Propane Separation

Article pubs.acs.org/IECR

Comparing SiCHA and 4A Zeolite for Propylene/Propane Separation using a Surrogate-Based Simulation/Optimization Approach Mona Khalighi, I. A. Karimi,* and S. Farooq Department of Chemical and Biomulecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117585 ABSTRACT: Propylene/propane separation is one of the most energy-intensive in the chemical industry. Adsorption may offer a low-energy alternative process. In this work, we compare 4A zeolite and a new 8-ring silica chabazite zeolite (SiCHA) for separating these mixtures in a pressure vacuum swing adsorption (PVSA) process. We base our assessment on a five-step PVSA cycle with concurrent pressurization, high pressure adsorption, rinsing with the heavy component (i.e., heavy reflux), forward blowdown, and reverse evacuation, which we simulate rigorously using a nonisothermal isobaric micropore diffusion model with concentration-dependent diffusivity developed by Khalighi et al. [Ind. Eng. Chem. Res. 2012 51, 10659−10670] We develop fast neuro-fuzzy surrogates for these simulations and estimate minimum energy consumptions per tonne of propylene using a genetic algorithm (GA). We show that the blowdown step, although widely used in the literature for 4A zeolite, is redundant for both 4A zeolite and SiCHA. While 4A zeolite requires lower separation energy per tonne of propylene, it admits lower throughputs due to lower diffusivities. Since energy costs outweigh capital costs for this separation, a comparison based on approximate total annualized cost also confirms that a process using 4A zeolite is cheaper than that using SiCHA. Between the two industrial propylene/propane feeds of 50:50 and 85:15 mol:mol, the latter requires lower energy and cost per tonne of propylene than the former for separation into two high-purity products.

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INTRODUCTION The separation of light olefins such as ethylene/ethane and propylene/propane from the off-gas of catalytic crackers is a key step in the petrochemical industry. The current method for these separations involves cryogenics. The US DOE has identified propylene/propane separation as the most energyintensive single distillation process practiced commercially.2 Thus, low-energy alternatives for these separations are highly desirable. Adsorption offers an attractive option due to its low energy demands. Pressure vacuum swing adsorption (PVSA) is a well-established technology for gas separation. Since commercial inception in 1950,3 it has progressed much in size, versatility, and complexity. It can handle multicomponent separation and purification and offers great flexibility in design and operation. In this work, we focus on the adsorption-based separation of industrially relevant propylene/propane mixtures into two highpurity products. For propylene, we target 99 mol % purity, as required for polypropylene production. For propane, we target 90 mol % purity, as used in engines, oxy-gas torches, barbecues, etc. In a previous work, we4 identified 4A zeolite and SiCHA as the two most promising adsorbents for this separation from those studied in the literature. They are the two top candidates, when all reviewed adsorbents are ranked according to the kinetic selectivity. While 4A zeolite is commercially available and well-studied, SiCHA is not. For 4A zeolite, Grande and Rodrigues5 suggested a five-step PVSA process with pressurization, high-pressure adsorption, rinsing with propylene product (also called heavy reflux), cocurrent blowdown, and countercurrent evacuation. Furthermore, Khalighi et al.1 developed a nonisothermal micropore diffusion model with concentrationdependent diffusivities for kinetically selective PVSA processes, which we validated with published data5 on propylene/propane separation with 4A zeolite. For SiCHA, Khalighi et al.4 © 2014 American Chemical Society

demonstrated the power of combining limited published data with molecular simulation estimates to assess process suitability of a new adsorbent. They showed that a four-step PVSA cycle with pressurization, high-pressure adsorption, rinsing with propylene product, and countercurrent evacuation can indeed yield 99% propylene and 90% propane. However, none of these studies offered a definitive conclusion on the relative merits of 4A zeolite and SiCHA. In fact, as we discuss later, such a conclusion is not possible without a detailed optimization of the PVSA processes for these two adsorbents. But, such an optimization study for propylene/propane separation does not exist in the literature. Our aim is to compare 4A zeolite and SiCHA for propylene/ propane separation based on extensive simulations and detailed optimization and identify the best adsorbent along with its best PVSA process. Our assessment criteria are energy consumption per tonne of propylene and total annualized cost for a fixed propylene/propane feed rate. We consider two industrially relevant propylene/propane feed mixtures.4 First is the 50/50 mol/mol mixture from the thermal cracking of liquid feedstocks such as naphtha, and second is the 85/15 mol/mol mixture from the off-gases of the fluid catalytic cracking (FCC) units. While both sources are at about 2−3 atm and 600−800 K, we assume a lower temperature of 353 K to increase kinetic selectivity and a pressure of 2 atm for our feeds. We neglect the pressure drops through the adsorption columns and use the nonisothermal, concentration-dependent micropore diffusion Special Issue: Jaime Cerdá Festschrift Received: Revised: Accepted: Published: 16973

December 26, 2013 July 6, 2014 August 25, 2014 August 25, 2014 dx.doi.org/10.1021/ie404392j | Ind. Eng. Chem. Res. 2014, 53, 16973−16983

Industrial & Engineering Chemistry Research

Article

model of Khalighi et al.1 along with the equilibrium and kinetic parameters from Khalighi et al.4 for simulating various PVSA processes.

nitrogen from air, and used a nonlinear programming approach to minimize the cost of producing nitrogen. Other surrogate models such as ANFIS (adaptive network-based fuzzy inference system) and Kriging21−24 are also attracting increasing attention. The black-box approaches have one major disadvantage. The details of process dynamics are not fully integrated within or transparent to the optimization algorithm. While this does reduce the complexity of the optimization model, it compromises the nature and progress of the optimization algorithm. If a black-box approach uses a surrogate model, then it has one more major disadvantage. The surrogate model being less complex than the rigorous one, does speed up the optimization algorithm, but its predictions of process performance, especially in extrapolated situations, are often inaccurate. In contrast to the black-box approach, the equation-oriented and simultaneously tailored approaches embed the PDAEs for the PVSA process explicitly inside the optimization formulation. Nilchan and Pantelides25 proposed complete discretization (CD) involving a third order orthogonal collocation on finite elements for the spatial domain and a first order backward finite difference method for the temporal domain. They imposed simple periodic boundary conditions on process variable profiles to ensure CSS and used SQP (sequential quadratic programming) for optimization. Agarwal et al.9 presented a novel superstructure for the optimal cycle configuration of PVSA processes. They formulated an optimal control problem, and employed complete discretization for its solution. They used a first-order finite volume method for the spatial domain and orthogonal collocation on finite elements for the temporal domain. They used IPOPT26 to solve the large nonlinear program. Nikolić et al.16 reported an optimization framework for complex PSA processes with multibed configurations and multilayered adsorbents, and illustrated it for hydrogen recovery from SMR (steam methane reforming) off-gas.27 They used orthogonal collocation for the spatial domain and solved the PDAEs in gPROMS.28 They employed a state transition network (STN) approach for efficient simulation and optimization using the gOPT toll with reduced sequential quadratic programming (rSQP) algorithm. The STN approach has simpler and linear implementation in multibed PSA systems, where states are represented by operation steps (such as pressurization, adsorption, etc.) and inputs are the step durations and operating parameters. Jiang et al.29 proposed the simultaneous tailored approach for PVSA process optimization. Instead of solving the PDAEs to the full CSS condition at each iteration as in the black-box approach, they imposed just the CSS condition as a constraint in the optimization problem. At each iteration, they solve PDAEs in an inner loop for exactly one cycle to obtain the values of the constraints and objective function. In other words, the algorithm attains CSS only when it achieves the optimal solution. Initially, they used a modified finite volume (van Leer) method with smooth flux delimiters to decrease the oscillations for steep fronts. Then, they employed the DAE solver DASPK 3.0 to solve and integrate the bed equations. Finally, they used reduced-space successive quadratic programming (rSQP) for optimization.

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OPTIMIZATION OF PVSA PROCESSES A PVSA process is inherently transient and cyclic and has no true steady state. Its true performance, and thus design, is dictated by the cyclic steady state (CSS) that it achieves after many cycles of continuous operation. In addition to the adsorbent properties such as equilibrium isotherm, isosteric heat of adsorption, and diffusional time constants, the performance at CSS depends on both structural and operational parameters of a PVSA process. The former include the numbers and dimensions of the adsorption beds, while the latter include the operational steps (e.g., pressurization, highpressure adsorption, rinse, blowdown, and evacuation), their sequence, pressure levels, and durations. Thus, unlike a continuous plant, one cannot design a PVSA process without fixing or optimizing its operational details. Because the true measure of an adsorbent is in the performance of its PVSA process at the CSS, one cannot assess or compare adsorbents without finding the best process for each. Thus, to compare 4A zeolite and SiCHA and identify the best, we must first develop/ design the best PVSA process for each separately. This highlights the need for a full-fledged synthesis and optimization6,7 of the relevant PVSA processes. The full-fledged synthesis and optimization of a PVSA process is a major challenge for several reasons. Adsorption is a highly nonlinear phenomenon. Its modeling, simulation, and optimization in the context of a PVSA process involves repeated solution of complex hyperbolic partial differential and algebraic equations (PDAEs). This is extremely time-consuming and requires efficient numerical simulators8 and sophisticated optimization algorithms.9 Many cycles of operation must be simulated to arrive at the cyclic steady state (CSS) describing the actual performance of a PVSA process at each point during optimization. Several optimization studies10 using a variety of approaches for several practical separation problems (e.g., the works of Agarwal et al.9,11,12 for CO2 capture and concentration; Lewandowski et al.13 and Cruz et al.14,15 for air separation; Nikolić et al.16 for hydrogen recovery) exist in the literature, but none on propylene/propane separation. Biegler et al.10 classified the various optimization approaches into four groups: (1) simplified, (2) black-box, (3) equation-oriented, and (4) simultaneous tailored. While the simplified approach of Smith and Westerberg17 assumes a sequence of bed operations and bed design parameters such as bed length and pressure levels to find the minimum number of beds and a cyclic operating schedule, the other approaches address much wider and varying scopes for the design, operation, and optimization. The black-box approach is essentially simulation-based optimization,18,19 in which a series of separate (black-box) simulations of a PVSA process guides the optimization algorithm. The simulations may involve either a fully rigorous model of the PVSA process, or an approximate or surrogate model derived and updated with continuous help from the rigorous model. For instance, Kapoor and Yang20 used polynomial expressions to fit the outputs (product purities and recoveries) of a rigorous simulation model in terms of the inputs (feed pressure, depressurization pressure, and throughput) for CO-H2 separation. Lewandowski et al.13 developed an artificial neural network (ANN) model for the separation of

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ASSESSMENT APPROACH Based on the arguments and observations of Khalighi et al.,4 we expect the four-step cycle with pressurization, high-pressure adsorption, rinsing with propylene, and countercurrent 16974

dx.doi.org/10.1021/ie404392j | Ind. Eng. Chem. Res. 2014, 53, 16973−16983


Article

Figure 1. (a) Five-step PVSA process and (b) four-step PVSA process with 4A zeolite and SiCHA.

evacuation to be the simplest cycle for both SiCHA and 4A zeolite. However, Grande and Rodrigues5 allowed an additional step of cocurrent blowdown in their study of 4A zeolite. To be fair, we adopt the five-step cycle of Grande and Rodrigues5 as the base cycle on which to compare SiCHA and 4A zeolite. However, to show that cocurrent blowdown is suboptimal for both 4A zeolite and SiCHA, we allow it to have zero duration, enabling it to vanish during optimization. In other words, the optimizer would be able to automatically choose the best between the five-step and the four-step cycles. Strictly speaking, we must find the best PVSA process for each adsorbent for us to compare the two adsorbents, as it is possible that the best PVSA cycle for 4A zeolite is not the same as that for SiCHA. However, this requires the synthesis of an optimal cycle for each adsorbent, which is a challenge in itself. Therefore, instead of full cycle synthesis optimization, we allow limited synthesis option of four-step versus five-step cycle. Thus, in this study, we optimize the five-step cycle (Figure 1a) for both SiCHA and 4A zeolite separately. It involves (1) pressurization, (2) high-pressure adsorption, (3) rinsing with recycled heavy product from step 5 (called heavy reflux), (4) cocurrent blowdown, and (5) countercurrent evacuation. Steps 2, 3, and 4 produce propane, and step 5 produces propylene. Our assessment is purely based on the nonisothermal isobaric micropore model of Khalighi et al.,1 which they validated on the experimental data5 of 4A zeolite. Table 1 summarizes the parameters used in this study. For more details, please refer.1,4 As indicated earlier, we target 99% pure propylene and 90% propane. Recall that recoveries are fixed by the purities in a binary separation, when there are no waste streams such as in our chosen five-step cycle. Since energy consumption is a key consideration in this separation, we use energy use per tonne of propylene as the first criterion for judging a PVSA process. As an alternate criterion, we use total annualized cost for a given feed flow. We compare the two adsorbents based on both these two criteria.

Table 1. Physical Property Data for Various PVSA Simulations parameter

value

unit

DC0 for propylene on SiCHA DC0 for propane on SiCHA DC0 for propylene on 4A zeolite DC0 for propane on 4A zeolite λ′ (clash with another in GA) Cp for propylene Cp for propane Kw h0 hi D0 ϵp ϵ Cps ρs ρp Cpw ρw

9.03 × 10−11 1.80 × 10−14 5.5 × 10−12 2.7 × 10−14 1.11 × 10−02 73 85 0.21 2.40 × 10−03 6.00 × 10−03 2.5 0.34 0.43 0.917 1.45 1.21 0.5 8.238

cm2/s cm2/s cm2/s cm2/s W/cm·K J/mol·K J/mol·K W/cm·K W/cm2·K W/cm2·K cm

J/g·K g/cm3 g/cm3 J/g·K g/cm3

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IMPLEMENTATION OF SIMULATION MODEL We solved the model equations using COMSOL Multiphysics software.30 COMSOL uses the finite element method. We prepared a separate COMSOL file for each of the five steps of pressurization, adsorption, rinsing, blowdown, and evacuation. We programmed a MATLAB procedure to cycle through these steps sequentially. Each cycle begins with the pressurization step, and the first cycle assumes that the column has propylene at the evacuation pressure. We judge the convergence to CSS by monitoring propylene purity. When propylene purity for five successive cycles differs by less than 0.1%, we assume that the CSS is reached. Each simulation run required about 50−60 cycles to reach the CSS and needed 3−4 h of CPU time on a Dell Optiplex 780 with 2.66 GHz Intel Core 2 Quad Q9400 16975



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Then, the total energy consumption by the vacuum pump is given by

CPU and 8 GB of RAM. From the exit velocity and composition profiles at CSS, we computed product purities.

WVT = W Vbd + W Vev

propylene purity (%) =

100∫

tev

0

Again, each right side term in eq 7 is computed by the following generic expression: τ 1 γ WV = Fin(t ) min[Pin(t ), Patm] η1 − γ 0 ⎧ ⎫ ⎞1 − γ / γ ⎪⎛ ⎪ Patm ⎨⎜ − 1⎬ dt ⎟ ⎪ min[P (t ), P ⎪ in atm] ⎠ ⎩⎝ ⎭ (8)

CC3H6v|z = 0 dt

t

t

∫0 ev CC3H6v|z = 0 dt + ∫0 ev CC3H8v|z = 0 dt

(1)

∫

propane purity % =

100∫

tad

0 tad

t ri

CC3H8v|z = 0 dt + ∫ CC3H8v|z = 0 dt + ∫ 0 0 t ri

t bd

CC3H8v|z = 0 dt

t bd

∫0 Ctotalv|z = 0 dt + ∫0 Ctotalv|z = 0 dt + ∫0 Ctotalv|z = 0 dt (2)

With this, the total energy consumption for the cycle in Figure 1a is given by

For a binary separation, recoveries are fixed by specified purities,4 when there is no waste stream. Rei =

W = (WCT + WVT)/(3.6 × 42 × F1) kWh per tonne propylene fed (9)

Fj Pu i(1 − Pu j) − Fi Pu iPu j

1 (1 − Pu i)(1 − Pu j) − Pu iPu j Fi

where, F1 is the total moles of propylene entering the process during pressurization and adsorption. For rinsing, we collect propylene in a buffer tank during evacuation and recycle a fraction (G) from the tank as heavy reflux. For given rinse duration (tri) and reflux ratio (G), we compute the velocity of propylene entering the feed during step 3 as follows.

(3)

where, Pui, Rei, Fi are the purity, recovery, and molar feed composition (mol) of component i with j as the other component. For 99% pure propylene and 90% pure propane, propylene (propane) recovery is 89% (99%) for the 50/50 propylene/propane feed and 98% (94%) for the 85/15 propylene/propane feed. Let PH denote the final pressure in step 1 and the pressure during steps 2 and 3. Let PM denote the blowdown pressure in step 4, and PL denote the evacuation pressure in step 5. Figure 1a uses one compressor for steps 1 and 2, another for step 3, one vacuum pump for step 4, and another for steps 3 and 5. Since the feed is at 2 atm, the compressor must pressurize the feed to PH during steps 1 and 2, if PH exceeds 2 atm. In step 3, it must pressurize the rinse stream from 1 atm to PH. Since we are assuming an isobaric system, pressure drops through the beds are zero and the compressor needs no additional energy. Thus, work done by the compressor for the five-step cycle is given by WCT = WCpr + W Cad + WCri

Wpr C

where expression

and

Wad C

vri = GMgR gTg /(triεAPH)

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OPTIMIZATION ALGORITHM We use a surrogate-based black-box approach for optimization. Our primary reason for using this approach is as follows. Micropore diffusion controls the transport in 4A zeolite and SiCHA. Therefore, the micropore diffusion model with concentration-dependent diffusivities developed by Khalighi et al.1 is appropriate for simulating our five-step process. The discretization of this model is much more complex than the ones that are based on the usual linear driving force assumption. Using the micropore diffusion model with an equation oriented or simultaneous tailored optimization approach seems intractable at this time. Thus, a black-box approach seems the best and most expedient choice, as the primary aim of this study is relative comparison of two promising adsorbents. As mentioned earlier, each simulation run for the five-step process in COMSOL takes about 3−4 h of CPU time. Thus, a SimOpt strategy using the rigorous simulation model is also not advisible. Maguire et al.31 showed that a neuro-fuzzy model such as ANFIS (adaptive network-based fuzzy inference system) is more accurate than an ANN (artificial neural network) model. It reduces training time, and may be better for optimization. Thus, we preferred to use an ANFIS model. A neuro-fuzzy model is the product of a hybrid intelligent system that combines artificial neural network (ANN) and fuzzy logic.32 It uses a layer of hidden neurons for fuzzy inference. Jang33 implemented Takagi−Sugeno fuzzy rules34 in an adaptive network-based fuzzy inference system (ANFIS). Their ANFIS architecture uses the following layers of operations. The first layer generates fuzzy membership values for the input variables. The second layer multiplies the incoming signals from the previous layer, and computes the

(4)

are given by the following generic

∫

(5ab)

where, η = 0.72, γ = 1.4, τ is the step duration, Fin(t) is the flow of gas entering the compressor, and Pin(t) is the pressure of gas entering the compressor. WriC is computed via the following: 1 γ = η1 − γ

∫0

τ

(10)

where, Mg is the moles of gas collected in the tank, A is column cross section area, Rg is the universal gas constant, ε is the bed porosity, and Tg is gas temperature.

τ ⎧1 γ ⎫ Fin(t )Pin(t ) ⎪ ⎪ ⎪ ⎪ η 1 − γ 0 1−γ/γ ⎫ ⎧ ⎪ ⎪ ⎪⎛ P ⎞ ⎪ H ⎬ WC = ⎨ ⎨⎜ − 1⎬ dt ⎟ ⎪ ⎪ ⎪ ⎪⎝ Pin(t ) ⎠ ⎭ ⎩ IF PH > 2 atm ⎪ ⎪ ⎪ IF PH ≤ 2 atm ⎪ ⎭ ⎩0

WCri

(7)

1−γ/γ ⎧ ⎫ ⎪⎛ P ⎞ ⎪ H Fin(t )Pin(t )⎨⎜ − 1⎬ dt ⎟ ⎪ P ⎪ ⎩⎝ atm ⎠ ⎭

(6)

where, Patm is the atmospheric pressure. We assume that PM ≤ 1 atm and the vacuum pump always delivers gas at 1 atm. The vacuum pump will reduce the bed pressure from PH to PM in step 4 and from PM to PL in step 5. 16976



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firing strength of the rule (T-norm operation). The third layer computes the normalized firing strength. The fourth layer has several nodes, where node k computes the contribution of the kth rule in the model output based on the first-order Takagi− Sugeno rules. Lastly, the fifth layer computes the weighted global output of the system. Our selection of GA (genetic algorithm35) as an optimization algorithm is mainly for its simplicity and ease/speed of implementation. ANFIS Model. The following ten variables constitute the input variables for our ANFIS model: PH, PM, PL, G, tri, inlet velocity (ν0), pressurization time (tpr), adsorption time (tad), blowdown time (tbd), and evacuation time (tev). For each input variable, we select appropriate lower and upper bounds (Table 2). Purity of propylene, purity of propane, and total energy Figure 2. Improvement in ANFIS purity predictions versus COMSOL results with progress in optimization. (Solid fill symbols are for propylene and empty symbols are for propane.)

Table 2. Minimum-Energy PVSA Processes for the 50/50 and 85/15 Feeds Using 4A Zeolite and SiCHA and 4A Zeolite SiCHA

4A zeolite

its true value from the COMSOL simulation, then we retrain the ANFIS model by including this set of input variables. Now, we start a freshly randomized run of GA again, in which the initial population is not biased by the previous best results. It took 4−5 such GA runs to get an accurate GA solution matching the COMSOL simulation. This constitutes just one iteration of our optimization algorithm. To ensure that we get the best overall solution, we repeat this iteration five times, and then take the best of all solutions. While our overall approach for comparing two adsorbents is sound and applicable to other adsorbents, some assumptions and simplifications inherent in our modeling and optimization do introduce some uncertainty. First, our use of the ANFIS surrogate model along with GA-based optimization precludes any theoretical guarantees of optimality (local or global) for the results presented in this work. Furthermore, isobaric model, specific choice of the five-step cycle, and simplified capital cost estimation may introduce uncertainties in our estimates that some more rigor may be able to improve in the future. However, while the exact numerical results may vary, we feel that the relative comparisons and inferences would remain largely valid and robust.

variable bounds

parameter

50/50

85/15

50/50

85/15

both feeds

v0 (cm/s) tad (s) tri (s) tbd (s) tev (s) PH (kPa) PL (kPa) PM (kPa) G W (kWh/tonne propylene) propane recovery (%) propylene recovery (%) propane purity (mol %) propylene purity (mol %) feed rate (mol/h)

14.43 195 58 0 329 296.43 27.09 NA 0.51 108

11.72 251 62 0 403 348.03 30.02 NA 0.42 101

10.41 145 53 0 256 257.09 33.91 NA 0.58 81

7.41 179 49 0 312 275.78 45.38 NA 0.43 72

1−50 20−1000 20−1000 0−1000 20−1000 101.3−1013 5.065−50.65 50.65−101.3 0.1−1.0

99.18

99.12

99.14

99.17

88.99

89.02

89.03

88.99

90.01

90.03

90.04

90.01

99.09

99.02

99.04

99.08

11.08

10.56

6.93

5.29

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consumption of a cycle comprise the three output variables of the ANFIS model. Recall that recoveries are fixed by the purities. To build the initial ANFIS model, we synthesize 200 sets of input variables using Latin hypercube sampling (LHS).36 For each point, we simulate the five-step process with a bed of 2.5 cm diameter and 75 cm length using COMSOL and MATLAB until CSS and compute the three output variables. From the 200 points and their solutions, we randomly choose 150 sample points to train the ANFIS model, and the remaining 50 sample points to validate it. We have an initial ANFIS model based on 200 rigorous simulations. As we discuss later, we use solutions from our optimization procedure to continually retrain and improve our ANFIS model. Figure 2 shows how the prediction errors of ANFIS reduce with optimization. Figure 3 shows the schematic of our optimization algorithm. Using the initial ANFIS model inside GA in MATLAB, we optimize the five-step PVSA process. Then, we simulate in COMSOL the process corresponding to the best values for the ten optimization/decision variables. If any of the three outputs (two purities and energy consumption per tonne of propylene) predicted by the ANFIS model differs by more than 0.1% from

COMPARISON BASED ON ENERGY CONSUMPTION We compare the two adsorbents using a five-step process with a bed diameter d0 = 2.5 cm and length L0 = 75 cm but allow the feed rate to vary for minimizing the specific energy consumption. For each adsorbent-feed combination, we identify the best process operating parameters that achieve minimum energy consumption per tonne of propylene feed, by using the following objective function in GA. minimize Z = W + λ(min[0, 99 − P1] + min[0, 90 − P2])

(11)

where, λ = 1500 for SiCHA and λ = 1000 for 4A zeolite are penalty parameters, P1 is propylene purity, and P2 is propane purity. No penalty is needed for the bounds on the other variables, as they are handled naturally within the framework of a GA algorithm. The optimization results for the four adsorbent−feed combinations are presented in Table 2. The best values for all variables are far from their bounds, thus the imposed bounds 16977



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Figure 3. Optimization algorithm used in this work.

Khalighi et al.4 asserted that the 85/15 feed was easier to separate into two high-purity products than the 50/50 feed, because it required less energy. Our optimization results in Table 2 confirm this. For SiCHA, the 85/15 feed needs 101 kWh/tonne of energy as compared to 108 kWh/tonne for the 50/50 feed. Similarly, for 4A zeolite, the 85/15 feed requires 72 kWh/tonne of energy versus 81 kWh/tonne for the 50/50 feed. The lower concentration of propylene in the feed necessitates a higher feed velocity, higher high-pressure, higher rinse time, and lower evacuation pressure. All these result in higher energy consumptions for the compressors and vacuum pumps. The lower energy coupled with the lower productivity of 4A zeolite raises an important question. Should adsorbent selection be based purely on energy consumption at the process level? If the plant cost is comparable to energy cost, then it is likely that the higher productivity of SiCHA may offset the higher energy costs, and SiCHA might prove better than 4A zeolite! In other words, one cannot decide solely on the basis of energy consumption, and it is worthwhile to consider a comparison based on total annualized cost. The total annualized cost of separation must be the ultimate and fool-proof criterion for comparing these two adsorbents. Again, this can only be done by optimizing the entire processes for minimum total annualized cost.

are acceptable. All processes yield the desired purities, but the blowdown step has zero duration. Adsorption and rinse are sufficient to produce 90% propane. This confirms our assertion that the four-step process is better than the five-step process for both SiCHA and 4A zeolite, as far as energy demand per tonne of propylene fed is concerned. The SiCHA-based processes require 108 (101) kWh of minimum energy per tonne of propylene fed for the 50/50 (85/15) feeds. In contrast, the 4A-based processes require 81 (72) kWh of minimum energy respectively for the two feeds. Clearly, 4A zeolite demands less energy than SiCHA. While we can explain this conclusion based on the much higher kinetic selectivity of 4A compared to SiCHA (224 vs 28), we cannot be sure until we compute the minimum energy requirements by optimizing the full process. Majumdar et al.37 have also discussed the limitation of the ideal kinetic selectivity in representing the separation factor of an adsorbent and shown that time-dependent effective selectivity taking into account the equilibria and diffusional interactions should be calculated for assessing the potential of an adsorbent. While we agree that the latter is a better indicator than the former, we suggest that full process optimization is the most unambiguous way to assess an adsorbent. The optimization approach discussed in this work provides the necessary speed and efficiency to enable reliable and systematic assessment of adsorbents. The energy advantage of 4A, however, comes at the cost of throughput. As we see from Table 2, the SiCHA-based processes allow 11.07 mol/h of the 50/50 feed and 10.56 mol/h of the 85/15 feed. In contrast, the 4A-based processes allow only 6.92 mol/h of the 50/50 feed and 5.29 mol/h of the 85/15 feed into the same column. Thus, SiCHA is superior from the perspective of throughput. This higher productivity of SiCHA can be explained by the faster diffusion of propylene and propane in SiCHA than 4A zeolite.

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COMPARISON BASED ON TOTAL ANNUALIZED COST (TAC) We design a separate five-step process for each adsorbent, and then compute its minimum TAC. To ensure a fair comparison, each process must have the same capacity or feed rate. Our objective is a process that separates a given propylene/propane feed into 99% propylene and 90% propane. Since our interest is only a relative comparison, we assume the following for simplicity. 16978



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Figure 4. Effect of bed length on the minimum energy for SiCHA and 4A for 50/50 and 85/15.

Heuristic 1. The energy consumption of the five-step PVSA process with bed length L and inlet interstitial velocity v depends on L/v only. In other words, changes in L and v do not affect the energy consumption, as long as L/v remains the same. To show the above heuristic, we tuned a separate ANFIS model for several L over a wide range of 20−200 cm. For each L, we minimized the energy consumption by varying v and other parameters. Figure 4 shows the optimal L/v ratios for the four adsorbent-feed combinations at different Ls. As we can see, the optimal L/v is roughly constant at 5.14 for the 50/50 feed on SiCHA, 6.40 for the 85/15 feed on SiCHA, 7.21 for the 50/ 50 feed on 4A zeolite, and 10.11 for the 85/15 feed on 4A zeolite. Figure 4 also shows that the minimum energy consumption also remains constant with L for a given L/v. Note that the optimal L/v ratios for 4A are higher than those for SiCHA. This suggests a longer L (thus larger column and higher capital cost) for 4A than SiCHA at a given feed rate. Heuristic 2. The energy consumption (kWh per tonne of propylene) of the five-step PVSA process remains practically unchanged with bed diameter d as long as L and other parameters (v, bed pressures, and step durations) remain constant. For this, we simulated the four minimum-energy processes from Table 2 for various d using COMSOL. Figure 5 shows that energy consumption is practically independent of d for each solution. In other words, for any given L, the largest diameter (or minimum L/d ratio) will maximize the feed rate and capacity. Lastly, the column in our ANFIS model was small and nonisothermal, i.e. allowed heat losses. In contrast, industrial columns are large and nearly adiabatic. Therefore, we need the following heuristic to account for the heat effects.

1. 2. 3. 4.

The monetary unit is 2012 US$. Capital annualization factor is 0.1. The process operates 8000 h per annum. It uses N ≥ 2 identical beds of length L and diameter d. Multiple columns are necessary to receive the propylene/ propane feed in a continuous manner. 5. A buffer with negligible cost collects the propylene product from the evacuation step and decouples the operations of the evacuation and rinse steps. 6. 3d ≤ L ≤ 8d holds. This is based on expert observations38,39 from practice that most adsorption columns in the industry obey these limits on L/d ratio. This is largely to limit pressure drop in a real column. 7. The annual operating expenditure (OPEX) for the fivestep process is solely from the energy required for separation. 8. The electricity tariff is 0.0671 in 2012 US$/kWh.40 9. The total capital cost of the process is seven times the purchase cost of N columns. Using the above, the fewest columns required for a continuous feed are N = 1 + ⌈(tbd + tri + tev )/(tad + t pr)⌉

(12)

where, ⌈x⌉ represents the integer ceiling of x. Recall that we used a bed with diameter d0 = 2.5 cm and length L0 = 75 cm in our ANFIS model and allowed the feed flow (or inlet interstitial velocity v0) to vary. This may be too small to achieve a desired flow of F mol/s. Thus, we need a larger column with diameter d and length L, which must now be additional variables in our cost optimization along with v0, bed pressures, and step durations. To avoid a new ANFIS model with L and d as variables, we devise a scale-up procedure based on the following three heuristics. 16979



Article

transfer coefficient zero. The energy consumptions for these two limits are also shown in Figure 4. As we can see, the effect of heat transfer on energy consumption is practically negligible. This validates the use of our ANFIS model for designing systems with larger columns. Heuristic 4. For this kinetically controlled PVSA process, adsorption during column pressurization (step 1) should be negligible. In other words, a frozen bed assumption holds for this separation. From various simulations, the average ratio of the amount of feed entering the column during pressurization to that entering a frozen bed is 1.01 for both SiCHA and 4A zeolite. This confirms that adsorption during pressurization can be neglected. Then, we can fix tpr in terms of PH, PL, and v0 from our small ANFIS column as follows:

Figure 5. Effect of bed diameter on the minimum energy for SiCHA and 4A for 50/50 and 85/15.

t pr =

Heuristic 3. Our ANFIS model for a nonadiabatic, nonisothermal, five-step PVSA process predicts very well the energy consumption of an industrial adiabatic column. In other words, the impact of heat effects on energy consumption is negligible. To understand heat effects, we simulated the minimumenergy nonisothermal processes reported in Figure 4 for various L under isothermal and adiabatic conditions. For the former, we fixed the inside and outside heat transfer coefficients to be very large, and for the latter, we made the inside heat

V0 ⎛ P ⎞ ⎜1 − L ⎟[ε + εp(1 − ε)] εA 0v0 ⎝ PH ⎠

(13)

where, V0 = πd02L0/4. Equation 13 fixes tpr, so it ceases to be an optimization variable. The first three heuristics enable us to size a large column with length L, diameter d, and inlet interstitial velocity v to accommodate a feed of F mol/s based on the simulation of our small ANFIS column with a feed of F0 mol/s. First,

Table 3. Minimum-TAC PVSA Processes for 10 mol/s of the 50/50 and 85/15 Feeds Using SiCHA and 4A Zeolite SiCHA parameter v0 (cm/s) tad (s) tri (s) tbd (s) tev (s) PH (kPa) PL (kPa) PM (kPa) G propane recovery (%) propylene recovery (%) propane purity (%) propylene purity (%) W (kWh/tonne propylene) L0/v0 F0 (mol/s) tpr (s) F (mol/s) N volume (m3) CAPEX ($/y) OPEX ($/y) TAC ($/y) TAC ($/tonne propylene) d (cm) L (cm) v (cm/s)

4A zeolite

50/50 33.23 231 43 0 356 401.32 31.03 NA 0.64 99.19 89.02 90.03 99.1 110 2.26 9.59 × 3.05 10 3 0.3838 6.88 × 4.46 × 5.15 × 7.78 54.62 163.9 72.59

10−3

103 104 104

85/15 24.56 261 51 0 411 432.69 36.82 NA 0.47 99.12 89.05 90.05 99.02 104 3.05 7.64 × 4.09 10 3 0.4817 7.48 × 7.17 × 7.92 × 7.04 58.91 176.7 57.87 16980

10−3

103 104 104

50/50 18.78 168 36 0 289 321.35 21.54 NA 0.67 99.11 89.07 90.07 99.01 83 3.99 4.34 × 5.45 10 3 0.8482 9.42 × 3.37 × 4.31 × 6.51 71.14 213.4 53.44

10−3

103 104 104

85/15 15.73 197 40 0 363 371.82 38.93 NA 0.39 99.17 89.04 90.05 99.08 75 4.77 4.21 × 6.25 10 3 0.8752 9.55 × 5.17 × 6.13 × 5.44 71.88 215.7 45.23

10−3

103 104 104



Article

Table 4. Minimum-Energy PVSA Processes for the 50/50 and 85/15 Feeds Using SiCHA and 4A Zeolite under the Frozen Bed Assumption SiCHA parameter v0 (cm/s) tad (s) tri (s) tbd (s) tev (s) PH (kPa) PL (kPa) PM (kPa) G propane recovery (%) propylene recovery (%) propane purity (%) propylene purity (%) W (kWh/tonne propylene) L0/v0 F0 (mol/s) tpr (s) F (mol/s) N volume (m3) CAPEX ($/y) OPEX ($/y) TAC ($/y) TAC ($/tonne propylene) d (cm) L (cm) v (cm/s)

4A zeolite

50/50 15.01 196 57 0 333 300.01 28.01 NA 0.52 99.16 89.01 90.02 99.04 109 5.00 3.24 × 6.63 10 3 1.137 1.07 × 4.41 × 5.48 × 8.28 78.43 235.3 47.09

85/15 12.31 253 60 0 405 345.65 31.21 NA 0.43 99.06 89.05 90.05 99.00 102 6.09 3.06 × 8.11 10 3 1.203 1.10 × 7.01 × 8.11 × 7.20 79.93 239.8 39.36

10−03

104 104 104

⎡ v (cm/s) ⎤ F0(mol/s) = εV0(cm 3)⎢ 0 ⎥ ⎣ L0(cm) ⎦ ⎛ ⎞ PH(kPa) ⎟ ×⎜ 3 ⎝ R(kPa· cm /K· mol)T0(K) ⎠

10−03

104 104 104

85/15 8.06 182 46 0 315 277.64 46.19 NA 0.45 99.12 88.98 90.02 99.07 73 9.31 1.61 × 11.36 10 3 2.288 1.52 × 5.03 × 6.55 × 5.82 99.02 297.1 31.92

10−03

104 104 104

log(PCref ) = 3.4974 + 0.4485log(V ) + 0.1074[log(V )]2 (14a)

CAPEX(2012$/y) = 0.7

586 N PCref 382

(16)

From eqs 15 and 16, we get TAC = CAPEX + OPEX as the objective function for our GA-based optimization.

⎡ v (cm/s) ⎤ F(mol/s) = εV (cm 3)⎢ 0 ⎥ ⎣ L0(cm) ⎦

minimize Z = OPEX + CAPEX + λ(min[0, 99 − P1] + min[0, 90 − P2])

⎞ ⎛ PH(kPa) ⎟ ×⎜ 3 ⎝ R(kPa·cm /K ·mol)T0(K) ⎠

(17)

where, λ = 15 000 for SiCHA and λ = 10 000 for 4A zeolite. Note that L and D are not in the objective function and V = (F/ F0)V0. Thus, the variables in our optimization are v0, bed pressures, and step durations except tpr. From the best solution, we compute d = (4 V/(3π))3/2 and L = 3d. For F = 10 mol/s (12 700 tonne/year of the 50/50 feed and 12 500 tonne/year of the 85/15 feed), our optimization gives the minimum-TAC five-step processes in Table 3 for the four feed-adsorbent scenarios. First, step 3 (blowdown) again has zero duration. Thus, the five-step process is worse than the four-step process for SiCHA and 4A zeolite from both energy and cost perspectives. Second, the minimum-TACs (7.78 $/tonne propylene for the 50/50 feed and 7.04 $/tonne propylene for the 85/15 feed) for SiCHA are higher than those (6.51 $/tonne propylene for the 50/50 feed and 5.44 $/tonne propylene for the 85/15 feed) for 4A zeolite. Thus, separation

(14b)

where, V = πd2L/4 cm3, V0 = 368.2 cm3, T0 = 353 K is the feed temperature, and R = 8314 kPa·cm3/K·mol. The annual OPEX for the five-step process of capacity F mol/s is OPEX($/y) = 28.8z1FM × W (kWh/tonne propylene) × electricity tariff($/kWh)

104 104 104

11.18 146 50 0 259 300.21 35.28 NA 0.6 99.11 89.04 90.05 99.05 82 6.71 2.41 × 8.67 10 3 1.525 1.23 × 3.32 × 4.56 × 6.88 86.50 259.5 38.68

For computing the annual capital expenditure (CAPEX), we use the following correlation41 for the purchase cost (PC) of a column:

Heuristic 1 tells us that as long as we maintain L/v = L0/v0, the energy consumption of the large column will be the same as that of the ANFIS column. Then

= (V /V0)F0

10−03

50/50

(15)

where, z1 is the mole fraction of propylene in the feed, M is its molecular weight (g/mol), and W is the specific energy consumption. 16981



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Table 5. Comparison of COMSOL Results and ANFIS Predictions for the Small and Large (Scaled up) Columns for SiCHA COMSOL result small column

ANFIS prediction large column

small column

large column

output

50/50

85/15

50/50

85/15

50/50

85/15

50/50

85/15

energy (kWh/tonne propylene) propane purity (mol %) propylene purity (mol %)

108.0 99.21 89.00

99.9 99.20 89.99

108.1 99.14 89.02

100.1 99.13 88.96

107.0 99.41 89.96

99.5 98.63 88.91

108.5 99.48 89.21

100.2 98.71 88.61

literature abounds with screening based on specific thermophysical properties such as equilibrium/kinetic selectivity, capacity, heat of adsorption, Henry’s constant, etc. This work suggests that reliance on and screening based on such criteria cannot be fool-proof, and adsorbents must be compared based on their performances at the process level. Furthermore, this performance can only be obtained by fully optimizing the process with a suitable objective such as minimum energy or minimum total annualized cost. In this work, we have proposed a systematic simulation-optimization based approach using a surrogate ANFIS model to compare 4A zeolite and SiCHA adsorbents for separating two industrially relevant propylene/ propane feeds of 50/50 and 85/15 mol/mol. The key conclusion of this work is that 4A zeolite is superior to SiCHA for adsorption-based separation of propylene/ propane mixtures. While kinetic selectivity seems a good indicator of the energy need (OPEX) in this separation process, it is a poor indicator of the process productivity (CAPEX). In this process, the higher kinetic selectivity of 4A zeolite (224 vs 28) translates well into lower separation energy per tonne of propylene (25% less for the 50/50 feed and 29% less for the 85/15 feed) compared to SiCHA. However, the minimum energy process for a 4A zeolite needs larger columns (more capital cost) than SiCHA. Unless the capital costs for this separation are comparable to the operating costs, 4A zeolite seems a better adsorbent. Our total annualized cost optimizations based on some simple assumptions confirm this conclusion, as the total cost of separation for 4A zeolite is lower than that for SiCHA. The minimum-TAC processes use slightly higher energy (kWh per tonne of propylene fed) than the minimum-energy processes to reduce capital costs. In addition to the above, this work has shown that the blowdown step in the five-step process commonly studied in the literature for this separation is redundant. Furthermore, the separation of 85/15 propylene/propane feed into 99% pure propylene and 90% pure propane is less energy-intensive and cheaper than that of the 50/50 feed, when compared based on tonne of propylene fed.

using 4A zeolite is cheaper than that using SiCHA zeolite, and the 85/15 feed is cheaper to separate than the 50/50 feed. Since we did not assume frozen bed for the minimum energy results in Table 2, we ran our optimizations again with the frozen bed assumption. Table 4 lists the minimum-energy processes under the frozen bed assumption. First, the minimum energies and other parameters are quite close to those obtained without the frozen bed assumption. This confirms that frozen bed assumption is valid for this kinetically controlled separation process. Comparing the processes for minimum energies and minimum TACs, we see that the energy consumptions for the minimum-TAC processes are slightly higher than those for the minimum-energy processes, as the optimizer increases energy consumption slightly to reduce column size. However, they are not too far away from the minimum energy consumptions, as OPEX dominates CAPEX in this separation. As expected, the TACs for the minimum-energy processes are higher than those for the minimum-TAC processes. To confirm that the energy predictions remain valid through our scale up procedure, we simulate both the small and the large (scaled-up) column using both COMSOL and ANFIS models for SiCHA. The first two columns in Table 5 are the ANFIS model predictions for the small and the large columns. The third and fourth columns are results from rigorous COMSOL simulations. The ANFIS predictions are in close agreement with the COMSOL results, which validate our ANFIS model. Furthermore, the results for the small column are similar to those for the large column, whether we use ANFIS or COMSOL. This validates our scale up procedure.

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SUMMARY OF ASSUMPTIONS/LIMITATIONS In addition to those specifically stated in the previous section on cost-based comparison, we hereby summarize some assumptions and/or limitations that may impact the conclusions from this work. 1. Our comparison of SiCHA and zeolite 4A is based on the five-step process with propylene-propane feeds at 353 K. We did not attempt to synthesize the best cycle for this separation except for those subsumed by the five-step process. Our choice of feed temperature is to take advantage of greater kinetic selectivity. 2. Our use of the ANFIS surrogate model along with GAbased optimization precludes a theoretical guarantee of strict optimality for our optimization results. 3. Adsorption columns have no pressure drops. 4. For a PVSA process with micropore diffusion, a surrogate-based optimization approach is less computeintensive than that using an equation oriented or simultaneous tailored approach.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +65 6516-6359. Fax: +65 6779-1936. Email: cheiak@ nus.edu.sg. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors acknowledge that this work is a revised, more complete, and fuller version of a conference paper42 presented at PSE2012 (11th International Symposium on Process Systems Engineering) held in Singapore, July 15−19, 2012.

■

CONCLUSION Adsorbent screening is inevitable when considering an adsorption-based separation application. The adsorption 16982



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