# Membrane-Based Processes: Optimization of Hydrogen Separation by Minimization of Power, Membrane Area, and Cost

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

_{2}separation from off-gases in hydrocarbons processing plants to simultaneously attain high values of both H

_{2}recovery and H

_{2}product purity. First, for a given H

_{2}recovery level of 90%, optimizations of the total annual cost (TAC) are performed for desired H

_{2}product purity values ranging between 0.90 and 0.95 mole fraction. One of the results showed that the contribution of the operating expenditures is more significant than the contribution of the annualized capital expenditures (approximately 62% and 38%, respectively). In addition, it was found that the optimal trade-offs existing between process variables (such as total membrane area and total electric power) depend on the specified H

_{2}product purity level. Second, the minimization of the total power demand and the minimization of the total membrane area were performed for H

_{2}recovery of 90% and H

_{2}product purity of 0.90. The TAC values obtained in the first and second cases increased by 19.9% and 4.9%, respectively, with respect to that obtained by cost minimization. Finally, by analyzing and comparing the three optimal solutions, a strategy to systematically and rationally provide ‘good’ lower and upper bounds for model variables and initial guess values to solve the cost minimization problem by means of global optimization algorithms is proposed, which can be straightforward applied to other processes.

_{2}separation; membranes; multi-stage process; optimization; design; operation; cost; membrane area; energy; mathematical programming; NLP; GAMS

## 1. Introduction

_{2}) of industrial-grade is produced purposefully. However, H

_{2}can also be recovered from H

_{2}-rich off-gas streams from petrochemical facilities or refineries, which is mostly burned as a residual gas [1]. Since industry tendencies will increase the need for more profitable sources of H

_{2}for a variety of applications, H

_{2}recovery from these off-gas streams becomes an interesting alternative to make more effective use of these existing facilities concomitantly. Some hydrogen uses or applications require ultra-high purity supply (e.g., semiconductor industry) but other applications require less pure feed stocks (e.g., hydrodesulphurization and hydrocracking). The achievable H

_{2}purity levels depend on the used gas separation/purification technologies.

_{2}separation/purification has attracted considerable attention owing to the inherent advantages over other traditional separation technologies such as pressure swing adsorption and cryogenic adsorption processes. Membrane gas separation does not require moving parts; it has small footprint and it is a compact system; it provides operating flexibility to feed fluctuations; it demands comparatively lower energy requirement leading to lower operating costs; it does not involves chemicals, make-up, and solvents; it is easy start-up and shut-down; it requires minimal maintenance and operator attention; it allows a modular design; it requires minimal utilities; and it is easy to control. Among the main drawbacks, it can be mentioned no economy of scale due to the modular design; pretreatment of streams with particulates, organic compounds, or moisture can be difficult and/or expensive; sensitivity to chemicals can be problematic in some cases; requirement of electrical power for compression (high-quality energy) [2].

_{2}separation, recovery and/or purification, four different membrane types have been commercialized or are being considered for development and commercialization. They are polymeric membranes, porous (ceramic, carbon, metallic) membranes, dense metal membranes, and ion-conductive membranes [3]. The polymeric membranes have achieved a comparatively high degree of industrial application and commercialization [3]. Indeed, Permea (currently a division of Air Products) was the first company to successfully use membranes for gas separation at a large industrial scale, using a polysulfone hollow-fiber (HF) membrane (commercially known as Prism) for the separation of H

_{2}from NH

_{3}reactor purge gas, in 1980 [4]. Now, there are several hundred polymeric membrane systems for H

_{2}separation and recovery installed by Medal/Air Liquide (Paris, France, polyimide HF), Separex/UOP (Des Plaines, IL, USA, cellulose acetate, spiral wound SW), UBE Industries (Tokyo, Japan, polyimide HF), GENERON/MG (Houston, TX, USA, tetrabromopolycarbonate HF), Permea/Air Products (Allentown, PA, USA, polysulfone HF), IMS/Praxair (Danbury, CT, USA, polyimide HF), among other companies [5]. Dense metal membranes, such as palladium and palladium-based alloys, have been commercially applied to special markets since they offer inherently a very high selectivity of H

_{2}. Currently, a lot of research and development efforts are dedicated to porous membranes, such as ceramic and carbon compositions. Among the mentioned membrane types, ion-conducting membranes are the least studied for H

_{2}separating, despite many fuel cells use a proton-conducting membrane as electrolyte [3].

_{2}capture ([6,13,14,15]), and H

_{2}separation ([9,16,17]). For instance, Xu et al. [17] studied the potential applications of membrane-based processes for H

_{2}purification and pre-combustion CO

_{2}capture. They investigated single-stage and two-stage configurations, and two membrane types: CO

_{2}selective membranes and H

_{2}selective membranes (HSMs). Among other results, the authors found that a minimum cost selectivity can be obtained by fixing the membrane permeability along with the H

_{2}product purity level. Another important result indicated that it is difficult to reach a stable operation mode of the two-stage system with HSM because it is strongly influenced by the variation of the operating conditions. The authors highlighted the need for further investigation in this matter. By using a nonlinear mathematical programming (NLP) model implemented in GAMS (General Algebraic Modeling System) software, Zarca et al. [9] evaluated a two-stage membrane process for H

_{2}recovery from the tail gas generated in carbon black manufacturing process, considering two types of membranes: polymeric membranes and ionic liquid-based membranes. The authors assumed that the retentate streams are at atmospheric pressure and proposed the net present value as the objective function to be minimized. Results show that ionic liquid-based membranes are promising to achieve a H

_{2}-rich syngas stream at a minimal cost and also to mitigate CO

_{2}emissions.

_{2}from a CO

_{2}/CO/H

_{2}/N

_{2}gas mixture generated in hydrocarbons processing plants to attain desired H

_{2}product purity levels ranging between 0.90 and 0.95 mole fraction and a H

_{2}recovery of 90% by minimization of the total annual cost (TAC). To this end, a NLP problem is solved using the algebraic equation-oriented optimization tool GAMS, considering simultaneously all the trade-offs existing between the model variables. Compared to the study of Zarca et al. [9], the model considers the possibility of combining vacuum pumps and compressors to create the driving forces in the membrane stages, which may lead to a reduction of the required total membrane area for a given fixed electric power level, or a reduction of the demanded electric power for a fixed value of total membrane area.

_{2}separation, as well as to elucidate the exiting techno-economic trade-offs that are difficult to distinguish at first glance.

_{2}separation. Section 3 summarizes the main model assumptions and considerations and presents the mathematical model employed in this research. Section 4 states the optimization problems to be solved. Section 5 discusses the optimization results obtained by cost minimization (Section 5.1) and total power minimization and total membrane area minimization (Section 5.2). Also, in Section 5.2, a strategy to systematically and rationally provide ‘good’ lower and upper bounds for model variables and initial guess values to solve the cost minimization problem by means of global optimization algorithms is proposed. Finally, Section 6 draws the conclusions of this work.

## 2. Process Description

_{0}reaches the operating pressure (p

^{H}) and temperature (T

_{MS}) in C1 and HEX1, respectively. Then, F

_{0}can be optionally mixed in M1 with a fraction of the retentate obtained in MS1 (RR

_{MS1}) and/or with a fraction of the retentate obtained in MS2 (RR

_{MS2_MS1}). Afterwards, the resulting stream is fed to MS1, where it is separated into two streams: permeate stream (rich in H

_{2}) and retentate stream. The permeate membrane side can operate under vacuum to create the driving force for component separation through the vacuum pump VP1. The permeate stream P

_{MS1}leaving the VP1 decreases its temperature in HEX3 and increases its pressure in C2. Afterwards, it reaches the operating temperature T

_{MS2}in HEX2, and it can be optionally mixed in M2 with a fraction of the retentate obtained in MS2 (RR

_{MS2}). Finally, the resulting stream is fed to MS2, where it is separated into the corresponding retentate and permeate streams.

^{H}− p

^{L}

_{MS}) depends on many factors such as membrane material, membrane areas, costs, and design specifications. For instance, the higher the operating pressure ratio (p

^{H}/p

^{L}

_{MS}), the higher the electric power requirement but the lower the membrane area. The optimal operating pressure values p

^{H}, p

^{L}

_{MS1}, and p

^{L}

_{MS2}depend on the relationships between investment and operating costs not only of the compressors and vacuum pumps but also of the remaining process units. Thus, it is clear the importance of optimizing simultaneously all the techno-economic trade-offs that exist between the process variables. The proposed model includes the following three alternative ways to create the pressure difference as driving force for permeation: (i) by compressing the feed F

_{0}and the permeate P

_{MS1}by means of C1 in the first stage and C2 in the second stage (i.e., no vacuum is applied at the permeate side of the membranes); (ii) by applying vacuum at the permeate side of the membranes (i.e., no compression of the feed and permeate streams is applied); and (iii) by combining both compression and vacuum. Then, the selection i.e., presence or absence of compressors C1 and C2 and vacuum pumps VP1 and VP2 in the process configuration results from solving optimization model.

## 3. Process Modeling

#### 3.1. Assumptions and Process Mathematical Model

#### 3.2. Cost Model

^{−1}), capital expenditures (CAPEX, in M$), annualized capital expenditures (annCAPEX, in M$ year

^{−1}), and operating expenditures (OPEX, in M$ year

^{−1}) are calculated by Equations (1)–(5).

_{1}(4.98) in Equation (4), and f

_{2}(0.464), f

_{3}(2.45), and f

_{4}(1.055) in Equation (5) can be found in [15], which were estimated based on the guidelines given in [19] and [20]. In Equation (5), OPEX takes into account the manpower and maintenance costs (OLM). The total investment cost (C

_{INV}, in M$) is calculated by Equation (6), where the investment costs of the individual process units are estimated by Equations (7)–(10):

_{RM}, in M$ year

^{−1}) used in Equation (5) is calculated by Equation (11). It depends on the cost of electricity (C

_{EP}), cooling water (C

_{CW}), and membrane replacement (C

_{MR}), which are expressed by Equations (12)–(14), respectively:

_{EP}, cru

_{CW}, and cru

_{MR}are, respectively, 0.072 $ kW

^{−1}, 0.051 $ kg

^{−1}, and 10.0 $ m

^{−2}. An operation period (OT) of 6570 h year

^{−1}was considered.

## 4. Problem Statement

**x**is the vector of model variables;

**h**

_{s}(

**x**) refers to the mass and energy equality constraints, and correlations for physicochemical properties estimation, design specifications, and cost estimation;

**g**

_{t}(

**x**) refers to inequality constraints which are employed to avoid concentration and temperature crosses in the process units. The H

_{2}product purity target specification is parametrically varied between 0.90 and 0.95 through the parameter α, which is a fixed value in a particular optimization run.

- Minimal TAC.
- Optimal TAC distribution between the annualized capital expenditures (CAPEX) and operating expenditures (OPEX).
- Optimal sizes of the process units (membrane unit areas, heat exchanger areas, compressor and vacuum-pump power capacities).
- Optimal values of temperature, pressure, composition, and flow rate of all process streams.

**x**and constraints

**h**

_{s}(

**x**) and

**g**

_{t}(

**x**) have the same meanings as in the problem given in Equation (15). In this case, the optimization problem is solved for a H

_{2}product purity target specification of 0.9.

## 5. Results and Discussion

_{2}product purity are discussed. In Section 5.2, optimal solutions obtained by minimizing the total membrane area and the electric power are presented and compared to the obtained by minimizing the total annual cost for the same design specifications.

#### 5.1. Optimal Solutions Corresponding to the Minimization of the Total Annual Cost

_{2}recovery target level of 90% and H

_{2}product purity target values in the range 0.90–0.95 are presented in Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10.

_{2}purity increases since the H

_{2}permeate flow rate in the first stage increases to satisfy the increased purity, as shown in Figure 7, Figure 8 and Figure 9 for H

_{2}product purity levels of 0.90, 0.91, and 0.94, respectively. For instance, compared to 0.90 H

_{2}product purity, the minimum TAC value obtained for 0.95 H

_{2}purity increases by 26.2% (from 1.764 to 2.227 M$ year

^{−1}) as consequence of the increase of both the OPEX value by 25.1% (from 1.095 to 1.370 M$ year

^{−1}) and the annCAPEX value by 28.1% (from 0.669 to 0.857 M$ year

^{−1}). On the other hand, it can be observed in Figure 2b that the contribution ratio between OPEX and annCAPEX to the TAC remains almost constant with increasing H

_{2}purity values. Certainly, the contribution of OPEX to the TAC varies slightly from 62.1% to 61.6% for H

_{2}product purity values of 0.90 and 0.95, respectively.

_{2}product purity in 0.01 determines different percentage variations in costs depending on the purity level itself. For instance, an increment of H

_{2}purity from 0.90 to 0.91 implies an increase of TAC in 3.74 × 10

^{−2}M$ year

^{−1}(from 1.764 to 1.802 M$ year

^{−1}, i.e., 2.1%) while the same increment from 0.94 to 0.95 implies an increase of TAC in 0.173 M$ year

^{−1}(from 2.054 to 2.227 M$ year

^{−1}, i.e., 8.4%).

_{2}purity from 0.90 to 0.94 increases the permeate flow rate (from 0.008 to 0.013 kmol s

^{−1}) and H

_{2}concentration (from 0.710 to 0.774 mole fraction) in the first stage, but decreases the permeate flow rate in the second stage (from 4.986 × 10

^{−3}to 4.774 × 10

^{−3}kmol s

^{−1}). It is interesting to note that, in order to reach these flow rate values and H

_{2}purities, the electric power requirement by compressors and vacuum pump increases in total 0.108 MW (0.026 MW, 0.049 MW, and 0.033 MW in C1, C2, and VP1, respectively) while the optimal total membrane area decreases 332.1 m

^{2}(58.0 m

^{2}and 274.1 m

^{2}in the first and second stage, respectively). Thus, the optimal cost-based trade-offs indicate that it is more beneficial to increase the total electrical power (to operate the process at higher operating pressure values p

^{H}as shown in Figure 5) rather than to increase the total membrane area.

_{2}product purity is increased from 0.94 to 0.95. In this case, it is necessary to increase both the total membrane area about 67.0 m

^{2}(from 5369.7 to 5436.7 m

^{2}) and the electric power about 0.065 MW (from 0.406 to 0.471 MW) in order to satisfy a desired H

_{2}purity of 0.95. It is interesting to note that the increase of the total membrane area results from an increase of the area of the first stage in 115.2 m

^{2}and a decrease of the area of the second stage in 48.2 m

^{2}, which is a trend opposite to the one observed when the H

_{2}purity increases from 0.90 to 0.94 (Figure 3 and Figure 4), where the area of MS1 and MS2 decreases and increases, respectively, with increasing purity levels. This behavior can be better understood by observing in Figure 7 the individual variation of the area of both membranes with increasing product purity levels. This figure interestingly shows that the curve of the membrane area corresponding to MS1 has a minimum value at a H

_{2}purity value of 0.93, and that the one corresponding to MS2 decreases practically linearly in the studied purity variation range. This is one of the reasons of why dissimilar trade-offs between the same process variables are established at different values of H

_{2}purity levels.

_{2}product purity values. It is followed by the compressor C2 used in the second stage for compressing the permeate leaving the vacuum pump VP1. In contrast to C1, the contribution of C2 increases exponentially with increasing H

_{2}product purity values, showing a behavior similar to the one observed for the optimal high operating pressure p

^{H}values (Figure 5). The third contributor to the total investment is the membrane area required in the first stage A

_{MS1}, with an investment that remains almost constant with increasing H

_{2}product purities. The vacuum pump VP1 is the fourth contributor, whose investment increases more importantly at high H

_{2}purity values. The contributions of the remaining process units are comparatively less important or practically insignificant.

_{RM}shown in Figure 8b, the cost of electricity for running the compressors and the vacuum pump is by far the major contributor, and it increases more rapidly with increasing H

_{2}product purity levels.

_{2}purity levels. The area increases in HEX1 and HEX3 are mainly due to the increase in the compression ratio of the compressors which rises their outlet temperatures, thus requiring more area for heat transfer to reach the operating temperature of the stages (313.15 K). On the other hand, the increase of the heat transfer area of HEX2 (located after the vacuum pump VP1) and its corresponding heat load is only due to the increase in the permeate flow rate since the first stage operates with a vacuum level of 0.020 MPa, what implies the same pressure ratio (5.065) and, therefore, the same output temperature (497.8 K) for all the H

_{2}product purity levels.

#### 5.2. Influence of the Objective Functions on the Optimal Design and Operating Conditions

^{2}, which is, respectively, 49.9% and 83.5% lower than the value obtained in osTAC and osTW, but the electric power required in osTMA is 30.2% and 79.1% higher than the required in osTAC and osTW, respectively. Table 3 shows that the minimization of TMA (2854.23 m

^{2}) implies the highest TW value (0.387 MW) reaching the upper bound for p

^{H}(1.01320 MPa). Also, Table 3 shows that the minimization of TW (0.216 MW) implies the highest TMA value (17,316.96 m

^{2}).

_{2}separation studied in this paper (which in fact can be straightforward applied to other processes). More precisely, in order to determine tight variable bounds, the idea behind is to use the information predicted by the same model of the process but considering two different situations: membrane area minimization and power minimization, which represent two extremes that can be used efficiently to narrow the feasible region of the cost optimization problem. Unlike other works, it is here intended to establish a systematic bounding procedure using information inherent to the process obtained in a rational way instead of exploiting the nature of the associated constraints (at the beginning of the methodology) without applying any rational criterion.

_{MS1}, A

_{MS2}, W

_{VP1}, p

^{L}

_{MS1}, HTA

_{HEX2}, Q

_{HEX2}, and ∆TML

_{HEX2}are provided as lower bounds to solve the minimization of TAC while the optimal values of W

_{C1}, W

_{C2}, A

_{HEX1}, A

_{HEX2}, Q

_{HEX1}, Q

_{HEX2}, ∆TML

_{HEX1}, ∆TML

_{HEX2}, and p

^{H}are provided as upper bounds. The second step consists on the minimization of TW; the optimal values of W

_{C1}, W

_{C2}, A

_{HEX1}, A

_{HEX2}, Q

_{HEX1}, Q

_{HEX2}, ∆TML

_{HEX1}, ∆TML

_{HEX2}, and p

^{H}are now provided as lower bounds while the values of A

_{MS1}, A

_{MS2}, W

_{VP1}, p

^{L}

_{MS1}, HTA

_{HEX2}, Q

_{HEX2}, and ∆TML

_{HEX2}as upper bounds. Thus, if the minimization of TMA provides a lower bound for a given decision variable, then the minimization of TW provides an upper bound for it, and vice versa. It is said that the pre-processing phase provides bounds in a rational way because they represent limits for the sizes of the pieces of equipment and/or process operation conditions. They can be used to identify smaller search spaces for the cost optimization problem and reduce the number of iterations, and consequently, the computing time. In addition, one of the two solutions (osTMA or osTW) can be used as an initial guess point in the global optimization algorithm because they are both feasible solutions for the cost optimization problem, thus facilitating the model convergence.

## 6. Conclusions

_{2}separation by minimization of the total annual cost, the total membrane area, and the total electric power as single objective functions, employing a nonlinear mathematical model implemented in GAMS environment.

_{2}product purity target levels. In fact, it was found that different trade-offs are established between the required total electric power and the total membrane area when the H

_{2}product purity is increased from 0.90 to 0.94 and from 0.94 to 0.95. In the former case, the total electric power increases and the total membrane area decreases with the increasing of the H

_{2}purity. The optimal cost-based trade-offs indicated that it is more beneficial to increase the total electric power (to operate the process at higher operating pressure values) rather than to increase the total membrane area. However, in the last case, it was observed that both the total membrane area and the total electric power increase with the increasing of the H

_{2}product purity.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A_{MS#} | membrane area required in the membrane stage MS#, m^{2} |

annCAPEX | annualized capital expenditures, M$ year^{−1} |

CAPEX | capital expenditures, M$. |

CRF | capital recovery factor, year^{−1} |

C_{RM} | raw material and utility cost, M$ year^{−1} |

cru_{CW} | specific cost of the cooling water, M$ kg^{−1} |

cru_{EE} | specific cost of the electricity, M$ kW^{−1} |

cru_{MR} | specific cost of the membrane replacement, M$ m^{−2} |

F_{0} | feed flow rate, kmol s^{−1} |

F_{MS#} | feed flow rate in the membrane stage MS#, kmol s^{−1} |

I_{MS#} | investment for membrane area of the stage MS#, M$ |

I_{HEX#} | investment for the heat exchanger HEX#, M$ |

I_{VP#} | investment for the vacuum pump VP#, M$. |

I_{C#} | investment for the compressor C#, M$ |

OPEX | operating expenditures, M$ year^{−1} |

p^{H} | high operating pressure (retentate side), MPa |

p^{L}_{MS#} | operating pressure in the permeate side of the membrane stage MS#, MPa |

P_{MS#} | permeate flow rate obtained in the membrane stage MS#, kmol s^{−1} |

R_{MS#} | retentate flow rate obtained in the membrane stage MS#, kmol s^{−1} |

TAC | total annual cost, M$ year^{−1} |

T_{0} | feed temperature, K |

T^{out} _{C#} | outlet temperature from the compressor C# associated with the membrane stage MS#, K |

T_{MS#} | operating temperature in the membrane stage MS#, K |

T^{out} _{HEX#} | outlet temperature from the heat exchanger HEX#, K |

TW | total power, MW |

W_{C#} | power required by the compressor C# associated with the membrane stage MS#, MW |

W_{VP#} | power required by the vacuum pump VP# in the membrane stage MS#, MW |

x_{i,0} | mole fraction of component i in the feed stream, dimensionless |

x_{MS#,i} | inlet composition of the component i in the membrane stage MS#, dimensionless |

x_{MS#,i,j} | mole fraction of the component i in the retentate stream of the membrane stage MS# at the discretization point j, dimensionless |

x_{MS#,R,i} | mole fraction of the component i in the retentate stream leaving the membrane stage MS#, dimensionless |

y_{MS#,i} | mole fraction of the component i in the permeate stream leaving the membrane stage MS#, dimensionless |

y_{MS1,i,j} | mole fraction of the component i in the permeate stream of the membrane stage MS# at the discretization point j, dimensionless |

## Appendix A. Process Mathematical Model

#### Appendix A.1. Main Model Assumptions

- All components can permeate.
- The component permeability is not affected by the operating pressure.
- The pressure drop is negligible at both membrane sides.
- The pressure of the feed and retentate streams is the same.
- Plug-flow pattern is considered at both membrane sides.
- Each membrane module operates isothermally.
- The Fick’s first law is used.

#### Appendix A.2. Mathematical Model

#### Appendix A.2.1. Mass Balances

_{i}and A

_{MS1}are the permeance of component i and membrane surface area, respectively. p

^{H}and p

^{L}

_{MS1}are the operating pressures in the retentate and permeate sides, respectively. The index j refers to a discretization point which varies from 0 to 19 (J = 19, i.e., 20 discretization points is considered).

#### Appendix A.2.2. Power Requirement

_{c}, and P

_{0}are the adiabatic expansion coefficient (1.4), efficiency (0.85), and atmospheric pressure (0.1013 MPa), respectively.

#### Appendix A.2.3. Energy Balances and Transfer Areas of Heat Exchangers

^{−2}K

^{−1}for all heat exchangers.

#### Appendix A.2.4. Connecting Constraints

#### Appendix A.2.5. Performance Variables

## References

- Benson, J.; Celin, A. Recovering hydrogen—And profits—From hydrogen-rich offgas. Chem. Eng. Prog.
**2018**, 114, 55–59. [Google Scholar] - Favre, E. Polymeric Membranes for Gas Separation. In Comprehensive Membrane Science and Engineering; Drioli, E., Giorno, L., Eds.; Elsevier: Amsterdam, The Netherlands, 2010; Volume II, pp. 155–212. ISBN 978-0-444-53204-6. [Google Scholar]
- Edlund, D. Hydrogen Membrane Technologies and Application in Fuel Processing. In Hydrogen and Syngas Production and Purification Technologies; Liu, K., Song, C., Subramani, V., Eds.; Wiley-Blackwell: Hoboken, NJ, USA, 2009; pp. 357–384. ISBN 978-0-471-71975-5. [Google Scholar]
- Baker, R. Membrane Technology in the Chemical Industry: Future Directions. In Membrane Technology; Pereira Nunes, S., Peinemann, K.-V., Eds.; Wiley-Blackwell: Hoboken, NJ, USA, 2001; pp. 268–295. ISBN 978-3-527-60038-0. [Google Scholar]
- Shalygin, M.G.; Abramov, S.M.; Netrusov, A.I.; Teplyakov, V.V. Membrane recovery of hydrogen from gaseous mixtures of biogenic and technogenic origin. Int. J. Hydrog. Energy
**2015**, 40, 3438–3451. [Google Scholar] [CrossRef] - Ramírez-Santos, Á.A.; Bozorg, M.; Addis, B.; Piccialli, V.; Castel, C.; Favre, E. Optimization of multistage membrane gas separation processes. Example of application to CO
_{2}capture from blast furnace gas. J. Membr. Sci.**2018**, 566, 346–366. [Google Scholar] [CrossRef] - Ohs, B.; Lohaus, J.; Wessling, M. Optimization of membrane based nitrogen removal from natural gas. J. Membr. Sci.
**2016**, 498, 291–301. [Google Scholar] [CrossRef] - Robeson, L.M. The upper bound revisited. J. Membr. Sci.
**2008**, 320, 390–400. [Google Scholar] [CrossRef] - Zarca, G.; Urtiaga, A.; Biegler, L.T.; Ortiz, I. An optimization model for assessment of membrane-based post-combustion gas upcycling into hydrogen or syngas. J. Membr. Sci.
**2018**, 563, 83–92. [Google Scholar] [CrossRef] - Ahmad, F.; Lau, K.K.; Shariff, A.M.; Murshid, G. Process simulation and optimal design of membrane separation system for CO
_{2}capture from natural gas. Comput. Chem. Eng.**2012**, 36, 119–128. [Google Scholar] [CrossRef] - Chowdhury, M.H.M.; Feng, X.; Douglas, P.; Croiset, E. A new numerical approach for a detailed multicomponent gas separation membrane model and AspenPlus simulation. Chem. Eng. Technol.
**2005**, 28, 773–782. [Google Scholar] [CrossRef] - Ghasemzadeh, K.; Jafari, M.; sari, A.; Babalou, A.A. Performance investigation of membrane process in natural gas sweetening by membrane process: modeling study. Chem. Prod. Process Model.
**2016**, 11, 23–27. [Google Scholar] [CrossRef] - Giordano, L.; Roizard, D.; Bounaceur, R.; Favre, E. Energy penalty of a single stage gas permeation process for CO
_{2}capture in post-combustion: A rigorous parametric analysis of temperature, humidity and membrane performances. Energy Procedia**2017**, 114, 636–641. [Google Scholar] [CrossRef] - Turi, D.M.; Ho, M.; Ferrari, M.C.; Chiesa, P.; Wiley, D.E.; Romano, M.C. CO
_{2}capture from natural gas combined cycles by CO_{2}selective membranes. Int. J. Greenh. Gas Control**2017**, 61, 168–183. [Google Scholar] [CrossRef] - Arias, A.M.; Mussati, M.C.; Mores, P.L.; Scenna, N.J.; Caballero, J.A.; Mussati, S.F. Optimization of multi-stage membrane systems for CO
_{2}capture from flue gas. Int. J. Greenh. Gas Control**2016**, 53, 371–390. [Google Scholar] [CrossRef] - Franz, J.; Scherer, V. An evaluation of CO
_{2}and H_{2}selective polymeric membranes for CO_{2}separation in IGCC processes. J. Membr. Sci.**2010**, 359, 173–183. [Google Scholar] [CrossRef] - Xu, J.; Wang, Z.; Zhang, C.; Zhao, S.; Qiao, Z.; Li, P.; Wang, J.; Wang, S. Parametric analysis and potential prediction of membrane processes for hydrogen production and pre-combustion CO
_{2}capture. Chem. Eng. Sci.**2015**, 135, 202–216. [Google Scholar] [CrossRef] - Arias, A.M. Minimization of Greenhouse Gases (GHGs) Emissions in the Energy Sector Employing Non-Conventional Technologies. Ph.D. Thesis, Universidad Tecnológica Nacional, Córdoba, Argentina, 2017. [Google Scholar]
- Abu-Zahra, M.R.M.; Niederer, J.P.M.; Feron, P.H.M.; Versteeg, G.F. CO2 capture from power plants: Part II. A parametric study of the economical performance based on mono-ethanolamine. Int. J. Greenh. Gas Control
**2007**, 1, 135–142. [Google Scholar] [CrossRef] - Rao, A.B.; Rubin, E.S. A technical, economic, and environmental assessment of amine-based CO
_{2}capture technology for power plant greenhouse gas control. Environ. Sci. Technol.**2002**, 36, 4467–4475. [Google Scholar] [CrossRef] [PubMed] - General Algebraic Modeling System (GAMS); Release 24.2.1; GAMS Development Corporation: Fairfax, VA, USA, 2013.
- Drud, A. CONOPT 3 Solver Manual; ARKI Consulting and Development A/S: Bagsvaerd, Denmark, 2012. [Google Scholar]
- Puranik, Y.; Sahinidis, N.V. Domain reduction techniques for global NLP and MINLP optimization. Constraints
**2017**, 22, 338–376. [Google Scholar] [CrossRef][Green Version] - Sherali, H.D.; Totlani, R.; Loganathan, G.V. Enhanced lower bounds for the global optimization of water distribution networks. Water Resour. Res.
**1998**, 34, 1831–1841. [Google Scholar] [CrossRef][Green Version] - Ruiz, J.P.; Grossmann, I.E. A New Theoretical Result for Convex Nonlinear Generalized Disjunctive Programs and its Applications. In Computer Aided Chemical Engineering; Bogle, I.D.L., Fairweather, M., Eds.; 22 European Symposium on Computer Aided Process Engineering; Elsevier: Amsterdam, The Netherlands, 2012; Volume 30, pp. 1197–1201. [Google Scholar]
- Kirst, P.; Stein, O.; Steuermann, P. Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints. TOP
**2015**, 23, 591–616. [Google Scholar] [CrossRef]

**Figure 2.**TAC minimization. Optimal costs vs. H

_{2}product purity for a H

_{2}recovery of 90%: (

**a**) TAC; (

**b**) OPEX, annCAPEX, and percentage contribution of OPEX to TAC. (TAC: total annual cost; OPEX: operating expenditures; annCAPEX: annualized capital expenditures)

**Figure 3.**TAC minimization. Optimal solution for a H

_{2}product purity of 0.90 and H

_{2}recovery of 90%.

**Figure 4.**TAC minimization. Optimal solution for a H

_{2}product purity of 0.94 and H

_{2}recovery of 90%.

**Figure 5.**TAC minimization. Optimal high operating pressure p

^{H}(retentate side) versus H

_{2}product purity.

**Figure 6.**TAC minimization. Optimal solution for H

_{2}product purity of 0.95 and H

_{2}recovery of 90%.

**Figure 7.**TAC minimization. Optimal membrane areas of stages MS1 and MS2 versus H

_{2}product purity.

**Figure 8.**TAC minimization. Optimal costs vs. H

_{2}product purity for H

_{2}recovery of 90%: (

**a**) Process-unit investments; (

**b**) Raw material and utility cost C

_{RM}, with cost for electric power EP, cooling water CW, and membrane replacement MR.

**Figure 10.**TAC minimization. Optimization results for heat exchangers: (

**a**) Heat transfer areas and (

**b**) heat loads, versus H

_{2}product purity.

**Figure 11.**Schematic of a variable bounding and solution strategy proposed for solving the cost optimization problem via global optimization.

**Table 1.**Numerical values of model parameters [9].

Parameter | Value |
---|---|

Feed specification | |

Flow rate, kmol h^{−1} | 100 |

Temperature, K | 313.15 |

Pressure, kPa | 101.32 |

Composition (mole fraction) | |

CO_{2} | 0.04 |

CO | 0.16 |

H_{2} | 0.18 |

N_{2} | 0.62 |

Membrane material (Polymer) | |

Permeance (mole m^{−2} s^{−1} MPa^{−1}) | |

CO_{2} | 8.444 × 10^{−3} |

CO | 7.457 × 10^{−4} |

H_{2} | 2.871 × 10^{−2} |

N_{2} | 4.078 × 10^{−4} |

**Table 2.**Minimization of TAC, TMA, and TW for 90% H

_{2}recovery and 0.90 H

_{2}product purity: Costs. (TAC: total annual cost; TMA: total membrane area; TW: total power).

Cost Item | Min TMA (osTMA) | Min. TAC (osTAC) | Min TW (osTW) |
---|---|---|---|

TAC (M$ year^{−1}) | 1.851 | 1.764 | 2.116 |

OPEX (M$ year^{−1}) | 1.158 | 1.095 | 1.262 |

annCAPEX (M$ year^{−1}) | 0.692 | 0.669 | 0.853 |

C_{INV }(M$) | 1.481 | 1.431 | 1.826 |

I_{C1} | 0.852 | 0.694 | 0.489 |

I_{C2} | 0.365 | 0.316 | 0.274 |

I_{MA_MS1} | 0.134 | 0.269 | 0.831 |

I_{VP1} | 6.93 × 10^{−2} | 7.67 × 10^{−2} | 0.1043 |

I_{HEX1} | 2.19 × 10^{−2} | 2.03 × 10^{−2} | 0.018 |

I_{MA_MS2} | 1.84 × 10^{−2} | 3.40 × 10^{−2} | 8.49 × 10^{−2} |

I_{HEX3} | 1.10 × 10^{−2} | 1.07 × 10^{−2} | 1.14 × 10^{−2} |

I_{HEX2} | 9.87 × 10^{−3} | 1.04 × 10^{−2} | 1.26 × 10^{−2} |

C_{RM }(M$ year^{−1}) | 0.193 | 0.155 | 0.139 |

C_{E} | 0.183 | 0.141 | 0.102 |

C_{MR} | 5.71 × 10^{−3} | 1.14 × 10^{−2} | 3.46 × 10^{−2} |

C_{CW} | 3.66 × 10^{−3} | 2.79 × 10^{−3} | 2.06 × 10^{−3} |

**Table 3.**Minimization of TAC, TMA, and TW for 90% H

_{2}recovery and 0.90 H

_{2}product purity: Process-unit sizes and operating conditions.

Cost Item | Min TMA (osTMA) | Min. TAC (osTAC) | Min TW (osTW) |
---|---|---|---|

TMA (m^{2}) | 2854.23 | 5701.66 | 17316.96 |

MA_{MS1} | 2510.80 | 5063.60 | 15714.90 |

MA_{MS2} | 343.43 | 638.06 | 1602.06 |

TW (MW) | 0.387 | 0.298 | 0.216 |

W_{C1} | 0.277 | 0.197 | 0.110 |

W_{C2} | 6.75 × 10^{−2} | 5.32 × 10^{−2} | 4.20 × 10^{−2} |

W_{VP1} | 4.29 × 10^{−2} | 4.75 × 10^{−2} | 6.46 × 10^{−2} |

HTA_{HEX1 }(m^{2}) | 8.839 | 7.802 | 6.378 |

HTA_{HEX2 }(m^{2}) | 2.305 | 2.6 | 3.5 |

HTA_{HEX3 }(m^{2}) | 2.813 | 2.680 | 2.997 |

Q_{HEX1} (MW) | 0.210 | 0.147 | 8.09 × 10^{−2} |

Q_{HEX2 }(MW) | 4.10 × 10^{−2} | 4.50 × 10^{−2} | 6.00 × 10^{−2} |

Q_{HEX3 }(MW) | 6.68 × 10^{−2} | 5.05 × 10^{−2} | 3.80 × 10^{−2} |

∆TML_{HEX1} (K) | 85.533 | 67.908 | 45.676 |

∆TML_{HEX2} (K) | 62.871 | 62.871 | 61.236 |

∆TML_{HEX3} (K) | 85.533 | 67.908 | 45.676 |

p^{H} (MPa) | 1.01320 | 0.59834 | 0.30396 |

p^{L}_{MS1} (MPa) | 2.00 × 10^{−2} | 2.00 × 10^{−2} | 2.10 × 10^{−2} |

p^{L}_{MS2} (MPa) | 0.10132 | 0.10132 | 0.10132 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mores, P.L.; Arias, A.M.; Scenna, N.J.; Caballero, J.A.; Mussati, S.F.; Mussati, M.C. Membrane-Based Processes: Optimization of Hydrogen Separation by Minimization of Power, Membrane Area, and Cost. *Processes* **2018**, *6*, 221.
https://doi.org/10.3390/pr6110221

**AMA Style**

Mores PL, Arias AM, Scenna NJ, Caballero JA, Mussati SF, Mussati MC. Membrane-Based Processes: Optimization of Hydrogen Separation by Minimization of Power, Membrane Area, and Cost. *Processes*. 2018; 6(11):221.
https://doi.org/10.3390/pr6110221

**Chicago/Turabian Style**

Mores, Patricia L., Ana M. Arias, Nicolás J. Scenna, José A. Caballero, Sergio F. Mussati, and Miguel C. Mussati. 2018. "Membrane-Based Processes: Optimization of Hydrogen Separation by Minimization of Power, Membrane Area, and Cost" *Processes* 6, no. 11: 221.
https://doi.org/10.3390/pr6110221