Optimization of Adsorption-Based Natural Gas Dryers - ACS Publications

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Optimization of Adsorption based Natural Gas Dryers Yasser Fowad Al Wahedi, Arwa Rabie, Abdulla Al Shaiba, Frank Geuzebroek, and Prodromos Daoutidis Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b00374 • Publication Date (Web): 24 Mar 2016 Downloaded from http://pubs.acs.org on April 2, 2016

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Industrial & Engineering Chemistry Research

Optimization of Adsorption based Natural Gas Dryers Yasser Al Wahedia*, Arwa H. Rabieb, Abdulla Al Shaibac, Frank Geuzebroekb, Prodromos Daoutidisd* a

Department of Chemical Engineering, Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates b

Department of Research & Technology, Abu Dhabi Gas Industries Ltd. (GASCO), Abu Dhabi, P.O. Box 665, Abu Dhabi, United Arab Emirates c

Projects and Engineering Division, Al Yasat Petroleum Operations Company Ltd., P. O. Box: 44476, Abu Dhabi, United Arab Emirates d

Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN-55455, USA * Corresponding authors, E-mail addresses: [email protected] & [email protected] Keywords: Optimization, Natural Gas, Adsorption, Zeolites, Dehydration ABSTRACT Common approaches in designing natural gas dryers are based on empirical algebraic correlations and design heuristics. Such approaches fail to capture the process physics and are generally not optimal. In this work a new method for the design of natural gas dryers is presented. The method formulates a Mixed Integer Nonlinear Programming (MINLP) problem where the objective is to minimize the net present value of ensued costs (NPVC) of the drying system throughout its life time, while meeting all process constraints. Two process schemes based on common industrial conditions are considered, which differ in the source of the regeneration gas. Both schemes are shown to attain an optimal NPVC in the range of 4.5 to 5.4 $/MMSCF. When compared to conventional methods, this represents a reduction in the range of 17- 37%. The cost savings are primarily achieved from the optimization of the adsorption time, regeneration time, and the regeneration gas flow rate, thus illustrating the advantages of the proposed optimal design. 1 ACS Paragon Plus Environment


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1. INTRODUCTION Dehydration of gas streams is a commonly applied practice in various fields of gas processing such as natural gas processing, air drying, nitrogen liquefaction, and natural gas liquefaction (LNG).1, 2 The level of removal (maximum allowable water content in the product gas) is set by the target products. In the case of natural gas processing and shallow natural gas liquids recovery (i.e. recovery of C3+ components), tri-ethylene glycol systems are the preferred technology for dehydration.3-6 In ethane recovery and LNG processes, deeper water removal is needed to prevent freeze out, making it a necessity to use solid desiccants.1, 2

Zeolites are preferred over other solid desiccants due to a multitude of advantageous properties. First, zeolites achieve the deepest removal of water up to levels meeting LNG processing requirements.2 Second, the molecular sieving attributes of zeolites render them highly selective towards adsorption of water molecules and rejection of all other species commonly existing in natural gas (e.g. methane, CO2 and heavier hydrocarbons).7 Finally zeolite-based drying systems are a mature and well known technology with a wealth of data being continuously generated from operating units. Commonly used adsorbents for drying systems are Zeolite 3A and Na-X.8, 9

The current practice in designing solid desiccant dryers relies on empirical correlations and rules of thumb.1 The earliest work reported on the design of natural gas dryers was by Wunder in 1962.10 The approach uses an experimentally determined adsorbent capacity to compute the total mass of the adsorbent needed to dehydrate a given gas feed. The diameter of the vessel is set by pressure drop constraints. Prior to regeneration, the dryer is heated to an experimentally determined temperature. Dryer regeneration is assumed to occur isothermally. Subsequently, the bed is cooled down to the target operating temperature. The approach assumes a fixed cycle time

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that is commonly used in industry.1 Considering the limited computational power available at the time, these assumptions rendered the problem tractable and easily solvable. The work of Wunder was expanded by Manning and Thompson.1 They introduced two corrections to Wunder’s approach to account for mass transfer limitations and the deterioration of the adsorbent capacity with continuous operation. Following Manning and Thompson, several groups have reported the design and assessment of operating drying units.11,

12

High fidelity

modeling studies of gas drying processes were conducted by several groups with the main objective of assessing mass transfer correlations or experimental data fitting.13,14 To the best knowledge of the authors, high fidelity model based optimal design of natural gas dryers with the objective of minimizing the Net Present Value of all Costs (NPVC) ensued during the life cycle of the unit, has not been performed in the reported literature. Minimizing the NPVC requires addressing three main challenges. First, cyclic adsorption systems are dynamic and hence are governed by dynamic Partial Differential Equations (PDEs).15 The solution of the governing PDE model is required in order to precisely determine the design constraints of adsorption time, breakthrough time, and the required regeneration time.15, 16 Secondly, the attainment of the cyclic steady state condition at the optimal point has to be guaranteed.15,

16

Finally, the objective

function is nonlinear, contains both integer and continuous decision variables, and may also contain discontinuities.17

Optimization of adsorption swing systems has been attempted in the literature through three different approaches: the black box approach, the equation-oriented approach, and the simultaneous tailoring approach.15 The black box approach requires numerous simulations, each achieving the cyclic steady state condition, in order to arrive at a predictive model. The high



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computational expense of this approach renders it applicable only to small-scale optimization problems.15 The equation-oriented approach utilizes discretization techniques to transform the governing PDEs into sets of algebraic equations. The discretization techniques include finite differences and orthogonal collocations.18-22 The discretized algebraic equations and the boundary conditions are incorporated within the optimization program. The equation-oriented approach can consider an expanded space of decision variables. Still, the computational expense is high. For instance, Sankararao et al. considered a multi-objective optimization of a Pressure Swing Adsorption (PSA) system and reported a computational time of 720 hours using a Pentium 4 2.99 GHz CPU.23 Furthermore, the approach is limited to reduced complexity kinetic models due to the numerical instabilities that arise from modeling steep front profiles.15 The simultaneous tailoring approach attempts a middle ground. The achievement of the cyclic steady state condition is incorporated as a constraint within the optimization engine while the bed simulations are performed separately.15 This approach allows for higher complexity bed models, but the computational expense is high. For example, a single objective function optimization of a PSA system considering seven decision variables took 122 hours on a 2.4 GHz CPU machine for complete convergence.15 Overall the major hurdle in optimizing adsorption systems is the solution of the governing PDEs. Furthermore, the problem can be exacerbated by the nature of the objective function. Objective functions tackled in the literature include product recovery maximization23, power consumption minimization21, and cost minimization24. To date, none of the literature studies have considered the NPVC as the objective function.


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In a recent manuscript, we have reported a novel methodology for optimizing the design of temperature swing adsorption systems for Claus tail gas cleanup.17 The methodology formulates a Mixed Integer Nonlinear Program (MINLP) to optimize the design of the adsorption system while minimizing the NPVC. The solution of the optimization problem entails a two-step approach. Initially the governing PDE model is replaced with a semi-empirical nonlinear algebraic model obtained from the equilibrium solution of Rhee, Aris and Amundson25 and corrected with an efficiency factor in order to account for mass transfer effects. The MINLP problem is transformed into a set of NLPs corresponding to all possible combinations of the integer variables. The resulting NLPs are optimized for a set of randomly generated initial guesses. In the second step, optimization is performed based upon the governing high fidelity PDE with the initial guess being the optimal solution obtained from step 1. In the present work, we adopt the same methodology for the design of natural gas dryers. Two schemes commonly implemented in industry are studied: Scheme A which utilizes fuel gas for regeneration and Scheme B which utilizes a slip stream taken from the dry gas for regeneration.1 The selected adsorbent is zeolite 3A whose properties are reported by Simo et al.26 A real plant feed is considered as the optimization input. The problem constraints include cycle timings, cycle time balance, and pressure drop. Several case studies are conducted to probe the impact of the pressure drop constraint on the objective function and its elements.

2. PROCESS DESCRIPTION AND OPTIMIZATION PROBLEM 2.1 PROCESS DESCRIPTION The two process schemes investigated in this work are depicted in Figure 1. In both schemes, the feed gas is first introduced to the vessel(s) undergoing adsorption dehydration operation (ADS Tower). Downward flow is commonly the preferred flow arrangement for the feed gas. Effluent 5 ACS Paragon Plus Environment


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dry gas is then routed to the next unit via the dry gas outlet header. Following the adsorption operation, the ADS tower undergoes regeneration via temperature swing. In process scheme A, fuel gas is used for regeneration; it is first heated to the desired regeneration temperature and subsequently introduced to the vessels undergoing regeneration from the bottom nozzle. The effluent regeneration gas is subsequently cooled via a water-cooled heat exchanger before being routed to the regeneration gas separator. In the separator, condensed liquids are separated from the gas phase and subsequently routed to other units for further processing. In process scheme B, the regeneration gas source is the product dry gas. A slip stream is taken from the dry gas stream and is depressurized to the regeneration pressure conditions. The resulting gas temperature is then increased to the desired regeneration temperature. The regeneration gas then follows the same pathway as in process scheme A. Finally, the gas effluent of the separator is routed to a centrifugal compressor as a means of recycling the gas back to the wet gas inlet manifold.

Table 1 presents the composition and critical parameters of the feed and regeneration gas streams for both schemes. The major difference in the regeneration gas specifications of schemes A and B is the temperature of the regeneration gas. The gas pressure will be assumed to be equivalent for both cases and a fixed design input.


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(2)

(1)

Figure 1. Schematic description of the processes considered - Scheme A (1) and Scheme B (2)



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Table 1. Feed and regeneration gas specifications (compressibility factors were computed using the Peng Robinson equation of state.)

Category

Feed Gas

Regeneration Gas Process Scheme A

Process Scheme B

Pressure (bar)

69.3

23

23

Temperature (oC)

28

28

3.35

Compressibility Factor

0.82

0.95

0.95

Total Molar Flow (kmol h-1)

31,525 (632 MMSCFD)

Design Variable

Design Variable

Methane (Mole Fraction)

8.31E-01

8.31E-01

8.31E-01

Ethane (Mole Fraction)

8.73E-02

8.73E-02

8.73E-02

Propane (Mole Fraction)

4.22E-02

4.22E-02

4.22E-02

i-Butane (Mole Fraction)

8.31E-03

8.31E-03

8.31E-03

n-Butane (Mole Fraction)

1.57E-02

1.57E-02

1.57E-02

i-Pentane (Mole Fraction)

4.27E-03

4.27E-03

4.27E-03

n-Pentane (Mole Fraction)

3.93E-03

3.93E-03

3.93E-03

n-Hexane (Mole Fraction)

3.20E-03

3.20E-03

3.20E-03

Nitrogen (Mole Fraction)

3.19E-03

3.20E-03

3.20E-03

H2O (Mole Fraction)

7.05E-04

0

0

2.2 OPTIMIZATION FORMULATION The NPVC objective function is shown in equation (1) (definitions of symbols can be found in the Nomenclature section). It is consists of three components: the Total Capital Investment (TCI), the net present value of operating cost (OPEX), and the net present value of bed replacement costs (BED). The TCI is equal to the sum of the major equipment cost multiplied by


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the appropriate Lang factor. In this work, we have used a Lang factor of six.27 The cost of the vessels and the centrifugal compressor were obtained from Matches engineering company website (www.matches.com).28 The remaining TCI cost correlations are from Peters and Timmerhaus.27 For the case of scheme A, equation (1) is used to compute the process economics, excluding the components pertaining to the compression cost, namely Pcomp and PW. For scheme B, equation (1) is utilized as is. NPVC = 6 ⋅ (Pbed + Pv + PFHR + Pcomp + PHxC + PSep ) + 14444444244444443 TCI j

j

1+ r  (PW + PHDR + PCW ) inf  ∑ 1+ r  j =1 1 4444424444dis 43

 1 + rinf   + ∑ (Pbed ) 1 + r j = n* f dis  1444 42444 4 3

OPEX

BED

J

J

(1)

where,

(

[ (

Pv = ( N ads + N reg ) ⋅ − 1 .28 ⋅ 10 − 7 ρ v π D (L + Lint )th + πD 2 th

(

[ (

PSep = − 1 .28 ⋅ 10 − 7 ρ v πD (LSep + Lint )th + π D sep th

Pbed = Pads ⋅ (Nads + Nreg ) ⋅ ρc (1− εb )π

2

)]

2

[ (

)] + 1.024 ⋅ [ρ (πD (L 2

v

CEPCIcurrent 0.752⋅log( HDR)+2.29 10 CEPCI2002

PHxC =

CEPCIcurrent 0.11(log10 Ac )2 +0.17log10 Ac +3.3 10 CEPCI2002


)]

+ Lint )th + π D sep th + 77060 2

Sep

D2 L 4

PFHR =

)]

+ 1 .024 ⋅ ρ v πD (L + Lint )th + πD 2 th + 77060

)

)


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    Pfeed 5 W= Qreg RTenvi   2η   Penvi  

CregG , P

  

−1 CregG ,V C regG ,P C regG ,V

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   − 1   

(

)

Pcomp = −1.56⋅10−8W 2 + 0.5205⋅W + 94620

TregG

PHDR = PFG ⋅ HDR = PFG ⋅ Qreg ∫ CregG,P dT Tenvi

PW = 8760PEP B PCW = 8760QCW PWater

The cost of the separator (Psep) is computed as follows. The separator under design is assumed to be vertical. As such, the diameter of the vessel is governed by the settling velocity of a chosen liquid droplet size. The velocity of the gas in the separator must not exceed the settling velocity. A liquid droplet size of 125 µm is assumed to be the cut off target for separation.29 The separator length (Lsep) is computed by assuming a slenderness ratio of 3 (the ratio of the separator length to its diameter).29 The separator is a pressure vessel, therefore its cost is based upon its weight.

Eight decision variables and four process constraints are considered, as listed in Tables 2 and 3. The decision variables are: (i) the bed length (L), (ii) the vessel inside diameter (i.e. Bed Diameter D), (iii) the number of vessels undergoing adsorption (Nads), (iv) the number of vessels undergoing regeneration (Nreg), (v) the regeneration gas molar flow rate (Qreg), (vi) the regeneration temperature (Treg), (vii) the allocated time for regeneration (treg) (removal of contaminants from the bed at the regeneration temperature), and finally (viii) the allocated time for adsorption. The ranges of all the decision variables were chosen based on common industrial


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practice.30 The four constraints , following our previous work and the work of Manning and Thomspon,1, 17 are:

1) Breakthrough Constraint: The assigned adsorption time tads should not exceed the breakthrough time tads,max which is computed by solving the PDEs comprising the governing kinetic model.

2) Cycle Balance Constraint: The combined time for the whole regeneration cycle (i.e. bed heating, removal of contaminant, and bed cooling) must allow for continuous operation by ensuring the availability of a fully regenerated bed(s) to interchange operations with a saturated bed and begin adsorption. For the case when the number of beds undergoing adsorption and regeneration are equivalent (Nads=Nreg), the combined time for the regeneration cycle must not exceed the assigned adsorption time.

3) Regeneration Constraint: The allocated time for the regeneration treg should assure complete removal of contaminants from the bed by meeting or exceeding the minimum time required for regeneration treg,min. The latter is determined by solving the PDEs comprising the governing kinetic model.

4) Pressure Drop: The pressure drop across the bed during adsorption is constrained by the adjacent units’ pressure requirements and/or product gas specifications. Herein, Ergun equation is used in estimating the pressure drop across the bed.



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Table 2. Design variables Design Variable

Description

LB

UB

L

Length of the Bed (m)

0

70

D

Internal Vessel Diameter (m)

2

5

Nads

Number of Vessels undergoing adsorption. (Integer)

1

4

Nreg

Number of Vessels undergoing regeneration. (Integer)

1

4

Qreg

Molar flow of regeneration gas (kmol·h-1)

0

3500

TregG

Temperature of regeneration gas (oC)

Treg

550

treg

Allocated time for regeneration (h)

0

70

tads

Allocated time for adsorption (h)

0

70

Table 3. Governing constraints

Constraint Description

Mathematical Expression

Breakthrough constraint

t ads ≤ t ads , max

(2)


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N ads (t reg + t heating + t cooling ) (3) N reg

Cycle Balance

t ads ≥

Regeneration Constraint

treg ≥ treg,min (4)

Pressure Drop

∆ max

 150µ (1 − ε b )2 U f 1.75ρ f (1 − ε b )U f 2   (5) ≥ L + 2 3 3   R ε R ε 4 2 P b P b  

The number of vessels undergoing adsorption and regeneration are assumed to vary independently. This is taken into account by the introduction of the ratio of the adsorption vessels to the regeneration vessels (Nads/Nreg) in inequality (3). Moreover, the cooling time tcooling is defined as the time required to lower the bed temperature to a maximum of 10oC higher than the feed gas temperature. The minimization of the NPVC, equation (1), subject to the above constraints results in a MINLP.

2.3 KINETIC MODEL

The cycle timing constraints are directly linked to the governing kinetic model. We defined the breakthrough time tads,max to be the time at which the water concentration reaches 1 ppm in the outlet gas. The minimum regeneration time is defined as the minimum time required to reduce the adsorbate solid phase water concentration to 1E-06 of its saturation concentration. The kinetic model employed is from Ko and Moon work.31 The processed gas exhibits non-ideal behavior due to its high pressure. As such, the compressibility factor is introduced to account for the non-ideality. Furthermore, the following assumptions are invoked:



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a. Constant temperature, concentration, and pressure profiles in the radial direction (i.e. only axial and temporal variations are allowed).31 b. Langmuir adsorption isotherm model.31 c. The compressibility factor is independent of space or time. d. Water is the only adsorbing species. Based on these assumptions, the model comprises of the following equations: 1) Mole balance of water in the bulk phase is given by

∂C i ∂ (uC i ) 1 − ε b ∂qi * ∂ 2Ci + + = D z ,i ∂t ∂z ε b ∂t ∂z 2

(6)

Ci (t = 0,z ≠ zB ) = Ci,ini Ci (t,z = zB ) = CiBC uCi (t,z = zB ) = uCiBC − Dz,i

∂Ci ∂z

z=z B

2) The concentration corrected for non-ideal behavior is given by Ci =

yi P ZRT

(7)

3) The water dispersion coefficient is given by32

ε b Dz,i Dm,i

= 20+ 0.5ReSci (8)

4) The linear driving force expression due to Ko and Moon yields31

∂q*i = kmass,i (qi − q*i ) (9) ∂t

where kmass,i is given by31 14 ACS Paragon Plus Environment

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k mass ,i

 qi R = + P  y i k fi ρ f a b / P 5a b / P 

 1 1  + D  e ,i D mac ,i

   

−1

(10)

The kfi correlation due to Yang yields33 k fi =

0 . 357

εb

Re 0 .64 Sc i

033

D m ,i

D mac , i =

2RP

ε P D m ,i τ

(11 a,b)

6) The following energy balances hold: a) In the bulk phase, the energy balance is 1− εb a ∂ T ∂ (uT ) + + h s b / P  C fg ρ f  ε b ∂t ∂z

 − 4 hs  (T − T P ) = (T − T s ) D ε b C fg ρ f 

(12)

T(t, z = zB ) = TBC T(t = 0, z) = Tini

b) The energy balance in the solid sorbent is

a ∂TP 1 = hs b / P (T − TP ) − ∂t CP ρc CP ρc

Nu

∑ ∆H i i =1

∂qi* ∂t

(13)

c) The energy balance of the vessel steel is ∂ Ts a = h s b / P (T − Ts ) (14) ∂t C P ,v ρ v

d) The heat transfer coefficient is33

hs =

0.357

εb

Re0.64 Pr033

kth,g 2RP

(15)

e) The pressure dependency on axial dimension is modelled using the Ergun equation



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2 ∂ P 150 µ (1 − ε b ) u 1 .75 ρ f (1 − ε b )u − = + 2 3 3 ∂z 4RP ε b 2RPε b

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2

(16)

f) The equilibrium concentration is given by

 ∆H i  1   − 1  qis C i K i exp  R  TP Tref      qi =  ∆H i  1   − 1  C i 1 + K i exp  R  TP Tref     

(17)

2.4 OPTIMIZATION PROTOCOL

The NPVC objective function is discontinuous. This stems from the bed replacement term, which introduces cost at distinct points in the NPVC function. The period at which the bed must be replaced (f) is strongly dependent on the total cycle time and is given by

 N ⋅t  f = int R ads  (18)  4380  where the function int rounds the argument to the nearest integer. An infinitesimal increase in the adsorption time cycle tads can lead to a significant increase in the value of f due to the int function, hence leading to more frequent bed replacements over the course of the plant life. The optimization protocol utilized herein involves the two-step approach reported in our previous work. The first step is to recast the PDE model into a set of nonlinear algebraic equations.

Using the following protocol, the optimal solution for this set of equations is

determined and is used as the first approximation: 1) The adsorption step is assumed to be isothermal.


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2) To determine the breakthrough time, the equilibrium based analytical solution as described by Rhee, Aris and Amundson is utilized.25 An efficiency factor is introduced in order to account for mass transfer effects. The empirical form described by the expression (19) below was found to capture this deviation. Values of fitting parameters are available in Table S1 (See the Supporting Information). The regeneration step is modeled as a pure substance phase change. First, the bed and the vessel steel are heated to an experimentally determined regeneration temperature. Then, isothermal removal of the absorbed contaminants occurs. Finally the bed and the vessel steel are cooled down to the original operating temperature. X4

 L  X1 ⋅ X 2 ⋅ − X 3  ⋅ LX 5 U /ε   f b  (19) ζ = X4  L  1+ X 2 ⋅ − X3  U /ε  f b  

3) An analytical solution is used to compute the required heating and cooling times based upon energy balances where the lumped capacitance model is invoked. The regeneration time (i.e. the time at which the adsorbed contaminants are removed isothermally) is computed using the same approach described earlier for adsorption. 4) Instead of the adsorption time (tads) the bed replacement period f is utilized as an integer design variable. The upper and lower bounds for f are set to 3 and 15 years, respectively. This is in line with the general norms of a gas processing plant’s shut down frequencies. As a result, the optimization problem now includes two integer variables (f and N) with a narrow range of possible values. The original objective function remains unchanged. The governing constraints after this modification take the form:



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t ads ≤

min (K i ,ads ⋅ qis,ads )  ζ ads L  1 − ε b  1+ ρC (U f / ε b )  ε b 1 + K i ,ads CiF 

t reg ≥

 1− εb L 1 + ρ C max K i ,reg ⋅ qis,reg ζ reg (U reg / ε b )  εb

t ads ≥

N ads (t reg + t Heating + tCooling ) N reg

∆ max

(

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(22 a-g)

) 

 150 µ (1 − ε b )2 U f 1.75 ρ f (1 − ε b )U f 2   ≥ L + 2 3 3   ε ε 4 R 2 R P b P b  

[

]

LB ≤ L, N reg , N ads , D, Qreg , t reg , TregG , f ≤ UB 5) The MINLP is thus transformed into a set of multiple NLP sub-problems. These NLPs span all possible combinations of f and N. An SQP based algorithm coupled with a multistart subroutine that generates 100 random initial guesses is used to solve the NLPs. The resulting NLPs are solved using the fmincon Matlab™ function with the SQP option.

The solution is then used as an initial guess in the second step, during which the full-scale PDE model found in section 2.2 is optimized for the set of continuous variables. gPROMS™ version 4.0 CVB_SS optimization routine is used for the solution. The PDEs are discretized to 100 finite sections using fourth order central finite differences. The resulting system is integrated in time using the DASOLV solver.

3. RESULTS AND DISCUSSION

3.1 MODEL INPUTS

The adsorbent under study is zeolite 3A. During regular operations, the adsorbent capacity to dry natural gas deteriorates with time. This is caused by the numerous regeneration cycles the adsorbent undergoes. Once the capacity of the adsorbent reaches 50 % of its fresh capacity, the 18 ACS Paragon Plus Environment

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adsorbent should be replaced. In this work, we take the conservative approach and assume that the adsorbent capacity is 50% of its fresh feed capacity. A summary of the relevant zeolite 3A properties reported by Simo et al. are presented in Table S2 (See the Supporting Information).26 The economic and other auxiliary parameters are listed in Tables S3 and S4 (See the Supporting Information).

3.2 CASE STUDY - PRESSURE DROP IMPACT ON UNIT DESIGN AND COST

Among the constraints considered, the maximum allowable pressure drop across the dryers is the only constraint imposed on the system under study by external factors such as downstream unit requirements, the product specifications, and the overall plant economics. In this work we studied the impact of the pressure drop on the optimal design of the system as well as on the economics. Five different pressure drop values were used for both process schemes A and B (a total of ten cases). All cases were solved over an Intel™ i7 5600U processer clocked at 2.6 GHz. The average computational time for each case is in the order of two hours.

The results of the ten cases are presented in Figure 2, Tables 4 and 5. With respect to process economics, the NPVCs of Scheme A are lower compared to Scheme B with an average difference of ~6%. The operating cost of the system for both schemes is the major contributor to the process economics. In scheme B, a dehydrated slip stream is used for regeneration. After regeneration, the saturated gas is cooled and compressed prior to recycling back to the feed stream. This scheme introduces cost elements not present in scheme A, i.e. the compressor capital cost and the compression power cost. On the other hand, in Scheme B the regeneration gas temperature is substantially lower (3.4 oC vs. 28oC) than that of scheme A. This leads to a



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cost reduction in cooling, and compensates for the recompression cost. As a result, the two schemes show minor differences in the final NPVC value.

The optimization results show that longer absorption and regeneration cycles improve the economics of the process. As mentioned previously, the OPEX dominates the NPVC function. Larger adsorption beds allow for a longer adsorption cycle prior to breakthrough, resulting in a longer available time for regeneration. This leads to lower rates of regeneration energy supply and hence lower OPEX. Furthermore, the optimal NPVC shows a substantial increase (>10%) when the maximum allowable pressure drop is lowered from 100 kPa to 80 kPa. This is caused by an increase in the optimal number of vessels. Lowering the pressure drop from 100 kPa to 80 kPa requires increasing the vessel diameter beyond 5 m in order to accommodate the new constraint. Since the diameter upper bound is 5 m, the optimizer seeks the other option for decreasing the pressure drop; i.e. by increasing the number of vessels. Lowering the pressure drop beyond 80 kPa doesn’t lead to substantial change since the required increase in diameter is compensated by a decrease in the bed length which in turn maintains the mass of the adsorbent unchanged while still maintaining the diameter bounds.

Next, we analyze the optimal sets of design variables determined using the optimization protocol. The optimal values of the vessels’ internal diameter and length ranged between 4 to 5 m and 12 to 20 m respectively. For all of the studied cases, the lowest NPVC was found to occur at the upper boundary of the regeneration gas temperature (TregG). The regeneration gas temperature impacts the NPVC of the process through two unit operations: the regeneration gas heater and the regeneration gas cooler. High regeneration gas temperatures lead to faster regeneration and thus a lower regeneration gas flow rate. Decreasing the regeneration gas flow


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rate (Qreg) leads to a direct decrease in the cost of all the unit operations with the exception of the adsorption vessels in scheme A (not impacted). As such, the optimizer will always seek the highest possible regeneration temperature assuming that thermal impact on construction material or on the adsorbent life is not limiting.

Figure 2. Optimal cost figures for process scheme A (A) and process scheme B (B) at varying maximum allowable pressure drops.



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Table 4. Suggested sets of optimal design variables for process scheme A.

Process Scheme A P. drop. (kPa)

100

80

60

40

20

L (m)

15.65

18.57

17.04

15.10

12.27

D (m)

5.08

4.06

4.26

4.56

5.14

1146.46

1092.61

1089.98

1081.05

1047.10

350

350

350

350

350

f (yr)

8

14

14

14

14

tads (h)

35.04

61.32

61.32

61.32

61.32

Nads

1

2

2

2

2

Nreg

1

2

2

2

2

Qreg (kmol·h-1) Treg (oC)

NPVC ($)

3.11E+07 3.45E+07 3.46E+07 3.45E+07 3.44E+07


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Table 5. Suggested sets of optimal design variables for process scheme B.

Process Scheme B P. drop. (kPa)

100

80

60

40

20

L (m)

20.47

19.15

17.58

15.58

12.66

D (m)

4.00

4.15

4.36

4.67

4.29

789.89

776.58

761.60

760.18

774.51

350

350

350

350

350

15

15

15

15

15

Qreg (kmol·h-1) Treg (oC) f (yr) tads (h)

65.70 65.70

65.70

65.70

65.70

Nads

2

2

2

2

3

Nreg

2

2

2

2

3

NPVC ($)

3.60E+07 3.57E+07 3.54E+07 3.55E+07 3.76E+07

Furthermore, the optimization results show that the lowest NPVC values are ensued when the number of vessels undergoing adsorption is equal to the number of vessels undergoing regeneration (i.e. Nads = Nreg). For a given feed gas flow rate, decreasing the number of regeneration vessels leads to a decrease in the total capital investment (TCI). On the contrary, the required regeneration gas flowrate has to increase to compensate for the decrease in available time for regeneration and efficiencies losses ( ζ reg ). As a consequence, this leads to an increase 23 ACS Paragon Plus Environment


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in OPEX and TCI (via capacity increase in the compressor, fire gas heater, separator, and water cooler). The latter factor dominates the economics and hence forces the optimizer towards increasing the number of regenerating vessels. Due to the cyclical and interchanging nature of the vessels’ operation, increasing the number of regeneration vessels beyond the number of adsorbing vessels does not lead to any cost advantage. As such the optimal NPV is achieved when Nads = Nreg. Finally, we compare the optimized results with the conventional design approach proposed by Manning and Thompson.1 An adsorption cycle time of 8 hours is assumed in the Manning and Thompson approach. The comparison is made based upon Scheme B since it is the more common industrially. A sample calculation using the conventional approach is presented by Manning and Thompson.1 Figure 3 presents a comparison of the two methods for process scheme B. Substantial reductions in NPVC (up to 36%) are realized in the optimization approach, especially

at lower pressure drops (60-20 kPa). The savings arises from major

reductions in the OPEX and BED cost contributions.


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Figure 3. Optimal cost figures (O) vs. Manning and Thompson design (C) for process scheme B at varying allowable pressure drop.

4. CONCLUSIONS

This paper proposed an optimization-based framework for the optimal design of natural gas, adsorption based drying systems the optimization approach followed overcomes challenges arising due to the cyclic nature of the process and discontinuities of the objective function. The computed optimal cost figures of the process schemes considered suggest that the NPVC and OPEX range from 4.5 to 5.4 $/MMSCF and 2.4 to 2.9 $/MMSCF respectively. Compared with the conventional design approach proposed by Manning and Thompson, substantial reductions in the NPVC are documented (up to 36%) due to reductions in the OPEX and BED contributions. These results were obtained under the conservative assumption that the adsorbent capacity was 25 ACS Paragon Plus Environment


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equal to 50% of its fresh capacity. The incorporation of the dynamics of the adsorbent capacity and its variation upon successive regeneration cycles can allow for further optimization of the design and reduction of the overall cost. This work will be pursued in the near future.

NOMENCLATURE ab / P

Outer surface area of sorbent pellets per unit volume of bed

Ac

Heat transfer area of the water cooling exchanger

B

Conversion factor

BED

Net present worth of bed replacement costs in $

CEPCI

Chemical Engineering Plant Cost Index

Cfg

Constant volume heat capacity of gas used in PDE model (feed gas during adsorption, and regeneration gas during regeneration)

Ci

Concentration of species i in the bulk phase

Ci,ini

Initial concentration of species i within the bed

CiBC

Concentration of species i at the boundary

CiF

Concentration of species i in the feed gas

Cp

Heat capacity of the adsorbent

CP,v

Heat capacity of vessel steel

CregG,P

Constant pressure heat capacity of regeneration gas

CregG,V

Constant volume heat capacity of regeneration gas

D

Bed diameter

De,i

Average diffusion coefficient of species i within the pellet excluding macropore

Dm,i

Gas phase diffusion coefficient of species i

Dmac,i

Diffusion coefficient of species i within the macropore

Dsep

Internal diameter of the Separator

Dz,i

Dispersion coefficient of species i in the axial direction

f

Period of bed replacement in years

HDR

Heating duty for regeneration gas

hs

Heat transfer coefficient 26 ACS Paragon Plus Environment

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J

Plant life-time in years

j

Index running in expression (1) from 1 to J

kfi

Film mass transfer coefficient for species i

Ki

Equilibrium constant of species i. Subscripts (ads) for adsorption and (reg) for regeneration

kmass,i

Overall mass transfer coefficient for species i

kth,g

Thermal conductivity of gas phase

L

Bed length

Lint

Vessel length dedicated for internals

Lsep

Seam to Seam length of the Separator

Nads

Number of vessels undergoing adsorption

Nreg

Number of vessels undergoing regeneration

NPVC

Net Present Value of Costs

NR

Number of regeneration cycles after which bed replacement is due

OPEX

Net present worth of operating costs

P

Pressure in the PDE model

Pads

Adsorbent price in $·kg-1

Pbed

Cost of the adsorbent bed

PComp

Cost of the compressor,

PCW

Cost of water coolant in $ year -1 basis

PDE

Partial Differential Equation model

Penvi

Pressure of the regeneration gas

PEP

Price of electrical power

PFG

Price of Fuel gas

PFHR

Cost of the regeneration gas heater

PHDR

Cost of the regeneration heater duty in $·year-1 basis

PHxC

Cost of the water cooling exchanger

Pr

Prandtle number

PSep

Cost of the separator

Pv

Cost of the adsorbent vessels 27 ACS Paragon Plus Environment


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Pv,hyd

Cost of the hydrogenation reactor vessel

PW

Cost of the compressor duty in $·year -1 basis

Pwater

Cost of cooling water in $·m-3

QCW

Volumetric flowrate of cooling water in m3·h-1

qi

Equilibrium concentration of the adsorbed phase in mole·m-3 solid

qi *

Concentration of adsorbed phase in mole·m-3 solid

qis

Saturation capacity of the sorbent towards species i. Subscripts (ads) for adsorption and (reg) for regeneration

Qreg

Regeneration gas molar flow in kmol·h-1

R

Universal gas constant

rdis

Discounting rate

Re

Particle based Reynolds number

rinf

Inflation rate

Rp

Pellet radius

Sci

Schmidt number of species i

t

Time

T

Temperature in bulk phase in the PDE model

tads

Assigned time for adsorption step

tads,max

Breakthrough time computed based on kinetic simulation

TBC

Temperature boundary condition in bulk phase energy balance

TCI

Total Capital Investment

tcooling

Required time for cooling the bed and the vessel from regeneration temperature to adsorption temperature

Tenvi

Inlet Temperature of the regeneration gas to the feed gas heater

Tfeed

Temperature of feed gas

th

Vessel thickness

theating

Required time in h-1 for heating the bed and the vessel to the regeneration temperature

Tini

Initial temperature of the bed

Tp

Temperature of adsorbent pellet


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Tref

Reference temperature used in equilibrium constant temperature dependency expression

treg

Assigned time for regeneration step

TregG

Regeneration gas temperature

treg,min

Minimum regeneration time computed based on kinetic simulation

Ts

Temperature of vessel steel

u

Interstitial velocity of the fluid

Uf

Fluid superficial velocity

X1

Constant used in efficiency factor correlation, expression (18)

X2


X3


X4


X5


yi

Mole-fraction of species i

Z

Compressibility factor

z

Axial dimension

zB

Axial dimension at which the boundary condition applies. For adsorption zB=0 , for regeneration zB = L.

Greek ∆Hi

Heat of adsorption of species i

∆max

Maximum allowable pressure drop

εb

Bed Porosity

εP

Pellet porosity

ζ

Efficiency factor accounting for mass transfer in adsorption or regeneration steps. Subscripts (ads) for adsorption and (reg) for regeneration

η

Compression adiabatic efficiency

µ

Gas viscosity (for feed gas during adsorption and for the regeneration gas during regeneration)

ρc

adsorbent density



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ρf

Gas density (for feed gas during adsorption and for the regeneration gas during regeneration)

ρv

Steel density

τ

Tortuosity

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ACKNOWLEDGMENT The authors would like to acknowledge the financial support of the Gas Sub-Committee R&D arm of Abu Dhabi National Oil Company United Arab Emirates.

SUPPORTING INFORMATION List of adsorbent specifications, economic and auxiliary parameters are available in the Supporting information section. This information is available free of charge via the Internet at http://pubs.acs.org/.

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Al Wahedi, Y.; Torres, A. I.; Al Hashimi, S.; Dowling, N. I.; Daoutidis, P.; Tsapatsis, M., Economic assessment of Temperature Swing Adsorption systems as Claus Tail Gas Clean Up Units. Chemical Engineering Science 2015, 126, 186-195.

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Schematic description of the processes considered - Scheme A (1) and Scheme B (2). 208x269mm (300 x 300 DPI)

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Schematic description of the processes considered - Scheme A (1) and Scheme B (2). 218x268mm (300 x 300 DPI)



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Optimal cost figures for process scheme A (A) and process scheme B (B) at varying maximum allowable pressure drops. 451x290mm (300 x 300 DPI)


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Optimal cost figures (O) vs. Manning and Thompson design (C) for process scheme B at varying allowable pressure drop. 451x352mm (300 x 300 DPI)



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Graphical Table of Content 28x10mm (300 x 300 DPI)


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Optimization of Adsorption-Based Natural Gas Dryers - ACS Publications

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