Techno-economic assessment of the one-step CO 2 conversion to dimethyl ether in a membrane-assisted process

This study investigates the impact of the membrane reactor (MR) technology with in-situ removal of water to boost the performance of the one-step DME synthesis via CO 2 hydrogenation at process scale. Given the higher efficiency in converting the feedstock, the membrane reactor allows for a remarkable decrease in the main cost drivers of the process, i.e., the catalyst mass and the H 2 feed flow, by ca. 39% and 64%, respectively. Furthermore, the MR-assisted process requires 46% less utilities than the conventional process, especially in terms of cooling water and refrigerant, with a corresponding decrease in environmental impact (i.e., 25% less CO 2 emissions). Both the conventional and MR-assisted plants were found effective for the mitigation of the CO 2 emissions, avoiding ca. 1.4 – 1.6 ton CO 2 / ton DME . However, given the higher reactor and process efficiency, the membrane technology contributes to a significant reduction (i.e., 25%) in the operating costs, which is a remarkable improvement in this OPEX intensive process. Nevertheless, the calculated minimum DME selling price (i.e., 1739 € /ton and 1960 € /ton for the MR-assisted and the conventional process, respectively) is over 3 times greater than the current DME market price. Yet, with the predicted decrease of renewable H 2 price and a zero-to-negative cost for the CO 2 feedstock, the MR-assisted system could become competitive with the benchmark between 2025 and 2050.


Introduction
The anthropogenic CO 2 emissions must be drastically reduced in order to tackle the urgent issue of global warming, which is the top priority challenge of our times [1,2].In this scenario, the CO 2 capture and storage (CCS) is widely recognized as the most effective way to mitigate the CO 2 concentration in the atmosphere in short term [3].Nevertheless, processing the captured CO 2 to obtain more valuable products, according to a carbon capture and utilization (CCU) approach, is even more attractive as a long term solution.This would allow, at the same time, to synthesize carbon-based products (e.g., methane, methanol, olefins), reducing our dependency on fossil fuels [4][5][6][7].Among the different products that can be produced from CO 2 , dimethyl ether (DME) is very attractive.DME is an alternative clean fuel which can be used in replacement of diesel or LPG with limited changes to the current engines [8,9].We can identify two distinct DME production routes: 1) the indirect route, where methanol is first produced and then dehydrated in a separate step; 2) the direct route, which is more efficient, where the methanol synthesis and dehydration occur simultaneously in a single reactor [10].Currently, the feedstock for the methanol production is syngas, which is in turn a product of either steam reforming of natural gas, or gasification of crude oil, coal, or more rarely biomass and municipal solid waste (MSW) [11,12].Thus, the benchmark DME process is mostly fossil-based and has a CO 2 footprint in the range of 89-98 gCO 2 /MJ DME [13][14][15] .Furthermore, the DME production cost from natural gas was estimated to range between 0.12 and 0.16 USD/kg DME (i.e., a relatively low production cost), as reported by Yoon and Han (2015) [16].
Taking this into account, producing DME from captured CO 2 and renewable H 2 is not only a valid route for CO 2 valorisation and/or H 2 storage [17,18], but also a way to render the process more sustainable [19].
The CO 2 direct (or one-step) hydrogenation to DME can be summarized by the following reaction scheme: CO 2 hydrogenation: CO 2 + 3 H 2 ⇄ CH 3 OH + H 2 O ΔH 0 = − 49⋅5 kJ/mol (1) Reverse water gas shift: CO 2 + H 2 ⇄ CO + H 2 O ΔH 0 = +41⋅2 kJ/mol (2) The overall process is exothermic and is thermodynamically favoured by high pressures and low temperatures.Both the methanol synthesis (1) and the reverse water gas shift (r-WGS) reaction (2) are carried out over a Cu-ZnO-Al 2 O 3 catalyst [20,21] although novel catalyst formulations to improve the CO 2 activity have been proposed in the last few years [22][23][24] On the other hand, the methanol dehydration reaction (3) requires acid catalysis, which is often given by materials such as γ-Al 2 O 3 , silico-aluminates and zeolites (e.g., HZSM-5, FER, MOR.) [25,26] As a result, the one-step DME synthesis requires a bi-functional catalyst, which normally is a physical mixture of the methanol synthesis and dehydration catalyst.All the reactions (1-3) lead to the formation of large volumes of water as a by-product, which contributes to the strong thermodynamic limitations of the system, as well as to catalyst deactivation in long term operation [27][28][29].Thus this process would enormously benefit from the in-situ removal of water from the reaction environment.
The integration of water selective membranes in a so-called membrane reactor (MR) has proved to be an effective strategy to overcome the thermodynamic limitations in the DME synthesis [9,[30][31][32][33].In our recent study, we demonstrated that removal of ca.96% of the water produced leads to an improvement of the CO 2 conversion and DME yield of 36% and 46%, respectively [34].We proposed a fixed bed membrane reactor configuration with a co-current circulation of a sweep gas containing the reactants (i.e., CO 2 and H 2 ), and studied the effect of the reaction conditions based on ideal membrane properties.To the best of our knowledge, only two studies have investigated the integration of the membrane reactor technology for the DME synthesis at flowsheet level.De Falco et al. [35] introduced a specific plant architecture named "Double Recycling Loop DME production" (DRL-DME), which is based on the simultaneous recycle of the CO 2 streams from the permeation zone and the unconverted gas from the reaction zone.In this study, the authors proposed the use of zeolite membranes to promote the water separation, using a CO 2 rich syngas as feedstock.More recently, Hamedi et al. [36] proposed a comparison of the conventional (i.e., with packed beds) direct DME synthesis via CO 2 hydrogenation route with its MR-assisted counterpart, based on an energy assessment of the two technologies.The authors found that the MR technology allows for a reduction of the heating and refrigerant demands of ca.44.5% and 69.4%, respectively.Nevertheless, neither of these studies has investigated the economics of the two process configurations and, especially the impact of the MR technology on both capital investment and operating costs.As a matter of fact, some researchers have already identified the cost of hydrogen as the main bottleneck of any CO 2 hydrogenation process [19,[37][38][39] which is the main factor that currently holds back industries from investing in these technologies.
Therefore, this study proposes a comparison on a techno-economic level of two routes for the one-step DME synthesis via CO 2 hydrogenation: 1) the conventional route, based on a packed bed reactor (PBR) technology; and 2) the MR-assisted route, based on the packed bed membrane reactor technology (PBMR).The two processes are designed at relatively large scale (i.e., 10 kton/y of DME), and optimized with the objective of minimizing the energy requirement and the H 2 consumption; as well as maximizing the efficiency at both reactor and process scale, reducing as much as possible the utilities consumptions.The main goal is to assess whether the membrane reactor technology can significantly improve the performance at process scale, and therefore increase the industrial attractiveness of this CO 2 valorisation route.Furthermore, we propose a detailed analysis of the possible conditions which could render our technology more competitive with the DME market price in the future.We consider different routes for the H 2 production, as well as different scenarios regarding the price of the CO 2 feedstock based on the relationship between the carbon capture cost and the carbon tax.Finally, based on these scenarios and on cost predictions, we aim at identifying the moment in which this technology will be industrially appealing and the factors which could delay/anticipate its applicability at large scale.

Methodology and assumptions
Mass and energy balance calculations were carried out via process flow modeling using Aspen Plus V11 and MATLAB R2019a software.Process intensification strategies (i.e., the use of membrane reactors), and heat integration were proposed as a way to improve the energy efficiency of the process.Afterwards, the impact of the capital investment (CAPEX) and operational cost (OPEX) on the minimum DME selling price (MDSP) necessary to make the system profitable was assessed.

System boundaries
▪ This analysis focuses on the DME production while the CO 2 capture, purification and transport, as well as the H 2 generation and transport are out of the scope of this work.As a base case, we assumed that CO 2 is obtained via sorption enhanced water gas shift (SEWGS) process from iron and steel off-gases [40], while H 2 is assumed to be supplied by an integrated pipeline network and produced via a range of the most cost efficient technologies, as determined by the JRC-EU-TIMES model [39,41].The H 2 production technologies identified by this model are mostly based on steam methane reforming, coal and biomass gasification, coupled with the CCS.Next, we propose a sensitivity analysis on the cost of H 2 and CO 2 to evaluate different alternatives as well as to consider sustainable production methods, in strive for a lower carbon footprint of the entire supply chain.The H 2 and CO 2 streams are assumed to enter the plant at 3.5 MPa and 25 ⁰C, and ambient conditions, respectively.The purity of both streams entering the plant is assumed 100%, since the purification of such streams generally take place at the site of generation.This assumption is stronger for the CO 2 stream, where the purification can significantly affect its cost.However, the effect of the purification is incorporated in the sensitivity analysis on the feedstock price.▪ The DME production process comprises the following sections: 1) two multistage compression sections for the H 2 and CO 2 , respectively, 2) DME synthesis reactor via one-step CO 2 hydrogenation in either PBRs or PBMRs, 3) DME purification via condensation and distillation train, 4) recycle of unconverted gas and recovery of by-product; and 5) the heat exchanger network.All these sections constitute the plant inside battery limits (ISBL).The outside battery limits (OSBL) comprises: 1) the HP-steam generation system, 2) a cooling tower and 3) a refrigeration cycle based on propylene.The electricity is assumed to be derived from the grid.▪ Both plants target a DME productivity of 10 kton/ year (kTA).
Typical methanol production plants have productivity ranging from 0.03 to 800 kTA [42].Being methanol the conventional feedstock for the DME production (2CH 3 OH⇌CH 3 OCH 3 + H 2 O), the proposed plant size falls in the range of typical industrial scale plants.Furthermore, we assume a plant lifetime of 20 years, with a production time of 8000 h per year, which corresponds to a capacity factor of 91.3% [39].▪ Both technologies are designed to obtain DME fuel grade, according to the specification given by the ISO16861 normative developed in 2015 [43].

S. Poto et al.
▪ The plant is considered to be built in The Netherlands, where the average temperature is 11 ⁰C and can go up to 19.5 ⁰C during summer, with an average humidity of 79% [44].The current carbon tax in the Netherlands is above average when compared to the rest of Europe [45], making our study more conservative on this aspect.Thus, we propose a sensitivity analysis also on this parameter to evaluate different scenarios and to reflect various geopolitical situations.

Basis and assumptions for reactor design and sizing
▪ The packed bed reactor (PBR) and packed bed membrane reactor (PBMR) design is based on a 1D pseudo-homogeneous plug flow reactor model, assuming a unitary catalyst effectiveness (i.e., no internal diffusion limitations), no external mass transfer limitation, and no temperature gradients at the particle scale as well as in the reactor radial direction.▪ The reactor model consists of mass and energy balances, coupled with the Ergun equation for the estimation of the pressure drops in the catalytic bed.Details on the model equations are reported in the supplementary information (S.I.).▪ The catalytic bed includes a bifunctional catalyst based on a physical mixture of 90 wt% Cu/ZnO/Al 2 O 3 for the methanol synthesis and 10 wt% of HZSM-5 for the methanol dehydration, which follows the kinetics proposed by Portha et al. [46] and Ortega et al. [47], respectively.The reaction kinetics was considered to be unaffected by the presence of the membranes.Details on the reaction pathway and kinetics are reported in S. I., together with the experimental validation and optimization of the composition of the catalytic bed (i.e., mass ratio of the Cu/ZnO/Al 2 O 3 and HZSM-5).To prevent hot spots, silicon carbide (SiC) is added to the catalyst bed with a volumetric dilution factor of 2/3.An average particle size (d p ) of 3 mm was assumed for both catalyst and diluent.The solid hold-up (ε s ) is set to 0.6 m 3 solid /m 3 reactor .▪ A H 2 :CO 2 stoichiometric ratio of 3, and a total pressure of 40 bar, based on our previous work [34].▪ Circulating boiling water in an external reactor shell was selected as heat management solution to guarantee a nearly isothermal operation.Therefore, the temperature of the boiling water (T w ) was optimized accordingly.The flow rate of the boiling water ( ṁw ) was determined in such a way that the heat removed from the reaction environment could be used for the production of medium pressure (MP) steam (i.e., latent heat exchange).▪ The membrane module of the PBMR consists of tubular ceramic-supported carbon molecular sieve membranes (CMSMs), which show promising performance in terms of vapor/gas separation and stability in hot and humid environment, according to our previous work [48].The properties of the membranes in terms of permeance of H 2 O, H 2 , CO 2 , CO and CH 3 OH as a function of temperature were determined experimentally and fitted with an Arrhenius law [49] (details in S.I.).DME permeance was assumed to be 50 times lower than that of H 2 O [50].A relatively low gradient in total pressure (ΔP = 5 bar) between the reaction and permeation zone was selected to ensure the selective removal of water and, at the same time, to retain the reactants in the reaction zone.To the same scope, the reactants (i.e., CO 2 , H 2 with H 2 :CO 2 of 3) are circulated in the permeation zone as a sweep gas [34].The SW ratio, defined as the ratio between the flow rate of the sweep gas and the feed flow rate, is another parameter regulating the driving force for the water removal.In a previous study, we proposed an optimal value for SW of 20 to remove effectively both the water and the heat from the reaction environment.However, this would require an excessive H 2 make-up for the sweep gas recirculation, which has been identified as the most critical cost driver of the CO 2 hydrogenation processes [19,39].Thus, this works assumes a SW of 1 to reduce H 2 consumption, while the heat management of the PBMR also relies on the circulation of boiling water in an external mantle.▪ The reactor operating conditions (i.e., temperature and GHSV) were first optimized for the PBR.Thereafter, the PBMR was assumed to operate in the same conditions and a sensitivity analysis was carried out to determine the optimal normalized membrane area (NA m ), as defined in Eq. 4, as well as the composition of the sweep gas in terms of methanol molar fraction.
▪ The PBR and PBMR were sized to meet the target plant productivity, accounting for the DME recovery in the separation section.The length and diameter of the reactors were determined assuming an aspect ratio (L/D) of 5.The maximum reactor length was set to keep the average temperature equal to the optimal value without the need to increase the boiling water flow.As a result, the number of parallel reaction units was calculated.The reactor shell (or cooling mantle) diameter for the circulation of boiling water was designed assuming a maximum pressure drops of 0.5 bar [51].

Basis and assumptions for process modelling
▪ The flash drums design was based on sensitivity analyses to determine the temperature and pressure necessary to achieve a 95% recovery of DME in the liquid phase.A 95% approach to the thermodynamic equilibrium was assumed.▪ The distillation columns design and optimization was carried out using the DTSW and RadFrac models in Aspen Plus.The number of stages (N), reflux ratio (R), feed position and the distillate-to-feed ratio (D/F) were first estimated via the DSTW and later optimized by means of a more rigorous model (Rad-Frac), which allows to determine the mass and energy balance of the system.We assumed a pressure drop per-stage of 7 mbar [52], a Murphee efficiency of 85% to account for deviation from the equilibrium.Column internals are trayed and the column diameter, tray spacing and hole area/active area ratio were optimized to avoid drying up and with a 80% approach to flooding.▪ The heat exchanger network (HEN) was designed based on the pinch analysis [53].Counter-current shell and tube heat exchangers were modeled in Aspen Plus, using a shortcut method on design basis.A minimum temperature difference (ΔT min ) of 5 ⁰C was assumed for mild temperature conditions.For temperatures below 0 ⁰C and above 200 ⁰C, the ΔT min was increased to 10 ⁰C.▪ All the turbomachines (compressors, pumps and steam turbines) were modeled in Aspen Plus assuming an isentropic and a mechanical efficiency to determine the thermodynamic conditions of the outlet stream and the energy balance.The isentropic and mechanical efficiency was assumed to be 0.85 and 0.95 for compressors and pumps, respectively.For the MPsteam turbine, an isentropic and mechanical efficiency of 0.8 and 0.99 are assumed, respectively [54].▪ HP steam at 40 bar and 250 ⁰C is produced pressurizing and vaporizing the waste water stream from the separation train.The required heat duty for the boiler is generated by the combustion of natural gas in a furnace.The combustion temperature was set at 1100 ⁰C and the flow of air was determined by assuming a concentration of O 2 in the exhaust of 4 vol%, to ensure complete combustion.The net thermal efficiency of the industrial boiler was set at 90% [55].▪ A cooling tower is used to reduce the costs of the cold utilities via the recirculation of the cooling water in the system.The required air flow as well as the amount of water which evaporates were calculated assuming a relative humidity of the air of 79% and an average air temperature of 20 ⁰C, to design the tower in the worst-case scenario.The cooling water outlet temperature from the tower was set at 25 ⁰C.The make-up of fresh water that needs to be fed to the system corresponds at least to the amount of water that evaporates in the cooling tower.

Basis and assumption for the economic analysis and economic indicators
The CAPEX was estimated via the factorial method based on Lang factors, according to which the CAPEX is a factor of the purchase equipment cost (PEC), as reported in Table 1 [56][57][58].
For the calculation of the PEC, correlations from W. D. Seider [59] and R. Smith [60] were used, based on 2000 and 2002 as reference year, respectively.The PEC is then actualized to the base year of this study (i.e., 2020) using the Chemical Equipment (CE) index, as reported in Eq. 5, where C P is the purchase cost of equipment.
Details on the correlations used for the calculation of the purchase equipment cost of all the equipment are reported in SI.
The OPEX is defined as the sum of the variable and fixed operating costs OPEX variable and OPEX fixed , respectively.The OPEX variable depends on the cost of the feedstock (i.e., CO 2 and H 2 ), utilities (i.e., electricity, cooling water, natural gas), the waste water treatment and the annualized cost for the catalyst and membranes, for which a lifetime of 2 and 5 years was assumed, respectively [19,61].The values used for these costs are reported in Table 2.
The OPEX fixed are calculated on an annual basis and the methodology adopted for their estimation is summarized in Table 3.The labor requirement is calculated based on the number of operators required on site and on the average yearly salary in the Netherlands (i.e., 55,000 € [65]), as reported in SI.
To compare the impact of CAPEX and OPEX and to evaluate the total annual cost (TAC), the CAPEX is calculated on an annual basis (ACA-PEX), according to the methodology reported in SI.The total annual cost (TAC) is determined via Eq.6, as follows: The minimum DME selling price (MDSP) or levelized cost of the DME produced was determined based on the discounted cash flow (DCF) analysis, reported in SI.All the financial parameters and assumptions required for the calculation of the ACAPEX and the MDSP are reported in Table 4.The plant is assumed to be financed in a 50/50 debt/equity split.Considering a 4% interest rate on debt according to the recent interest rate charges [66], and a cost of equity of 12%.The capital investment is assumed to be spent in a three-year construction period as follows: 20%, 50% and 30% for each consecutive year.The price of raw materials, utilities, product and by-products are estimated for the year 2020 and are considered constant for the next 20 years, as a base case.The best method of depreciation was evaluated within the analysis, based on the expected cash flow for the generic year n.The plant is expected to be fully depreciated at the end of its life, so no salvage value is expected.a The price of methanol was used to determine the selling price of the methanol as a by-product

Technical and environmental key performance indicators (KPIs)
The definitions of the CO 2 conversion and DME yield at both reactor (i.e., per-pass) and process scale (i.e., taking into account the recycle streams) are reported in Eqs.7-10.In the performance evaluated at reactor scale, the subscript R and P stand for either reaction and permeation zone, respectively.The loss or cofeeding of CO 2 (i.e., through back-permeation of sweep gas in the reaction zone) was considered in the terms F CO2,tmb and F * CO2,tmb [34].Another important KPI of the membrane reactor is the efficiency of the water removal (WR, Eq. 11), which represents how effectively the membrane removes the water produced by the reaction system.This last indicator can be derived for each species permeating through the membrane.
The plant performance was then evaluated in terms of efficiency indexes, as described below.
The cold gas efficiency (CGE, Eq. 12), defined as the ratio of the energy content of the valuable products (i.e., DME and methanol) and the energy content of the feed (i.e., H 2 ), where the energy content refers to the low heating value (LHV).
A low H 2 consumption reflects a high potential for the commercialization of the process.As a result, we defined (Eq.13) an index representing the H 2 consumption per unit of hydrogenation product (η H2 toDME ).The η H2toDME can assume a minimum value of 0.26 ton/ton, which corresponds to a complete conversion of H 2 to DME.
The chemical energy (W chem ) and the energy of the feed (W feed ) correspond to the energy content of the product and of the H 2 , respectively, defined in terms of LHV, as in Eq. 12.The denominator of η tot represents the energy input to our system, necessary for the production of the chemical energy (W chem ) contained in the products.As a result, besides the energy corresponding to the H 2 (W feed ), we need to account for the energy of the natural gas (W NG ) necessary for the production of the HP-steam and the net electricity consumed/produced (W El,in ↔ out ).Since we did not account for the production of electricity in our process, we assumed that electricity is produced with a natural gas combined cycle, with a net efficiency (η El ) of 58.4% [54].
Next, the level of heat integration of the process is assessed with the efficiency of the utilities (Z utilities ), which represents the amount of cooling (i.e., propylene used as refrigerant and cooling water) and heating (i.e., HP-steam) utilities compared to the amount of DME produced (Eq.15 (12)).(15) where F propyl., F CW and F steam are the molar flow rate of propylene, cooling water and steam and F DME is the molar flow of DME produced by the industrial plant.
The carbon footprint of the produced DME was evaluated in terms of net CO 2 emissions ( ṁCO2,emissions ), and CO 2 avoided or used ( ṁCO 2,avoided ), as in Eqs.16 and 17.The direct CO 2 emissions ( ṁCO2,direct ) include both the unconverted CO 2 which is not recycled (i.e., purge streams), and the CO produced after the combustion of the natural gas for the HP steam generation.The second term of Eq. 16 (W El,in • ṁCO2,CC ) represents the indirect CO 2 emissions related to the production of the electricity, assumed on average as 330 g CO2 /kWh as in a natural gas combined cycle [68].The indirect fraction of ṁCO2,emissions only accounts for the generation of the utilities.The CO 2 emissions related to the feedstock (i.e., H production, CO 2 capture, as well as their storage and transport) are neglected, being a thoroughly life cycle assessment out of the scope of this work.

Packed bed reactor design
Fig. 1 evaluates the effect of the reaction temperature and GHSV under isothermal conditions on the conversions and yields.Given the exothermicity of the desired reactions, temperature has a negative effect on DME yield (Y DME ) and CO 2 conversion (X CO2 ) in favor of the CO yield (Y CO ), as depicted in Fig. 1a.Indeed, being the r-WGS reaction (reaction 2) endothermic, an increase in the reaction temperature favors the production of CO.On the other hand, the catalyst requirements to reach the optimal gas hourly space velocity (GHSV) decrease exponentially with temperature (i.e., the catalyst mass decreases by 82% from 200 to 220 ⁰C), while the change in DME yield is almost linear.As a result, a reaction temperature of 220 ⁰C was selected as a trade-off.The optimal GHSV which maximizes Y DME at these conditions is 64.3 h − 1 (Fig. 1b), which is comparable to the range of space velocities reported in literature for similar systems [19].A boiling water temperature (T w ) of 196 ⁰C and a corresponding pressure of 14.3 bar was found optimal, keeping an average temperature of 220 ⁰C.Based on these results, the reactor was sized to meet the target DME productivity.Size characteristics and operating conditions of the reaction unit of the conventional DME production process are summarized in Table 5. Pressure drops were found negligible (ca.0.025 bar), given the low gas superficial velocity and the large catalyst particle size.

Conventional process description
Fig. 2 depicts the process flow diagram of the one-step CO 2 conversion to DME using conventional packed bed reactors.CO 2 enters the plant at ambient conditions (i.e., 1 bar and 25 ⁰C) as stream 28 and it is compressed to 40 bar (i.e., working pressure of the PBR reactor units) via a multistage compressor unit (MCU) comprised of four compressors (C1 to C4) with intermediate cooling.The outlet temperature of each heat exchanger of the MCU is ca.35 ⁰C.Then, H 2 is fed to the system at 35 bar and 25 ⁰C (stream 36), and it is compressed to 40 bar via a single stage compressor (C6).The pressurized H 2 and CO 2 feed streams (stream 38) mix with the recycle (stream 23), and the resulting stream (stream 25) is first pre-heated to 195 ⁰C in E1 using the heat of the effluent gas S. Poto et al. from the reaction section, and then to 200 ⁰C (i.e., reactor inlet temperature) in E13 using HP steam.Once conditioned, the gas stream (stream 27) is fed to the reaction section, which comprises two parallel PBRs working at average temperature of 220 ⁰C and pressure of 40 bar.The outlet stream from the reaction zone (stream 0) is then recompressed to 40 bar to overcome the pressure drops encountered in the reactors (i.e., 0.025 MPa) prior to the recycle.This also allows a high DME recovery (≥ 95%) in the condensation step, which, given the high volatility of DME, takes place in the flash drum V1 at − 33.4 ⁰C.To minimize the cooling requirements, this is done in five consecutive heat exchangers (i.e., E1-E5) that allow integration of the heat generated in the reaction in other parts of the process, namely the pre-heating of the inlet stream to the reactor (E1) and heating of the liquid produced at the flash drum V1 (E2).The remaining heat is used to heat up cold utilities (i.e., cooling water for E3 and E4 and propylene for E5).The flash drum V1, separates a vapor phase containing CO, H 2 and part of the CO 2 at the top (stream 8), from a liquid phase stream containing DME, methanol, water and a large portion (i.e., CO 2 mass fraction of 44.1%) of CO 2 at the bottom (stream 7).The gaseous stream (stream 8), together with the CO 2 separated within the distillation train (stream 13), is recycled back to the reactor, with a recycle ratio of 99% (i.e., 1% of the stream is purged as gas waste).The liquid stream from V1 (stream 7)., instead, is first heated to 90 ⁰C (E2) and fed to the first distillation tower (T1).The distillation tower T1 operates at 40 bar in a temperature range of 64.7 ⁰C-235.4⁰C to separate DME and CO 2 over the top (stream 10) and methanol and water at the bottom (stream 11).The DME/CO 2 stream is cooled down to 45 ⁰C (E6) and fed to the column T2, operating at 40 bar and 4.8 ⁰C-110.6 ⁰C, to separate CO 2 at the top (stream 13) and to produce a fuel grade DME (i.e., purity of 99.91 wt%) at the bottom (stream 15).The pure DME stream is then depressurized to 10 bar and cooled down to 35 ⁰C (E11), which are the typical DME liquid storage conditions.Finally, stream 11, bottom product of T1, is depressurized to 30 bar and fed to the last distillation tower (T3), which operates in a temperature range of 185-234 ⁰C, to separate 99.92 wt% pure water at the bottom (stream 21) and industrial grade methanol at the top (stream 18), which is then depressurized to 10 bar and cooled down to 35 ⁰C (E10).Details on the mass balance of the plant (i.e., stream tables) are reported in S.I.The generation and usage of the utilities are also reported in the scheme in Fig. 2 with dotted lines.

Packed bed membrane reactor design
The packed bed membrane reactor was designed according to the procedure described in Section 2. The operating pressure and temperature of the reaction zone are the same as those identified for the conventional packed bed reactor, while, the conditions regulating the driving force across the membrane (i.e., ΔP and SW) were selected from our previous study [34].To prevent any loss of reactant (especially the costly H 2 ) across the membrane, a sweep gas with a similar composition and pressure as those in the feed stream is fed to the permeation zone.An extensive discussion on this configuration is given in our previous work [34].Nevertheless, this strategy alone is not effective to prevent methanol removal (MR), which can achieve values above 50% (Fig. 3a, right axes), resulting in an increase in Y MeOH and a decrease in Y DME , lowering the efficiency of the membrane reactor.A sensitivity analysis was carried out to determine the normalized membrane area (NA m ) that maximizes Y DME (Fig. 3a).The Y DME displays an optimum corresponding to NA m of ca.3.65⋅10 − 2 m 2 ⋅h/Nm 3 .Greater membrane areas lead to a decrease in Y DME due to the removal of methanol from the reaction zone.Alternatively, the concentration of methanol in the sweep gas can also be optimized to prevent losses.Therefore, we optimized the methanol concentration in the sweep gas to keep the Y MeOH close to zero, which means that all the methanol produced is effectively converted to DME and does not permeate through the membrane.We found that a molar fraction of methanol of 6.37%, together with a normalized membrane

Table 5
Characteristics of the PBR-based reaction section in terms of size of reactors, number of reactors, catalyst bed properties and operating conditions.The inlet catalyst mass, the inlet volumetric flow and the boiling water mass flow are reported as the sum of the two PBR.area of 4.11⋅10 − 2 m 2 ⋅h/Nm 3 maximizes Y DME .The gas composition in the permeation zone (Fig. 3b) obtained in these conditions shows that only water is effectively removed from the reaction environment.Indeed, the concentration of the component in the sweep gas (i.e., H 2 , CO 2 and methanol) slightly decreases only due to the dilution effect caused by the permeation of water.The optimal temperature of the boiling water (T w ) in this case was 178 ⁰C (i.e., lower than that for the PBR), with a corresponding pressure of 9.6 bar.As a matter of fact, the PBMR achieves higher conversion, leading also to greater heat production.Details on the reaction unit and operating conditions of the MR-assisted DME production process are summarized in Table 6.Pressure drops are negligible (ca.0.025 bar), similarly to the PBR.

MR-assisted process description
Fig. 4 shows the process flow diagram of the one-step CO 2 conversion to DME process via packed bed membrane reactors.CO 2 enters the plant at ambient conditions as stream 77 and it is compressed to 35 bar (i.e.,  pressure of the sweep gas of the PBMR units) via the same MCU previously described (i.e., four compressors with intermediate cooling to 35 ⁰C).H 2 is fed to the system at 35 bar and 25 ⁰C as stream 90 and it is split in two streams: 1) stream 91 for the reaction zone feed (51% of stream 90) and 2) stream 92 for the sweep gas make-up (49% of stream 90).With similar proportion, also the CO 2 stream at 3.5 MPa (stream 85) is split in: 1) stream 86, for the reaction zone and 2) stream 87, for the sweep gas.The H 2 and CO 2 streams directed to the reaction zone are both compressed to 40 bar via C6 and C5, respectively, and then mixed with the recycle (stream 20).The resulting stream 43 is first pre-heated to 180 ⁰C via E1, using the heat of the effluent gas from the reaction section, and then to 200 ⁰C (i.e., reactor inlet temperature) via E7 using HP steam.The H 2 and CO 2 streams directed to the sweep gas mixed with two recycle streams: 99% of stream 27 and the methanol separated at the top of T3 (stream 35).The resulting stream 40 is first pre-heated to 193 ⁰C, via E4, using the heat of the permeated stream from the PBMR, and then to 200 ⁰C via E6 using HP steam.Stream 45 and 42 are respectively fed to the reaction and permeation zone of the PBMR, which works at an average temperature of 220 ⁰C and a pressure of 40 bar and 35 bar, respectively.The outlet stream from the reaction zone (stream 0) is re-compressed to 40 bar and cooled down to − 26 ⁰C to recover DME in the liquid phase.This is done via three heat exchangers: E1, used to pre-heat the inlet stream to the PBMR reaction zone, and E2-E3 using cold utilities (i.e., cooling water and propylene).The flash drum (V1) separation is similar to that in the conventional plant, as well as the recycle of the gaseous stream, combined with the CO 2 recovered from the liquid phase.
The permeate stream from the PBMR (stream 21) is cooled down to 36 ⁰C via three heat exchangers, first pre-heating the sweep gas stream (E4), then for heating the liquid phase produced via the second flash drum V2, prior to the distillation (E9) and finally with cooling water (E5).The resulting stream 24 is fed to the flash drum V2, which separates the permanent gas at the top (stream 25) from a liquid stream containing 55.6 wt% of water and 35.8 wt% of methanol at the bottom (stream 26).About 70% of the gaseous stream (stream 25) is recycled to the permeation zone (stream 27), together with the methanol stream recovered from the distillation section (stream 35), as previously mentioned.The remaining 30% (stream 28) is recycled to the reaction zone, after being compressed to 40 bar (C5).
The liquid stream from V1 (stream 6) is first used as internal utility stream in the CO 2 MCU and then fed at 70 ⁰C to the first distillation tower T1.The distillation tower T1 operates at 40 bar and in a temperature range of 80.1 ⁰C-220.4⁰C to separate DME and CO 2 over the top (stream 12) and methanol and water at the bottom (stream 13).The DME/CO 2 stream is cooled down to 40 ⁰C and fed to the column T2, operating at 40 bat and between 9.4 ⁰C-111 ⁰C, to separate CO 2 at the top (stream 15) and to produce a fuel grade DME (i.e., purity of 99.91 wt %) at the bottom (stream 16).The pure DME stream is then depressurized 10 bat and cooled down to 35 ⁰C (E16), to achieve the DME liquid storage conditions.The liquid stream from V2 (stream 26), is heated up to 200 ⁰C (E9, E26 and E10) and then mixed with the water/methanol stream from T1, previously depressurized to 30 bar (stream 31).The resulting stream 33 is then heated to 220 ⁰C (E11) and fed to the last distillation tower (T3), which operates at 35 bar and in a temperature range of 185-241 ⁰C, to separate 99.9 wt% pure water at the bottom (stream 36) and 99.9 wt% pure methanol at the top (stream 35), which is recycled to the sweep gas stream, as already mentioned.Details on the mass balance of the plant (i.e., stream tables) are reported in S.I.As for the process flow diagram of the conventional process, the generation and usage of the utilities are also reported in the scheme in Fig. 4 with dotted lines.Furthermore, to facilitate their identification, the sweep gas and permeate stream (before the separation) are represented as dashed lines.

Heat integration and generation of the utilities
Fig. 5a and b depict the hot and cold composite curves obtained for the conventional and MR-assisted process, respectively, using the pinch method developed by Linnhoff [53] with a ΔT min of 10 ⁰C.The process minimum energy targets in terms of hot (Q h ) and cold (Q c ) duty were determined for both processes, starting from the stream thermal data (i.e., mass and energy balances).The Q h for the conventional and MR-assisted process was very similar (i.e., 455 kW and 444 kW, respectively), with the latter being ca.2.4% lower.As a matter of fact, the DME synthesis is an exothermic process and with the membrane reactor technology, an extra hot stream is produced (i.e., the permeate), from which it is possible to recover the heat for the cold streams.On the other hand, the Q c of the MR-assisted process is much higher than that of the conventional process (i.e., 421 kW vs 99.3 kW), for the same reason.Indeed, also the permeate stream undergoes some separation (i.e., condensation and distillation of the liquid product), which mainly requires cooling duty.The maximum heat recovery which corresponds to the minimum energy targets is 1588 kW and 1527 kW for the conventional and MR-assisted process, respectively.The heat management of the reaction unit was not included in the construction of the composite curves.However, we should consider that the conventional process has one more reaction unit than the MR-assisted process, requiring ca.10% more cooling duty.
Following this calculation, the heat integration within the two processes was carried out through the maximization of the internal heating and cooling (i.e., using process streams instead of external utilities) and using cooling water, refrigerants and steam when necessary.As a result, the energy saving (i.e., fraction of the maximum heat recovery target)

Table 6
Characteristics of the PBMR-based reaction section in terms of size of reactors, number of reactors, catalyst bed and membrane properties and operating conditions.was 62.1% and 75.7% for the conventional and MR-assisted process, respectively.A general overview of the HEN of the two processes is given in Table 7.The minimum number of heat exchangers (U min ) was determined according to Eq. 18, where N s is the total number of hot and cold streams, L is the number of independent loops and S is the number of independent subsystems.In our case, L = 0 and S = 1, which give the same formula proposed by Linnhoff.The amount of heat exchangers used is higher than U min , due to the internal heat exchange, which allows for a reduction of the utilities and of the OPEX.

Geometrical properties of the PBMR section
The remaining heat exchangers are based on external utilities.As described above, the flash drum V1 operates at − 33.4 ⁰C and − 26 ⁰C in the conventional and MR-assisted process, respectively, while the  condenser of the tower T2 operates at 5 ⁰C in both cases.Thus, propylene is selected as cooling medium.Propylene can cool down streams till − 48 ⁰C with a less energy intensive refrigeration cycle, when compared to ethylene.As a matter of fact, propylene requires a lower pressure to achieve its dew point at 35 ⁰C.An overview of the refrigeration cycle is given in Table 8.
The remaining cooling duty is supplied via cooling water.Instead of using continuously fresh water, a cooling tower is implemented in both systems to further reduce the OPEX.The cooling tower cools down the water by evaporating a small portion of it, mixing warm water with air.Therefore, the outlet temperature of the water is limited by the air temperature, which in the Netherlands is 11.7 ⁰C as yearly average, or 20 ⁰C in the summer.For a conservative design, the air inlet temperature is set at 20 ⁰C, which limits the water outlet temperature to 25 ⁰C.For the heat exchangers that require a slightly lower water temperature (i.e., 15 ⁰C), extra fresh water is fed to the system at 15 ⁰C.This is to avoid the use of more refrigerant, which would otherwise result in a higher OPEX and CO 2 footprint.Instead, the use of more fresh water than the required make-up to the cooling tower results in some purge of warm water before being recycled to the tower.A schematic representation of the cooling water (CW) usage and recycle is given qualitatively in Fig. 6.Fresh CW enters the system at 15 ⁰C with a flow of 9.91 ton/h and 5.40 ton/h for the conventional and MR-assisted process, respectively, to be then mixed with the corresponding 157 ton/h (43.6 ⁰C) and 87.6 ton/h (52 ⁰C) warm water stream from the heat exchangers network (HEN).
In both process configurations, a small portion of the warm water which is not recycled to the cooling tower is fed to a pump and a furnace, which burns natural gas and produces HP steam (i.e., steam at 40 bar and 250 ⁰C).The HP steam production and usage is represented in detail in S.I.As the HP steam is used in the HEN, its quality decreases down to high temperature boiling water, which is used in the reaction unit for the heat management.The medium pressure (MP) steam obtained in this way is fed to a steam turbine to produce electricity.The exhaust gases produced at the furnace are used for the condenser of the tower T2 (E8) and for the pre-heating of the sweep gas (E6) in the conventional and MR-assisted process configurations, respectively.Further details on the natural gas input and electricity produced from the steam turbine are reported in Table 9.

Technical analysis
The two technologies proposed in this study are first compared at the reactor scale (Table 10).The membrane reactor, removing ca.72% of the water produced in the reaction zone, allows for an increase of 41% and 63% in the X CO2 per pass and Y DMEper pass , respectively.Most importantly, the PBR and PBMR work at the same GHSV, which means that the PBMR requires ca.40% lower mass of catalyst and flow of reactants to achieve the same DME productivity, given the higher performance of the PBMR.As a result, the membrane reactor technology allows for a reduction in the number of reaction units required to achieve a specific productivity (i.e., with the PBMR we can remove one parallel reactor).Another important aspect is that the PBMR requires 64% less H 2 per unit mass of DME produced, η H2to DME , (i.e., 0.47 and 0.78 for the PBMR and PBR, respectively).This means that the PBMR converts H 2 more efficiently, reducing the impact of one of the main cost driver, as well as bottleneck, of the hydrogenation processes.The PBMR is not only more efficient in terms of conversion/yield, but also in terms of energy efficiency and CO 2 footprint.The amount of boiling water required for the heat management is 17.3% lower than that for the PBR, which means that less energy and natural gas are required for the production of the reactor utility.Finally, the PBMR shows a CGE of 88% versus the 76% of the PBR, which confirms that also the energy conversion of the PBMR is more efficient.

Table 7
Heat exchangers network specifications of the conventional and MR-assisted processes.

Table 9
Input and output of the HP steam generation and cycle for the conventional (a) and MR-assisted (b) one-step DME production process.Table 11 compares the two process configurations (i.e., considering reactor as well as feeding and product separation section) based on their technical performance indicators evaluated from the mass and energy balances.The MR-assisted process allows for a reduction in the H 2 requirement by 15.2%, which is significantly lower that the savings anticipated based on reactor performance alone.This is due to the H 2 make-up required for the sweep gas stream.In terms of product, the two plants were designed to achieve the same productivity (i.e., 10 kton/y of fuel grade DME).However, the conventional process also produces 2.6 kton/y of industrial grade methanol as sellable product.On the contrary, the methanol produced in the PBMR is 100% recycled as sweep gas after its purification, to improve the DME selectivity per pass, as reported in Section 3.2.1.Thus, the resulting CGE of the two plants remains very similar, with only ca.1.77% improvement of the MR-assisted over the conventional process (i.e., 89.8% vs 91.3%).Nevertheless, the energy consumption of the MR-assisted process is strikingly (i.e., 49%) lower than the conventional counterpart, mostly due to a 52% reduction of the energy requirements in the compression of the refrigeration cycle.Similarly, given the difference in size of the recycle streams (Table 10), the compression of the reactor unit effluents requires only 2.06 kW for the MR-assisted process versus the 5.01 kW of the conventional process.The pump (P1) required for the HP steam production shows a similar consumption for the two processes, while the electricity produced via the steam turbine (TURB) is ca.24.3% lower for the MR-assisted technology, given the lower boiling water requirement for the reaction unit.The MR-assisted plant has also a lower requirement of HP steam, which corresponds to a natural gas usage ca.11.3% lower than in the conventional plant.Overall, the MR-assisted process achieves a total energy efficiency of 72.9% versus the 69.9% of the conventional process.
When comparing the two plants in terms of the usage of the utilities per unit of DME produced (Table 12), the MR-assisted process always require a lower amount of any utility (i.e., propylene, cooling water and steam), with an overall Z utilities of 45.9% lower, which is mostly attributed to the lower requirement of cold utilities.
The analysis of the carbon footprint is also relevant to underline the advantage of using membrane reactor technologies.Fig. 7a shows that the direct CO 2 emissions of the two plants is very similar (i.e., 0.04 ton CO2 /ton DME ), in both cases attributed to the residual (ca.1%) of the unconverted reactant streams which is not recycled.However, the direct emissions only contribute ca.5-7% to the total CO 2 emissions.The main contributors are the electricity and steam generation (i.e., indirect emissions), which for the MR-assisted plant are 48.1% and 25.3% lower than for the conventional plant, respectively.The lower carbon footprint of the MR-assisted plant is in line with the energy balance and with the utilities requirement (Table 11).
Overall, the conventional and the MR-assisted processes emit 0.71 and 0.53 ton CO2 /ton DME respectively.However, when the CO 2 emissions are compared to the CO 2 fed to the plant, these numbers becomes negligible, being our technologies based on CO 2 utilization.As a result, since the conventional plant converts the feedstock with a lower efficiency at the reactor scale, thus requiring more CO 2 per unit of DME produced, the CO 2 avoided is slightly higher for the conventional plant than for the MR-assisted one (1.56 vs 1.39 ton CO2 /ton DME ).Therefore, considering the size of the plants, the conventional and MR-assisted process avoid ca.170 kton/y and 152 kton/y of CO 2 , respectively.
Furthermore, when the one-step DME production via CO 2 hydrogenation is compared to the benchmark process (Fig. 7b), where DME synthesis is based on fossil fuels (i.e., syngas produced via steam reforming of natural gas), the CO 2 footprint of our technologies is between 73% and 80% lower.This means that the DME production technology proposed in this study is much more sustainable.Indeed, the CO emissions for the industrial DME production range between 89 and gCO 2 /MJ DME [13][14][15].This number accounts for the NG-to-DME production pathway, independently on the direct or indirect route.When translated in terms of ton CO2 /ton DME , it results in an average value of 2.63.Thus, the technology we propose here is, from one hand, a valuable CO 2 utilization route and, from the other hand, a more eco-friendly pathway for the production of DME.

Economic analysis
The results of the economic analysis are summarised in Table 13.The purchase equipment cost (PEC) is the same for both process configurations (i.e., 1.809 M€ vs 1.802 M€).As a matter of fact, the MR-assisted process has an extra flash drum (V2) for the permeate stream and a larger number of heat exchangers of the HEN, which result in a PEC contribution increase from 3.82% to 6.53% and from 20.57% to 26.53% for the flash columns and heat exchangers, respectively.On the other hand, the MR-assisted process displays a 45.9% lower cost for the reactor section with respect to the conventional process, due to the removal of one reaction unit.The distributed PEC is graphically represented in Fig. 8a, where we can observe that the main contribution to the PEC is given by the compressors (i.e., 36.8% and 32.1%), followed by the heat exchangers (i.e., 20.6% and 26.5%), distillation towers (i.e., 15.1% and 15.4%) and finally the turbine (18% and 14.7%).
Considering the operating costs, the MR-assisted process has a total variable cost of 15.15 M€/y versus the 19.59 M€/y of the conventional plant, in line with the higher efficiency in converting the feedstock and   the lesser utility requirement of the MR-assisted process.As shown in Fig. 8b, the largest contribution to the OPEX is given by the H 2 make-up, which amounts to 57.8% and 62.91% for the conventional and MRassisted process, respectively.The second contributor to the OPEX is the catalyst cost, with a 29.2% and 22.8% of the total variable cost for the conventional and MR-assisted process.On the other hand, the cost of the utilities (mostly determined by the cost of natural gas and electricity) has a lower impact.Nevertheless, this cost is strongly affected by the geopolitical situation, which introduces some uncertainties on this number (see Section 6.6).In the base case, no carbon tax is considered, while a dedicated analysis on this subject is reported in Section 6.Therefore, the only cost related to the waste material (i.e., water in our case) is included in the utilities and consists of ca.4% of the total utilities cost.
When comparing the OPEX with the annualized CAPEX (ACAPEX), it is clear that the impact of the capital investment on the annual costs is negligible.As a result, the TAC follows the same trend as the OPEX, with a value of 24.32 and 20.08 M€/y for the conventional and MR-assisted process, respectively.As a consequence, the minimum DME selling price (MDSP) amounts to 1960 and 1739 €/ton, respectively (i.e., ca. 11.2% reduction in MDSP in the case of the MR-assisted process).These MDSP values align with the range identified by Michailos et al. [19] (i.e., 1828-2322 €/ton).The average MDSP they found is 2193 €/ton for a two-steps DME synthesis process using conventional packed bed reactors and, likewise in this study, using captured CO 2 and H 2 from PEM as feed.By combining the two steps in a single reaction unit and with the use of the membrane reactor technology, we were able to decrease the Fig. 7. CO 2 emissions and usage of the conventional and MR-assisted one-step DME production process (b) CO 2 emissions of the conventional and MR-assisted process compared to the emissions of the benchmark DME production from natural gas.

Table 13
Overview of the economic analysis for the for the conventional and MR-assisted and one-step DME production process.MDSP by 1.26 times, which is a great achievement.
Nevertheless, DME is currently sold for a price of 520 €/ton, which is more than 3 times lower than our MDSP.However, the market price refers to a chemical grade DME, commonly sold as aerosol propellant or as a solvent, thus with a different market value than the fuel grade DME, despites its similar purity specification.The fuel grade DME is not on the market yet, but it is expected to be soon [69].Thus, it is difficult to predict its value, although it would be reasonably higher than the current DME market price, to be in line with the price of diesel/LPG.Another important aspect to consider is that the DME produced via CO 2 hydrogenation would have a higher value in the perspective of a decarbonization of the fuel and chemical industry, since it derives from an alternative feedstock/waste (i.e., the captured CO 2 ), rather than from fossil fuels.Despites this, in the current market conditions, the production of DME from CO 2 and renewable H 2 with our technology would not be profitable.Thus, it is crucial to analyze the system in more depth, to understand the bottlenecks and to identify the conditions in which this process would become an attractive solution at industrial level.

Forecasting and sensitivity analysis
The economic analysis (Section 5) showed that the one-step DME production via CO 2 hydrogenation route is not yet competitive with the benchmark route (i.e., DME from steam methane reforming or SMR), given the current market conditions.However, the market conditions are expected to change due to the environmental concerns and the needs of decarbonizing the chemical industry.Therefore, in this section, we provide a detailed analysis of the possible conditions which could render our technology industrially appealing in the future.
As we learned already in Section 5, the one-step DME production via CO 2 hydrogenation is an OPEX intensive process.As a matter of fact, the ACAPEX is ca. the 5.67% and 6.66% of the TAC for the conventional and MR-assisted process, respectively.This means that the MDSP is mainly affected by the OPEX.Fig. 9 shows that the H 2 feedstock price is largest contributor to the MDSP, followed by the cost of the catalyst, which strongly depends on its lifetime.Furthermore, the cost of the natural gas as well as of the CO 2 feedstock, both show a minor and similar impact.Finally, both the membrane lifetime and the cost of the electricity do not affect the MDSP significantly.Based on this preliminary analysis, in this section we propose some sensitivity analyses on the main cost drivers, as well as further process optimization strategies to reduce the operating costs.
Finally, we suggest different realistic scenarios which could decrease the MDSP in the next few years at the point in which the DME production cost via CO 2 hydrogenation in membrane reactors balances with the forecasted DME market value.

Forecasting of H 2 price according to different production methods
The H 2 price is extremely influenced by the production method.An overview of the available technologies, together with their current cost and its prediction in 2050 is given in Table 14.The H 2 production methods can be summarized as follows: 1) H 2 from fossil fuels, which include the widely used steam methane reforming (SMR), but also higher hydrocarbon cracking, reforming and gasification; 2) H 2 from electrolysis of water, either from renewable energy and using electricity from the grid (i.e., mostly fossil fuel based).In 2010, about 96% of the H 2 used in industry was produced from fossil fuels (i.e., natural gas, coal and oil) [70].Currently, this value is still close to 90%, being the SMR technology the cheapest on the market.The remaining 10% is mostly produced via water electrolysis, which still leads to considerable indirect CO 2 emissions, given the electricity requirement.Furthermore, these technologies are 3-10 times more expensive than the SMR, especially because these methods are still under development/optimization and they are mainly affected by the price and source of the electricity.
In our base case scenario, we assumed that H 2 is supplied by an integrated pipeline network (i.e., H 2 price of 2.95 €/kg, as reported by Fortes et al. [39]), with H 2 being mostly produced via steam methane reforming and coal and biomass gasification coupled with CCS.Despites the CCS technology, these production routes are energy intensive, thus, not environment-friendly.The goal of this research is to promote a sustainable production method of DME, as well as a route for the CO 2 utilization.As a result, we should also consider the impact of any indirect CO 2 emission source, such as the emission related to the H 2 production.The only production method which can potentially be 100% renewable is the electrolysis.However, when the electricity from the grid is used, H 2 cannot be considered as renewable.As a matter of fact, nowadays, still 80% of the electricity in the Netherlands is produced using fossil fuels with a CO 2 footprint of 330 gCO 2 /kWh [71].a H 2 from 100% renewable resources is classified as REN-H 2 [72].
b In some studies grid-electricity is used, sometimes in combination with renewable energy, so the H 2 production is not 100% renewable.

S. Poto et al.
To remove any source of CO 2 emission, H 2 must be produced via electrolysis based on 100% renewable resources, which makes the H 2 production much more expensive (Table 14).At the moment, the alkaline electrolysis (AE) is the most mature technology and, as a consequence, the cheapest sustainable route.Polymer electrolyte membrane (PEM) electrolysis is approaching the cost of the AE and even the MWscale systems are currently market ready [72].On the other hand, the solid oxide electrolyser (SOE) technology is not yet ready for the industrial scales.Detz et al. [72] predicted the H 2 price from different sustainable technologies in the time span from 2015 to 2050, considering that phenomena such as learning-by-doing, learning-by-searching, economies-of-scale, and automation can reduce the renewable H 2 manufacturing costs.According to their prediction, both PEM and SOE are the techniques that in the future (i.e., by 2050) will be able to produce H 2 at comparable prices (i.e., 1.3 €/kg) to the fossil fuel based technologies.
Therefore, we implemented in our economic analysis the function derived by Detz et al. describing the decrease in the H 2 price within the years for both the PEM and SOE technologies.The effect of changing the H 2 price on the MDSP for both the conventional and MR-assisted process is depicted in Fig. 10, where it is clear that the choice of the electrolysis method between PEM and SOE has a large impact on the MDSP and that, despites the readiness of the technology, the SOE is much more promising in terms of economics.Furthermore, we observe that the MDSP of the MR-assisted technology is always much lower than the one related to the conventional process.As a result, in the next analyses, we will consider only the MR-assisted technology with the H 2 obtained via SOE as a new base case scenario.

Effect of the carbon tax
As learned in Section 6.1, with the prediction of the H 2 price by SOE, the MDSP of the MR-assisted technology can be reduced to 1376 €/ton in 2050.This price cannot be directly compared to the DME market price, which corresponds to the benchmark technology.As a matter of fact, the DME production cost from SMR is expected to increase in the next years, due to the extra costs related to the emissions and the corresponding carbon tax.Indeed.the carbon tax in the Netherlands and in Europe (on average) is expected to increase linearly over the years (Fig. 11a) [45].With this data, the DME market price can be estimated over the years, considering an average emission of 93 gCO 2 /MJ DME [13][14][15] and assuming that after 2030, the carbon tax will continue to increase linearly (i.e., linear extrapolation).However, in this analysis we assume that no carbon tax is included in the current DME market price (year 2020) and that the price of other feedstock, like natural gas, are not influenced by the carbon tax significantly.On the other hand, the effect of the carbon tax on the MDSP related to the one-step DME production via CO 2 hydrogenation is more complex to analyse.We should consider that our system uses CO 2 as a feedstock.This implies that the carbon tax can have: 1) a negative effect, due to the CO 2 total emissions and 2) a positive effect on the reduction of the CO 2 feedstock price.The latter effect is described in Section 6.5.When considering, at the same time, the reduction in the H 2 price from SOE and the negative effect of the carbon tax on the MDSP of the MR-assisted technology, as well as the effect of the carbon tax on the DME market price, a competitiveness curve can be obtained (Fig. 11b) showing that the novel technology based on CO 2 utilization will be competitive with the benchmark method in 2050.

Effect of the catalyst lifetime (scenario 1)
The Cu/ZnO/Al 2 O 3 -HZSM-5 catalyst we selected in this study has a lifetime of ca. 2 years, as reported in literature [19,75].Its deactivation phenomena usually arise from copper crystallization and aluminum leaching with hot water, possible poisoning from sulfur based compound (i.e., impurities in the feedstock) and coke formation, which is faster and enhanced at higher temperatures (i.e., above 300 ⁰C [76]).However, the catalytic bed of the membrane reactor operates in an almost dry environment, given the removal of water by means of the membrane module.Furthermore, we promote a low temperature operation process (i.e., an average reactor temperature of 220 ⁰C, with a peak at 260 ⁰C), given the more severe thermodynamic limitations when using pure CO 2 as the sole carbon source and the higher efficiency of the PBMR.As a result, the catalyst deactivation could be reasonably delayed and its lifetime can be extended from 2 to 5 years, to be compatible with the lifetime of the membranes.Considering a catalyst lifetime of 5 years, the MDSP curve referred to the MR-assisted technology of Fig. 11b will shift downwards of ca.192 €/ton (scenario 1), becoming even more attractive than the conventional technology and crossing the DME market price already in 2043 (i.e., 7 years earlier).

Optimization of the HP steam cycle and natural gas usage (scenario 2-4)
The third important cost contributor to the MDSP is the cost of natural gas (NG), which also directly influences the CO 2 emissions related to the combustion.The natural gas requirements can be reduced by optimizing the use of the HP steam, which is mainly required at the reboiler of columns T1 and T3.As seen also in Table 13, the CAPEX has a small impact on the TAC and on the MDSP.Therefore, we could increase the number of stages of the distillation tower T1 to reduce the reflux ratio and, as a result, the reboiler duty.An increase in the number of stages from 18 to 22 corresponds to a decrease in the reflux ratio from to 4 (beyond 22 stages, the reflux ratio changes are not significant).This condition corresponds to a reduction of 15.5% and 12% in the HP steam flow and natural gas requirement, respectively, as well as to a CAPEX increase of 0.06%, which has a negligible effect on the MDSP.On the other hand, we did not find any beneficial effect in increasing the height of the column T3.
Based on the optimized usage of the HP steam, multiple scenarios can be built, on top of scenario 1 (i.e., considering a catalyst lifetime of years): • Scenario 2: Natural gas is used for the production of the HP steam in the optimized conditions (i.e., 12% NG usage less than the base case); • Scenario 3: The purge stream of the unconverted gases, which still contains a heating value of ca.1175 MJ/h due to the presence of H (70 mol.%) and traces of CO, methanol and DME, can be fed to the burner, in combination with a reduced flow of natural gas.This solution further reduces the NG usage of 20%; • Scenario 4: The natural gas required in scenario 3 is completely replaced with green H 2 .As a result, the purge stream is fed to the burner together with H 2 .This solution also minimizes the CO 2 emissions.
An overview of the NG requirement and the alternative fuels used for the production of the HP steam in the base case and three scenarios is given in Table 15, together with the impact on the direct CO 2 emissions.The impact of the three scenario on the competitiveness curve is depicted in Fig. 12.The MDSP curve related to scenario 2 and 3 decrease over the years with the same trend of the base case (i.e., curve of Fig. 11b).However, these curves are only slightly shifted downwards due to the lower NG consumption, since in general we saw that the impact of the NG cost on the total OPEX is not that significant.On the other hand, the curve representing scenario 4 decreases with a quite different slope, due to the implementation of the H 2 decreasing function, together with the reduction of the NG usage and the CO 2 emissions.For the same reason, scenario 4 has initially a higher MDSP than the other scenario, because of the higher cost of H 2 used for the combustion.Nevertheless, with the decrease in the H 2 price over the years and with the increase in the carbon tax, the MDSP decreases faster than the other cases from the year 2025, anticipating the moment from which our technology will be competitive with the benchmark of ca. 3 years (i.e., 2040 instead of 2043).

Effect of the CO 2 feedstock price: carbon capture vs carbon tax (scenario 5-7)
Although the CO 2 feedstock price does not play a significant role on the MDSP, similarly to the natural gas, we believe that this variable needs a dedicated section.As a matter of fact, the technology we propose here uses CO 2 as the sole carbon source for the synthesis of DME.Therefore, we could easily imagine a future scenario in which, heavy CO 2 emitting companies would be keen to buy our CO 2 utilization technology to make profit from a waste rather than paying a tax.In our base case, we assumed a CO 2 feedstock price of 33 €/ton (i.e., CO 2 from SEWGS).Nevertheless, the CO 2 price is expected to change over the years due to the development of the CO 2 capture technologies and to the environmental concerns and the corresponding carbon tax policy.From the moment in which the carbon tax will be higher than the carbon capture price (CCP), companies will start to capture their CO 2 and either sell it or use it directly.We define this moment as t 1 , which allows us to identify two different time regions: 1) Before t 1 , the price of the CO feedstock for our technology corresponds ca. to the CCP, since we have to buy it from industries/companies which decide to capture CO 2 and sell it with a certain profit.Indeed, industries will not capture their CO for "free", since paying a carbon tax would be cheaper; 2) After t 1 , the situation is more complex and we can identify three scenario: • Scenario 5: after t 1 the CO 2 feedstock price will be zero; • Scenario 6: after t 1 the CO 2 feedstock price will correspond to the difference between the carbon tax and the CCP.As a result, the CO feedstock will be seen as a revenue instead of a cost.Indeed, companies would prefer to capture the CO 2 , rather than paying a tax, and

Table 15
Overview of NG requirement and the alternative fuels used for the production of the HP steam in the base case and the three scenarios, together with the corresponding direct CO 2 emissions.would pay the difference for the CO 2 utilization process, which could be seen as a waste treatment technology.• Scenario 7: it is similar to scenario 6, but with a slightly different revenue.The company which decides to capture the CO 2 instead of paying the carbon tax, would prefer to pay for the CO 2 utilization technology less than the difference between the carbon tax and the CCP.This scenario is much more realistic, since it is easy to imagine that if the CO 2 waste treatment and the carbon tax come with the same price, one would still prefer to pay a tax and avoid further capital investments in CO 2 capture technologies.In this scenario we assume that the CO 2 emitting companies would pay 14.1% less than the difference between carbon tax and CCP.This % corresponds to the average gross profit margin of primary metal industry [77].
These scenario can be built on top of scenario 4, described in the previous section, where the usage of the HP steam and of the fuels to produce it are optimized.
Within these scenario, we do not consider the case in which, after t 1 , the CO 2 emitting companies would decide only to sell it with a profit margin, since this will correspond exactly to our scenario 4, with the CO 2 feedstock price of the base case.Nevertheless, it is easy for us to see the CO 2 feedstock as a revenue, since when the CCP is lower than the carbon tax, it is worth for the companies to capture the CO 2 .When more and more companies will capture their CO 2 , the market will be saturated and if they cannot sell it, they would still need to emit it and pay the carbon tax on top of the CCP.As a result, these companies would be willing to pay a difference between carbon tax and CCP to the CO 2 consumers.
The competitiveness curve related to the new scenario (5, 6 and 7), together with the one of scenario 4 (see Section 6.5), are depicted in Fig. 13.Scenario 5, 6 and 7 were all built on top of scenario 4, which was the best scenario found in view of the optimization of the HP steam generation and usage.Starting from 2022 the curves related to the new scenario show a discontinuity, due to a drop in the price of the of CO 2 feedstock.As a result, the year 2022 corresponds to t 1 , where the carbon tax has achieved the CCP (i.e., 33 €/ton for the SEWGS).From this point on, it is clear that scenario 6 is more convenient, followed by scenario 7 and scenario 5.In case of scenario 6 and of the more realistic scenario 7, our MR-assisted process could become competitive with the benchmark already in 2032 and 2033, respectively.In case of scenario 5, instead, our process would be competitive in 2038.

Overview and uncertainty analysis
Table 16 gives an overview of the scenario built in Sections 6.4 and 6.5, in terms of the MDSP, year and carbon tax corresponding to the intersection point between the MDSP curve and the DME benchmark market price (i.e., moment in which the one-step DME synthesis via CO 2 hydrogenation using membrane reactors will become competitive with the benchmark DME synthesis).According to this analysis, our technology could become profitable, and thus industrially applicable, between 2040 and 2032.As a matter of fact, scenario 1 considers a longer catalyst lifetime, which is realistic thanks to the advantages of the membrane reactor technology, as discussed in Section 6.3.Furthermore, scenario 2-4 depends on an optimization of the fuel used for producing HP steam.Therefore, it is reasonable to consider scenarios on top of scenario 4. Nevertheless, the results reported in Table 16 also show that the moment in which our technology will become competitive with the benchmark not only depends on the different scenarios, but also on the value of the carbon tax.Currently, the carbon tax policy has not been accepted all over the world and its value depends on national regulations.As an example, if we focus on the European countries who have already imposed a carbon tax, we can have a value ranging from 116.33 €/ton CO2 for Sweden, to a value of 0.07 €/ton CO2 for Poland [78].If we consider the carbon tax corresponding at year 2020 as a variable and consider a linear increase with time as in Fig. 11a, the point of intersection of the MDSP of scenario 6 (i.e., the more realistic) shifts.As a result, the year of competitiveness and the corresponding carbon tax value correlates as depicted in Fig. 14, from which we can observe that the carbon tax has to be at least 118 €/ton CO2 to have a MDSP equal to the DME market price by 2050.
The results that we show in this section are based on several hypotheses.Although all the variables are based on previous studies and information retrieved from literature, there are some uncertainties which will surely affect the moment in which the technology would become competitive with the DME market value.A list of some of the unknown variables or data which have not been included or have been assumed in this research and that we believe could reduce the accuracy of our prediction is given here: • The salary change over the years was not taken into account.The salary could increase due to the inflation and increase in the welfare, as example.As a result, it is very difficult to predict its future trend.• Currently, only the price of the DME chemical grade is known.
However, our technology produces a fuel grade DME, which is expected to have a higher market value.• In case the H 2 production would be integrated in the DME synthesis, the heat generated in the hydrogen production step could be used to replace HP steam completely.As a matter of fact, the SOE process operates at temperature of 500-850 ⁰C and the heat corresponding to the H2 stream could be used for the reboilers in the distillation towers.Furthermore, the maximum working pressure of the SOE and PEM can vary in a wide range (35-200 bar) [79,80].This indicates that the cost of compression could be further reduced.However, the electricity cost, as well as the CAPEX, did not show a large impact on the MDSP.• Our analysis does not take into account the possible subsidies related to the use of renewable feedstock/energy.This could reduce our cost significantly and make our system more competitive with the benchmark.
• The carbon tax in the Netherlands (30 €/ton CO2 ) is above the European average (24 €/ton CO2 ), which makes it harder for our technology to be competitive.• The carbon capture price is also expected to be dependent on the technology adopted and on the composition of the waste stream from which the CO 2 needs to be purified.A more expensive technology would delay the moment from which CO 2 could become a cost zero feedstock or even a revenue (t 1 ).However, as for the H 2 , also the CCP is expected to decrease with time, due to the development of the existing or even more efficient technologies.As an example, the use of membrane separation technologies can reduce the cost of solvent based technologies of ca.28% [81].• Changes in the price of natural gas over the years have not been considered in this study.However, the scenarios 4-7 are not affected by this cost, given that the natural gas has been completely replaced with renewable H 2 .

Conclusions
This work demonstrates that CO 2 can be upgraded from a polluting agent into a valuable feedstock at industrial scale.The use of a membrane reactors (MR) in the direct CO 2 hydrogenation to dimethyl ether (DME) shifts the single pass conversion from 39% to 55%, together with a shift in the DME yield from 32% to 53%.The higher efficiency in the conversion of the packed bed membrane reactor (PBMR) allows for a remarkable decrease in both the catalyst mass and in the H 2 feedstock flow to produce 1 ton of DME of ca.39% and 64%, respectively.Overall, the PBMR displays a cold gas efficiency (CGE) of 88% with respect to the 76% of the packed bed reactor (PBR).On a process perspective, the MRassisted plant requires less energy input to produce the same amount of DME.
On the economic aspect, both processes revealed to be OPEX intensive, with the operating costs of the MR-assisted process significantly lower (ca.23%), due to the lower requirement of H 2 , which covers more than 60% of the OPEX.
The minimum DME selling price (MDSP) was found to be 1739 €/ton and 1960 €/ton for the MR-assisted and the conventional process, respectively, in the base case scenario, where no carbon tax is taken into account and the CO 2 feedstock is considered as a cost.This result proves that the combination of the two steps in a single reactor, together with the use of the membrane reactor technology, allows for a reduction in the MDSP of 1.26 times with respect to what reported in literature.
Nevertheless, the MDSP of the MR-assisted technology is still 3.3 times higher than the current DME market value.As a result, we carried out a feasibility study to predict the moment in which this technology would become competitive with the benchmark.Our analysis showed that if we consider the reduction in the H 2 price produced using the solid oxide electrolysis (SOE) technology, together with an increase in the catalyst lifetime from 2 to 5 years and an optimization of the high pressure steam and natural gas usage, our system can be competitive with the benchmark in 2040, if the carbon tax would increase linearly.In addition, if the CO 2 feedstock is considered as a revenue rather than a cost, our process could be profitable ca.7 years earlier.The result of the competitiveness analysis strongly depends on the carbon tax policy, which varies from country to country.Overall, we conclude that, given the uncertainties related to this prediction, we can identify a region, more than an exact moment, which goes from 2025 to 2050 where the CO 2 direct hydrogenation to DME in membrane reactors will be economically competitive with the benchmark process.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Table 16
Overview of the different scenario in terms of MDSP, year and carbon tax corresponding to the intersection point between the MDSP curve and the DME benchmark market price.Fig. 14.Carbon tax corresponding at the year in which our technology will be competitive with the benchmark according to scenario 6, depending on the initial policy on the carbon tax (i.e., at 2020).

Fig. 1 .
Fig. 1.CO 2 conversion, DME yield and CO yield (left side bars) and on the catalyst mass (right side line) as a function of temperature (a) and DME yield as a function of the GHSV at 220 ⁰C (b).

Fig. 2 .
Fig. 2. Process flow diagram of the one-step CO 2 conversion to DME process via packed bed reactors.

Fig. 3 .
Fig. 3. PBMR performance in terms of Y DME and Y MeOH (on the left) and water removal (WR) and methanol removal (MR) (on the right) as a function of the normalized membrane area (a); composition of the sweep gas/permeate stream as a function of the normalized reactor length (z/L) when 6.37 mol% of methanol is incorporated in the sweep gas (b).

Fig. 4 .
Fig. 4. Process flow diagram of the one-step CO 2 conversion to DME process via packed bed membrane reactors.

Fig. 5 .
Fig. 5. Hot (red) and Cold (blue) composite curves obtained for the conventional (a) and for the membrane reactor (MR) assisted (b) one-step DME production process, obtained applying the graphical approach of the Linnhoff method [59] with a ΔT min of 10 ⁰C.

Fig. 6 .
Fig. 6.Schematic representation of the cooling water usage and recycle via the cooling tower for both processes.

Fig. 8 .
Fig. 8. Distributed PEC (a) and distributed OPEX (b) for the MR-assisted and conventional one-step DME production process.

Fig. 9 .
Fig. 9. Effect of the higher impact cost drivers of the OPEX on the MDSP of the MR-assisted one-step DME production process.

Fig. 10 .
Fig. 10.MDSP for the conventional (dashed lines) and MR-assisted plant (solid lines) as a function of time (years) considering different H 2 production technologies: PEM (black lines) and SOE (red lines), implementing the H 2 price predicted by Detz et al. [72].

Fig. 11 .
Fig. 11.The expected carbon tax for the coming years on average in Europe (grey bars) and in the Netherlands (orange bars) (a); MDSP of the MR-assisted plant (solid lines) as a function of time (years) when compared with the DME market price prediction (red line).

Fig. 12 .
Fig. 12. MDSP of the MR-assisted plant (black lines) as a function of time (years) when compared with the DME market price prediction (red line), using REN-H 2 from SOE, a catalyst life time of 5 years in the three scenario for the HP steam production.

Fig. 13 .
Fig. 13.MDSP of the MR-assisted plant (black lines) as a function of time (years) when compared with the DME market price prediction (red line), using REN-H 2 from SOE, a catalyst life time of 5 years, H 2 and purge streams for the HP steam production in the three scenario identified for the CO 2 feedstock price.The blue dashed vertical line represents the time t 1 .

Table 2
Prices assumed for the variable operating costs (OPEX variable ).

Table 3
Methodology for the estimation of the OPEX fixed .

Table 4
Financial parameters and assumptions.
S.Poto et al.

Table 8
Details of the propylene usage via the refrigeration cycle for the conventional and MR-assisted process.

Table 10
Key performance indicator (KPI) at the reactor level: comparison of the PBR and PBMR unit for the DME synthesis via CO 2 one-step hydrogenation.
S.Poto et al.

Table 11
Technical performance comparison of the conventional and MR-assisted onestep DME production process.

Table 12
Efficiency of the utilities compared to the amount of DME produced for the conventional and MR-assisted process.

Table 14
Current Price of H 2 and its prediction in 2050 according to different production methods.