Article pubs.acs.org/IECR
Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Industrial Scale Propylene/Propane Separation Using Pressure Vacuum Swing Adsorption Wee Chong Kuah, Surya Effendy,† and Shamsuzzaman Farooq* Department of Chemical & Biomolecular Engineering, National University of Singapore, Singapore 117585 S Supporting Information *
ABSTRACT: Conventional propylene/propane separation via distillation is capital- and energy-intensive. Pressure vacuum swing adsorption (PVSA) is a potential low-cost alternative to C3 distillation. In this work, a new 7-step PVSA cycle is developed using 4A zeolite as the adsorbent, capable of separating 84.4/15.6 propylene/ propane (wt %) mixture to produce high purity (>99.5 wt %), high recovery (>99%) propylene at a low energy consumption. The proposed PVSA unit is simulated and costed together with its peripheral units using industrially relevant feed condition and product specifications. The lost opportunity cost arising from the presence of propylene in the raffinate product is also included in the costing algorithm. The proposed PVSA unit is optimized using a global stochastic optimizer, giving a minimum total cost of US$20.86 per tonne of propylene. This is significantly lower than the cost of an equivalent distillation unit, which is found to be US$41.07 per tonne of propylene. The use of PVSA for propylene/propane separation can thus lead to a significant improvement in profitability. The net present value (NPV) of PVSA over distillation for a 450 KTA propylene plant is found to be US$76.79M.
1. INTRODUCTION Propylene is an important feedstock for the manufacture of polypropylene.1 Propylene is primarily produced via fluidized catalytic cracking or steam cracking, the latter accounting for 56% of the global propylene production.1 The composition of propylene/propane product from steam cracking depends upon the severity of the cracking; Moulijn et al.2 provided examples of propylene/propane cracking at several representative severities, and the reported product compositions ranged from 88 wt % to 97 wt % propylene (balance propane). In a typical olefin plant, naphtha is fed into a furnace for steam cracking. The furnace effluent is cooled, and subsequently compressed to 3.5 MPa.3 The compressed gas is then chilled and sent through a series of distillation columns where hydrogen, methane, ethane and ethylene are recovered. The remaining products are fed into a depropanizer, where the C3 fraction is recovered as the distillate. The C3 fraction is then sent to a C3H4 hydrogenation unit where methyl acetylene and propadiene are selectively hydrogenated to propylene. The reaction products are liquefied and sent to the C3 splitter where propylene and propane are separated. A schematic of the processes in an olefin plant is provided in Figure 1. Propylene/propane separation is conventionally effected via distillation. However, the relative volatility of propylene and propane is close to unity (1.0 to 1.1), and hence the production of polymer-grade propylene (>99.5 wt % purity) requires a large number of theoretical plates (>100) and a high reflux ratio. Consequently, C3 distillation is a capital- and energy-intensive process. © XXXX American Chemical Society
Pressure vacuum swing adsorption (PVSA) is a potential alternative to distillation that could reduce the capital and energy requirement of propylene/propane separation. Grande and Rodrigues4 performed experimental and simulation studies on propylene/propane separation using a 5-step PVSA cycle and 4A zeolite adsorbent. They obtained propylene purity of 99.40 wt % and recovery of 84.3% using a 46.3/44.1/9.6 propylene/propane/nitrogen (wt %) feed. To improve propylene recovery, Grande et al.5 designed a 2-stage PVSA unit that used 4A zeolite of different crystal size in each stage. The 2-stage unit separated a 38.9/61.1 propylene/propane mixture to give 99.58 wt % purity propylene, with 95.9% recovery. However, its energy consumption was 20% higher than distillation. Khalighi et al.6 developed a nonisothermal micropore diffusion model for kinetically selective PSA separation. The model allowed for concentration dependence of micropore diffusivity, with chemical potential gradient as the driving force, implemented for a dual-site Langmuir isotherm. It was used to study propylene/propane separation on silica chabazite zeolite (SiCHA).7 Using SiCHA, they were able to obtain a 99 wt % purity propylene stream at 98% recovery from 84.4/15.6 propylene/propane (wt %) feed. They also identified SiCHA and 4A zeolite as two promising candidates for propylene/propane separation due to Received: January 21, 2018 Revised: April 12, 2018 Accepted: April 14, 2018
A
DOI: 10.1021/acs.iecr.8b00289 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research
Figure 1. Block flow diagram of a typical olefin plant modified from Benali and Aydin.3
made in this model. The gas-phase is assumed to be ideal, and Darcy’s Law is used to describe the pressure drop along the length of the column. It has been checked later that the Reynolds number in all the simulations in this study is indeed in the laminar range to justify the use of Darcy’s law.
their high kinetic selectivity among the adsorbents screened for the purpose. In a subsequent study, Khalighi et al.8 used a surrogate-model-based simulation and optimization approach to show that 4A zeolite adsorbent offers a more economical option due to its higher kinetic selectivity. Choice of 4A zeolite is retained in this study while improving on some of the drawbacks of the aforementioned studies. One significant drawback is the lack of a rigorous costing algorithm that takes into account the scheduling of the PVSA cycle, as well as the cost of the peripheral equipment of the PVSA unit, i.e., heat exchangers, compressors, vacuum pumps, etc. It is also unclear if the cycles used in these studies can be further improved. The current study is undertaken in conjunction with a detailed optimization and costing study of propylene/propane separation by distillation9 in order to fully appraise the potential of adsorption technology for the same separation. First, the micropore diffusion-based simulation model of Khalighi et al.6 is extended to include the effect of pressure drop. This extension ensures that the model can reliably capture the process performance for industrial scale operations. Next, using the more complete simulation model, a new PVSA cycle is identified. This cycle is more energy efficient than the cycles used by Grande et al.5 and Khalighi et al.8 for the feed and product specifications they had chosen. The cycle is then used to study the separation of an 84.4/15.6 propylene/propane mixture to obtain polymer grade propylene at recoveries in excess of 99%. Industrial feed and product conditions are used to demonstrate the possibility of directly substituting the C3 splitter with a PVSA unit in a typical olefin plant. The cost of the proposed PVSA unit, including the relevant peripheral equipment, is optimized using a global stochastic optimizer. The performance of the PVSA unit and the cost are discussed, and the adequacy of heat integration is evaluated. A proper investment analysis is also carried out to fully assess the economic potential of replacing the conventional C3 splitter with a PVSA process.
2 150 1 ⎛ 1 − εb ⎞ ∂P − = ⎜ ⎟ μv 4 rp2 ⎝ εb ⎠ ∂z
(1)
Plug flow is assumed in the column. In this kinetically controlled process, the spreading of the mass transfer zone is completely dominated by the high diffusional resistance in the micropores of 4A zeolite. Adding the axial dispersion term does not make any difference. This assumption is acceptable due to the high Peclet number of the proposed PVSA unit. The adsorbent bed is assumed to be a collection of isotropic, spherical, microporous crystals, which are compacted into adsorbent particles using a binder. The average value of the ratio of microand macropore resistances for propylene and propane in 4A zeolite in the temperature range 323 to 423 K considered in this study is 103 and 105, respectively. Clearly, the micropore resistance is completely dominant for both gases. The chemical potential gradient is assumed to be the driving force for diffusion in the micropore and the adsorption equilibrium is represented by the multisite Langmuir isotherm model. The temperature gradients along the radii of the column and microparticle are assumed to be negligible. Furthermore, the gas and adsorbent particles are assumed to be at an approximate thermal equilibrium at any axial position along the bed. Lumped heattransfer coefficients are used to account for heat transfer between the bed and column wall, and between the column wall and the surrounding. 2.2. Model Equations. The following mass and energy balance equations are used to simulate the PVSA unit: 2.2.1. Component Mass Balance.
2. THEORETICAL BACKGROUND 2.1. Assumptions. A nonisothermal, nonisobaric, bidispersed pore diffusion model with chemical potential as the driving force (CPDF) implemented for a multisite Langmuir isotherm is used to simulate the PVSA unit. Several assumptions are B
⎛ (1 − εb)(1 − εp) ∂qc̅ i 1 − εb ⎞ ∂Ci + ρc εp⎟ ⎜1 + εb ∂t εb ⎝ ⎠ ∂t ∂ = − (Civ) ∂z
(2)
ρp qp̅ i = εpCi + (1 − εp)ρc qc̅ i
(3) DOI: 10.1021/acs.iecr.8b00289 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research Here Ci is the concentration of component i (A = propylene, B = propane) in the bulk phase, v is the interstitial velocity, εb is the bed porosity, εp is the adsorbent particle porosity, ρp is the particle density, ρc is the crystal density, qp̅ i is the average number of moles of component i adsorbed per unit particle mass and qc̅ i is the average number of moles of component i adsorbed per unit crystal mass. The two terms on the left-hand side of eq 2 correspond to the accumulation of component i in the gas- and adsorbed-phases of the column, while the term on the right-hand side of corresponds to the flux of component i due to convection. eq 3 defines the relationship between qp̅ i and qc̅ i. 2.2.2. Gas and Solid Phase Energy Balance.
Note that eq 6a is the transient mass balance of a spherical crystal including chemical potential gradient as the driving force for diffusion. 2.2.5. Multisite Langmuir Model.10 ⎛ = biPi ⎜⎜1 − qsi ⎝
qc*i
−
(4)
a wi
(5b)
2(R w + e) e(2R w + e)
(5c)
a wo =
PuA =
PuB =
∂t
=
qci ∂piim ⎞ 1 ∂ ⎛⎜ 2 ⎟ r D c0i im pi ∂r ⎟⎠ r 2 ∂r ⎜⎝
∫0
t HPA
(8a)
C Bvout dt
t
∫0 HPA CTvoutdt
(8b)
PuA (yA,feed − PuA )(1 − PuB) (1 − PuB) − yA,feed t
ProdA = 3600
(8c) t
∫0 CnEv CAvoutdt − ∫0 CoR CAvindt tcycleLρp
1 − εb εb
(8d)
Here PuA is the mole fraction purity of propylene, PuB is the mole fraction purity of propane, RecA is the fractional recovery of propylene, yA,feed is the mole fraction of propylene in feed to PVSA, ProdA is the productivity of propylene in mol/(kg·h). The parameter values used for simulation are given in the Supporting Information. 2.3. Seven-Step PVSA Cycle. The steps involved in the PVSA cycle determine the performance of the proposed PVSA unit. To design suitable steps for the PVSA process, the 4-step PVSA cycle used by Khalighi et al.8 is used as the base case. It is observed that to obtain 99.6 wt % propylene, the column has to be thoroughly rinsed with propylene product in order to minimize the amount propane in the gas-phase (5 will be needed if PH is greater than 400 000 Pa. Therefore, PH = 400 000 Pa is set as the upper limit of the operating pressure of the PVSA unit. The condensed product is then pumped to 2.5 MPa and heated to 50 °C for polymerization. Part of this is refluxed back to the PVSA unit as CoR feed. This stream requires expansion, followed by heating to satisfy the process condition. Heat integration is performed to minimize the amount of utility needed for heating and refrigeration. The vapor CnEv product is the hot stream, whereas the FP/HPA feed, CoR feed and condensed CnEv product are the cold streams. The sensible heating of FP/HPA feed and CoR feed is set to occur in exchangers directly downstream of the compressor at E-102 and E-107. This is to ensure a large logarithmic temperature difference to compensate for the small vapor-to-vapor heat
Ffeed,T × yA,feed × RecA × ProdA ρp (1 − εb)
(11a)
Here Ffeed,T is the specified feed flow rate in mol/h. The number of trains required is the volume of bed required divided by the total volume of the columns in 1 train, rounded up to a whole number. 0 log10 C p,col = 3.4974 + 0.4485log10 Vcol + 0.1074
× [log10Vcol]2
Fp,col
(11b)
2P HR w ⎧ ⎫ ⎪ ⎪ ⎡ 1000000.6P H ⎤ + 0.00315 ⎪ ⎪ 2⎣850 − 100000 ⎦ , 1.25⎬ = max⎨ 0.0063 ⎪ ⎪ ⎪ ⎪ ⎭ ⎩
0 C BM,col = C p,col (2.25 + 1.82Fp,col)
(11c) (11d)
0 CGR,colT = [1.18C BM,col + 0.5C p,col (2.25 + 1.82)]
× NT
CEPCI 397
(11e) 3
C0p,col
Here Vcol is the volume of 1 column in m , is the purchased cost for 1 column, Fp,col is the pressure factor, CBM,col is the bare module cost of 1 column and CGR,colT is the grassroots cost of all the column in US$, NT is the total number of columns. Chemical Engineering Plant Cost Index (CEPCI) is used to account for inflation and a value of 556.8 (Jan 2016)18 is used for CEPCI. 2.5.4.2. Vacuum Pump. Each vacuum pump can only serve 1 column at a time. At the end of each counter-current evacuation step, the waiting time before the start of another evacuation step in a separate column in the train is tDPE + tCoR. Hence the total number of vacuum pumps needed can be calculated by Nvac =
(tCnEv + t DPE + tCoR ) × N × Ntrain tcycle
(12a)
0 ̇ Cp,vac = 7185.9 + 6.428VCnEv
(12b)
0 C BM,vac = 3.4Cp,vac
(12c)
CGR,vacT = 1.68C BM,vacNvac
CEPCI 576.1
(12d)
Here C0p,vac is the purchased cost of the vacuum pump, V̇ CnEv is the volumetric flow rate during the evacuation step in m3/h, CBM,vac is the bare module cost of the vacuum pump and CGR,vacT is the grassroots cost of all the vacuum pumps. Equation 12b is a correlation developed in another study from our laboratory.19 G
DOI: 10.1021/acs.iecr.8b00289 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research 2.5.4.3. Centrifugal Pump. The cost of the centrifugal pumps can be calculated using the following equations: Wpump = Ẇpump × mean(nCnEv (t )) (13a)
heat exchangers can be calculated using the following equations: 0 log10 Cp,E10 X = 4.1884 − 0.2503log10 AE10X
+ 0.1974 × [log10AE10X ]2
0 log10 Cp,pump = 3.3892 + 0.0536log10 Wpump 2
+ 0.1538 × [log10Wpump]
(13b)
log10 Fp,E10X = 0.03881 − 0.11272log10 PE10X + 0.08183 × [log10PE10X ]2
log10 Fp,pump = − 0.3935 + 0.3957log10 Ppump 2
− 0.00226 × [log10Ppump] C BM,Pump =
0 Cp,pump (1.89
+ 1.35Fp,pump)
CGR,Pump = [1.18C BM,pump + ×
(13c)
0 C BM,E10X = Cp,E10 X (1.63 + 1.66Fp,E10X )
(13d)
0 0.5Cp,pump (1.89
CEPCI 397
+ 1.35)]
×
(14a)
0 log10 Cp,comp = 2.2897 + 1.3604log10 Wcomp
− 0.1027 × [log10Wcomp]
WCnEv =
(14b)
0 0 C BM,compT = 2.7Cp,comp + 1.5Cp,driver
CGR,compT = 1.68C BM,compT ×
CEPCI 397
(14c) (14d)
γ ηCnEv 1 − γ 1
×
(14e)
∫0
tCnEv
fCnEv (t )PCnEv(t )
8000 1000
(16a)
tCnEv + t DPE + tCoR W × CnEv tCnEv tCnEv (16b)
Here WCnEv is the energy consumption in 1 evacuation step of a column in J, ηCnEv is the efficiency of the vacuum pump, which is taken to be 0.6, f CnEv(t) is the evacuation outlet molar flow for 1 column, PCnEv(t) is the pressure at the outlet of the column during evacuation step, and WvacT,annual is the annual electrical consumption for all the vacuum pumps in kWh. Equation 16b is required to account for the additional power consumption as the vacuum pumps will still be running even while waiting for another evacuation step to start. Low-pressure steam (LPS) is used in E-101, E-104, and E-108 to supplement the heating requirement and cooling water is used in E-109 to cool the propylene product, while refrigerant at −20 °C is used to condense the propylene product in E-106. The cost of LPS, cooling water and refrigeration are US$13.28/GJ, US$0.354/ GJ, and US$7.89/GJ, respectively.17 The adsorbent cost is an operating cost since it is assumed that the adsorbent is changed annually. The cost of zeolite 4A used in this cost calculation is US$350/tonne.22 Other costs associated with adsorbent change is found to be insignificant compared to the total operating cost.
Q E10X ,exch,max 0.9Tlm,E10XUE10X
(15e)
WvacT,annual = N × Ntrain ×
Here Wcomp is the electrical energy required for the compressor in kW, C0p,comp is the purchased cost of the compressor, C0p,driver is the purchased cost of the driver, CBM,compT is the combined bare module cost and CGR,compT is the combined grassroots cost for the compressor unit. 2.5.4.5. Heat Exchanger. The heat exchanger cost is largely dependent on the heat exchange area. The area (in m2) is calculated from AE10X =
CEPCI 397
⎡⎛ ⎤ ⎞1 − γ / γ Patm ⎢ × ⎜ − 1⎥dt ⎟ ⎢⎣⎝ min{PCnEv(t ), Patm} ⎠ ⎥⎦
0 log10 Cp,driver = 1.9560 + 1.7142log10 Wcomp
− 0.2282 × [log10Wcomp]2
(15d)
Here C0p,E10X is the purchased cost of the heat exchangers, Fp,E10X is the pressure factor, PE10X is the design pressure (see Supporting Information), CBM,E10X is the bare module cost and CGR,E10X is the grassroots cost of the heat exchangers. CAPEX is calculated by adding up the grassroots costs of all the equipment and annualizing it. A 20-year operating lifespan and 10% weighted average cost of capital is assumed, giving an annualization factor of 0.1175. 2.5.5. Operating Cost. The operating cost consists of electricity, utilities and adsorbent cost. A total of 8000 operating hours per year is assumed. The cost of electricity in USA for August 2016 is used (US$0.0723/kWh).21 The annual electrical consumption for the vacuum pumps is calculated as
Here Wpump is the electrical energy required for the pump in kW, C0p,pump is the purchased cost of the pump, Fp,pump is the pressure factor, Ppump is the design pressure of the pump (set at 29 barg), CBM,Pump is the bare module cost of the pump and CGR,Pump is the grassroots cost of the pump. Note that mean() is the integral average operator. 2.5.4.4. Centrifugal Compressor. The cost of the centrifugal compressor consists of the compressor and driver costs. They can be calculated using the following equations:
2
(15c)
0 CGR,E10X = [1.18C BM,E10X + 0.5Cp,E10 X (1.63 + 1.66)]
(13e)
̇ Wcomp = Wcomp × mean(nCnEv (t ))
(15b)
(15a)
Here QE10X,exch,max is the maximum heat exchange required in kW. The maximum, instead of the time-averaged heat exchange is used for a more conservative estimate of the area. Here UE10X is the overall heat transfer coefficient in kW/(m2·°C). The cost correlations given by Turton et al.17 for heat exchanger is only valid for area up to 1000 m2. Hence, 2 or more equal-sized heat exchangers in parallel will be used if the area exceeds this value. The heat transfer coefficient of all the exchangers is provided in the Supporting Information.17,20 The cost of the H
DOI: 10.1021/acs.iecr.8b00289 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research 2.5.6. Lost Opportunity Cost. The propylene recovery for the proposed PVSA unit is less than 100%. To obtain a fair comparison, the cost of propylene lost in the raffinate product must be factored in. In this study, we have opted to include the effect of recovery via lost opportunity cost (LOC). Lost propylene is sold as propane, which is of lower value (US$305/ tonne23 for propane versus US$782/tonne24 for propylene), leading to an LOC of US$477 per tonne of unrecovered propylene. Consequently, the annual LOC incurred (in US$) can be calculated as
It is found that 3 of the optimized decision variables: HPA pressure, CnEv minimum pressure, and PVSA feed temperature are approaching the upper, lower, and lower bounds of the prescribed range, respectively. These bounds cannot be further relaxed. For example, the upper bound for the HPA pressure is the limit prescribed by the heat integration discussed in Section 2.5.3. The lower bound for the CnEv minimum pressure is 10 kPa, based on the observation that industrial PVSA columns undergo unacceptable leakage at low vacuum pressures. The lower bound of the PVSA feed temperature is set as 323 K, following the recommendation made by Ramachandran and Dao.27 Furthermore, the adsorption kinetics and adsorption equilibrium equations used are correlated from experiments conducted at 373 K to 473 K.11,12 The lower bound temperature is set to 323 K to limit extrapolation, which may lead to inaccurate results. A separate simulation is carried out using the decision variable values in Table 1 and the PVSA feed temperature fixed at 373 K. The proposed PVSA unit remains capable of producing 99.5 wt % propylene at >99% recovery, but the total annual cost (TAC) increases by about 25% due to the additional heating of the feed gas. This implies that the process performance may not be very sensitive to the inaccuracies arising from extrapolating the kinetic and equilibrium data The time-evolution of propylene, propane partial pressures, and the total pressure at the product end of the column at CSS for the minimum-cost case is depicted in Figure 7. At the start
LOCannual = 477 × ṁ feed × 8000 × yA,feed,mass × (1 − RecA )
(17)
Here ṁ feed is the specified mass feed rate in ton/h and yA,feed,mass is the propylene mass fraction in feed. 2.5.7. Optimization Method. The total annual cost, which consists of the annualized capital cost, the operating cost and the LOC is set as the objective function. There are a total of 8 decision variables: column length (l), mole flux scaling factor (GJ), adsorption pressure (PH), rinse velocity scaling factor (GvCoR,0), evacuation velocity scaling factor (GCnEv), evacuation minimum pressure (PL), PVSA feed temperature (Tfeed) and propylene outlet mole fraction condition (GHPA,out). The definitions and selection of these decision variables may be found in the Supporting Information. Optimization is done using Non-Dominated Sorting Genetic Algorithm II (NSGA II),25,26 downloaded from MATLAB Central, with 12 parallel cores. Optimization is done in two stages. The initial stage is a relatively brief process intended to explore the objective function surface, using a population size of 100 and 10 generations. The initial optimization took 3 days. The upper and lower bounds are then identified for the second round of optimization, with a population size of 80 and 40 generations. The latter optimization takes 10 days to complete.
3. RESULTS AND DISCUSSIONS 3.1. Minimum-Cost Result. The decision variables corresponding to the minimum cost result is presented in Table 1.
Figure 7. Partial pressures at the product end of the column.
of the FP step, the total pressure decreases slightly before increasing linearly with time. The slight decrease in pressure occurs due to rapid adsorption of propylene that entered the column during the previous CoRR step. Consequently, the assumption of linear pressure profile made elsewhere4,6,7 will not be appropriate in this study. During CnEv, the column pressure seems to decrease exponentially over a long duration. This implies that an exponential pressure profile could be used to model the decrease in evacuation column pressure. However, the speed of the exponential decay will not be known a priori. For example, the coefficient of the exponential decay term used by Khalighi et al.7,8 would result in an inappropriately rapid pressure decrease, which casts doubt on the calculation of productivity. Note also that the use of an exponential pressure profile would result in a time-varying evacuation velocity, which would be overstated at the start of the CnEv step, and understated toward the end. Figure 7 also shows that PPE and CoRR provide almost half the required pressurization in a fraction of the time FP would otherwise take. This demonstrates that PPE and CoRR not only reduce the amount of heavy reflux needed and increase propylene recovery respectively, but they also increase productivity.
Table 1. Decision Variable Values of the Minimum Total Annual Cost Variables
Values
Decision variables Length, l (m) Mole flux scaling factor, GJ Adsorption pressure, PH (Pa) Rinse velocity scaling factor, GvCoR,0 Evacuation velocity scaling factor, GCnEv Evacuation minimum pressure, PL (Pa) PVSA feed temperature, Tfeed (K) Propylene outlet mole fraction condition, GHPA,out
7.38 0.357 400000 0.475 0.451 10000 324.5 0.0463
The simulation demonstrated the capability of the proposed PVSA unit for producing high purity (99.6 wt %), high recovery (99.34%) propylene product at low cost. The optimizer also eliminated the usage of E-101, E-107, and E-109. The lowest possible total annual cost is found to be US$9.38M/year or US $20.86 per tonne of propylene. A summary of the minimum total annual cost, including the breakdown, is provided in the Supporting Information. I
DOI: 10.1021/acs.iecr.8b00289 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
Figure 8. Average number of moles of component i adsorbed along the dimensionless length of the column at the end of HPA and CnEv.
propylene leakage to the propane product stream. Even though the LOC is only 15% of the total cost, it is very sensitive to changes in recovery. A 0.3% decrease in recovery will result in a 7% increase in total cost. The inclusion of peripheral units and LOC into the total cost leads to a more comprehensive objective function, which is then minimized through optimization. 3.2. Process Capability. In an actual chemical plant, feed composition fluctuates over time. The robustness of the proposed PVSA unit is investigated by simulating different feed compositions. FP duration is allowed to vary and FP terminates when column pressure reaches 400 kPa. HPA duration is adjusted such that total FP and HPA duration is kept constant at 265.6s. The durations of other steps are kept constant according to the values stated in Table 1. Fixing the step durations is necessary because scheduling cannot be adjusted easily when the PVSA is in operation. Figure 10 presents the results of
Figure 8 shows the end-of-step bed temperature and average adsorbed-phase concentration profiles along the length of the column. The average adsorbed-phase concentration of propylene after adsorption and evacuation steps are 2.0 and 1.7 mol/kg respectively, indicating incomplete bed regeneration. This arises due to heat loss from the column to the surrounding, which incentivizes low operating temperature, leading to slow diffusion during the regeneration step. When the outside heat transfer coefficient is decreased from 24 to 0 W/(m2·K), using the decision variable values reported in Table 1, the vacuum pump power consumption decreases by 2.5%, while propylene recovery and productivity remain relatively constant. Following the same logic, the performance of the column can also be improved by reducing the crystal size. When the crystal radius is decreased from 1.9 to 1.3 μm, using the decision variable values reported in Table 1, the vacuum pump power decreases by 11.1%, while propylene recovery and productivity remain relatively constant. However, there are challenges associated with the use of very small adsorbent crystals. Grande et al.28 noted the difficulty in producing high purity propylene product using small adsorbent crystals. In this work, when the crystal radius is decreased to 1.0 μm, the desired 99.6 wt % propylene stream is no longer obtained. The breakdown of the total cost is shown in Figure 9. The main PVSA unit, which is typically used as the sole determinant
Figure 10. Propylene product purity at different feed compositions.
the study. The additional 0.1 wt % purity buffer (see Section 2.5.2) allows the propylene mass fraction in the feed to decrease by 2.1 wt % without compromising downstream polymerization unit feed specification. Moreover, as discussed earlier, the feed composition of 84.4 wt % used in this study is already a conservative estimate. Thus, the proposed PVSA unit seems robust against modest fluctuation in the feed composition. 3.3. Sensitivity Analysis. Electricity, low pressure steam and −20 °C refrigerant are consumed in the operation. During the lifetime of the chemical plant, the cost of utility is expected to fluctuate. The sensitivity of the total cost to cost of these utilities are briefly investigated. Total annual cost increases linearly with electricity cost. For the cost of electricity assumed in this study (US$0.0723/kWh), a 1% increase in electricity cost will lead to an approximately 0.3% increase in TAC. Total annual cost also increases linearly with lowpressure steam (LPS) and refrigeration costs. At the assumed
Figure 9. Pie chart showing the cost breakdown of the main PVSA unit, peripheral units, and LOC.
of the cost reported in the literature, takes up only 42% of the total cost. Evidently, the total cost will be significantly understated if the peripheral units are not considered. The LOC is also included in the objective function. It is not a true cost, but provides a good representation of the revenue lost due to J
DOI: 10.1021/acs.iecr.8b00289 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
propylene can be produced as long as the propylene feed composition is above 82.3 wt %. This demonstrates the resilience of the proposed PVSA unit against modest fluctuation in feed composition, thus highlighting its potential to replace the conventional C3-splitter in chemical plants. PVSA performance improves with column insulation and reduction in crystal size. It is also found that the peripheral units contribute to 43% of the total cost, demonstrating their significance in cost estimation procedures. The effect of LOC, which captures the effect of propylene recovery, is likewise shown to be significant. The heuristics used for heat integration in this work achieves 98.2% of the maximum possible recovery found in pinch analysis. The minimum total cost is found to be US$20.86 per tonne of propylene, which is significantly lower than that of the C3 splitter (US$41.07 per tonne of propylene) found in a separate study from our laboratory. The net present value (NPV) of the proposed PVSA unit over the C3 splitter for a 450 KTA propylene plant is US$76.79M, ignoring taxation. The proposed unit can be further optimized, primarily by allowing alternative arrangement of the peripheral units. The cost reduction is expected to increase the NPV further.
LPS cost of US$13.28/GJ, a 1% increase in LPS cost results in only a 0.03% increase in TAC. At the assumed refrigerant cost of US$7.89/GJ, a 1% increase in refrigerant cost leads to a 0.07% increase in TAC. It is evident that TAC is largely insensitive to price changes in LPS and the refrigerant. The LOC is calculated based on the difference in propylene and propane prices. Fluctuation in the relative price can also affect the minimum cost parameters. It is observed that TAC increases linearly with the price difference of propylene and propane. At the price difference of US$477, a 1% increase in price difference leads to a 1.6% increase in TAC. This high sensitivity implies that a change in average price difference is expected to modify the optimal design parameters significantly. 3.4. Adequacy of Heat Integration. The adequacy of the heat integration proposed in Section 2.5.3 is verified using pinch analysis. Pinch analysis cannot be directly applied in this system because of the fluctuating flow rates. Instead, a timeaveraged constant molar flow rates of 438.0 mol/s, 450.6 mol/s and 80.0 mol/s for FP/HPA feed, CnEv product, and CoR feed are used, respectively. The hot pinch temperature is found to be −0.33 °C, while the corresponding cold pinch temperature is found to be −10.33 °C. Pinch analysis shows that the proposed heat exchanger network is capable of heat integrating 98.2% of the maximum recoverable energy. The remaining 1.8% is primarily due to heat transfer across the pinch, i.e., the heating of CoR feed from −28.44 to −10.33 °C with the vapor product stream at E-107. Ideally, the heating should be done using the condensing product stream, but this would require an additional heat exchanger. In practice, it will not be possible to integrate 100% of the maximum recoverable energy due to fluctuations in flow rates, especially that of the CnEv product stream. 3.5. Cost Comparison with C3 Distillation Unit. A separate costing study was undertaken in our laboratory to calculate the lowest possible cost of a C3 distillation unit (heretofore called C3 splitter), taking into account heat integration of peripheral units, using the same feed and product specifications.9 The C3 splitter produces 99.6 wt % pure propylene and 95 wt % pure propane, equivalent to a 99.05% propylene recovery. The total annual cost (excluding LOC) for the 450 ktonne per annum (KTA) propylene plant is US$16.36 M/year or US $36.50 per tonne of propylene. With the LOC factored in, the revised total annual cost is US$18.40 M/year or US$41.07 per tonne of propylene. The net present value (NPV) of the proposed PVSA unit over the C3 splitter is US$76.79M, ignoring taxation. The cost reduction arises due to the high kinetic selectivity of propylene over propane (ca. 30), versus the relative volatility used in distillation (ca. 1.1). There are reductions in both energy and capital cost contributions. The distillation process uses mechanical vapor recompression to perform heat integration, and consequently uses more equipment to reduce utility consumption. The cost reduction (of PVSA versus distillation) is thus affected more by capital cost reduction than energy reduction.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.8b00289. Boundary conditions, model parameters, comparison with 2-stage PVSA, cyclic steady state profile comparison with and without update procedure, correlations for peripheral units sizing, heat exchanged in peripheral heat exchangers, selection of decision variables, summary and breakdown of minimum total annual cost (PDF)
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AUTHOR INFORMATION
Corresponding Author
*S. Farooq. Email:
[email protected]; Tel: (65)-6516 6545; Fax: (65)-6516 1936. ORCID
Shamsuzzaman Farooq: 0000-0002-6501-5540 Present Address †
Department of Chemical Engineering, Massachusetts Institute of Technology, 25 Ames Street, Cambridge, MA 02142, USA Notes
The authors declare no competing financial interest.
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4. CONCLUSION In this work, a 7-step PVSA cycle has been developed, costed, and optimized. Under the minimum cost condition, the proposed PVSA unit produces 99.6 wt % propylene product at 99.34% recovery, assuming an 84.4 wt %/15.6 wt % propylene/ propane feed. These operating parameters allow for a certain degree of fluctuation in the feed composition. Polymer grade K
NOMENCLATURE AE10X = heat transfer area for heat exchanger (m2) bi = adsorption constant (Pa−1) b0i = pre-exponential constant for the temperature dependence of bi (Pa−1) Ci = concentration of component i (A = propylene, B = propane) in the bulk phase (mol/m3) Ċ p,CoR = molar specific heat capacity of CoR feed (kJ/(mol·K)) Ċ p,feed = molar specific heat capacity of FP and HPA feed (kJ/(mol·K)) Cpg = molar specific heat capacity of gas mixture in PVSA (J/(mol·K)) Ċ pg,prod = molar specific heat capacity of vapor product (kJ/(mol·K)) Ċ pl,prod = molar specific heat capacity of liquid propylene (kJ/(mol·K)) DOI: 10.1021/acs.iecr.8b00289 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research
QE10X,annual = annual utility consumption for the exchanger (GJ) QE10X,exch(t) = amount of heat exchange in E-10X, where “X” is the exchanger number (kW) QE10X,exch,max = maximum heat exchange required (kW) Qs,CoR(t) = sensible heat needed to heat the CoR feed (kW) Qs,feed(t) = sensible heat needed to heat the FP/HPA feed (kW) Qsg,prod(t) = sensible heat from cooling the vapor product (kW) Qsl,prod(t) = sensible heat needed to heat the liquefied product (kW) Qvap,CoR(t) = sensible heat needed to vaporize the CoR feed (kW) Q̇ vap,feed = energy required to vaporize a mole of FP/HPA feed (kJ/mol) Qvap,feed(t) = latent heat needed to vaporize the FP/HPA feed (kW) Q̇ vap,prod = specific latent heat of vaporization of product (kJ/mol) Qvap,prod(t) = latent heat from condensing the product (kW) r = radial coordinate of the crystal (m) rc = crystal radius (m) rp = particle radius (m) R = ideal gas constant (J/(mol·K)) Rw = column internal radius (m) RecA = fractional recovery of propylene tj = duration of step j (s) tCnEv,k = duration of the evacuation step at cycle k (s) tcycle = total duration of a cycle (s) tgap = time gap between consecutive FP steps in a train (s) T = temperature of the column (K) Tamb = ambient temperature (K) Tcomp,out = temperature at outlet of compressor (K) Tfeed = temperature of FP/HPA feed (K) ΔTlm,E10X = logarithmic mean temperature difference of the heat exchanger (K) Tvap,CoR = temperature of CoR feed after passing through expansion valve (K) Tvap,feed = temperature of FP/HPA feed after passing through expansion valve (K) Tw = wall temperature (K) UE10X = overall heat transfer coefficient (kW/(m2·°C)) v = interstitial velocity (m/s) vCnEv,k = evacuation velocity at cycle k (m/s) vCnEv,CSS = actual evacuation velocity (m/s) vin = interstitial velocity for flow into the column (m/s) vout = interstitial velocity for flow out of the column (m/s) vp̅ ipe = velocity of gas flowing through the pipe during equalization (m/s) Vbed,T = volume of bed required (m3) Vcol = volume of 1 column (m3) V̇ CnEv = volumetric flow rate during the evacuation step (m3/h) WCnEv = energy consumption in 1 evacuation step of a column (J) Wpump = electrical energy required for the pump (kW) Wcomp = electrical energy required for the compressor (kW) WX,annual = annual electrical consumption of equipment “X” (kWh) Ẇ comp = electrical energy required to compress a mole of product (kW/mol) Ẇ pump = electrical energy required to pump a mole of product (kW/mol)
Cps = specific heat capacity of adsorbent (J/(kg·K)) Cpw = specific heat capacity of the column wall (J/(kg·K)) CT = total concentration of the bulk gas phase (mol/m3) C̅ T,pipe = average concentration in the pipe during pressure equalization (mol/m3) C0p,x = purchased cost of equipment “x” (US$) CBM,x = bare module cost of equipment “x” (US$) CGR,x = the grassroots cost of equipment “x” (US$) Dc0i = temperature-dependent limiting micropore diffusivity at zero adsorbate concentration (m2/s) 2 D∞ ci = limiting crystal diffusivity at high temperature (m /s) Dpipe = diameter of the pipe connecting 2 columns during pressure equalization (m) e = wall thickness (m) Ei = activation energy of the crystal diffusion (J/mol) f pipe = Fanning friction factor of the pipe f CnEv,(t) = evacuation outlet molar flow for 1 column (mol/s) Ffeed,T = specified feed flow rate (mol/h) Fp,x = pressure factor of equipment “x” GCnEv = evacuation velocity scaling factor GHPA,out = propylene outlet mole fraction condition GJ = mole flux scaling factor GvCoR,0 = rinse velocity scaling factor ho = heat transfer coefficient between wall and external surrounding (W/(m2·K)) hw = heat transfer coefficient between bed and wall (W/(m2·K)) ΔHi = isosteric heat of adsorption for component i (J/mol) JT = mole flux for FP/HPA (mol/m2) l = column length (m) Lpipe = length of the pipe connecting 2 columns during pressure equalization (m) LOCannual = annual LOC incurred (US$) ṁ feed = specified mass feed rate (ton/h) nCnEv(t) = molar flow rate of CnEv product (mol/s) nCoR(t) = molar flow rate of CoR feed (mol/s) nfeed(t) = molar flow rate of FP and HPA feed (mol/s) N = number of column per train NT = total number of column Nvac = number of vacuum pump P = gas phase total pressure (Pa) PCnEv(t) = pressure at the outlet of the column during evacuation step (Pa) PCoR = pressure at the outlet of the column during cocurrent rinse step (Pa) Pi = partial pressure of component i (Pa) pim i = imaginary partial pressure of component i (Pa) PH = high-pressure adsorption pressure (Pa) PL = evacuation minimum pressure (Pa) Ppump = design pressure of the pump (barg) Pout = pressure at product end of the column (Pa) PuA = mole fraction purity of propylene PuB = mole fraction purity of propane ProdA = productivity of propylene (mol/(kg·h)) qci = number of moles of component adsorbed per unit crystal mass at position r (mol/kg) qc̅ i = average number of moles of component i adsorbed per unit crystal mass (mol/kg) q*ci = equilibrium number of moles of component i adsorbed per unit crystal mass (mol/kg) qp̅ i = average number of moles of component i adsorbed per unit particle mass (mol/kg) qsi = number of moles of component i adsorbed per unit crystal mass at saturation level (mol/kg) L
DOI: 10.1021/acs.iecr.8b00289 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
(15) Wu, W.; Li, Y.-L. Selective Hydrogenation of Methylacetylene and Propadiene in an Industrial Process: A Multiobjective Optimization Approach. Ind. Eng. Chem. Res. 2011, 50 (3), 1453. (16) Sato, H.; Ogawa, H. Review on Development of Polypropylene Manufacturing Process. Sumitomo Kagaku 2009, II, 1. (17) Turton, R.; Bailie, R. C.; Whiting, W. B.; Shaewitz, J. A.; Bhattacharya, D. Analysis Synthesis and Design of Chemical Processes, 4th ed.; Prentice Hall International Series in the Physical and Chemical Engineering Sciences; Prentice Hall: Ann Arbor, MI, 2012. (18) Current Economic Trends - March 2016 - Chemical Engineering. http://www.chemengonline.com/current-economictrends-march-2016/?printmode=1 (accessed March 12, 2018). (19) Khurana, M. Integrated Adsorbent and Process Design for Carbon Capture from Power Plant Flue Gas. Ph.D. Thesis, National University of Singapore, Singapore, 2016. (20) Overall Heat Transfer Coefficient Table Charts and Equations. http://www.engineersedge.com/thermodynamics/overall_heat_ transfer-table.htm (accessed March 12, 2018). (21) EIA-Electricity Data. https://www.eia.gov/electricity/monthly/ epm_table_grapher.cfm?t=epmt_5_6_a (accessed March 12, 2018). (22) Granular Zeolite 4a. https://www.alibaba.com/product-detail/ granular-zeolite-4a_60413265368.html?spm=a2700.7735675.30.235. iIEBsR&s=p (accessed March 12, 2018). (23) Propane - Daily Price - Commodity Prices - Price Charts, Data, and News - IndexMundi. http://www.indexmundi.com/commodities/ ?commodity=propane (accessed March 12, 2018). (24) PolymerUpdate.com. https://www.polymerupdate.com/news/ ps/25Jan2018/5322/polystyrene-ps-export-prices-continue-tojourney-north-in-the-usa (accessed March 12, 2018). (25) Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 2002, 6 (2), 182. (26) Deb, K.; Sundar, J.; Udaya Bhaskara, R. N.; Chaudhuri, S. Reference Point Based Multi-Objective Optimization Using Evolutionary Algorithms. International Journal of Computational Intelligence Research 2006, 2 (3), 273. (27) Ramachandran, R.; Dao, L. H. Method of producing unsaturated hydrocarbons and separating the same from saturated hydrocarbons. Patent US5365011 A, 1994. (28) Grande, C. A.; Basaldella, E.; Rodrigues, A. E. Crystal Size Effect in Vacuum Pressure-Swing Adsorption for Propane/Propylene Separation. Ind. Eng. Chem. Res. 2004, 43 (23), 7557.
yA,feed = propylene mole fraction in FP/HPA feed yA,feed,mass = propylene mass fraction in FP/HPA feed yi = mole fraction of component i z = axial coordinate of the column (m) Greek Letters
αi = number of sites occupied per molecule awi = ratio of the internal column wall surface area to column wall volume (m−1) awo = ratio of the external column wall surface area to column wall volume (m−1) εb = bed porosity εp = particle porosity ηCnEv = efficiency of the vacuum pump γ = Cpg/Cvg μ = viscosity (Pa·s) ρc = crystal density (kg/m3) ρp = particle density (kg/m3) ρ̅pipe = average density of the gas in the pipe during equalization (kg/m3) ρw = column wall density (kg/m3)
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REFERENCES
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DOI: 10.1021/acs.iecr.8b00289 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
