elsevier Ltd. All rights reserved. Keywords: Pressure swing adsorption; Fuel ethanol; Water adsorption; 3 Å zeolite; Method of lines; Modeling 1. Introduction In the past, extractive or azeotropic distillation processes have been used to break the water ethanol azeotrope (Black, 1980). Since distillation routes are energy intensive and expensive, lower energy separation alternatives such as liquid liquid extraction, adsorption and membrane processes have been analyzed. The pressure swing adsorption (PSA) process has succeeded on the industrial scale. Ethanol can be produced by fermentation of practically any starch containing feedstock. Fermented liquor is distilled in a series of distillation columns including a stripping column, rectifying column, and in some processes an added side stripper. To produce anhydrous ethanol, water is removed with an appropriately sized molecular sieve sorbent. A 3 Å zeolite possesses micro-pores, where due to the small size of the pores, the water molecules are adsorbed while the ethanol molecules are not. The Corresponding author. address: msimo2@eng.buffalo.edu (M. Simo). rectifying column is used to produce high ethanol content vapor, which is fed to a PSA unit; a 99.5% (by weight) ethanol stream leaves the operation as the final product. The PSA process has proven to be much more energy efficient compared to the classical processes and presently is commercially well established as a separation process for dewatering the mixture of ethanol and water. The typical PSA cycle includes a production step in which vapor flows into the vessel from the top at a high pressure; water is adsorbed while the ethanol vapor passes through the column and is collected as the high pressure product at the bottom of the bed. After the production step, the bed must be regenerated and prepared for the next cycle. First, the pressure in the bed is reduced while some water is desorbed. This step is referred to as the depressurization step. In the next regeneration step, water is desorbed from the bed under the vacuum. Near the end of the regeneration step, a portion of product gas (99.5% ethanol) is used to purge the vessel to remove the adsorbed water that had been adsorbed during the production step. Then, the vessel is re-pressurized with product ethanol vapor from the operating vessel. The adsorbent bed has then completed its pressure /$ see front matter 2007 Elsevier Ltd. All rights reserved. doi: /j.compchemeng

3 1636 M. Simo et al. / Computers and Chemical Engineering 32 (2008) Nomenclature c fluid phase molar concentration (mol m 3 ) c p isobaric specific heat (J kg 1 K 1 ) c s speed of sound (m s 1 ) d p particle diameter (m) D bed diameter (m) D ax axial effective dispersion coefficient (m 2 s 1 ) D eff effective diffusion coefficient (m 2 s 1 ) F mass flow rate (kg h 1 ) G mass velocity (kg m 2 s 1 ) k ef axial effective thermal conductivity (W m 1 K 1 ) k f external mass transfer coefficient (m s 1 ) k LDF linear driving force mass transfer coefficient (s 1 ) K Langmuir isotherm equilibrium constant (Pa 1 ) M molar weight (kg mol 1 ) Mach Mach number P pressure (Pa) q molar loading in adsorbed phase (mol kg 1 ) q s saturation loading (mol kg 1 ) q* equilibrium loading (mol kg 1 ) Q isosteric heat of adsorption (J mol 1 ) r p adsorbent particle radius (m) R universal gas constant (J mol 1 K 1 ) Re Reynolds number t time variable (s) T temperature (K) u superficial fluid velocity (m s 1 ) Y fluid phase molar fraction z spatial coordinate (m) Greek symbols α pressure ratio (=P F /P P ) ε gas void fraction κ ratio of isobaric and isochoric specific heats ρ density (kg m 3 ) Subscripts b bulk or packed bed F feed stream (or high pressure step) conditions g gas (fluid) phase i adsorbing component (water) p particle P purge stream (or low pressure step) conditions s solid (adsorbed) phase 0 nozzle inlet conditions or reference state for isotherm 1 nozzle exit conditions swing cycle and is ready to enter a new production step. Numerous PSA cycles have been devised using two or more adsorbent beds; all of them use the steps described above with slight variations. A precise design of the PSA unit is a difficult task because of many interacting operational parameters characterizing this separation process. Laboratory scale experiments are time consuming and economically demanding. These reasons have lead to the development of mathematical models which are used for initial evaluation of the PSA process. Reliable models enable us to calculate the basic operational characteristics, size the system, and evaluate different scenarios of operation. 2. PSA simulation model The mathematical model describing the five-step PSA process, involving high-pressure adsorption, depressurization, regeneration with purge and pressurization, has been used in the present study for the simulation of the water ethanol separation. A non-isothermal non-adiabatic dispersed plug flow model with variation of axial velocity has been used. The model assumes non-linear adsorption equilibrium. The mass transfer rate is described by the linear driving force (LDF) approximation. Based on assumptions of the adsorbing system, PSA bed models can be described by models having different levels of characterization of the system. Several transport effects, including the mechanisms of intra-particle diffusion and external mass transfer need to be considered. In our analysis, the LDF model will be used as a compromise between accuracy and calculation efficiency. To have a reasonable description of the transient adsorption system following balances and relations should be considered: 1. Mass balance for each component. 2. Energy balance for the gaseous and adsorbed phase and the solid adsorbent matrix. 3. Description of the component transfer rates in the gas and adsorbed phase. 4. Adsorption equilibrium relationship for each component. 5. Equation of state for the gas phase. 6. Momentum balance Mass conservation equations The conservation equations for mass consider the convection flow term, axial eddy diffusion term, accumulation and source term caused by the adsorption process on the solid matrix. The equations are represented by a set of highly non-linear parabolic partial differential equations. The term representing the axial dispersion is very small compared to the convection term and therefore the equations show the properties of hyperbolic nonlinear differential equations of the first order. However, the dispersion term eliminates the shock-like behavior and it is easier to solve these equations compared to those where the dispersion term is eliminated. The spatial discretization must be done carefully to suppress the numerical dispersion. A material balance for component i over a differential volume element yields c i = D ax 2 c i z 2 1 ε z (uc i) (1 ε) q i ρ s ε (1)

4 M. Simo et al. / Computers and Chemical Engineering 32 (2008) When the column pressure changes with time, the overall material balance equation is C = C ε u z (1 ε) ε ρ s n i=1 q i Eq. (1) can be substituted to Eq. (2) in order to remove the derivative u/ z: c i 2 c i = D ax z 2 u c i ε z + c 1 C i C ( (1 ε) q i n ρ s Y i ε i=1 After applying the ideal gas law and assuming only one adsorbate Eq. (3) becomes Y i = D ax 2 Y i z 2 u Y i ε z + Y 1 i P q i P ) (2) (3) (1 ε) RT q i ρ s ε P (1 Y i) (4) The last equation represents the component material balance. The term containing the P/ derivative is identically zero for constant pressure steps such as adsorption and the regeneration steps. This term is non-zero only for variable pressure steps. However, we have neglected it completely in our model since its contribution was very small Energy balance The energy balance considers an accumulation term, axial effective heat conduction term, convection term and source term due to adsorption desorption process. We have considered here an idealized effective temperature that would correspond to a temperature in the system of solid particle fluid phase, where the heat transfer coefficient between the particle and adjacent fluid is infinite: [ ρ g c pg + 1 ε ] T ρ s c ps ε = k ef 2 T z 2 u ε ρ gc pg T z ε) q i + Q(1 ρ s ε This type of model is referred to as the one-phase model. The axial effective thermal conductivity (k ef ) may play an important role for the system water ethanol. The second order term is relatively small outside the adsorption front; however, since the adsorption is strongly exothermic, the temperature fronts can be very steep with high values of the second derivative. As a result, this term can be very large in the front and can change the velocity of the front propagation. We have used the correlation proposed by Votruba to estimate the effective thermal conductivity (Votruba, Hlavacek, & Marek, 1972). (5) 2.3. Momentum balance Rigorous mathematical model needs to consider the momentum balance in the full form. However such a model would be complicated and as a result computational time may increase dramatically. According to other authors, the time constant for momentum balance is much smaller than the time constants for mass or heat transfer balances and therefore we have considered the momentum balance as a quasi-steady-state equation (Todd & Webley, 2005). For the description of the pressure velocity relation we have used the Ergun correlation that is routinely used in the design of catalytic and adsorption systems: dp dz = 1 ε ( b ε (1 ε ) b) ρg u 2 (z) ep R (z) (6) d b p 2.4. Adsorption equilibrium To describe the equilibrium relation between the gas and solid phase, Langmuir isotherm was used, see Table 1. For design purposes this isotherm was capable of describing the laboratory data with a reasonable accuracy. Equilibrium data for water uptake were provided by the adsorbent manufacturer. The parameters of the isotherm are given in Table Mass transfer rate The source term in the mass and energy balances should be calculated by solving the diffusion equation in the porous structure of the adsorbent matrix. In order to simplify the model, the linear driving force (LDF) approximation is adapted for the PSA applications. However, this lumped model works well only when the diffusional time constant r 2 p /D ef is small compared to the cycle time (Ahn & Brandani, 2005). In our case of the ethanol water separation the diffusional time constant is 5 s and the cycle time is 345 s, and thus the LDF rate model may be considered adequate. External mass transfer is also considered. This mechanism is not the rate controlling, but it makes a contribution to the overall resistance especially during the desorption stage: [ ] 1 r p rp 2 = + k LDF 3k f 15ε p D eff q i ρ p c i (7) We have used the LDF expression proposed by Gorbach, Stegmaier, and Eigenberger (2004). Their experimental results show that the major mass transport mechanism within the pore structure is molecular diffusion; Knudsen diffusion makes contribution to the overall resistance at low pressure steps and surface diffusion is completely negligible. The value of the external mass transfer coefficient was estimated from the correlation reported by Wakao and Funazkri (1978). The value of tortuosity was assumed to be equal to 2 according to the work of Teo and Ruthven (1986).

5 1638 M. Simo et al. / Computers and Chemical Engineering 32 (2008) Table 1 Governing equations and simplifications Mass balance for adsorbing component Overall mass balance LDF rate Energy balance Pressure drop Equilibrium Simplifications Y i = D ax 2 Y i z 2 1 P 1 T P T u ε Y i z = 1 u ε z 1 u ε P (1 ε) RT q i ρ s ε P (1 Y i) P z + 1 u T ε T z (1 ε) RT ρ s ε P [ ] q i = k LDF (qi q 1 rp rp 2 q i) = + i ρ p k LDF 3k f 15ε p D eff c i [ ρ g c pg + 1 ε ] T 2 T ρ s c ps = k ef ε z 2 u ε ρ T gc pg z dp dz = 1 ε ( b ε (1 ε ) b) ρg u 2 (z) ep R (z) d b p ( qi = qi s K(T )P i K ), ln = Q ( K(T )P i K 0 R T 1 ) T 0 n i=1 (1 ε) q i + Q ρ s ε 1. Ethanol is considered as inert (only one adsorbing component) 2. Local thermal equilibrium assumption one-phase model 3. Momentum balance follows quasi-steady-state model 4. Mass transfer mechanisms considered: external mass transfer and macro-pore diffusion 5. Flow through valves is isentropic 6. Ideal gas equation of state for vapor phase q i 2.6. Calculation of linear velocity An assumption of the constant velocity within the bed is acceptable for the trace systems; here the adsorbed component is present at low concentrations in a large excess of an inert carrier. Provided that the pressure drop is small the velocity can be considered as a constant. However, if the adsorbate concentration is high (in our case adsorbate concentration is 20 vol.%) we cannot assume linear velocity constant. Variation of velocity is given from overall mass balance (2); its rigorous form is C = 1 ε (1 ε) (Cu) z ε ρ s n i=1 q i After applying the ideal gas law Eq. (8) yields 1 P 1 T P T = 1 ε u z 1 u P ε P (1 ε) RT ρ s ε P z + 1 ε n q i i=1 u T T z This is the overall material balance in the most general form. For numerical purposes such equation is not convenient. The terms containing space derivatives and coefficients containing dependent variables are sources of numerical problems. In addition, two time derivatives in the left hand side of (9) would lead to an implicit system of differential equations; numerical integration would then be required to solve a system of algebraic equations at each integration step. The most convenient way to deal with the problems like this is to approximate this equation according to a general formula: [f (y) F(y)] n+1 [f (y)] n [F(y)] n+1 (10) (8) (9) Here f(y) represents the coefficients containing the dependent variable(s) and F(y) is the linear differential operator. For reasonably short time steps the approximation results in differential equations with locally constant coefficients. The approximation (10) yields significant saving in the computational time Compressible flow valve equation Flows are typically considered compressible when the density varies by more than 5 10%. The one-dimensional gas flow through nozzles, orifices and in pipelines is the most important application of the compressible flow. In the PSA technology we encounter the problem during the depressurization and repressurization of the bed. The speed of sound for an ideal gas and the Mach number can be calculated from: κrt c s = (11) M Mach = u c s (12) When Mach = 1, the flow is critical or sonic and the velocity equals to the speed of sound. The compressibility effects are important if the Mach number exceeds 0.1. In the process plant pipelines, the compressible flow is better approximated by adiabatic rather than isothermal conditions. An adiabatic discharge of an ideal gas through a frictionless (reversible) nozzle is isentropic (Perry, 1997). In terms of the exit Mach number (Mach 1 ) and the upstream stagnation conditions 0, the flow conditions at the nozzle exit 1 are given by ( P 0 = 1 + κ 1 ) κ/(κ 1) P 1 2 Mach2 1 (13) T 0 T 1 = 1 + κ 1 2 Mach2 1 (14)

6 M. Simo et al. / Computers and Chemical Engineering 32 (2008) ( ρ 0 = 1 + κ 1 ) 1/(κ 1) ρ 1 2 Mach2 1 (15) G = P 0 κm RT 0 Mach 1 (1 + ((κ 1)/2)Mach 2 1 )(κ+1)/2(κ 1) (16) The exit Mach number Mach 1 may not exceed the value of 1. Eqs. (13) (16) were used to estimate the exit velocity of the gas at the bottom of the bed for the depressurization and re-pressurization steps. The flow conditions during the first depressurization step are critical. First, critical pressure is calculated using Eq. (13) by setting Mach 1 = 1. The value of critical pressure is then compared to downstream (external) pressure (P 2 ). If P 1 > P 2 then the flow is choked and exit pressure is equal to critical pressure. Mass velocity is given by Eq. (16). Under choked flow conditions, sonic velocity must be evaluated at nozzle exit using proper values for temperature and density, Eqs. (14) and (15). IfP 1 < P 2 then the flow is subsonic and exit pressure equals to external pressure P 2. Mach number is evaluated using Eq. (13) and afterwards mass velocity is given by Eq. (16). In our program, valve sizes were adjusted such that the actual pressure history data were reproduced. The valve size is necessary to calculate the exit velocity as well as the mass flow rate of fluid entering or leaving the bed. In an ethanol plant, the rate of pressure changing steps is restricted due to limited mechanical stability of the adsorbent material; e.g. faster pressurization led to the occurrence of zeolite dust particles in the product stream. In case of depressurization steps, the size of the exhaust condensers and vacuum level used are the major limiting factors Governing equations and simplifications The governing equations describing the problem are summarized in Table 1 and the corresponding initial and boundary conditions in Table 2. It s known that as many as 10,000 cycles may be needed to get to periodic steady-state in a PSA process. Therefore it is desirable that the problem will be solved in a timely fashion. Following section discusses various solution techniques and their efficiency. 3. Solution of the governing equations The governing equations reported in Table 1 represent a system of partial differential equations (PDEs) that typically have a steady-state attractor. In the literature this attractor has been called cyclic steady state (CSS). However, owing to the highly non-linear behavior of the governing equations one can also expect multiplicity of CSS, oscillatory or chaotic behavior of the attractor. Stepanek, Rajniak, and Kubicek (1999) observed Table 2 Initial and boundary conditions for governing equations a Cycle step Note I. Adsorption step t =0 Ȳ = q = 0, T = T b, P = P F, Ȳ = Ȳ (V.), q = q (V.), T = T (V.), P = P (V.) First cycle/any other cycle z =0 Y = Y F, T = T F, u = u F, P = P F z = L Y T z = 0 II. First depressurization t =0 Ȳ = Ȳ (I.), q = q (I.), T = T (I.), P = P (I.) Any cycle z =0 z = L Y T z = 0 Y T u = u(valve) III. Second depressurization t =0 Ȳ = Ȳ (II.), q = q (II.), T = T (II.), P = P (II.) Any cycle z =0 z = L Y T z = 0 Y T u = u(valve) IV. Purge t =0 Ȳ = Ȳ (III.), q = q (III.), T = T (III.), P = P (III.) Any cycle z =0 Y = Y P, T = T P, u = u P z = L Y T P = P P V. Repressurization t =0 Ȳ = Ȳ (IV.), q = q (IV.), T = T (IV.), P = P (IV.) Any cycle z =0 Y = Y P, T = T P, u = u(valve) z = L Y z = 0. T z = 0 a Roman numerals in superscripts represent conditions at the end of corresponding step.

7 1640 M. Simo et al. / Computers and Chemical Engineering 32 (2008) multiple CSS; other types of attractors have not been determined so far. There are several strategies to solve the PSA equations. The first strategy is based on the idea that the initial value problem for parabolic equations can be transformed to an elliptic problem where the missing boundary condition is the unknown CSS. After the complete discretization both in time and space the algebraic non-linear equations can be solved by the Newton Raphson method. Nilchan and Pantelides (1998) used finite difference and collocation methods in both time and space to discretize these PDEs. This approach features several problems; among them are: huge dimension of the set on nonlinear algebraic equations, formulation of the nominal initial guess for the Newton and a possibility of divergence. The second strategy is based on an appropriate approximation of the space operator by finite differences; the resulting set of ordinary non-linear stiff differential equations can be solved as an initial value problem by the method of lines (MOL). The advantage of this approach is that space and time discretization steps are decoupled; high-order accuracy can be achieved in each dimension. The spatial discretization can be achieved in a number of other ways. In addition to finite differences, Galerkin finite element methods, orthogonal collocation and finite volume approximation have been tested, see Liu, Delgado, and Ritter (1998), Choong, Paterson, and Scott (2002), Jiang, Biegler, and Fox (2003). The steep adsorption fronts may cause significant numerical problems since the set of ODEs is stiff and anti-stiff integration routines must be used. To integrate these systems, integration packages such as LSODE (Hindmarsh, 1983), DASSL (Petzold, 1983), and DASPK (Li & Petzold, 1983) can be adopted Approximation of differential equations In our calculations, we have used finite differences to approximate the space operator. Since the adsorption of water on zeolites is a strongly exothermic process we can expect a very steep temperature and concentration gradients in the axial direction. To keep a high accuracy of the calculation it is necessary to flood the domain with the mesh points or to use a regridding technique (Hlavacek, 1985). In this technique the points are concentrated close to the adsorption front and a smooth expansion of the grid occurs toward the flat part of the profile. Such a technique can substantially reduce the computational time; however, a serious book keeping problem occurs. The most capable method for the calculation is to transform the equations to a form that does not produce steep gradients and solve the transformed equations. Similar strategy was suggested by Dimitriou, Puszynski, and Hlavacek (1989) to solve solid fuel combustion problems. In our calculations we have discretized the differential operator by the method of a high-order difference scheme with the degree of approximation of O(h 4 ). Due to the hyperbolic character of the problem the up-wind approximation has been used. The resulting system of ordinary differential equations was solved by a fourth-order Gear algorithm with a variable step size control strategy Calculation of the attractor The governing equations can be re-written in a discretized operator form as F 1 (y 1,y 1,y 1,g,t) = 0, y 1(t 0 ) = y 0, t [t 0,t 1 ]; F i (y 1,y 1,y 1,g,t) = 0, y i(t i 1 ) = y i 1 (t i 1 ), t [t i 1,t i ], i = 2,.., N; W(y(t),y 0,g) = 0; C(y 0,g) = y N (t N ) y 0 = Δ = 0 The form of the operator F depends on the type of discrete approximation (finite difference, Galerkin, finite volumes, etc.), y i are the state variables, g are design variables such as flow rates or valve constants, W(y(t), y 0, g) are design constraints which can include purity or pressure requirements and C(y 0, g) are the conditions characterizing the type of attractor. If Δ = 0 then we have the cyclic steady state, for Δ 0 the attractor is either periodic or chaotic. It is necessary to recognize that the equation Δ = 0 can feature a multiplicity of attractors. With the addition of appropriate boundary conditions, the bed equations for an N-step PSA cycle can now be written as a multi-stage DAE system Methods of solution of Δ = Successive substitution To carry out the simulation of PSA and to calculate the attractor we must solve the equation Δ = 0. The simplest method of solution is a method of successive substitutions, sometimes also called Picard iteration method. This approach represents a fixed point calculation. We can assume; as in recycle calculations, because of the mass and energy balance restrictions, that all the eigenvalues of the locally linearized F operator are λ i < 1. This cannot be proved but the convergence of the process represents an a posteriori proof. Eigenvalues close to the value one are responsible for the slow convergence. Here, we integrate the operator approximation F i, set y i (t i 1 )=y i 1 (t i 1 ) and solve until C(y 0, q) 2 is below a user pre-assigned tolerance ε. The fixed point iteration is a reliable and stable technique and the convergence trajectory mirrors the actual physical transient PSA process. In a case that a certain eigenvalue is close to the value 1 the governing equations can converge slowly. We would use an accelerating technique that has been studied in the past to improve the convergence of the recycle processes. In our simulation of the ethanol dewatering PSA process we never noticed an excessive number of iterations Methods of second order convergence Newton and quasi-type of Newton methods can be used if the number of iterations of the fixed point equation is very high. For detailed treatment and analysis we refer to papers by Smith and Westerberg (1992), Croft and Levan (1994), Ding and LeVan (2001) and Kvamsdal and Hertzberg (1997).

8 M. Simo et al. / Computers and Chemical Engineering 32 (2008) Fuel ethanol process PSA cycle Modeling of the cyclic PSA process makes use of the above-mentioned equations (Table 1), along with the equilibrium and kinetics data. Operating conditions are the same as for the industrial process (Table 2). Two or three bed PSA arrangements are used in the industry; in our study we have considered the two-bed cycle. The pressure history of the PSA cycle is shown in Fig. 1. The half cycle of ethanol PSA process, sequence of steps and interactions between beds is presented in Fig. 2. The PSA cycle can be divided into following stages: Fig. 1. Pressure history for PSA cycle in ethanol production. (1) Adsorption or production stage. The water ethanol vapor stream is fed to the bed from the top at kpa (55 Psia) and 440 K. The high pressure product stream is collected at the bottom of the bed (desirably dry ethanol). A part of the product stream is used to re-pressurize and purge the bed during the desorption stage. The adsorption stage takes about 345 s. Fig. 2. Half cycle for ethanol PSA process (345 s) (steps I. III.); step IV. represents the switch between the beds.

9 1642 M. Simo et al. / Computers and Chemical Engineering 32 (2008) Table 3 Summary of operational parameters for the basic case Feed gas Molar fraction of water, Y i (8 wt.%.) Flow rate, F F 20,410 kg h 1 Temperature, T F 440 K Production pressure, P F 379,212 Pa/55 psia Purge pressure, P P 13,790 Pa/2 psia Purge flow rate, F P 1360 kg h 1 Bed length, L 7.3 m Bed diameter, D 2.4 m Gas void fraction, ε 0.63 Bulk void fraction, ε b 0.4 Isosteric heat of adsorption, Q 51,900 J mol 1 Thermal capacity of gas, c p,g 1000 J kg 1 K 1 Thermal capacity of solid (zeolite), c p,s 1260 J kg 1 K 1 Axial effective dispersion coefficient, D ax m 2 s 1 Effective thermal conductivity, k ef W m 1 K 1 Initial bed temperature, T b 450 K Adsorbent-3 Å molecular sieve Bulk density, ε b 729 kg m 3 Adsorbent particle radius, r p m (1/8 in. beads) Langmuir isotherm parameters Water saturation capacity, qi S mol kg 1 Reference temperature, T K Equilibrium constant at ref. temp., K Pa 1 Diameters of valves Valve 1 (first depressurization) Valve 2 (second depressurization) Valve 3 (re-pressurization) m m m (2) Desorption stage. Follows after the production stage is completed. The bed must be depressurized, regenerated and re-pressurized to the adsorption pressure. First depressurization step. Initially, the pressure in the bed is kpa and declines to about kpa (20 Psia) in 60 s or less. The flow through the valve is critical and the pressure decrease is linear. In our model, the rate of the first depressurization is governed by the cross section of ball valve 1 located on the top of the bed (countercurrent depressurization), see Table 3. The vacuum used during this step is 37.9 kpa (5.5 Psia). For some processes the vacuum for the first and second steps are the same. Second depressurization step. Pressure at the outlet (top of the bed) is kpa and it declines exponentially to 13.8 kpa (2 Psia) in about 150 s. The rate of the second depressurization is governed by the cross section of ball valve 2 located on the top of the bed (counter-current depressurization), see Table 3. Regeneration step with purge. The bed is purged at 13.8 kpa from the bottom of the bed by using a portion of the product stream. This step is very short in the plant; it takes only 15 s. Pressurization. Initially the bed is under the vacuum 13.8 kpa and it is continually pressurized (from the bottom of bed) by the product stream all the way up to kpa in about 120 s. The rate of pressurization is governed by the cross section of ball valve 3, see Table 3. The set of parameters for the basic case, representing the actual operating conditions of the PSA process, is summarized in Table Results and discussion System of equations in Table 1 was solved together with the initial and boundary conditions. The results have been obtained for 100 mesh points in the axial direction and a time step of <0.5 s. The CSS was reached after few hundred cycles, but never more than 1000 cycles. Average computational time for one cycle was s using a standard Dell computer with 1.6 GHz processor Transient start-up of the PSA unit The adsorption of water on the zeolite is strongly exothermic process and consequently there is no difference in the qualitative behavior between the start-up of a chemical reactor with an exothermic catalytic reaction with the Langmuir Hinshelwood kinetic expression and an adsorber column used for de-watering of an ethanol-rich vapor on a zeolite sorbent. In Figs. 3 and 4,we displayed the temperature at the geometrical center of the bed, total amount of water adsorbed and molar fraction of water at the product end of the bed as a function of operation time during the start-up. Initially, total amount of water adsorbed in the bed is 0 kg and the bed is pressurized to feed conditions with ethanol vapor (379.2 kpa). The adsorbent is fully regenerated and the bed is preheated to 450 K by ethanol vapors. As soon as the wet ethanol vapor is introduced to the bed, a rapid water adsorption takes place accompanied by significant heat generation. The simulation results indicate that the initial temperature of the bed 450 K increased to 570 K shortly after the start-up of the process. This strong temperature overshooting during the start-up of an exothermic catalytic reactor is well known fact and steps should be taken to avoid it or at least to lower it. The technical solution here requires to start the operation with a pure ethanol feed stream and smoothly increase the concentra- Fig. 3. Transient start-up of the bed. Temperature in the center of the bed and the amount of water adsorbed in the bed is plotted against the operation time.

10 M. Simo et al. / Computers and Chemical Engineering 32 (2008) the cycle. This sequence will periodically repeat; the CSS was reached. As mentioned earlier, multiple solutions are possible for the system of interest. Few cases were started with different initial water loadings and saturated bed to check for multiple periodic states. In all cases tested, only one unique periodic state was exhibited Qualitative behavior of the PSA process Fig. 4. Molar fraction of water in product stream at the end (bottom) of the bed as a function of operation time during the start-up. tion of water until a required concentration of the ethanol water mixture is achieved (here 8 wt.%). Alternately, process starts with a low flow (F F ) of ethanol feed vapor (92 wt.%). As the bed is being gradually preheated and preloaded with water, the feed flow is slowly increased. It is important to notice that the CSS is approached after 67 h of operation (350 cycles). Fig. 5 shows the development of profiles in the solid phase as a function of the axial coordinate for different values of the operation time and for different cycle numbers. The water solid phase concentration wave travels through the bed until its position is fixed inside an envelope created by solid and dotted lines after 350 cycles. The position of the profile is periodically repeating within the defined envelope. At the end of the adsorption step, the bed is saturated with water (solid line, cycle 350). A desorption stage follows to remove the adsorbed water and at the end of the pressurization step the water loading corresponds to the dotted line; the bed is regenerated. The shaded area in Fig. 5 defined by the two solid phase concentration profiles is proportional to the amount of water removed in Understanding the bed dynamics and interpretation of cyclic steady-state profiles is very helpful to understand the process performance. The results for the basic case corresponding to the current plant operating conditions (Table 3) are presented first in Figs. 6 and 7. Fig. 6a indicates the development of the concentration profiles in the gaseous phase during the adsorption step after 350 cycles of operation. By this time the process reached the CSS. We can notice that the concentration wave has all the properties of a constant pattern propagating wave; the exit concentration of ethanol is greater than wt.%. We can also observe that a major part of the packed bed (close to 50%) is not utilized. Fig. 5. Solid phase loading profiles of water as a function of axial coordinate during the start-up of PSA unit plotted for different cycles. Axial coordinate at 0 m represents the top of the bed. Dotted line corresponds to the bed at the end of regeneration at CSS. Fig. 6. (a) Molar fractions of water in gaseous phase in the bed during adsorption step at CSS plotted as a function of axial coordinate. Position at 0 m represents the top of the bed and flow direction is from top to the bottom of the bed. (b) Temperature profiles in the bed during the adsorption step at CSS plotted as a function of axial coordinate. Position at 0 m represents the top of the bed and flow direction is from top to the bottom of the bed.

11 1644 M. Simo et al. / Computers and Chemical Engineering 32 (2008) Fig. 7a. As a result, the concentration in the solid phase decreases and the axial profiles of water concentration start to decrease as well, see profile 210 s (regeneration step). After the short purge, bed is re-pressurized and water molar fraction becomes very low (330 s), see Fig. 7a. Desorption is an endothermic process and consequently the temperature in the bed is decreasing, Fig. 7b. Again the temperature profiles move in the strip given by the two envelops and the hot spot is eventually eliminated. In the area of the initial hot spot the temperature value decreases by almost 30 K. The internal temperature in the portion of the bed between z = 3.5 and z = 7.3 m stays almost constant during the desorption step; this portion represents the bottom half of the bed. Flow direction is from the bottom of the bed towards the top during the desorption step Simulation results versus industrial data Fig. 7. (a) Molar fractions of water in gaseous phase in the bed during desorption step at CSS plotted as a function of axial coordinate. Position at 0 m represents the top of the bed and flow direction is from bottom to the top of the bed. (b) Temperature profiles in the bed during the desorption step at CSS plotted as a function of axial coordinate. Position at 0 m represents the top of the bed and flow direction is from bottom to the top of the bed. Fig. 6b displays the development of the temperature profiles; we can notice that at the beginning the heat generated close to the adsorber inlet is conducted towards the cold internal part (dt/dx < 0); at t 150 s the direction of the gradient is reversed and the heat wave propagates toward the inlet. A transient hot spot is produced and it moves in the direction of the flow. The temperature profiles move in the strip between two envelops and the temperature front is represented by a standing wave. The pressure drop during the adsorption step in the bed is small and the axial profile of the pressure is linear (data not shown here). Fig. 6 also shows that during the adsorption step Y and T curves track each other, indicating that their wave velocities are similar. This result suggests that temperature front sensing may be used to monitor the front as will be shown in the next section. Upon decreasing the pressure in the adsorber the partially saturated solid phase starts to release the adsorbed water and the concentration of the water vapor in the gaseous phase increases. The profile at 0 s in Fig. 7a corresponds to the profile at the end of adsorption step. In the early stages of desorption only small amount of water is released, see profiles at 30 and 60 s. Desorption rate increases dramatically as vacuum is reached and the axial profiles of the gaseous concentration of water are described by a standing wave (second depressurization step, s), The enthalpy of adsorption/desorption on 3 Å zeolite exhibits a high value. We can conveniently use this fact and follow the temperature rise/decrease inside the bed to track the adsorption/desorption front. The industrial packed beds in an ethanol plant were equipped with five resistance temperature detectors (RTD) in the axial direction from the top to the bottom of the bed. The RTD 1 was placed on the top of the bed followed by RTD 2, RTD 3, RTD 4 and RTD 5 at the bottom. All RTD s were evenly spaced. The temperature readings were recorded and the graphic output for one cycle is shown in Fig. 8. The plant operational data were recorded during the test operation; thus the operating parameters did not correspond to the current operating parameters. During the plant start-up; the production of ethanol increases until the desired throughput is achieved. Meanwhile the water concentration in the feed stream changes with the reflux ratio of rectifying column; cycle time and duration of individual steps, purge flow rate and feed temperature are adjusted to meet mainly one condition at least 99.5 wt.% of ethanol in the final product. The simulation results for the test operation are shown in Fig. 9. The feed flow rate was 15,875 kg h 1, purge stream Fig. 8. Online temperature measurements from an ethanol plant at five axial points within the bed from the top to the bottom. Data were recorded for the operation with cycle time 880 s and water content in the feed stream was 8 wt.%.

12 M. Simo et al. / Computers and Chemical Engineering 32 (2008) Table 4 Values of parameters used in simulations Run T F (K) t P (s) W F (wt.%) P F (kpa) P P (kpa) α Fig. 9. Temperatures profiles at five axial points within the bed from the top to the bottom obtained from our simulation program. Data were calculated for the operation with cycle time 690 s and water content in the feed stream was 8 wt.% (basic case see Table 3). flow rate was 227 kg h 1, the water content in the feed stream was 8 wt.% and the feed stream temperature was 430 K. Cycle time was longer compared to the current one: adsorption step 440 s, first depressurization 60 s, second depressurization 195 s, purge 20 s and pressurization 165 s. By comparing the profiles in Figs. 8 and 9; one can see that a significant temperature change occurs only in the top part of the bed see reading of T1 and T2. The temperature changes in the bottom part of the bed are small. The same conclusion can be made by looking at the axial temperature profiles in the bed for the adsorption and desorption stages depicted in Figs. 6b and 7b, respectively. According to this observation, one can conclude that the adsorption/desorption process takes place only in the top portion of the bed while the bottom part of the bed remains in equilibrium. The quality of the product and the pressure history were also monitored in the full scale plant; both measurements validate our simulation results. Industry requires that the ethanol plant product stream is 99.5 wt.%, we have calculated wt.% for the test cycle described above. The pressure history was also successfully reproduced (data not shown here). Due to the simplifications in our model, we did not expect a perfect match. We have neglected the heat exchange between solid and fluid phase. Accordingly, in the real system (Fig. 8) one can see the temperature oscillations in the equilibrium part of the bed (temperatures 3, 4 and 5) caused by above mentioned heat transfer. On the other hand, such oscillations are absent in the simulation results, see Fig. 9. Ethanol co-adsorption was neglected in the model; however, we know from the plant operation that the amount of ethanol recovered in the exhaust vapors (condensates) is higher than the amount predicted by our model. Reliable ethanol water equilibrium model together with corresponding values of isosteric heats of adsorption and binary kinetic model is necessary to obtain qualitative description of the PSA process Parametric study Developed model was used to investigate the effects of four operational parameters (T F, t P, Y F and α) on the process per formance. Fourteen simulations were carried out, where in each run only one parameter was changed from the basic case (Run 1) and others were kept constant. Set of all parameters used in the parametric study is summarized in Table Effect of feed stream temperature The effect of the feed stream temperature on the overall performance was investigated. Two scenarios have been calculated and compared with the basic case (Table 4, Runs 2 and 3). The feed stream temperature was decreased and increased by 20 K. Ethanol plants have usually a heat exchanger installed downstream of rectifying column in order to superheat ethanol-rich vapor if necessary. This unit can be used to adjust the feed temperature to desired value. The condensation point of 92 wt.% ethanol vapor is K at kpa. The results are shown in Figs. 10 and 11. The quality of the final product for the basic case, T F = 440 K, was wt.%. Fig. 10. Water molar fraction profile in the bed at CSS as a function of axial position for three different feed temperatures plotted at the end of adsorption step.

13 1646 M. Simo et al. / Computers and Chemical Engineering 32 (2008) Fig. 11. Water solid phase loading at CSS as a function of axial position in the bed for three different feed temperatures plotted at the end of adsorption step. Shaded areas are defined by profiles at the beginning and at the end of adsorption step half cycle. In the case of the lower feed temperature 420 K, the quality of product decreased to wt.%. For a higher feed temperature, 460 K, the quality of the product improved to wt.% ethanol content. The effect of the temperature on the water loading is displayed in Fig. 11. Here more heat is available to aid the endothermic desorption process at a higher feed stream temperature; adsorption process is still performing well due to the rectangular shape of the isotherm. These results indicate that desorption stage should be carried out more effectively in order to improve the PSA performance Effect of purging The PSA cycle in the industrial plant is using only 15 s for purging the bed, see Fig. 1. There is a tradeoff between a higher flow rate of the purge stream and the ethanol recovery since a part of the product stream is used as a purge. In our simulation, the flow rate of the purge stream was kept constant at 1360 kg h 1 and only the duration of purge step (t P ) was increased while the duration of second depressurization step was decreased accordingly. The results are summarized in Figs. 12 and 13. By increasing the purging time from 15 to 50 s the ethanol content in the exit product increased from wt.% for basic case to wt.%. For 100 s purge time, a 100% ethanol product is collected as the bottom product and according to Fig. 13 a shorter bed could be used. The improvement in the quality of the product seems to be small ( 0.4 wt.%) while the amount of the purge needed is tripled for a 50 s purge duration. The idea of using smaller bed, higher throughput or higher water content in the feed by increasing the purge is very attractive. Rectifying column operates close to the pinch point represented by azeotropic point at 95.6 wt.% of ethanol. By increasing the amount of water in PSA feed stream (currently 8 wt.%); significant amount of energy could be saved in the distillation process since one would need less trays and/or lower reflux ratio. On the other hand, extra heat is needed in the boiler of rectifying column since all exhaust Fig. 12. Water molar fraction in the bed at CSS as a function of axial position for different duration of purge step plotted at the end of adsorption step. vapors are recycled back there. The exhaust stream (condensate) from the first depressurization step is introduced at the top of the column due its high ethanol content. The condensates from the second depressurization step and purge step enter the rectifier together with the feed stream since the water content is significantly higher here. In general, it s requested by the plant personal that the amount of exhaust condensates is low. These recycle streams perturb the rectifying column and it s more difficult to maintain steady operation Effect of feed water concentration As mentioned earlier, it s very attractive to operate the PSA unit with higher water content in the feed stream. Runs 6 8 were calculated to study the effect of Y F on the process performance. The results are shown in Figs. 14 and 15. As the feed water concentration increased, water content in the product increased as well. For the Y F equal to 6, 8, 9 and 10 wt.% the correspond- Fig. 13. Water solid phase loading at CSS as a function of axial position in the bed for different duration of purge step plotted at the end of adsorption step. Shaded areas are defined by profiles at the beginning and at the end of adsorption step half cycle.

14 M. Simo et al. / Computers and Chemical Engineering 32 (2008) Fig. 14. Water molar fractions in the bed at CSS as a function of axial position for different water feed concentration plotted at the end of adsorption step. ing volume averaged product concentrations were 99.47, 99.28, and wt.% of ethanol, respectively. The bed utilization also increases with an increase in Y F, Fig. 15. At higher feed water concentrations, bed looses its ability to adsorb the necessary amount of water. Longer bed should be used to prevent the water breakthrough beyond the specified limit. The amount of water removed in one cycle is also higher as Y F increases. In the case of 6 wt.% it s only kg of water while for the 10 wt.% water content in the feed kg of water is removed in one cycle. This can be observed in Fig. 15, where the shaded area increases with the amount of water in the feed stream Effect of pressure ratio (α) The pressure ratio (α = P F /P P ) is a critical design parameter in conventional PSA processes because higher α allows less purge to be used, thus increasing the recovery of weak adsorptive (here Fig. 16. Water molar fractions in the bed at CSS as a function of axial position for different value of regeneration pressure (P P ) plotted at the end of adsorption step. ethanol). In the case of PSA fuel ethanol process, it s not always possible to choose the pressure values arbitrarily. High degree of heat integration between distillation and evaporation processes requires that any change in the pressure needs to be checked before the adjustment is made. Two sets of simulations were used to study the effect of α. First, P F was kept constant and P P was changed by ±3.4 kpa (0.5 Psia), see Figs. 16 and 17. The regeneration pressure (P P ) for the basic case was 13.8 kpa (2 Psia). The product purity increased as the regeneration pressure decreased; wt.% of ethanol content was calculated for 10.3 kpa while wt.% of ethanol content was calculated for P P = 17.2 kpa. The water loading profiles decreased as the P P decreased while the amount of water removed per cycle (shaded areas in Fig. 17) has increased as the regeneration pressure decreased. Later, P P was held constant and P F was changed by ±34.5 kpa (5 Psia), see Figs. 18 and 19. The increase in the feed stream pres- Fig. 15. Water solid phase loadings at CSS as a function of axial position in the bed for different feed water concentrations plotted at the end of adsorption step. Shaded areas are defined by profiles at the beginning and at the end of adsorption step half cycle. Fig. 17. Water solid phase loadings at CSS as a function of axial position in the bed for different regeneration pressures plotted at the end of adsorption step. Shaded areas are defined by profiles at the beginning and at the end of adsorption step half cycle.