On process intensification through storage reactors: A case study on methane steam reforming

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On Process Intensification Through Storage Reactors: A Case Study on Methane Steam Reforming John Lowd III , Theodore T. Tsotsis , Vasilios I. Manousiouthakis PII: DOI: Reference:

S0098-1354(19)30640-4 https://doi.org/10.1016/j.compchemeng.2019.106601 CACE 106601

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Computers and Chemical Engineering

Received date: Revised date: Accepted date:

17 June 2019 26 September 2019 14 October 2019

Please cite this article as: John Lowd III , Theodore T. Tsotsis , Vasilios I. Manousiouthakis , On Process Intensification Through Storage Reactors: A Case Study on Methane Steam Reforming, Computers and Chemical Engineering (2019), doi: https://doi.org/10.1016/j.compchemeng.2019.106601

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On Process Intensification Through Storage Reactors: A Case Study on Methane Steam Reforming John Lowd III Department of Chemical and Biomolecular Engineering, University of California at Los Angeles (UCLA), Los Angeles, CA, 90095 Theodore T. Tsotsis Mork Family Department of Chemical Engineering & Materials Science, University of Southern California, Los Angeles, CA, 90089 Vasilios I. Manousiouthakis (corresponding author) Department of Chemical and Biomolecular Engineering, University of California at Los Angeles (UCLA), Los Angeles, CA, 90095 Abstract In this work, the novel storage reactor (SR) process is introduced. A SR consists of two physically distinct domains, designated as the reactor domain and the storage domain, which are allowed to communicate with each other through a semipermeable boundary. It is envisioned that the SR is operated in a dynamic (periodic) manner, that enables the loading and unloading of the storage domain. In this introductory work, a 0-D first principle SR model is developed that quantifies SR dynamic behavior. The resulting governing equations are nondimensionalized, and two dimensionless groups are shown to uniquely determine SR performance, which is quantified through the use of several proposed metrics. An illustrative case study on Steam Methane Reforming is then carried out, involving

parametric studies on the two aforementioned dimensionless groups. It is established that the SR outperforms an equivalent Steady-State Reactor (SSR), in regard to the outlined performance criteria

1. Introduction As early as 1972 Roger Sargent proclaimed that, ―The trend of developments is therefore to make the art of chemical engineering obsolete‖ and made the forecast that ―there will be many generations of chemical engineers before this occurs.‖ (Sargent, 1972). He went on to describe the importance of dynamic models for several chemical engineering systems and associated solution techniques. Since that time, the modeling of dynamic processes in chemical engineering has been extensively practiced, thus fulfilling another Sargent prediction, ―It is necessary to be able to predict the effects of various changes on the system performance and this requires a computational model of the system which simulates its behavior. This model can then be used simply to check hypotheses concerning the behaviour, or in conjunction with a systematic procedure to determine the values of the adjustable parameters which meet the overall system objective with the minimum use of resources. The essence of success in this programme is the rigorous use of Ockham’s razor; the overall objective must be kept firmly in mind and the model should be as simple as is compatible with a satisfactory representation of those aspects of system behaviour which directly affect this objective.‖ (Sargent, 1972). In honor of Sargent’s encouragement for the rigorous use of Ockam’s razor, the objective of this work is to introduce the novel Storage Reactor (SR) concept as a process intensification tool, and to develop a simple mathematical model that effectively demonstrates the intensifying characteristics of the SR process. Over the course of the last four decades, process intensification (PI) has developed as an

area of chemical engineering research. Having first appeared in the literature in the early 1970’s, PI has continued to grow incorporating a variety of aspects in chemical engineering, including process safety (Mannan et al., 2016) and process systems engineering (Stankiewicz and Moulijn, 2003). While an exact definition has been difficult to pin down, most seem to agree that PI involves any strategy or chemical engineering development that leads to a substantially smaller, cleaner, safer and more energy-efficient technology or which combines multiple operations into fewer devices (Baldea, 2015). Historically, major advancements in PI have been the result of improvements based on iterative experimental design. Examples include membrane reactors for methane steam reforming (MSR) for hydrogen generation at lower temperatures (Basile et al., 2011), the so-called dividing-wall columns that combine multiple distillation columns into a single unit (Asprion and Kaibel, 2010), and compact catalytic plate reactors for use in Fischer-Tropsch synthesis (LeViness et al., 2014). However, in recent years there have also been numerous advances in systematic approaches and analytical tools for identifying, at the theoretical level, new PI methodologies. Mathematical formulation advances, such as the IDEAS framework (Ponce-Ortega et al., 2012), as well as multi-objective optimization techniques (Sharma and Rangaiah, 2013) have helped to introduce a more systematic approach in developing and identifying PI pathways for various chemical systems. Additionally, software has been developed (Carvalho et al., 2013) based on the implementation of an extended systematic methodology for sustainable process design for use in PI. Our own continuing commitment to PI has been demonstrated in recent years both theoretically and experimentally, through identification of potential intensification pathways in environmentallybenign power generation. In this area, we have analyzed intensified reactor configurations at the lab scale through the use of carbon molecular sieve membrane (CMS)-based reactors (Garshasbi et al., 2017) for the production of H2 via the Water Gas Shift (WGS) reaction. Additionally, we have

developed and experimentally studied a novel hybrid membrane reactor (MR) and adsorptive reactor (AR) configuration that produces high purity H2 with simultaneous CO2 capture (Chen et al., 2018) for application to Integrated Gas Combined Cycle (IGCC) power generation. In addition to our experimental efforts, we have also carried-out extensive research in developing and simulating models for PI. We have developed multi-scale models for modeling reactors in PI, whose constitutive equations are derived through application of the Reynolds Transport Theorem at the reactor and catalyst pellet scales (Karagöz et al., 2018), using Dusty Gas Model (DGM), Stefan-Maxwell model (SMM) and Chapman-Enskog theories to quantify mass and momentum transport (Cruz et al., 2017). We have also contributed to intensified process synthesis methodologies, through our Infinite DimEnsionAl StateSpace (IDEAS) framework, that can identify performance limits for reactive separation networks (da Cruz and Manousiouthakis, 2019), and can synthesize energy-intensified flowsheets (Pichardo and Manousiouthakis, 2017). The focus of this paper is a novel process, called a Storage Reactor (SR), which aims to intensify traditional, steady-state, reactor designs, by carrying-out simultaneously reaction, separation, and storage in a single unit, while avoiding the reliability shortcomings associated with high-temperature membrane tubes typically used in MR that also simultaneously carry-out reaction and separation. The proposed SR process can be used to intensify high temperature and pressure processes subjected to either reaction equilibrium or kinetic limitations (Dabir et al., 2017). In the remainder of this work, a dynamic model of the SR process is first developed, and then made dimensionless. Two dimensionless groups are then identified that govern the behavior of the SR process. A three-phase SR operating strategy is then identified, characterized as Partial Pressure Swing Operation (PPSO), and associated performance metrics are introduced. An illustrative case study on hydrogen production via MSR is then presented, for

which the PPSO SR process is compared to a conventional reactor operating at steady-state (SSR). Finally, conclusions are drawn and future work is discussed. 2. Mathematical Formulation In this introductory study, a composite 0-dimensional model for the intensified SR process is first derived that captures and highlights the basic characteristics of this novel reactor process. Following non-dimensionalization, it is established that two dimensionless groups govern SR behavior. The SR is considered to be a composite thermodynamic system comprised of two simple subsystems, the reactor gas domain  g  and the storage pellet domain  s  , which communicate with one another through a permselective layer, but are spatially exclusive. Considering that each domain is spatially uniform, that the storage domain is uniformly dispersed within the gas domain, that no reaction occurs within the storage domain, and that the composite system is isothermal, gives rise to the following, species conservation based, 0-dimensional model for the SR.  dn gj  t  NC g sg g g0  ninj  t   nout j  1,..., NC  j  t   rj  Pk  t k 1 , T V  c j  c  n j  t  , n j  0   n j  dt  s  dn j  t   n sgj  t  , n sj  0   n sj 0 j  1,..., NC   dt







1 

  2   

where the first and second terms on the right-hand side of (1) are the inlet and outlet molar flowrates respectively, the third term is the reaction based molar rate of generation of species j (with rj the reaction based rate of generation of species j , V the total reactor volume,  c the volume fraction of the reactor occupied by the catalyst pellets,  j the catalyst effectiveness factor of species j , and  c the apparent mass density of the catalyst pellets, i.e. pellet mass over pellet volume), and the fourth term is the molar flowrate of species j , leaving the reactor gas domain through the permeable storage domain boundary and entering into the storage domain. The storage domain is isolated from the inlet and outlet flows, and thus species j can only enter from the reactor to the storage domain through its boundary.

Thus, the right hand side of (2) only contains the molar flow rate of species j , entering the storage domain through the permeable storage domain boundary, having left the reactor gas domain (We assume here that the permselective layer is ideal allowing only species j to permeate through. A practical example of that would be a storage medium coated by a then Pd-alloy layer that allows only hydrogen to permeate through during MSR). Sieverts’ Law is typically employed in quantifying the molar flow rate of a species j through a Pd membrane layer (Dabir et al., 2017). For such membranes, it has been shown, both theoretically (Carapellucci and Milazzo, 2003) and experimentally (Caravella et al., 2013), that the molar flow rate is proportional to the difference of the nth power of the partial pressures across the membrane, where 0.5
nsgj   j Ags  Pjg  Pjs  j  1,..., NC

 3

where  j is the jth species molar permeance through the permselective layer, Ags is reactor gas-storage medium interfacial area, and Pjg , Pjs are the jth species partial pressures in the reactor gas and storage mediums. Considering an ideal gas mixture, and the volume fractions of the catalyst pellet solid, catalyst pellet gas, catalyst pellet, reactor void unoccupied by either catalyst or storage pellets, reactor gas, storage pellet gas, storage pellet solid, and storage pellet to be  sc ,  gc ,  c ,  r ,  g ,  gs ,  ss ,  s respectively, yields:

 PjgV  g  n gj RT , Pjg 0V  g  n gj 0 RT j  1,..., NC  s s s0 s0  Pj V  gs  n j RT , Pj V  gs  n j RT j  1,..., NC   sc   gc   c ;  gc   r   g ;  gs   ss   s ;  c   r   s  1

 4    5    6 

where R is the universal gas constant, and

T

is the common temperature in all considered domains.

Incorporating (3), (4), and (5) , into (1) and (2) then yields:   in  P g t  n j  t   n out  t  NC j     g  dPjg  t  RT   g0 Pk  t  g0      Pj  0   Pj j  1,..., NC k 1 dt V  g    NC    cV c j rj Pkg  t  , T  A gs  j  Pjg  t   Pjs  t    k 1     s  dPj  t   RT Ags  P g t  P s t P s 0 0  P s 0 j  1,..., NC j  j   j   j   j  dt V  gs 





   7      8   

Next, the above model is nondimensionalized, and dimensionless groups are identified governing the SR’s behavior. *

*

*

Introducing n , P , r , t

P*V  g

*

n* RT

as reference values of molar flowrate, pressure, reaction rate, and

time, allows the definition of the following dimensionless variables:

t

t P , t*

g j

Pjg P

*

s j

,P

Pjs P

*

,n

in j

ninj n

*

, n out

n out ,r n* j

P

g k

 t k 1 , T NC



rj

P

g k

 t   P* k 1 , T NC

r



*

with values for the reference parameters P* , n* , and r * to be specified by the particulars of the considered problem, since the choice of reference parameters can vary widely, (Conesa et al., 2016), can significantly affect the range of values of the resulting dimensionless groups, (Sánchez Pérez et al., 2017), and must be such that the resulting dimensionless problem’s solution is not adversely influenced, (Alhama Manteca et al., 2014). Equations (7), and (8) can then be written in dimensionless form as follows:

   in  Pjg  t  out n t  n t         j  NC g  dP g  t     Pk  t   g0 g0  j    P 0  P  j  1,..., NC 9     k 1 j j  dt      * gs *      r V c r P g  t NC , T  A 1 P  j  P g  t   P s  t    k j k 1    c j n* j  n* 1 j    dPjs  t   g Ags 1 P*  j  g s s0 s0  Pj  t   Pj  t   Pj  0   Pj j  1,..., NC 10    *  gs n 1    dt 





where the first species and its molar permeance through the permselective layer, 1 is employed in defining the dimensionless group that captures the effect of the storage domain on overall process performance. The operation of the proposed SR process must necessarily be dynamic (periodic) in nature, since the species stored in the storage medium must at some point in time be removed, otherwise the storage medium will ―fill-up‖ and no longer allow species permeation though its boundary. In this work, a ―Partial Pressure Swing Operation‖ (PPSO) of the SR is envisioned, which keeps reactor pressure and temperature constant. Such operation, aims to reduce reactor heating/cooling and compression costs. To this end, and for the sequel of this work, it is thus considered that the reactor outlet flowrate is adjusted NC

so that

 P t   constant . In turn, this suggests that, the following must hold at all times: k 1

g k

 



NC  r *V c NC Ags 1P* NC   k g g  r P t , T  Pk  t   Pks  t     0 t  0 11        k k  l * * l 1 n k 1 n k 1  1  To further simplify the above derived dimensionless model, the following reference value is selected,

n out  t   n in  t    c

and dimensionless groups are introduced:

P* 

The

NC

NC

k 1

k 1

 Pkg t   constant   Pkg  t   1 P* Ags 1 1  , Da  Pemem n

resulting

12 

r V  c c RT  c  * c r  t * * n P g

dimensionless

model,

and

outlet

13 flowrate

non-negativity

constraint

are:

     in  in g   n j  t   n  t  Pj  t      g   NC NC   g0 g  dPj  t     D  r P g  t NC , T  P g  t  k rk Pl  t l 1 , T  , Pj  0   Pjg 0 j  1,..., NC  k j k 1  dt  a  j j k 1     NC  k      j g s g g s       Pj  t   Pj  t    Pj  t      Pk  t   Pk  t      k 1  1      1  s  dPj  t   g  j    P g  t   Pjs  t   Pjs 0  0   Pjs 0 j  1,..., NC  dt  gs 1 j  NC NC  in NC   n  t   Da  k rk Pl g  t l 1 , T    k  Pkg  t   Pks  t     0  t  0 k 1 k 1  1    





 



 



    14        15   16     

The above equations suggest that two dimensionless numbers determine the PPSO SR’s dynamic behavior. The first,  

1 , provides a measure of how effectively the reference species is being Pemem

extracted from the reaction domain into the storage domain, compared to the employed molar flowrate reference value. Pemem is a Peclet number commonly employed by other authors, (Alavi et al., 2018; Tsuru et al., 2004), (Motamedhashemi et al., 2011), (Israni et al., 2009) for the analysis of membrane reactors. Da is

the commonly employed Damkohler number, which indicates the ratio of the reference reaction rate to the molar flowrate’s reference value, and encapsulates the reactor’s residence time. The performance of membrane reactor systems has been analyzed in terms of these dimensionless numbers, (Gokhale et al., 1995; Mohan and Govind, 1986).

As mentioned earlier, it is envisioned that the proposed SR process is operated in a dynamic (periodic) manner. A possible implementation of the proposed ―Partial Pressure Swing Operation‖ (PPSO) of the SR, which keeps the reactor pressure and temperature constant, involves three operating phases. In the first phase, the SR operates in a Loading-Reaction mode in the  g  domain (where the reactants are loaded into the SR and the desired reactions are carried out in  g  ), and in a Storage mode

in the  s  domain (where one or more desired species are preferentially transported from  g  to  s  , where they are stored). In the second phase, the SR operates in a Reactant-Flushing mode in the  g  domain (where the reactants are removed from  g  ), and in Storage-Maintenance mode in the

s

domain (where the desired species are maintained in storage within  s  ). Finally, in the third phase, the SR operates in an Emptying mode in the  s  domain (where the desired chemicals are emptied from storage within

 s  and transported into  g  ), and in Unloading-Production mode in the  g  domain

(where the desired species are removed from  g  , to yield the main SR products). Comparing the performance of the PPSO SR, which is a periodic process, with that of a traditional reactor, which is a steady-state process, requires that a number of process performance metrics be introduced. Since the PPSO SR is a periodic process that takes place over several phases, it is appropriate to define metrics over each phase separately and over all phases. When the inverse Peclet number  is set to zero, the second and third operating phases become obsolete, and as the duration of the first phase approaches infinity, its associated metrics must approach their steady-state counterparts. Thus, the following metrics are considered. Limiting Reactant Conversion A limiting reactant K will be typically fed in the SR, and will be removed from the SR in varying amounts during each phase. It is thus appropriate to define its conversion over all phases as follows: k  k in  n t dt  nKout,k  t dt    K ,k     k 1   0 0 XK   NP  k  in   nK ,k  t dt   k 1  0  NP

Desired Product Ratio

17 

Molar ratios of desired product over limiting reactant can also be introduced, for either a single phase, or all phases. The molar ratio, of j produced during phase i , over limiting reactant K fed over all phases, is: i

 j,i

i

out in  n j ,i  t dt   n j ,i  t dt 0

0

k

 in    nK ,k  t dt   k 1  0  NP

18

The molar ratio, of j produced during all phases, over limiting reactant K fed over all phases, is: k  k out  n t dt  n jin,k  t dt      j ,k   k 1  0 0   k NP   in   nK ,k  t dt   k 1   0 NP

j

19 

This is often referred to as product yield. It then holds NP

 j    j ,i

 20 

i 1

Finally, the molar ratios defined below, can be considered as product recovery percentages over each PPSO phase, and are thus referred to as the Product Recovery percentages.

R j ,i

 j ,i j

i  1, NP j  1,..., NC

 21

The above system of non-linear first order differential equations 14  , 15 can be used to simulate all three PPSO SR phases, and can be solved using a standard implicit multistep backward differentiation formulation (BDF) that can accurately capture the solution of stiff initial value problems. Simultaneously with the time evolution of 14  , 15 , the algebraic inequality 16  is monitored to ensure the positivity of the storage reactor’s outlet flow rate. The above solution strategy was implemented within the COMSOL Multiphysics software platform. The storage reactor concept is next

illustrated on a steam methane reforming (SMR) case study, in which the impact of both dimensionless parameters on the PPSO of an SMR SR is quantified. 3. Steam Methane Reforming (SMR) Case Study In this case study, the derived dimensionless SR model is applied to the design of a novel process intensification reactor for SMR based hydrogen production using a SR under PPSO. It will be shown that the proposed 3 phase PPSO of the SMR SR outperforms a conventional SMR reactor operating at steady state. Steam reforming of natural gas (and of other light hydrocarbons) is a process that is used extensively in petroleum refineries today to generate the hydrogen needed for their operation, for example, in the hydroprocessing of crude oil for the production of gasoline and other fuels. Indeed, approximately 95% of the hydrogen produced in the United States industrially was obtained via the SMR reaction (Wei et al., 2012). These SMR reactors typically operate near chemical reaction equilibrium, and represent a significant component of a refinery’s capital and operating costs. Membrane separation has attracted attention over the past three decades as a process intensification tool due to its low energy requirements compared to more conventional separation technologies like distillation. Polymeric membranes have been the most intensively investigated, and are now widely used commercially. Inorganic membranes on the other hand, which include metallic, carbon, and ceramic membranes, have received relatively less attention, despite the fact they also show good promise for broad applications (Dabir et al., 2017). There are presently several commercial liquid-phase separations employing such membranes, but commercial gas-phase applications are presently lacking. However, high-temperature and high-pressure gas-phase reactive separations are an area where inorganic membranes have, potentially, a distinct advantage over polymeric membranes, and thus such applications remain today key drivers for the continued development of inorganic membranes.

3.1 Problem Specification and Thermodynamic Data In the analysis that follows, the molar flowrate n * , and reaction generation rate r  reference nin  0  , r

values are selected as n*

*

k1

 P* 

0.5

. According to Xu and Froment, (Xu and Froment, 1989),

SMR is carried out through the following three reversible reactions R1 , R 2 , and R3 , with enthalpies of formation as shown below: CH 4  H 2O CO  H 2O

CH 4  2H 2O

CO  3H 2 H1 :206.1 kJ

mol

 R1

CO2  H 2 H 2 :  41.15 kJ

mol

 R2 

CO2  4H 2 H3 :164.9 kJ

mol

 R3

Alternative SMR models employing only the first two of the above reactions have also been developed(de Smet et al., 2001), which argue that the above three reactions are linearly dependent. Although this is true in a stoichiometric, and equilibrium sense, it is not true in a kinetic sense. Indeed, the kinetic rate expressions provided in (Rostrup-Nielsen, 1984), can be brought in dimensionless form, as suggested in (Sánchez Pérez et al., 2017). The resulting dimensionless reaction rates for R1, R2, and R3 become:

k1

R1 

R2 

P  g H2

k2 PHg2

 

3 g   PHg2 PCO g g P P   2.5  CH 4 H 2O  K1  

 DEN 

2

g  g g PHg2 PCO 2 P P   CO H 2O K 2 



DEN



2

  

 22 

 23

k3

R3

P   g H2

  Pg Pg 3.5  CH 4 H 2O 





2

 DEN 

P  

g  PCO   K3 

g H2

4

DEN=1  K P  K H2 P  KCH4 P g CO CO

 24 

2

g H2

g CH 4



K H 2O PHg2O

 25

PHg2

where 1.5  P*  k 2  1.5 K k K 3 1  K1  , K 2  K 2 , K3  , k1  1, k2    P *  , k3  3  2 2 k1 k1   P*   P*   * * *   KCO  KCO P , K H 2  K H 2 P , K CH 4  K CH 4 P , K H 2O  K H 2O

      

 26 

In the spirit of (Zhou and Manousiouthakis, 2008), considering the above reaction rate expressions as elements of the linear space of real valued functions of the five species’ partial pressures, yields that the reactions R1, R2, and R3 are linearly independent in a kinetic rate sense. Indeed, it can be readily verified that the only real numbers 1 , 2 , 3 for which the equation 1r1  2 r2  3 r3  0 is satisfied for g g g all possible partial pressures PCH must satisfy 1  0, 2  0, 3  0 . , PHg2O , PHg2 , PCO , PCO 4 2

The PPSO of the SMR SR is carried out in three phases, each of which is described by the activity occuring in the  g  and  s  domains and is designated as follows: Phase 1 (Loading-Reaction/Storage), Phase 2 (Decarbonization/Maintenance), and Phase 3 (Unloading-Production/Emptying). These three phases have a time duration designated as  1 ,  2 , and  3 , as illustrated in the figure below, and are described next.

Figure 1: Proposed PPSO 3 phase SR operation

Phase 1: SR Loading-Reaction/Storage Phase At the beginning of this phase,  g  is largely composed of steam and some hydrogen, while  s  only contains hydrogen at a pressure higher than the partial pressure of hydrogen in  g  . A mixture of methane and steam is then fed into the SR at a constant flow rate, the SMR reactions are carried-out, and the generated hydrogen begins to permeate into

 s  as its partial pressure in  g  exceeds the total

pressure of  s  . The outlet flowrate varies, as described by 11 , so as to maintain constant pressure in

g. Phase 2: SR Decarbonization/Maintenance Phase

Phase 2 begins at the final conditions of phase 1, and the feed is switched to a mixture of steam and hydrogen, the composition of which is selected so that the partial pressure of hydrogen in  g  is above the hydrogen pressure in  s  so as to maintain the stored hydrogen in  s  . Thus  g  is decarbonized, until its contents essentially consist of steam and hydrogen. Phase 3: SR Unloading-Production/Emptying Phase Similarly, Phase 3 begins at the final conditions of phase 2, and  g  is fed pure steam. This action empties the contents of  s  into  g  , and unloads the contents of  g  generating a mixture of hydrogen and steam as the MSR SR product, which is readily separable at high pressure, thus avoiding compression related operating costs. Comparing the performance of the PPSO SMR SR, which is a periodic process, with that of a traditional, SMR reactor, which is a steady-state process, requires that the above defined process performance metrics be specialized to the SMR case study. Designating methane as our limiting reactant, equation (17) becomes: k  k in  out n t dt  nCH    t dt    CH 4 ,k   4 ,k k 1   0 0 X CH 4   27   NP  k  in   nCH 4 ,k  t dt   k 1   0 Similarly, equations (18)-(21) can be expressed for all products, CO, CO2 , H 2 , and are listed below for NP

the species of interest. 1

CO ,1 2

1

n

out CO2 ,1

0

in  t dt   nCO ,1  t dt 2

0

 k in    nCH 4 ,k  t dt   k 1  0  NP

 28

k  k out  n t dt  nHin2 ,k  t dt      H 2 ,k   k 1   0 0  k NP   in   nCH 4 ,k  t dt   k 1   0 NP

YH 2

i

R H 2 ,rec 

 29 

i

 n  t dt   n  t dt out H 2 ,i

0

in H 2 ,i

 30 

0

k  k out  n t dt  nHin2 ,k  t dt    H 2 ,k     k 1   0 0 NP

Equation (28) captures the CO2 molar production ratio in phase 1 over the total amount of CH 4 fed over all three phases. Equation (29) quantifies the molar ratio of total hydrogen produced over natural gas raw material, and represents the hydrogen yield over all three phases of operation Finally, of significance is the hydrogen recovery ratio quantified by equation (30) during the 3 rd phase, i  3 , as it quantifies the molar ratio of readily purifiable (through water separation) hydrogen to total hydrogen produced. To determine the time duration  1 ,  2 , and  3 of the three PPSO phases, a stopping criterion for each phase must be selected. Two different stopping criteria are considered for phase 1, and the obtained results are compared in terms of the above listed performance metrics in the discussion section. The first selection for the duration of the first phase  1 is the time at which the function CO ,1 : 1  CO 2

reaches its maximum value, i.e. 1 values of  1 , the value of CO

CO

2 ,1

2 ,1

2 ,1

1 

arg max CO2 ,1 1  . The rationale for this decision is that for small 10, 

1  is close to zero, while for large values of  1 , the value of

1  approaches the corresponding product ratio of the steady-state, no storage, reactor. The above

 1 selection ensures that significant CO2 product generation has occurred during the first phase, leading

inevitably to significant H 2 hydrogen generation and storage, and also leaving the SR gas phase at the end of phase 1 in a CO2 rich state, increasing the decarbonization efficiency of the second phase. Our second selection for the duration of the first phase  1 is the time at which the hydrogen partial pressure inside the storage medium reaches 90% of the hydrogen partial pressure attained in the reactor for operating times approaching infinity (which is equal to the hydrogen partial pressure at the exit

of

the

1 : PHs 1   0.9   PHg 2

2

corresponding



ss

steady-state

reactor).

Mathematically,

0.9  lim PHs2 1  . 1 

The duration of the second phase  2 is selected as the time at which the function PCg  t



g PCO  t   PCHg 4  t   PCOg  t  is brought below a predefined decarbonization limit (e.g. 0.01). 2

This selection determines the level of carbon impurities in the H 2 product generated during phase 3. Similarly, the duration of the third phase  3 is selected as the time at which the function

PHs2  t s H2

P



   2

is

brought below a predefined depressurization limit (e.g. 0.05). This selection determines the pressure fluctuation experienced by the storage medium over the SR PPSO. Next, the time evolution of all SR state variables (species mole fractions in the gas and storage phases) are shown for the SR model parameter values and the summarized in the Tables below. Table 1: Simulation Parameters Description Species k effectiveness factor Species j permeance ratio Reactor gas void fraction to Storage gas void fraction ratio Membrane Permeation (Inverse Peclet) number

Parameter

Value 1

k  j 1

0 for all j  1

 g  gs

0.1



50

Damköhler number

Da

7

Table 2: Reactor Dimensionless Inlet Flow Rates Description Inlet methane flow rate: phase 1 Inlet water flow rate: phase 1

Parameter in CH 4 ,1

n

Value 0.25

nHin2O ,1

0.75

n jin,1 j  H 2 O, CH 4

0

Inlet water flow rate: phase 2

nHin2O ,2

0.85

Inlet hydrogen flow rate: phase 2

nHin2 ,2

0.15

n jin,2 j  H 2O, H 2

0

nHin2O ,3

6

n jin,3 j  H 2 O

0

Inlet flowrate of other species: phase 1

Inlet flow rate of other species: phase 2 Inlet water flowrate: phase 3 Inlet flow rate of other species: phase 3

Table 3: Reaction Kinetic Parameters for P*  26 105 Pa, T  900 K Description Dimensionless reaction rate constant 1

Parameter k1

Value 1

Dimensionless reaction rate constant 2

k2

662.6

Dimensionless reaction rate constant 3

k3

0.143

Dimensionless equilibrium constant reaction 1 Dimensionless equilibrium constant reaction 2 Dimensionless equilibrium constant reaction 2 Dimensionless adsorption coefficient

K1

0.002

K2

2.35

K3

0.005

KCO

26.97

K H2

0.01

KCH 4

2.88

K H 2O

1.26

CO Dimensionless adsorption coefficient H2 Dimensionless adsorption coefficient CH 4 Dimensionless adsorption coefficient H 2O

Table 4: Reactor Initial Dimensionless Partial Presssure Conditions Description g Phase 1 PCH 4

0.0002

Value

PHg2O Phase 1

0.9992

PHg2 Phase 1

0.0002

g Phase 1 PCO

0.0002

g Phase 1 PCO 2

0.0002

PHs2 Phase 1

0.019

In Figure 2, the phase-1 time evolution of all species mole fractions in the gas domain is shown. It can be seen that the CO2 mole fraction time function exhibits a maximum, while the CH 4 , CO , and

H 2 mole fractions increase with time, and the H 2O mole fraction decreases with time. This behavior is consistent with the reactor starting phase-1 in a completely decarbonized state, and largely full of H 2O . Thus, despite the vigorous transformation of CH 4 into CO , and CO2 , the CH 4 mole fraction in the gas phase increases. Additionally, the phase-1 time evolution of H 2 in the storage domain is also captured, in the form of the ratio of the hydrogen storage pressure over the total reactor pressure, which is a monotonically increasing function of time whose limit for long times becomes equal to the H 2 mole fraction in the gas domain. Figure 3 illustrates the positivity of the outlet molar flowrate throughout the phase-1 time evolution, confirming the physical realizability of PPSO during phase 1. Figure 4 illustrates the time averaged metric CO2 ,1 as a function of the potential phase-1 operating time  1 . Figure 4 also exhibits a maximum at 1  3.89 , similar to the CO2 mole fraction behavior shown in Figure 2, which according to the first stopping criterion 1

arg max CO2 ,1 1  is then chosen as the operating 10, 

time for phase-1, since it ensures significant CO2 product generation that is higher than that of an SSR.

Figures 5 through 9, illustrate the performance of the SR PPSO operation under the aforementioned stopping criterion 1  3.89 for phase 1. In Figure 5 the phase-2 time evolution of all species mole fractions in the gas domain is shown. Since the SR feed during phase-2 consists of only H 2 and H 2O the outlet mole fractions of all other species decrease over time. In Figure 5 the phase-2 ratio of the hydrogen storage pressure over the total reactor pressure, is also shown to be approximately constant, except at small times as the hydrogen partial pressure in the gas equilibrates to the lower total storage pressure. Figure 6 shows PCg  t



g PCO  t   PCHg 4  t   PCOg  t  as a function of time, and illustrates that the sum of all carbon 2

containing species mole fractions falls below 0.01 at  2  3.13 . As with phase 1, Figure 7 shows that the outlet molar flowrate positivity is maintained throughout phase 2. Finally, Figures 8 and 9 show the SR behavior during the Unloading Phase (phase 3) of operation, depicting the partial pressure of each species in the gas and storage domains.

Choosing a

depressurization limit of 0.05, the phase 3 operating time is then determined to be  3  4.42 . As with the other phases, Figure 9 shows the positivity of the outlet molar flow is maintained throughout phase 3 reactor operation. With the operational times calculated, it is now possible to calculate the metrics as described in equations 27-30. Conversion of methane increased over 100% by implementing the SR over a SSR, going from 0.32 to 0.68. The hydrogen recovery ratio is 0.81, indicating a large amount of hydrogen is recovered in phase 3 of SR operation, exceeding values of comparable metrics recently obtained by membrane reactors operating at steady state (Di Marcoberardino et al., 2015). The SR hydrogen yield of YH 2  1.92 is also significantly higher than its SSR counterpart of YH 2  1.08 . These high SR metric

values suggest that the SR outperforms the SSR based on the defined criteria, and that SR operation at

the designated temperature T  900 K (which is lower than traditionally used SMR temperatures (Rostrup-Nielsen, 1984)), may be economically viable and realizable using alternative fuel sources that

would reduce carbon dioxide emissions (Said et al., 2016). Next we investigate the effect of the inverse Peclet number on reactor performance. Figures 2-4 (Figures 10-12) summarize the results for reactor designs with   50 (   1 ), while keeping all other simulation parameters the same. In particular, Figure 4 (Figure 12) illustrate that the magnitude of CO2 ,1 has a peak value of 0.49 for   50 (0.31 for   1 ), indicating that less CO2 is being generated and that less reaction is occurring in the gas domain as  decreases. They are also used to identify 1  3.89 for   50 ( 1  8.01 for   1) according to the first stopping criterion 1

arg max CO2 ,1 1  . Figures 10, 

5-9 (Figures 13-17) summarize the remaining results for reactor designs with   50 (   1 ), while keeping all other simulation parameters the same and using the first stopping criterion. Methane conversion is reduced from 0.68 for   50 to 0.43 for   1 . As  is lowered, operational times increase in both phases one and three, from 1  3.89 and  3  4.42 for   50 to 1  8.01 and

 3  25.01 for   1 . The above suggest that a number of potential operational and energy savings can be attained by using storage medium material that can deliver large inverse Peclet numbers. The inverse Peclet number  has a minimal effect on  2 , as during this phase there is minimal hydrogen permeation through the gas-storage domain boundary, since the reactor is being flushed of reactants and undesirable products. The hydrogen yield and hydrogen product recovery are also both reduced from YH2  1.92 and R H2 ,rec  0.81 at   50 to YH2  1.35 and R H2 ,rec  0.47 at   1 , suggesting that the inverse Peclet

number should be increased as much as physically possible, to obtain the best reactor performance.

System Dimensionless Partial Pressure Phase 1

0.5

0

0

5

10

15

System Dimensionless Partial Pressure Phase 2

1

P_bar

P_bar

1

20

0.5

0 0

5 t_bar

t_bar CH4 CO

H2O CO2

CH4 CO

H2 Gas H2 Storage

Figure 2: Dimensionless time evolution of species’ partial pressure in composite reactor system Phase 1, Θ=50.

h(t_bar)

n_bar out

5 4 3 2 1 0

10

15

H2 Gas H2 Storage

Summation Carbon Species Phase 2

6

5

H2O CO2

Figure 5: Dimensionless time evolution of species’ partial pressure in composite reactor system Phase 2, Θ=50.

Total Exit Molar Flowrate Phase 1

0

10

0.3 0.25 0.2 0.15 0.1 0.05 0 0

20

5

15

t_bar

t bar

Figure 3:Total exit flowrate of reactor during operation of Phase 1, Θ=50.

10

Figure 6: Sum of carbon containing species mol fraction in reactor gas during phase 2 of operation, Θ=50.

Total Exit Molar Flowrate Phase 2 1.5

0.6 0.5 0.4 0.3 0.2 0.1 0

n_bar out

ω CO2

Reactor Phase 1

1 0.5 0 0

0

5

10

15

20

2

4

6

8

10

t_bar

t bar

Figure 4: Evolution of parameters Θ=50.

CO

2 ,1

during operation of Phase 1,

Figure 7: Total exit flowrate of reactor during operation of Phase 2, Θ=50.

Total Exit Molar Flowrate Phase 1 System Dimensionless Partial Pressure Phase 3 n_bar out

P_bar

1 0.8 0.6 0.4 0.2 0

0

5

10 t_bar

15

3 2.5 2 1.5 1 0.5 0 0

20

CH4

H2O

H2 Gas

CO

CO2

H2 Storage

20

40

60

t_bar

Figure 11: Total exit flowrate of reactor during operation of Phase 1, Θ=1.

Figure 8: Dimensionless time evolution of species’ partial pressure in composite reactor system Phase 3, Θ=50.

Reactor Phase 1 Total Exit Molar Flowrate Phase 3

1 0.8

ω CO2

8

n_bar out

6 4

0.6 0.4 0.2

2

0

0

0 0

5

10

15

20

40

60

t_bar

20

t_bar Figure 9: Total exit flowrate of reactor during operation of Phase 3, Θ=50.

Θ=1.

System Dimensionless Partial Pressure Phase 1

System Dimensionless Partial Pressure Phase 2

1 P_bar

1

P_bar

Figure 12: Evolution of parameters  during operation of Phase 1, CO2 ,1

0.5

0

0.5

0 0

20 CH4 CO

t_bar H2O CO2

40

60 H2 Gas H2 Storage

Figure 10: Dimensionless time evolution of species’ partial pressure in composite reactor system Phase 1, Θ=1

0

20 t_bar CH4 CO

H2O CO2

40 H2 Gas H2 Storage

Figure 13: Dimensionless time evolution of species’ partial pressure in composite reactor system Phase 2, Θ=1.

System Dimensionless Partial Pressure Phase 3

1.2 1 0.8 0.6 0.4 0.2 0

1 P_bar

n_bar out

Total Exit Molar Flowrate Phase 2

0.5

0 0

10

20

30

40

0

50

CH4 CO

Figure 14: Total exit flowrate of reactor during operation of Phase 2, Θ=1.

20

30

40

t_bar

t_bar

H2O CO2

H2 Gas H2 Storage

Figure 16: Dimensionless time evolution of species’ partial pressure in composite reactor system Phase 3, Θ=1.

Summation Carbon Species Phase 2

Total Exit Molar Flowrate Phase 3

0.25

8

0.2

6

n_bar out

h(t_bar)

10

0.15 0.1 0.05

4 2 0

0 0

10

20

30

40

50

0

20

30

40

t_bar

t_bar

Figure 15: Sum of carbon containing species mol fraction in reactor gas during phase 2 of operation, Θ=1.

10

Figure 17: Total exit flowrate of reactor during operation of Phase 3, Θ=1.

There are several process design and operational parameters that can be adjusted to increase  . First, the inlet flowrate can be reduced, thus increasing reactant residence time, and allowing for additional reactant conversion to occur within the gas domain.

Second, the gas-storage domain

interfacial area can be increased, allowing for increased transport between the two domains. Third, increased preferential hydrogen permeance through the storage medium’s permselective layer can be pursued, through appropriate selection of the layer’s pore structure and material. Finally, high reactor operating pressure would also lead to higher  values.

Table 5: Comparison of performance metrics for SSR and SR Metric

SSR

SR: Θ=1, Da=7

SR: Θ=50, Da=7

SR: Θ=50, Da=0.1

X CH 4

0.32

0.43

0.68

0.36

YH 2

1.08

1.35

1.92

0.74

RH2 ,rec

N/A

0.47

0.81

0.80

Table 6: SR Operating Times Metric

Θ=1, Da=7

Θ=50, Da=7

Θ=50, Da=0.1

 1*

8.01

3.89

4.624

 2*

3.19

3.13

3.053

 3*

25.01

4.42

3.488

The above Tables 5 and 6 summarize the effects of varying  on SR performance. They also quantify the effect of varying Da on SR performance. As shown in Table 5, for   50 , methane conversion, hydrogen production ratio and hydrogen product recovery are all reduced from X CH4  0.68 , YH2  1.92 and R H2 ,rec  0.81 at Da  7 to X CH4  0.36 YH2  0.74 and R H2 ,rec  0.80 at Da  0.1 .

These reductions are significant, suggesting that SR’s with high  , and low Da values may not be efficient, and reaffirming that both the reaction and separation characteristics of SR must be simultaneously considered to optimize SR performance. In regard to operating times, Table 6 illustrates that varying Da has a relatively small effect on operating times for each phase of the SR. In comparing the proposed SR process to existing periodically-operated reforming reactors (e.g., sorption-enhanced), it should be emphasized that the SR does not employ sorption to enhance reactor performance. Rather, it employs a storage medium whose outer surface is permselective to the desired species, which are thus preferentially transported from the reacting phase into the storage medium. The transport across this permselective layer can be driven by a variety of driving forces, depending on the nature of the particular storage medium chosen, that affect the chemical potential difference of the

preferentially-transported species across the aforementioned surface. This suggests, that the SR process can be applied to reactors in which the reaction and storage domains can be composed of any combination of gas-phase, liquid-phase and/or solid-phase media. In comparing the proposed SR process to existing membrane-assisted reactors (MR), it is important to emphasize that the SR process does not suffer from any potentially severe performance degradation induced by structural imperfections, as commonly encountered with large-area membranes employed in such MR. Since the storage medium is likely to be in a pellet form, it is expected that it will be a straightforward task to prepare defect-free permselective coatings (e.g., via dip-coating of preceramic precursors with subsequent pyrolysis to form ceramic surface films, see Deng et al. 2014). Indeed, any pinhole and/or crack that may form during operation on a given pellet’s surface coating is likely to have less of a detrimental effect on reactor performance than forming a similar size defect on a membrane tube. This means then that any reactor performance degradation that may occur, due to the storage medium’s decline in permselectivity is likely to be gradual and incremental, and performance recovery may be easier to implement than in the MR case. In comparing the effect of different stopping criteria for phase 1 on overall SR performance, it  was found that stopping criterion one  1 

1 : PHs 1   0.9   PHg 2

2



ss

 arg max CO2 ,1  1   was superior to stopping criterion two 10,   

0.9  lim PHs2 1  across all metrics. Indeed as can be seen in Table 7, 1 

methane conversion, hyrogen yield, and hydrogen recovery are all lower when the second phase 1 stopping criterion is employed. This is consistent with the stopping criterion effect on the operational times of all three SR phases, summarized in Table 8. In the limit of long SR operational times, the SR performance metric values approach those of the SSR, thus negating the potential SR benefits. This

further highlights the need for further studies aiming at identifying the optimal SR phase operational times for the optimization of various SR performance metrics. Table 7: Comparison of SR performance metrics for both phase 1 stopping criteria Metric

CR1: Θ=1, Da=7

CR2: Θ=1, Da=7

CR1: Θ=50, Da=7

CR2: Θ=1, Da=7

X CH 4

0.43

0.36

0.68

0.58

YH 2

1.35

1.23

1.92

1.69

RH2 ,rec

0.47

0.26

0.81

0.69

Table 8: SR Phase Operating Times for both phase 1 stopping criteria Metric

CR1: Θ=1, Da=7

CR2: Θ=1, Da=7

CR1: Θ=50, Da=7

CR2: Θ=1, Da=7

 1*

8.01

27.2

3.89

5.91

 2*

3.19

3.01

3.13

2.97

 3*

25.01

28.9

4.42

4.60

The long-term periodic behavior of the SR process is attained within a few operating cycles. Indeed, the reactor at the end of the regeneration phase is largely filled with water and low levels of desired species (hydrogen) in the storage medium. Using initial conditions of yCH4=0.01, yH2O=0.96, yH2=0.01, yCO=0.01, yCO2=0.01, yH2S=0.02, the process converges to its long-term behavior within 3 cycles. The associated evolution of stopping times for each phase for a reactor with Θ=50, Da=7 is shown in the table below. Table 9: Convergence of operating times for each phase. Metric

Cycle 1

Cycle 2

Cycle 3

 1*

3.76

3.88

3.89

 2*

3.09

3.13

3.13

 3*

4.40

4.42

4.42

This quick convergence can be readily explained by the dominant presence of water in the reactor domain at the end of the regeneration phase. 4. Conclusions A novel reactor process, termed the storage reactor (SR), was proposed, and a first principle based model capturing its behavior was presented. The SR process combines reaction and separation, and can deliver high purity products, and potentially overcome equilibrium limitations. It is envisioned that the SR will find applications in the energy and other sectors, where there is a great demand for process intensification. To assess SR behavior, a 0-dimensional dynamical model was developed, whose dimensionless form highlights that two dimensionless parameters, Da (Damkohler number) and

  1 Pemem (inverse Peclet number), determine SR behavior. A number of metrics were introduced for assessing SR behavior, which were easily amenable to comparison with conventional metrics of steadystate reactor (SSR) performance. A case study on hydrogen production through Steam Methane Reforming was carried out, and SR Conversion, Yield, and Hydrogen Recovery were all shown to be greater than their SSR counterparts. A parametric study was then carried out on the aforementioned ,

Da and   1 Pemem dimensionless groups, and it was shown that maximizing both groups led to improved SR performance. This work should be viewed as a proof of concept study, that introduces the SR process, and will be followed by modeling and optimization studies of increased complexity. One of the many advantages of the SR process is its flexibility in accommodating any desired production scale. For example, in the presented case study for steam methane reforming, it is envisioned that the SR could be applied at the refinery level to meet hydrogen raw material needs; but it is also quite feasible to apply the SR technology at the hydrogen-fueling station level for decentralized hydrogen generation.

The SR is amenable to retrofit implementation in existing plants, since all it requires is the loading of the reactor with the storage media in addition to the catalyst, so no reactor rebuilding and/or replacement is required, as would be the case, for example, for industrial implementation of MR. Further, additional feed and effluent lines may need to be constructed in order to appropriately direct material to and from the reactor at different times. Such construction is expected to be minimal, however, as the SR process does not require chemical components exogenous to the original process (e.g., extraction fluids). In addition, given the dynamic nature of the SR process, and since most conventional reactors operate at steady state conditions, there may be an increased need for additional dynamic control equipment. Thus, it appears that the SR may be more easily incorporated into existing units than many of the currently investigated process intensification technologies, such as those employing solid sorbents and/or membranes. The presented SR dynamic model considers the reactor and storage domains to be spatially uniform, and has been employed to demonstrate the novel SR concept. Future research will focus on the development of an SR model that can capture both spatiotemporal and multi-scale effects. Further, as the SR process is shown to offer significant advantages for equilibrium-limited reactions, often carriedout at high pressures and/or temperatures, the incorporation of gas compressibility factors and energy balance considerations in the SR model will also be pursued. Acknowledgements Financial support from the American Chemical Society Petroleium Research Fund under award #57511-ND9 titled ―A Novel Pressure Swing Steam Reforming Reactor‖ is gratefully acknowledged.

English Symbols Ags m2 : reactor gas-storage medium interfacial area

 

Da : Damköhler number  kmol bar 0.5   kmol   kmol bar 0.5  k1   , k2   , k3   : Rate coefficients for SMR reaction  kg cat hr   kg cat hr bar   kg cat hr 

K1  bar 2  , K2 , K3  bar 2  : Equilibrium constants for SMR reaction

KCH4  bar -1  , K H2  bar -1  , KCO  bar -1  , K H2O , : Species adsorption constants for SMR reaction k j : Dimensionless rate coefficient for reaction j

K j j  1, 2,3 : Dimensionless equilibrium constant for reaction j K j j  CH 4 , H 2O, H 2 , CO, CO2 : Dimensionless adsorption constant for species j n gj  mol  , n sj  mol  : jth species moles in reactor gas and in storage medium

n gj 0  mol  , n sj 0  mol  : jth species initial moles in reactor gas and in storage medium

 mol  out  mol  ninj  , nj   : jth species inlet and outlet molar flowrates  s   s  n jin : jth species dimensionless inlet molar flowrate

 mol  out  mol  nin  ,n   : total inlet and outlet molar flowrate  s   s  n in , n out : Total dimensionless inlet and outlet molar flowrates

 mol  n sgj   : jth species molar flowrate from the reactor gas to the storage medium  s   mol  n*   : Reference molar flowrate  s  NC : Number of species NP : Number of reactor operational phases Pjg  Pa  , Pjs  Pa  : jth species partial pressure in gas and storage medium

Pjg 0  Pa  , Pjs 0  Pa  : jth species initial partial pressure in gas and storage medium

Pjg , Pjs : jth species dimensionless partial pressure in gas and storage medium Pjg 0 , Pjs 0 : jth species dimensionless initial partial pressure in gas and storage medium P*  Pa  : Reference pressure

Pemem : Modified Peclet number for membranes

  mol j rj   : jth species reaction based generation rate  kg catalyst  s  rj : jth species dimensionless reaction based generation rate   mol r*   : Reference reaction generation rate  kg catalyst  s  R j ,i : Dimensionless Recovery Ratio of jth species in ith phase

R j : Dimensionless rate for jth reaction

 J  R  8.314462 : Universal Gas Constant  mol  K  t  s  : Time t : Dimensionless time t *  s  : Reference time

T  K  : Temperature in all reactor domains

V  m3  : Total reactor volume

X K :Conversion of limiting reactant K Y j ,i : Desired product yield in reactor operation phase i

Y j : Desired product yield of species j

Greek Symbols

 mol j  j   j  1, NC : jth species permeance through storage medium permselective 2  Pa  m  s  layer  sc ,  gc ,  c ,  r ,  g ,  gs ,  ss ,  s : volume fractions of catalyst pellet solid, catalyst pellet gas, catalyst pellet, reactor void unoccupied by catalyst, reactor void unoccupied by storage pellet, reactor gas, storage pellet gas, storage pellet solid, and storage pellet.  j : jth species catalyst effectiveness factor

 : dimensionless membrane permeation (inverse Peclet) number  kg catalyst   : catalyst density 3  m catalyst 

c 

 j ,k : molar ratio of species j produced during phase i , over limiting reactant K  j : summation of molar production ratio over all phases of operation

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