Gas-Separation Membranes (GSM)

Flat-sheet envelope type membrane modules are considered within this thesis.

A graphical representation of the module is shown in Figure 2.5. The module consists of a cylindrical pressure vessel with circular membrane envelopes posi-tioned in series around an internal permeate tube. The feed gas ow is directed by the ow diverters. Part of the gas permeates through the membrane and exits via the permeate pipe at lower pressure. The remaining gas ow exits through the retentate outlet. An important characteristic of this type of mod-ule, is that the spacing between envelopes and ow diverters can be arranged so that the gas velocity can be kept nearly constant along the module's length.

Since the ow on the retentate side is decreasing along the module's length, the spacing is also reduced.

Two dierent polymeric materials are applied as active separation layer in the membrane modules, namely Polyimide Membrane (PIM) (Matrimid^®) and Poly-(ethylene oxide) Membrane (PEOM) (PolyActive^®). Both are selective for CO₂, thus the permeate stream should have a higher CO₂ concentration than the inlet stream. The PIM oers a higher CO₂ selectivity towards other components, while PEOM oers higher permeances. Both materials and mod-ules are developed and fabricated in Germany by colleagues at the Helmholtz-Zentrum Geesthacht - Center for Materials and Coastal Research (Brinkmann et al., 2015).

Theoretical Background

Polymeric membranes are often regarded as dense membranes with gas trans-port being governed by a solution-diusion mechanism as depicted in Figure 2.6 (Melin and Rautenbach, 2007; Ohlrogge and Ebert, 2012). The gas components in the feed are dissolved in the membrane, diuses through the membrane, and desorbs on the permeate side. The dierence in the chemical potential between both sides acts as the driving force for the diusion. Mass-transfer resistance on both sides can also occur, leading to formation of lm layers (not shown), which reduce the driving force for separation.

The three eects (solution, diusion, and dissolution) are often lumped into a single coecient, i.e., permability or permeance, which can be understood

Figure 2.5: Schematic representation of an envelope type membrane module.

Figure 2.6: Graphical representation of the solution diusion mechanism aross a dense membrane. Adapted from (Ohlrogge and Ebert, 2012)

2.2 Carbon Dioxide Removal as overall mass transfer coecients across the membrane. The permeability is a component ux normalized for membrane thickness and driving force, and reported in Barrer¹ (Baker, Wijmans, and Huang, 2010). While permeability is a performance indicator for the membrane materials, it is dicult to accurately determine the membrane thickness. The permeance, which is a gas ux normal-ized for the driving force, can therefore be used instead (Baker, Wijmans, and Huang, 2010). The permeance of a component in a membrane layer, dened by Equation 2.9, is often reported in Gas Permeation Units (gpu)².

Li = Pi In Equations 2.9 to 2.11:

Li is the permeance of componentiinNm³m⁻²s⁻¹Pa⁻¹ P_i is the permeability of componentiinNm³m m⁻²s⁻¹Pa⁻¹ δ^M is the membrane thickness inm

ṅ^M_i is the ux of componentithrough the membrane in Nm³m⁻²s⁻¹ f_i^Randf_i^P are the fugacities of componentiin the retentate and permeate

sides respectively, given inPa

L^{P I,0}_i andL^{0,P EO}_i are the reference condition permeances of componenti for the PIM and PEOM respectively, given inNm³m⁻²s⁻¹Pa⁻¹

Ea^{P I}_i andEa^{P EO}_i are the activation energies for componentiin the PIM and PEOM respectively inJ mol⁻¹

R is the universal gas constant inJ mol⁻¹K⁻¹ T is the temperature inK

σ,m⁰, andm^T are the free volume parameters

11 Barrer =1×10⁻¹⁰Ncm³cm cm⁻²s⁻¹cmHg⁻¹ =7.519×10⁻¹⁵Nm³m m⁻²s⁻¹kPa⁻¹

21 gpu =1×10⁻⁶Ncm³cm⁻²s⁻¹cmHg⁻¹ =7.519×10⁻⁹Nm³m⁻²s⁻¹kPa⁻¹

The permeance can be determined experimentally and then used to calculate the gas ux through the membrane within a simulation model. The permeance can also be inuenced by temperature, pressure, and component concentrations depending on the membrane material. Pure gas experiments can be used to regress all the parameters required (Ohlrogge and Ebert, 2012).

For glassy polymers, i.e., those above their glass transition temperature, the permeance is practically independent from pressure and gas composition. It is, thus often assumed to be constant or function of temperature using an Arrhe-nius type of equation. This is the case for the PIM (Eq. 2.10). For rubbery poly-mers below the glass transition temperature, pressure and temperature have a stronger inuence because they change the space available between polymer chains (Melin and Rautenbach, 2007). An increase in the polymer volume can also be caused by the sorption of large quantities of some readily condensable gases such as CO2. This is referred to as membrane swelling and can cause a drastic reduction in component selectivities. Hence, the permeance of rubbery membranes is also frequently modeled as a function of the gas composition, e.g., as in the extended free-volume theory (Eq. 2.11) for the PEOM.

Besides the solution-diusion mechanism, secondary transport phenomena, i.e., pressure drop, Joule-Thomson eect, and concentration polarization, can also occur and reduce the separation eciency (Ohlrogge and Ebert, 2012).

Pressure drop occurs due to the gas ow around spacers and ow diverters and reduces the driving force for separation along the module. The Joule-Thomson eect is the cooling of the gas ux through the membrane due to its sudden adiabatic expansion and causes a reduction in the membrane permeance. Con-centration polarization is the formation of a boundary layer in the vicinity of the membrane, wherein gas concentrations dier from that of the bulk gas phase.

This reduces the separation driving force for the target most permeable com-ponent and increases the separation driving force for unwanted less permeable components, thus reducing selectivity towards the target component.

Modeling Gas Permeation

A steady-state, one-dimensional model for the at-sheet envelope type mem-brane module is developed based on the solution-diusion mechanism. A dif-ferential membrane segment is used as the balance volume as shown in Figure 2.7. The molar component balances for the retentate and for the permeate sides are shown in Equations 2.12 and 2.13 respectively. The component ux through the membrane is calculated based on the permeance as per Equation 2.14. Summation equations (Equations 2.15 and 2.16) on both retentate and permeate sides are added, allowing the calculation of mole fractions.

2.2 Carbon Dioxide Removal

Figure 2.7: Balance Volume: Membrane Cell

The component fugacities are calculated by the Peng-Robinson (PR) Equation of State (EoS) (Peng and Robinson, 1976). The component's permeance are assumed to be constant and are tted to experimental data from (Stünkel, 2013). For simplicity, the Joule-Thompson eect is approximated with a lin-ear dependency on the trans-membrane pressure (Equation 2.17) as originally proposed in (Esche, 2015), while the pressure drop is also linearly correlated to the inlet supercial gas velocity (Equation 2.18) based on the experimental data published in (Stünkel, 2013) as seen in Figure 2.8.

Figure 2.8: Pressure drop calculated by Equation 2.18 (line) and experimen-tal measurements from (Stünkel, 2013) (circles) for dierent inlet supercial gas velocities

dṄ^R

i (z)

dz =−ṅ^M_i (z)·w^M (2.12)

dṄ^P

i (z)

dz = +ṅ^M_i (z)·w^M (2.13)

ṅ^M_i (z) =ρ^N_i ·L_i(z)·

(︁φ^R_i (z)·y^R_i (z)·p^R(z)−φ^P_i (z)·y_i^P(z)·p^P(z))︁ (2.14) Ṅ^R

i (z) =y^R_i (z)·

N C

∑︂

i=1

Ṅ^R

i (z) (2.15)

Ṅ^P

i (z) =y^P_i (z)·

N C

∑︂

i=1

Ṅ^P

i (z) (2.16)

T^P =T^R+ 0.9887−1.1583·(p^R(z= 0)−p^P) (2.17) dp^R(z)

dz =−(0.116 + 0.695·uⁱⁿ_gas)·w^M (2.18) In Equations 2.12 to 2.16:

Superscripts R, P, and M denote retentate, permeate, and membrane respectively

Ṅ_i is the molar ow rate of componentiinmol s⁻¹ ṅ_i is the molar ux of component iinmol s⁻¹m⁻² w^M is the membrane width in m

ρ^N_i is the molar gas density of component iat normal conditions (273 K and 1 bar) in mol m⁻³

Li is the permeance of componentiinNm³s⁻¹m⁻²Pa⁻¹

ϕi is the fugacity coecient of componentiin the mixture given yi is the molar fraction of componentiinmol mol⁻¹

p is the total pressure given inPa T is the temperature given in K

uⁱⁿ_gas is the inlet gas supercial velocity inm s⁻¹

2.2 Carbon Dioxide Removal Implementation

The model utilized within this work is adapted from (Song, 2014) and (Esche, 2015). It has been extended to simulate industrial-scale systems by using a numbering up approach, e.g., adding several equal modules in parallel, as de-scribed in Section E.1. It is re-implemented in the software ACM. Discretiza-tion is achieved by Orthogonal CollocaDiscretiza-tion on Finite Elements (OCFE) with third-order polynomials. Figure 2.9 shows simulation results for a high CO₂ removal rate of 20 % carried out with the exact same input specications and only varying the number of nite elements. It is clear that results are nearly in-dependent of the number of nite elements and even a single one could be used for the simulations. This is in agreement with (Esche, 2015), which applied the same discretization method. The ACM model is exported as a unit operation (Block) into Aspen Plus for the simulations and optimization in Chapter 4.

Parameter Estimation and Model Validation

The permeances and pressure drop parameters have been tted to experimental data obtained from two campaigns performed in 2010 and 2011 using a0.5 m² PIM module (Stünkel, 2013). The experiments only applied the four most rel-evant components, i.e., CO₂, C₂H₄, CH₄, and N₂ under the range of conditions summarized in the Table 2.2. Parity plots for simulation vs. experimental re-sults are shown in Figure 2.10 in terms of CO2 removal and C2H4 recoveries in the retentate stream. The agreement between simulation and experiments in terms of ows, mole fractions, and outlet pressures in the retentate side is good, with most values within the plotted±30%condence interval.

0 5 10 15 20 25 30 35 40 45 50

Number of Finite Elements 0.199014

0.199016 0.199018 0.19902 0.199022 0.199024 0.199026 0.199028

CO2 Removal

Figure 2.9: Analysis on the number of nite elements required to solve the mem-brane module model

Table 2.2: Range of experimental conditions applied by (Stünkel, 2013) and used to regress the permeance calculation parameters

Variable Range Units

Membrane Material PIM

-Membrane Area 0.5 m²

Feed Flow 179 - 1.063 kmol h⁻¹ Feed Temperature 290 - 296 K

Feed Pressure 5 - 32 bar

Permeate Pressure 1 - 1.12 bar Inlet CO₂ fraction 0.13 - 0.25 mol mol⁻¹ Inlet C₂H₄ fraction 0.09 - 0.15 mol mol⁻¹ Inlet CH4 fraction 0.14 - 0.18 mol mol⁻¹ Inlet N₂ fraction 0.44 - 0.64 mol mol⁻¹

Figure 2.10: Parity plots of simulation and experimental results for CO₂ re-moval and C₂H₄ recovery using PIM module. Simulations per-formed with the ACM model developed in this work and the ex-perimental data is used as published in (Stünkel, 2013).

Membrane Modeling Outlook

The past experiments have only been carried out for the four main components and for inlet CO2 concentrations up to25 mol%. A major source of uncertainty is the fate of H₂ and CO. Due to the small molecular diameter, H₂ is likely to have a high permeance, while CO should behave similarly to N₂. Further experiments are, thus required to also include these components, extend the range of validity of the model, and allow for a more accurate and rigorous assessment of the permeation-based CO₂ removal process.

2.2 Carbon Dioxide Removal 2.2.2 Absorption and Desorption

Chemical absorption with a 30wt% Monoethanolamine (IUPAC: 2-aminoethan-1-ol) (MEA) aqueous solution is considered in this thesis. Chemical absorption implies that, apart from equilibrium between the vapor and liquid phases, a chemical equilibrium also occurs in the liquid phase. For the system of H2O, MEA, and CO₂, the set of equilibrium reactions assumed is shown in Equations 2.19-2.23.

2 H₂O_(l) −−↽−−⇀H₃O⁺_(aq)+ OH⁻_(aq) (2.19) HCO3−

(aq)+ H2O(l) −−↽−−⇀CO32−

(aq)+ H3O⁺(aq) (2.20) 2 H₂O_(l)+ CO_2(g) −−↽−−⇀HCO₃⁻_(aq)+ H₃O⁺_(aq) (2.21) H₂O_(l)+ MEACOO⁻_(aq)−−↽−−⇀MEA_(l)+ HCO₃⁻_(aq) (2.22) H₂O_(l)+ MEAH⁺_(aq)−−↽−−⇀MEA_(l)+ H₃O⁺_(aq) (2.23)

Modeling and Validation

To model the solution chemistry containing the ionic species, an electrolyte Non-Random Two Liquid (NRTL) model such as the one implemented in Aspen Plus by Chen and Evans, 1986 is required. An EoS, such as the Redlich-Kwong (RK) (Redlich and Kwong, 1949), is also often applied to the gas-phase if absorption is carried out at high pressures. Song and Chen, 2009 modied the original electrolyte NRTL model by Chen and Evans, 1986 to improve its numerical performance and to make it fully consistent with the regular non-electrolyte NRTL model. This option is available under the package ENRTL-RK in Aspen Plus and has been used in this work in combination with the PR-EoS.

The process conditions in the absorption section range between 40°C to 150°C and 1.1 bar to 32 bar, which means that all components i except the solvents H2O and MEA are above their critical point. The solubility of gases in water or other solvents can be accurately modeled by Henry's law, so that the iso-fugacity condition reduces to Equation 2.24. For the solvents j, the extended Raoult's law (Equation 2.25) is used. The temperature dependency for the Henry constant of componenti in solventj is given by Equation 2.26.

For a mixed solved system, Equation 2.27 is used with a weighting function (wj) based on the solvents' composition and molar volumes (Equation 2.28).

Equations 2.24 to 2.28 are iteratively solved simultaneously with the chemical equilibrium, which is obtained by Gibbs free energy minimization.

φ^V_i (T, p, y)·yi·p=xi·γ_i^∗(T, x)·Hi(T, x) (2.24)

In Equations 2.24 to 2.28:

Subscript i stands for gas components H₂, N₂, CH₄, C₂H₄, C₂H₆, CO, and CO2

Subscript j stands for solvents H2O and MEA

φ^V_i andφ^V_j are the fugacity coecients of gas components iand solvent j in the vapor phase respectively

y_i and y_j are the mole fractions of gas component iand solvent j in the vapor phase respectively, given in mol mol⁻¹

p is the total pressure in Pa T is the temperature inK

xi and xj are the mole fractions of gas component iand solventj in the liquid phase respectively, given inmol mol⁻¹

γ_i^∗ is the activity coecients of gas componentiin the liquid phase using the innite dilution in water as the reference state

γj is the activity coecients of solventj in the liquid phase

Hi and Hi,j are the Henry constants of gas component i in the solvent mixture and in pure solvent j respectively, given inPa

p^LV_j is the vapor pressure of solvent j inPa

A_i,j, B_i,j, C_i,j, D_i,j, E_i,j are the Henry parameters for gas component i in pure solvent j

2.2 Carbon Dioxide Removal wj is the weighting factor for solvent j in the mixing rule

γ_i^∞ andγ_i,j^∞are the innite dilution activity coecient of gas component iin the solvent mixture and in pure solventj respectively

v_j is the molar volume of solvent j inm³mol⁻¹

The table of Henry parameters for all components in H₂O is complete using Aspen Plus' in-built data-banks. However, these have mostly been regressed around 298 K and deviations from experimental data at higher temperatures have been observed. Hence, these parameters have been tted to additional experimental data sets including higher temperatures. Experimental measure-ments and model predictions for C2H4 solubility in H2O using the original Aspen Plus' and the newly tted parameters are shown in Figure 2.11. Further comparisons are shown in Appendix A.

Besides CO2, none of the gases had available Henry parameters to compute their solubility in MEA. The solubility of hydrocarbons in amine solutions is higher than in pure water, which is commonly referred to as salting-in eect (Carroll and Mather, 1997). This is essential to accurately model product losses in the absorption process. Therefore, Henry parameters for all components in MEA have been tted to experimental data. Unfortunately, a single publica-tion in Japanese has been found with nine data points on the solubility of the product C2H4 on varying concentrations of aqueous MEA close to ambient tem-perature and at atmospheric pressure (Sada and Kito, 1972). Hence, further measurements are recommended to improve the model in future studies. Figure 2.12 shows the modeled and experimental solubility of C2H4 in aqueous MEA.

Comparisons for the other components are shown in Appendix A.

Finally, the solubility of CO₂ in a 30 wt% aqueous MEA solution is also computed by the model and compared to the experimental data from (Jou, Mather, and Otto, 1995) at dierent temperatures. The comparison in terms of amine loading as a function of the CO₂ partial pressure in the gas phase is shown in Figure 2.13. A good agreement is achieved on the range of conditions relevant to the process. No attempt is made to reproduce the entire data-set, notably the high CO₂ loading cases above 0.6 molCO2mol⁻¹_MEA, since the pressures required would be unpractical.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Liquid Mole Fraction of Ethylene [mol/mol] ₁₀^-3 0

10⁶ Solubility of Ethylene in Water as a P-x Diagram 311K Davis al. 1960

360K Davis al. 1960 394K Davis al. 1960 310K Model - fitted parameters 360K Model - fitted parameters 394K Model - fitted parameters

310K Model - Aspen APV100 BINARY parameters 360K Model - Aspen APV100 BINARY parameters 394K Model - Aspen APV100 BINARY parameters

Figure 2.11: Solubility of ethylene in water as a P-x diagram at 310.881K, 360.901K, and 394.238K. Experimental data (crosses) from (Davis and McKetta, 1960), model predictions with tted parameters (continuous lines) and with APV-100 BINARY parameters (dashed lines).

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Liquid Mass Fraction of Amine [kg/kg]

0.8

Liquid Mole Fraction of Ethylene [mol/mol]

10^-4 Solubility of Ethylene in aqueous MEA solution

298K Sada and Kito (1972) 288K Sada and Kito (1972) 298K Model

288K Model

Figure 2.12: Solubility of Ethylene in aqueous MEA at dierent concentrations, atmospheric pressure, and at 288 Kand 298 K: Model predictions (dots with trend line) and experimental data from (Sada and Kito, 1972) (crosses)

2.2 Carbon Dioxide Removal

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 CO₂ Loading in the Amine Solution [mol_CO2/mol_MEA]

10^-5 10⁰ 10⁵

CO 2 Partial Pressure [kPa]

Solubility of Carbon Dioxide in 30wt% aqeuous MEA

313K Jou et al. (1995) 353K Jou et al. (1995) 393K Jou et al. (1995) 313K Model 353K Model 393K Model

Figure 2.13: Solubility of Carbon Dioxide in30 wt% aqueous MEA solution at 313 K,353 K, and393 K: Model predictions and experimental data from (Jou, Mather, and Otto, 1995).

Implementation

The newly created property method using the electrolyte NRTL model with the PR-EoS and the regressed Henry parameters is saved as a new property method named ENRTL-PR. This is made available as a supplemental material of this thesis as an Aspen Properties le. To simulate the absorption and desorption columns, the phase-equilibrium mode of the RadFrac block in Aspen Plus is applied. The module RadFrac is a generic model for separation columns, e.g., distillation, absorption, stripping, that may include 2 or 3 phases, reactions, and heat and mass transfer limitations (rate-based).

2.3 Distillation

The nal hydrocarbon separation is achieved in a series of two low-temperature distillation columns. The PR-EoS with the original alpha function and mixing rule (Peng and Robinson, 1976) is applied herein through Aspen Plus' PENG-ROB property package and binary interaction parameters retrieved from the APV100 EOS-LIT and NISTV100 in-built data banks. The model is suitable for properties and phase-equilibria of hydrocarbon mixtures. Comparisons of predicted and experimental Vapor-Liquid Equilibrium (VLE) for the pairs of key components, i.e., CH4-C2H4 for the demethanizer, and C2H4-C2H6 for the C2-splitter, are shown in Fugures 2.14 and 2.15.

The columns are simulated using the phase-equilibrium mode of a RadFrac block. Design-specs (see Section 3.2) are set to achieve target product purities and recoveries and the convergence method is switched to "Petroleum/Wide-boiling". This applies a sum-rates algorithm adapted from the inside-out method by (Boston and Britt, 1978), which is the default method named "Standard". It can simultaneously converge design-specs and the outer loop and outperforms the standard algorithm for hydrocarbon separations with wide-boiling mixture and/or sharp splits.

The multi-stream heat exchangers or cold-boxes are simulated using the block MHeatX. This module accounts for the overall energy balance, but not for the exchanger geometry. It is important to apply a zone analysis, which is a verication of the temperature dierence along the heat exchanger to ensure there is always driving force for heat transfer.

2.3 Distillation

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mole Fraction of Methane [mol.mol^-1] 0.0

1.0 2.0 3.0 4.0 5.0

Pressure [Pa]

10⁶ P-xy Diagram for Methane and Ethylene

150K Miller et al. (1977) 150K Model

190K Miller et al. (1977) 190K Model

Figure 2.14: Vapor-liquid equilibrium of methane and ethylene as a P-xy dia-gram at150.014 K and 190.012 K. Model predictions and experi-mental data from (Miller, Kidnay, and Hiza, 1977)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mole Fraction of Ethylene [mol.mol^-1] 0.5

1.0 1.5 2.0 2.5 3.0 3.5

Pressure [Pa]

10⁶ P-xy Diagram for Ethylene and Ethane

263K Fredenslund et al. (1976) 263K Model

233K Fredenslund et al. (1976) 233K Model

Figure 2.15: Vapor-liquid equilibrium of ethylene and ethane as a P-xy diagram at233.182 Kand263.1524 K. Model predictions and experimental data from (Fredenslund, Mollerup, and Hall, 1976)

2.4 Cost Estimation

The goals of the cost estimation are to provide the objective functions for the optimal design of the industrial-scale BG-OCM plant and to compare the result-ing bio-ethylene production cost to the market value of fossil-based ethylene.

Cost estimations for preliminary and conceptual design stages typically focuses on utility and equipment cost. These are the costs that can be more easily and accurately estimated based on a process simulation model, since several other inuential factors such as plant location, available infrastructure, terrain characteristics, etc. are still unknown. At this stage, other costs such as piping,

Cost estimations for preliminary and conceptual design stages typically focuses on utility and equipment cost. These are the costs that can be more easily and accurately estimated based on a process simulation model, since several other inuential factors such as plant location, available infrastructure, terrain characteristics, etc. are still unknown. At this stage, other costs such as piping,

Im Dokument Optimal Design and Evaluation of a Biogas-based Oxidative Coupling of Methane Process (Seite 83-0)