Modeling, simulation and economic analysis of CO2 capture from natural gas using cocurrent, countercurrent and radial crossflow hollow fiber membrane

International Journal of Greenhouse Gas Control 36 (2015) 114–134

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International Journal of Greenhouse Gas Control journal homepage: www.elsevier.com/locate/ijggc

Modeling, simulation and economic analysis of CO2 capture from natural gas using cocurrent, countercurrent and radial crossflow hollow fiber membrane S.S.M. Lock a , K.K. Lau a,∗ , Faizan Ahmad b,c , A.M. Shariff a a

Chemical Engineering Department, Universiti Teknologi PETRONAS, Bandar Sri Iskandar, 31750 Perak, Malaysia Department of Chemical Engineering, COMSATS Institute of Information Technology, Lahore, Pakistan c Process Systems Design and Control Lab, School of Chemical Engineering, Yeungnam University, Republic of Korea b

a r t i c l e

i n f o

Article history: Received 8 August 2014 Received in revised form 18 December 2014 Accepted 4 February 2015 Keywords: Hollow fiber membrane Process simulation CO2 Radial crossflow Countercurrent Cocurrent

a b s t r a c t A mathematical model has been developed to characterize the multi-component CO2 capture from natural gas adapting hollow fiber membrane module for the radial crossflow, countercurrent and cocurrent flow. The solution procedure can also be incorporated in a versatile manner within the Aspen HYSYS process simulator to constitute the entire CO2 /natural gas separation plant in order to assist in the process design and optimization. The study of the separation performance and process economics of the different flow mechanisms has been conducted along with parameter sensitivity of typical membrane selectivity and CO2 feed composition in industrial application. Based on the study’s findings, ideally the countercurrent configuration exhibits a slightly higher separative performance in comparison to the radial crossflow, while both being superior to the cocurrent. It is also found that flow with the most effective separative performance is not always the most economical. Under circumstances of excessive permeation, it can lead to extra membrane area, auxiliary equipment power and hydrocarbon lost that increase the gas processing cost. Therefore, a tradeoff must be determined among these parameters to determine the optimal flow configuration for efficient CO2 removal under different operating conditions. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction The ever-growing worldwide energy demand has directed the attention of energy companies toward uncovering contaminated natural gas reservoirs with high CO2 content to circumvent the volatility of fuel price in petrochemical market while meeting user demand (Dana and Yepez-Garcia, 2012; Rezaei et al., 2014). On the other hand, the International Energy Outlook 2013 (IEO, 2013) reference case reported that the world energy-related CO2 emissions are forecasted to increase from 31 billion metric tons in 2010 to 36 billion metric tons in 2020 and 45 billion metric tons in 2035, following the trend of more countries becoming industrialized (United-States-Energy-Information-Administration, 2013). Increment in CO2 emission as the largest contributor to global warming have urged continuous pressure on oil and gas companies to adopt practices that reduce carbon footprint in natural gas processing to mitigate the effect of climate change (Gnanendran and Hart, 2009). Aside from contributing to atmospheric pollution, the presence

∗ Corresponding author. Tel.: +60 53687589; fax: +60 53656176. E-mail address: [email protected] (K.K. Lau). http://dx.doi.org/10.1016/j.ijggc.2015.02.014 1750-5836/© 2015 Elsevier Ltd. All rights reserved.

of CO2 also reduces the heating value and causes the natural gas stream to be acidic and corrosive, which in turn minimizes the likelihood of gas compression and transportation (Zhang et al., 2013). Hence, pipeline specification for CO2 in natural gas has been enforced to be below 2%, which emphasizes the requirement of CO2 capture in this industrial application (Baker and Lokhandwala, 2008). Several techniques have been adapted for CO2 capture, such as chemical and physical absorption, cryogenics and membrane separation (He and Hagg, 2014). Among the available separation technologies, membrane based gas separation is an emerging process for CO2 separation from natural gas, ascribed to its various advantages, e.g., occupying a relatively smaller footprint, chemical free, cost effective, high process flexibility and high energy efficiency, in comparison to the conventional gas separation technologies (Hyun et al., 2011; Marriot and Sorensen, 2003). This enables efficient utilization of floor space, which is especially vital for offshore natural gas platform and remote location that have confined footprint for large unit operation and high CO2 composition (Rezaei et al., 2014). The membrane separation process also produces a highly concentrated CO2 permeate stream, which could be pumped deep underground through sequestration as a feasible

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Nomenclature List of symbols Af cross section area of fiber Am area of permeation for one cell Amodule cross section area of membrane module compressor cost CC CH4 LS cost of hydrocarbon lost in the permeate stream CRC capital related cost inner diameter of the hollow fiber di do outer diameter of the hollow fiber GPC gas processing cost L active length of the fiber bundle number of fibers nf PF feed pressure ph pressure on the shell side pl pressure on the tube side Qn mix gas permeance of each component in the feed permeate pressure Pp V˙ F feed flow rate V˙ s [i, j] shell side flow rate for the radial crossflow cell V˙ s [j] shell side flow rate for the countercurrent and cocurrent flow cell V˙ T [i, j] tube side flow rate for the radial crossflow cell tube side flow rate for the countercurrent and cocurV˙ T [j] rent flow cell r radius distance from the center of the fiber bundle R radius of the fiber bundle sum summation of all components composition in the tube side VOM variable operating and maintenance cost zF,n feed composition of each component xS,n [i, j] shell side composition for the radial crossflow cell xS,n [j] shell side composition for the countercurrent and cocurrent flow cell yT,n [i, j] tube side composition for the radial crossflow cell tube side composition for the countercurrent and yT,n [j] cocurrent flow cell Greek symbols ˇ ratio of the pressure on the shell side to the pressure on the tube side ı difference between the check conditions with the datum Q flow rate that permeates through the membrane thickness of cell in the radial direction r z thickness of cell in the axial direction ε porosity convergence criteria ∈ ∅ packing factor * local stage cut of each cell viscosity ω

alternative to treat the greenhouse gas emission (Zhang et al., 2013). The hollow fiber membrane module is finding a relatively widespread application since it has the ability to pack the largest effective membrane area for separation through the adaptation of many fine, tubular fibers within a bundle (Katoh et al., 2011). Since the membrane based gas separation is a recently emerged technology as compared to the conventional separation processes, mathematical modeling becomes an indispensable tool in the design process of the natural gas plant for CO2 separation. The availability of reliable mathematical models to predict the performance of the natural gas permeation system minimizes the technical risks

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that are inherent in the design of the new process (Ahmad and Lau, 2007; Makaruk and Harasek, 2009). In addition, it also eliminates the need of the time consuming and costly pilot plant and experimental studies to evaluate the operating conditions and membrane specification in order to optimize the natural gas sweetening plant. The vitality of mathematical modeling to characterize membrane permeation process has urged various modeling efforts with a long history adapting different methodologies. The major development of the methodology used to describe the gas separation process within the hollow fiber membrane module is summarized in Table 1 (Chen et al., 1994; Chowdhury et al., 2005; Coker et al., 1998; Makaruk and Harasek, 2009; Marriot and Sorensen, 2003; Pan, 1986; Pettersen and Lien, 1999; Thundyil and Koros, 1997). Mathematical modeling of hollow fiber membrane module that deals with different flow configurations (e.g. radial crossflow, countercurrent and cocurrent) has been regarded as an important application because commercial gas separation hollow fiber membrane module is operated in one of the mentioned flow configurations, depending on the way the feed is introduced to the module and the hollow fiber bundle geometries (Thundyil and Koros, 1997). Pan (1986) compared the separation performance of the co- and countercurrent flow configurations based on the assumption of crossflow mass transfer transport mechanism adapting the solution method for differential equations. Sengupta and Sirkar (1987) revised the mathematical model by Pan (1986) to describe the co- and countercurrent flow configurations by simplifying the solution algorithm but confined to merely a ternary gas mixture application. Sidhoum et al. (1988) compared the performance of the mathematical model between the initial crossflow formulation proposed by Pan (1986) and revised equations that took into consideration the effect of bulk flow configurations for both the co- and countercurrent hollow fiber membrane adapting the forth-order Runge Kutta numerical technique. Similarly, Donatelli (1991) developed a mathematical model based on mass balance differential equations proposed by Sidhoum et al. (1988) to characterize the cocurrent, countercurrent and crossflow hollow fiber membrane for multiple stages. The work by Sidhoum et al. (1988) and Donatelli (1991) highlighted that the assumption of crossflow to characterize all flow configurations might not be necessary since their revised models provide a better characterization of the actual experimental data. However, their solution algorithm was rather cumbersome and was limited to the binary gas separation. Coker et al. (1998) revised the differential equations solution procedure proposed by Pan (1986) based on the staged wise approach as described in Table 1 to simplify and to reduce the computational time for their co- and countercurrent membrane contactors with introduction of sweep gas. Makaruk and Harasek (2009) further extended the model to incorporate the co-, counter- and crossflow hollow fiber membrane based on the succession of states coupled with Gauss–Siedel methodology for multistage system with recycling. In all studies, they reported that the countercurrent flow mechanism would theoretically exhibit a higher separative performance than its counterpart. Based on review of the published literatures, the succession of states approach is an advanteagous numerical solution to describe the hollow fiber membrane system attributed to the fact that it can be easily implemented. The methodology merely reduces the membrane area into a succession of compartments with constant driving force, whereby the inlet conditions to which are clearly specific, and consequently the outlet conditions from the compartment can be conveniently obtained adapting mass transfer numerical solution (Thundyil and Koros, 1997). The simplicity of the methodology not only ensures stability and convergence of the algorithm, but also enables non-ideal effects to be implemented conveniently in conjunction with the mass balance equations. At current, the succession of states method has been applied in mathematical

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Table 1 Summary of major development in methodology adapted to characterize the separation performance of hollow fiber membrane module. Published literature

Study domain

Research gap

Pan (1986)

-Mathematical modeling of multi-component high-flux, asymmetric hollow fiber membranes by formulating numerical integration of governing differential equations over relevant boundary conditions. -Proposed that all gas separation performances can be approximated by the cross-flow regardless of the bulk flow configuration.

-Instability when solving the differential equations.

-Shortcoming in predicting higher stage cuts due to the assumption of negligible bulk flow configuration (Makaruk and Harasek, 2009).

Thundyil and Koros (1997)

-Succession of states method to characterize the mass balance of radial crossflow, countercurrent and cocurrent flow configurations by dividing the hollow fiber membrane into many finite elements.

-The equations presented were merely confined to the binary system separation.

Coker et al. (1998)

-Mathematical modeling of the multi-component hollow fiber membrane contactors for longitudinal flow adapting the stage wised approach to transform the conservation differential mass balance equations to a first order finite difference solution procedure.

-Required the conservation equations to be fitted into the form of a tri-diagonal matrix and to be solved simultaneously using the complicated Thomas algorithm. -Validation of the method and sensitivity of the technique to initial estimates were not provided (Makaruk and Harasek, 2009).

Chen et al. (1994), Pettersen and Lien (1999)

-Averaging method by using the logarithmic mean pressure driving force to describe the countercurrent hollow fiber module performance.

-Accuracy of the method was only in good agreement with the exact solution at lower stage cuts.

Marriot and Sorensen (2003)

-Develop rigorous mass, momentum and energy balances to characterize the system, which were solved simultaneously using the orthogonal collocation method.

-Required the knowledge of diffusion and dispersion coefficients in the fluid phase, which was not readily available at the initial stage of design process (Chowdhury et al., 2005).

modeling of hollow fiber membrane, such as work by Thundyil and Koros (1997) and Makaruk and Harasek (2009), by assuming that all the cells exhibit the same crossflow mass transfer behavior as proposed by Pan (1986). However, it has been demonstrated in experimental observations that the bulk flow configuration is an important parameter to characterize the mass transfer driving force rather than assumption of the crossflow model (Feng et al., 1999; Giglia et al., 1991; Narinsky, 1991). This implies that a more comprehensive study is required to describe the succession of states mathematical model with consideration of flow configurations effect since the computational approaches for (1) the state with feed on only the shell side and (2) the state with feed on both shell and tube sides are considerably different than that of pure crossflow assumption model that is applicable to all cells throughout the module. In addition, a review of the published literature indicated that most of the hollow fiber membrane mathematical models are confined to charactering the longitudinal flow mechanisms along the axial direction (e.g. cocurrent, countercurrent and crossflow) (Marriot and Sorensen, 2003). Nonetheless, this assumption is not valid for the radial crossflow configuration, which must be characterized in a two dimensional approach along the radial and axial directions (Marriot and Sorensen, 2003; Thundyil and Koros, 1997). In the shell side feed radial crossflow hollow fiber membrane, the feed gas flows radially inward perpendicular to the hollow fibers to be collected within a perforated pipe located in the center of the membrane bundle. In addition to fluid distribution along the radial direction attributed to driving force to the center perforated pipe, the feed gas also follows the path along the hollow fiber in the axial direction since it constitutes a small resistance to flow. Hence, by nature of the radial crossflow configuration, the flow rates and compositions of the shell and tube sides vary axially and radially (Marriot and Sorensen, 2003; Thundyil and Koros, 1997). In previous work, mathematical modeling of the one dimension crossflow configuration has been discussed and thought of representative of the radial crossflow behavior (Lock et al., 2014b; Thundyil and Koros, 1997). Nonetheless, a distinction must be drawn between the radial crossflow membrane, which refers to the radial bulk flow

with respect to the membrane for permeation as described in published literature by Thundyil and Koros (1997) and Marriot and Sorensen (2003); and the one dimension crossflow pattern, which refers to the flow of feed gas parallel to, and of permeate gas flowing perpendicular to the active layer of the membrane as described in published work by Sridhar et al. (2006). Ho and Sirkar (1992) proposed analytically that the countercurrent hollow fiber membrane would always outperform the radial crossflow and cocurrent based on their partial pressure distribution profile. Thundyil and Koros (1997) pioneered the mathematical modeling that considered the radial crossflow, countercurrent and cocurrent to compare the separation performance of the flow mechanisms based on product quality. However, the analysis is confined to only the separation efficiency of the flow patterns without further consideration of process economics and is limited to only the ideal binary system. Marriot and Sorensen (2003) also modeled the radial crossflow, countercurrent and cocurrent flow configurations adapting the high complexity methodology as discussed in Table 1. Nevertheless, no further discussion and analysis was provided to compare their separation efficiency quantitatively. Previously, we proposed a mathematical model applicable to the two dimensional radial crossflow hollow fiber membrane for a multi-component gas separation (Lock et al., 2014b), and compared the model prediction with that of Thundyil and Koros (1997) work. The comparison has been conducted to verify the validity of the binary assumption as compared to the real multi-component mathematical model and to characterize the difference between the two mathematical models quantitatively through the membrane area requirement. Nonetheless, since the study was an initial step to elucidate the importance of the multi-component mathematical model, idealistic assumptions, such as single stage and isobaric condition, have been adapted throughout the membrane module. Moreover, as highlighted in the review of published literature previously, the studies to compare the flow configurations are mostly confined to mere separation efficiency without further consideration of process economic, which is an important parameter for development of commercial hollow fiber membrane system. In this context, incorporation of mathematical models

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within industrial process simulator is deemed important since it allows combination of the membrane unit with other unit operations already implemented in the process simulators (e.g. heat exchanger and compressor) to constitute the entire process flow in order to determine the natural gas processing cost of the plant (Ahmad et al., 2012; Rautenbach et al., 1996). In addition, it also allows for utilization of the physical properties and thermodynamic databases of the process simulators for determination of utility cost (Rautenbach et al., 1996). Most importantly, the incorporation enables membrane system with recycling to be simulated because stages of modules arrange in parallel or series arrangement without recycle stream constitute a single stage membrane separation process, which constraints the applicability of the simulation model in industrial application (Lock et al., 2015). From the review of the published literature, Aspen HYSYS is found to be one of the favorable process simulators for modeling, simulation and process economics study of membrane separation processes because it provides a component based framework that can be easily customized, updated and maintained to meet changing user requirements (HYSYS, 2010). Aspen HYSYS also allows convenient adaptation of its intrinsic capabilities for calculation of material and energy balances for prediction of physical and thermodynamic properties, which are highly essential for optimization of process economics (Davis, 2002). A user-defined membrane model can be implemented along with the Aspen HYSYS solution procedure adapting the Visual Basic (VB) or C++ subroutine (Ahmad et al., 2013). Hussain and Hagg (2010) implemented a one dimension hollow fiber membrane model in Aspen HYSYS for the feasibility study of CO2 capture by comparing the process economics of several process configurations. Peters et al. (2011) performed a simulation analysis interfaced within Aspen HYSYS to compare the performance and economics of an amine absorption process and a simple membrane unit. He et al. (2009) and He and Hagg (2014) also adapted the Aspen HYSYS process simulator with integration of ChemBrane to evaluate the techno-economic feasibility of their respective membrane systems associated to hollow fiber carbon membranes and fixed site carrier membranes. Previously, we also developed a two dimensional crossflow hollow fiber membrane model in Aspen HYSYS confined to binary CO2 /methane separation (Ahmad et al., 2012, 2013). Nevertheless, incorporation of a multi-component hollow fiber membrane model that is capable of catering different flow configurations for industry economic feasibility analysis has not yet been conducted. In this work, a hollow fiber membrane model is developed to characterize the radial crossflow, countercurrent and cocurrent flow based on a revised succession of states methodology based on earlier work by Thundyil and Koros (1997) that has been confined to the ideal binary gas separation system. The simplified methodology is required for further implementation within Aspen HYSYS as a user defined unit operation using Visual Basic (VB) subroutine to simulate the actual natural gas sweetening plant with other auxiliary unit operations. The multi-component system is simulated to study CO2 capture from natural gas that contains many components such as methane, heavy hydrocarbons (e.g. ethane, propane and butane), acid gases (e.g. CO2 ) and inert gases (e.g. N2 ). The paper also demonstrates the case study of CO2 removal from natural gas through adaptation of hollow fiber membrane module to compare the performance of different flow configurations based on their separation efficiency and process economics. The novelty of current work is highlighted from two standpoints, whereby (1) the developed mathematical model, unlike previous work that adapted the assumption of crossflow model throughout the entire membrane module, has incorporated the effect of bulk flow pattern to the permeation rates from a one dimensional perspective for the longitudinal flow (co- and countercurrent) and two dimensional analysis for the radial crossflow (2) the developed mathematical

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Boundary Conditions Required for Numerical Solution Initialization of problem

Succession of States Algorithm Loop over Single Cell Computation of composition

Computation of flow rates

Computation of tube side permeate pressure

Convergence

Incorporate within Aspen HYSYS process simulator as a user defined unit operation

Results Fig. 1. Overall solution procedure for the hollow fiber membrane module simulation.

model has been incorporated within the Aspen HYSYS process simulator to cater the research gap of previous published literature that has been limited to merely one flow mechanism in order to compare the separation efficiency and process economics of the different flow configurations. 2. Methodology The methodology adapted in this work is categorized into the discussion of the mathematical modeling and the simulation methodology. The mathematical model is developed based on the solution algorithm as presented by the overall workflow in Fig. 1. 2.1. Mathematical modeling (succession of states methodology) The succession of states methodology involves reducing the problem into a number of cells, in which the mass transfer is assumed to be constant at each cell. Each cell is independent of one another. The outlet condition of the cell is computed based on the specified inlet condition provided and will be the inlet condition of the subsequent cell. Therefore, from one cell, the computation proceeds to the next and is completed over the entire membrane module. Thundyil and Koros (1997) highlighted that the countercurrent and cocurrent flow can be sufficiently described using the one dimension approach along the axial direction since the characteristic of the fibers in the radial direction can be assumed to be the same. However, the radial crossflow must be characterized using the two

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dimensions approach since the shell side composition, tube side composition, shell side flow rate and tube side flow rate vary along both the axial and radial directions attributed to the nature of the flow mechanism as described earlier (Marriot and Sorensen, 2003; Thundyil and Koros, 1997). Therefore, for the longitudinal flow configuration (countercurrent and cocurrent) hollow fiber membrane module, it is divided into cells in the axial direction (denoted by index j); while for the radial crossflow configuration, the membrane module is divided into cells in both the radial (denoted by index i) and the axial (denoted by index j) directions. In addition, the membrane bundle specifications are provided by the end user to determine the active membrane area of each cell based on the predetermined number of cells (x in the axial direction, y in the radial direction). The active membrane area of each cell is dependent upon the flow configurations that impact its shape and dimension. To characterize the multi-component separation within the hollow fiber membrane module, the following input variables are required for calculation of the mass balance and transport mechanism equations from one cell to the subsequent cell: (a) Membrane characteristics: mix gas permeance of each component in the feed, Qn (b) Feed gas characteristics: i. Feed composition, zF,n ii. Feed pressure, PF iii. Feed flow rate, V˙ F (c) Permeate gas characteristics: permeate pressure, Pp (d) Membrane module characteristics: i. ii. iii. iv.

Active length of the fiber bundle, L Radius of the fiber bundle, R Inner and outer diameter of the hollow fibers, di and do Packing factor, ∅, or porosity, ε, or number of fibers, nf , of the membrane module. Packing factor is defined as the fraction of the area occupied by fibers over the entire cross sectional area of the fiber bundle, while porosity is defined as the fraction not made up by fibers. The packing factor, porosity and number of fibers are related to one another, as depicted in Eq. (1) (Li et al., 2004).

∅ = 1 − ε = nf

Af Amodule

= nf

do2 (2R)2

(1)

Several assumptions have been outlined when developing the mathematical model to simplify the modeling approach, such as the following: i. The model assumes no mixing in the tube and shell sides and can be sufficiently described by plug flow. Therefore, the mass balance of each cell can be solved independently provided the previous cell state is known (Ahmad et al., 2012, 2013; Pan, 1986; Pan and Habgood, 1974; Stern and Walawender, 1969; Thundyil and Koros, 1997). ii. All fibers within the bundle are assumed to assemble the same characteristics. Thus, all fibers have uniform outer and inner diameter, and the thickness of the selective membrane area is also constant throughout (Chern et al., 1985; Marriot and Sorensen, 2003; Soni et al., 2009). iii. The shell side pressure variations are negligible due to continuous bulk flow in the axial direction (Coker et al., 1998; Noble and Stern, 1996; Pan, 1986; Thundyil and Koros, 1997). The permeate side pressure drop is attributed to the vicious friction (Antonson et al., 1977; Chern et al., 1985; Sidhoum et al., 1988) within the narrow channel of the hollow fibers lumen and can be adequately described using the Hagen–Poiseuille

Fig. 2. Schematic representation of (a) radial crossflow hollow fiber membrane module and (b) cells within the two dimensions succession of states methodology for mathematical modeling.

equation (Ahmad and Lau, 2007; Ahmad et al., 2013; Coker et al., 1998; Davis, 2002; Pan, 1986; Thundyil and Koros, 1997). The Hagen–Poiseuille expression has been demonstrated in published literature to be rather eligible to govern the tube side pressure drop with some reasonable assumptions within the hollow fiber membrane module such as laminar flow, ideal gas since the gas is at a considerably low pressure as well as vicious and incompressible gas flow in an impermeable tube (Shao and Huang, 2006). iv. Operation within the hollow fiber membrane module is isothermal (Chowdhury et al., 2005; Davis, 2002; Pan, 1986; Tessendorf et al., 1996; Thundyil and Koros, 1997).

2.1.1. Radial crossflow configuration The mathematical modeling of the radial crossflow configuration is provided in this section. It is subdivided into the discussion of the succession of states methodology that involves computation describing mass balance from one cell to the subsequent cell, and transport mechanism within each individual cell. Fig. 2(a) depicts the schematic representation of the radial crossflow hollow fiber membrane module with the feed introduced through the shell side. The feed stream flows radially inward perpendicular to the hollow fibers toward the center from the outside of the fiber bundle. The end of the fiber bundle near the feed gas is sealed using epoxy resin glue while the other end allows the fibers to protrude through the seal to enable the permeate stream to exit the membrane module. The retentate stream is accumulated in a perforated pipe located at the center of the module. Fig. 2(b) describes the schematic representation of the two dimensions succession of states approach to characterize the mass balance of the radial crossflow hollow fiber membrane module, in which the membrane module is divided into many predetermined finite cells in both the radial and axial directions.

2.1.1.1. Succession of states in radial crossflow configuration. The area calculation of each membrane module cell as described in Fig. 2(b) has been adapted from Thundyil and Koros (1997) and Rautenbach (1990) work. The ratio of the active area for permeation, Am , to the cell volume, V, is based on the packing fraction of the hollow fibers in the membrane bundle, 1 − ε, and the specification of the hollow fiber, do , as presented in Eq. (2). The volume of the cell, which is defined as a ring with radial thickness, r = R/y, axial thickness, z = L/x, and radius distance of the cell from the center

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of the fiber bundle, r, is presented in Eq. (3), while Am is determined from Eq. (4). 4(1 − ε) Am = V do

(2)

V = 2r(r)(z)

(3)

Am =

8r(r)(z)(1 − ε) do

(4)

For the type I and type II cells at various radial position along the closed end sheet, the permeate composition of each component, yT,n [i, 1] , is determined using the solution procedure outlined in the subsequent Section 2.1.1.2.1. After determining the permeate composition, the total flow rate into the permeate side, V˙ , the flow rate of each component into the permeate side, V˙ n , the shell side flow rate, V˙ s [i, 1], the tube side flow rate, V˙ T [i, 1], and the shell side composition leaving each cell, xS,n [i, 1], are provided by the following Eqs. (5)–(9) respectively: V˙ =

n 

Qn Am (ph xS,n [i − 1, 1] − pl yT,n [i, 1]) n = 1, 2, . . ., N

(6)

V˙ s [i, 1] = V˙ s [i − 1, 1] − V˙

(7)

V˙ T [i, 1] = V˙

(8)

xS,n [i, 1] =

xS,n [i − 1, 1]V˙ S [i − 1, 1] − V˙ n V˙ S [i, 1]

(9)

For the type I cell in direct contact with the feed side, the indices [i − 1, 1] are replaced with the feed condition, e.g. V˙ F /x and zF,n . Similarly, for type III and IV cells, the permeate composition of each component in the gaseous mixture, yT,n [i, j] , is determined using the algorithm proposed in Section 2.1.1.2.2, in which it is applicable to cells with feed on both the shell and tube sides. Later, the total flow rate into the permeate side, V˙ , the flow rate of each component into the permeate side, V˙ n , the shell side flow rate, V˙ s [i, j], the tube side flow rate, V˙ T [i, j], and the shell side composition, xS,n [i, j], contacting the subsequent cells are provided by Eqs. (10)–(14) respectively: V˙ =

N 

Qn Am (ph xS,n [i − 1, j] − pl yT,n [i, j])

(10)

n=1

V˙ n = Qn Am (ph xS,n [i − 1, j] − pl yT,n [i, j]),

n = 1, 2, . . ., N

(11)

V˙ s [i, j] = V˙ s [i − 1, j] − V˙

(12)

V˙ T [i, j] = V˙ T [i − 1, j] + V˙

(13)

xS,n [i, j] =

xS,n [i − 1, j]V˙ S [i − 1, j] − V˙ n V˙ S [i, j]

(14)

For the type III cells in direct contact with the feed side, the indices [i − 1, j] are replaced with the feed condition, e.g. V˙ F /x and zF,n . The tube side pressure drop is characterized by the Hagen Poiseuille equation, as presented in Eq. (15), while incorporation of the Hagen Poiseuille equation within the succession of states approach is depicted in Eq. (16) (Thundyil and Koros, 1997). Viscosity of the gas mixture is calculated adapting the Wilke’s method while viscosity of the pure components is determined using the Lucas method (Reid et al., 1977). dp2l dz

=

25.6RTω di4



V˙ T nf

 pl [i, j] =

2

pl [i, j − 1] −

25.6RTω di4



V˙ T [i, j] nf



 z

(16)

For the Hagen Poiseuille equation applicable to the countercurrent and cocurrent flow discussed in the subsequent sections, Eq. (16) is merely reduced to a one dimension problem.

(5)

n=1

V˙ n = Qn Am (ph xS,n [i − 1, 1] − pl yT,n [i, 1]),

Fig. 3. Schematic diagram of the radial crossflow hollow fiber membrane module cell with feed on the shell side only.



(15)

2.1.1.2. Mass balance of one radial crossflow cell. In order to determine the composition of the permeate stream for a multicomponent system in this work, an iterative solution procedure is adapted. To apply the solution procedure, the hollow fiber membrane module cell is generally divided into two types, which are cell with feed on the shell side and cell with feed on both the shell and tube sides. For the radial crossflow pattern, the shell side feed and permeate streams flow perpendicularly in relation to one another, as explained in published literature by Thundyil and Koros (1997) and Marriot and Sorensen (2003), which determines the driving force for separation to occur. In this work, the driving force for separation of the radial crossflow is determined as the partial pressure of the shell side feed to the local tube side permeate partial pressure. The solution procedure for cells within the radial crossflow pattern is presented in Sections 2.1.1.2.1 and 2.1.1.2.2, characterizing the types of cell with feed on only the shell side and cell with feed on both the shell and tube sides respectively. 2.1.1.2.1. Cell with feed on the shell side for radial crossflow. Fig. 3 shows the radial crossflow hollow fiber membrane module cell with feed on only the shell side. The transport mechanism across the membrane unit can be described using the solution-diffusion model. The solution-diffusion model has emerged over the past 20 years as the most widely accepted explanation of transport in gas permeation (Graham, 1866). In this model, the permeable components dissolve within the membrane material in the high pressure side of the membrane, diffuse across the membrane through a driving force and evaporate from the low pressure side of the membrane (Graham, 1866; Wijmans and Baker, 1995). The separation is achieved among different components because some gases are more soluble in the membrane material, and pass more readily through the membrane than other components in the gas. The governing flux equation of the solution-diffusion model that characterizes the transport mechanism of component n for cell [i, j] within the radial crossflow hollow fiber membrane module is given by the Fick’s law of diffusion. It is described using the partial pressure driving force of the shell side feed to the tube side permeate (Wijmans and Baker, 1995), as presented in expression (17). yT,n [i, j]V˙ T [i, j] = Qn Am (ph xS,n [i − 1, j] − pl yT,n [i, j])

(17)

The local stage cut, *, is defined as the ratio of the local tube side flow rate to the feed side flow rate for that particular cell, as presented in (18). ∗ =

V˙ T [(i, j)] ˙Vs [(i − 1, j)]

(18)

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By introducing the local stage cut term, Eq. (17) is reformulated to (19): yT,n [i, j] ∗ V˙ s [i − 1, j] = Qn Am (ph xS,n [i − 1, j] − pl yT,n [i, j])

(19)

The solution procedure to determine the permeate composition is presented below: (1) The permeate composition of the first component, yT,1 [i, j], is assumed. (2) The local stage cut, *, is estimated from Eq. (19). (3) V˙ T [i, j] is computed based on the estimated * and the shell side feed flow rate, V˙ s [(i − 1, j)], from Eq. (18) (4) The permeate composition of other components, yT,n+1 (i, j), is determined from equation (20), which followed from derivation of equation (19). yT,n+1 [i, j] =

(ph xS,n+1 [i − 1, j]) ((V˙ T [i, j]/Am Qn+1 ) + pl )

,

n = 1, . . ., N − 1

Fig. 4. Schematic diagram of the radial crossflow hollow fiber membrane module cell with feed on the shell and tube sides.

(20)

(5) The sum of all the compositions in the permeate stream is calculated from (21). sum =

n 

yT,n [i, j]

(21)

n=1

(6) The summation of the permeate stream composition for all components is compared to unity, as provided in (22). ı = sum − 1

(22)

(7) Steps (1)–(6) are iterated with a new guess of the first component permeate composition, yT,1 [i, j], until the summation of the permeate composition obtained equals to unity within satisfying criteria, ∈. In order to ensure high accuracy of the solution procedure, ∈ has been set to be a small value (e.g., ∈ = 0.0001). The criterion to terminate the iteration process is provided in (23). ı ∈

(23)

The Newton’s bisection methodology is adapted to allow quick computation of the permeate stream composition for each cell in this work (Woodford and Philips, 1997). By setting the appropriate boundary conditions for the first component permeate composition as initial guesses of the low and high sides of the Newton’s bisection procedure, the approach is found to converge quickly to satisfy the criteria in (23) for all cases. For the cells along the closed end sheet, the lower end of the boundary condition have been set as the shell side feed composition, while the higher end at the maximum value 1 since the cells are expected to have the highest permeate composition attributed to the rich shell side composition that optimizes the driving force for permeation. As for the other cells that are not in direct contact with the closed end sheet, the lower boundary condition has been set as the shell side feed composition, while the higher boundary at the tube side permeate from previous contacting cell since the permeate composition of current cell is expected to be lower due to depletion in the shell side composition that reduces the driving force for separation. 2.1.1.2.2. Cell with feed on shell and tube sides for radial crossflow. Fig. 4 depicts the schematic representation of the radial crossflow hollow fiber membrane module cell with feed on the shell and tube sides. Similar to the previous case, the transport of components across the membrane by the Fick’s law of diffusion is provided in (24): yT,n [i, j] ∗ V˙ S [i − 1, j] − yT,n [i, j − 1]V˙ T [i, j − 1] = Qn Am (ph xS,n [i − 1, j] − yT,n [i, j])

(24)

Fig. 5. Schematic representation of (a) cocurrent hollow fiber membrane module, adapted from Rautenbach and Albrecht (1989) and (b) cells within the one dimension succession of states methodology for mathematical modeling.

The same solution procedure described in Section 2.1.1.2.1 is used to determine the permeate composition. The permeate composition of other components, yT,n+1 [i, j], is determined from (25) after obtaining the guessed local stage cut, *. yT,n+1 [i, j] =

ph xS,n+1 [i − 1, j] + ((yT,n+1 [i, j − 1]V˙ T [i, j − 1])/Am Qn+1 ) , (V˙ T [i, j]/Am Qn+1 ) + pl

n = 1, . . ., N − 1

(25)

2.1.2. Cocurrent configuration This section describes the mathematical modeling of the cocurrent configuration within the hollow fiber membrane module. Similarly, it is subdivided into the discussion of the succession of states approach from one cell to the subsequent cell, and transport mechanism characterizing separation within each individual cell. Fig. 5(a) shows the schematic representation of the cocurrent hollow fiber membrane module with the feed introduced through the shell side adapted for mathematical modeling (Rautenbach and Albrecht, 1989). The feed gas flows in the axial direction parallel to the hollow fibers until the retentate end, while the permeate stream diffuses into the fibers in the same direction with the feed. The end of the fiber bundle near the feed gas is sealed with epoxy glue while the other end allows fibers to protrude the seal for permeate gas to be separated from the retentate. On the other hand, Fig. 5(b) depicts the schematic representation of the one dimension succession of states approach to characterize the mass balance of the cocurrent hollow fiber membrane module. The module is divided into finite cells in only the axial direction. 2.1.2.1. Succession of states in cocurrent configuration. The volume of each cocurrent cell, as depicted in Fig. 5(b), which is a disk with radius, R, and axial thickness, z = L/x, is calculated from (26), while

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121

the active membrane area for permeation, Am is determined from (27). V = (R)2 (z) Am =

(26)

4R2 (z)(1 − ε)

(27)

do

The solution algorithm of the cocurrent hollow fiber membrane module involves computation proceeding from the feed end using the feed known composition to the retentate end. For the type I cell with feed on only the shell side, the local permeate composition of each component, yT,n [1], is determined from the solution procedure provided in Section 2.1.2.2.1. Later, the local retentate composition is determined from (28), which followed from the type I cell mass balance. xS,n [1] =

zF,n −  ∗ yT,n [1] 1 − ∗

(28)

As for the type II cells with feed on the shell and tube sides, the solution procedure in Section 2.1.2.2.2 is adapted to determine the local permeate composition, yT,n [j], followed by the local retentate composition of each cell using expression (29). xS,n [j] =

xS,n [j − 1] − yT,n [j] ∗ +yT,n [j − 1]V˙ T [j − 1]/V˙ S (j − 1) 1 + (V˙ T [j − 1]/V˙ S [j − 1]) − ∗

(29)

The flow rates of the hollow fiber membrane module are determined adapting the following equations from (30) to (33) for the total flow rate into the permeate side, V˙ , the flow rate of each component into the permeate side, V˙ n , the shell side flow rate, V˙ S [j], the tube side flow rate contacting the subsequent cells, V˙ T [j], respectively. V˙ =

N 

Qn Am (ph xS,n [j] − pl yT,n [j])

(30)

n=1

V˙ n = Qn Am (ph xS,n [j] − pl yT,n [j]),

Fig. 6. Schematic representation of the cocurrent flow hollow fiber membrane module cell with feed on only the shell side.

n = 1, 2, . . ., N

(31)

V˙ S [j] = V˙ S [j − 1] − V˙

(32)

V˙ T [j] = V˙ T [j − 1] + V˙

(33)

For the type I cocurrent flow cell in direct contact with the feed, the indices [j − 1] are replaced with the feed condition, e.g. V˙ F and zF,n , without tube side feed, e.g. V˙ T [j − 1] = 0. 2.1.2.2. Mass balance of one cocurrent cell. To apply the solution procedure for the cocurrent cell, the hollow fiber membrane module cell is similarly divided into two types of cell like the radial crossflow configuration, which are cell with feed on the shell side and cell with feed on both the shell and tube sides. As mentioned earlier, the cocurrent configuration involves dividing cells into only the axial directions. In addition to the dimension (e.g. 1-D or 2-D) when resolving the mass balance and transport mechanism, the distinction between the radial crossflow and the cocurrent flow, which is regarded as a longitudinal configuration, is that the shell side feed and permeate streams flow perpendicularly in relation to one another for the radial crossflow pattern, while flowing in the parallel direction for the cocurrent pattern. This difference distinguishes the driving force for separation to occur between the two configurations. The driving force of the parallel flow configuration is determined as the local shell side retentate partial pressure to the local tube side

yT,n [j] ∗ V˙ S [j − 1] − yT,n [j − 1]V˙ T [j − 1] = Qn Am

Fig. 7. Schematic representation of the cocurrent hollow fiber membrane module with feed on both the shell and tube sides.

permeate partial pressure leaving each cell as described by Barrer et al. (1962), Coker et al. (1998), Ghosal and Freeman (1994) and Graham (1866). The solution procedure for the cocurrent pattern is presented in Sections 2.1.2.2.1 and 2.1.2.2.2 that describes cell with only the shell side feed and cell with both shell and tube sides feed respectively. 2.1.2.2.1. Cell with feed on the shell side for longitudinal flow. Fig. 6 depicts the schematic diagram of the parallel flow hollow fiber membrane module cell with feed on the shell side. The transport of components across the parallel flow hollow fiber membrane is also described using the Fick’s law of diffusion equation. However, the driving force is the partial pressures of the shell side retentate to the tube side permeate leaving each cell [j], as provided in the following expressions of (34) and (35): yT,n [j] ∗ V˙ s [j − 1] = Qn Am (ph xS,n [j] − pl yT,n [j])

(34)

yT,n [j] ∗ VS [j − 1] = Qn Am

 p h

1 − ∗



(xS,n [j − 1] −  ∗ yT,n [j]) − pl yT,n [j]

(35)

The same solution procedure described in Section 2.1.1.2.1 has been adapted to determine the permeate composition. The permeate composition of other components, yT,n+1 [j], is calculated from (36). yT,n+1 [j] =

ph xS,n+1 [j − 1]/(1 −  ∗ ) , ˙VT [j]/(Am Qn+1 ) + ( ∗ ph /(1 −  ∗ ) + pl

n = 1, . . ., N − 1

(36)

2.1.2.2.2. Cell with feed on shell and tube sides for longitudinal flow. Fig. 7 shows the schematic representation of the parallel flow hollow fiber membrane module cell with feed on both the shell and tube sides. The characterization of the transport across the parallel flow hollow fiber membrane module cell with shell and tube sides feed using Fick’s law of diffusion is described in (37).



ph (xS,n [j − 1] − yT,n [j] ∗ +yT,n [j − 1]V˙ T [j − 1]/V˙ s [j − 1]) − pl yT,n [j] 1 + (V˙ T [j − 1]/V˙ S [j − 1]) −  ∗

(37)

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The same solution procedure described in Section 2.1.1.2.1 is applied to determine the permeate composition, followed by the permeate composition of other components, yT,n+1 [j], from (38).



yT,n+1 [j] =

since the cells in Fig. 9 are identified as the type with feed on only the shell side.

ph xS,n+1 [j − 1] ph yT,n+1 [j − 1]V˙ T [j − 1]/V˙ S [j − 1] yT,n+1 [j − 1]V˙ T [j − 1] + + Am Qn+1 1 −  ∗ + V˙ T [j − 1]/V˙ s [j − 1] 1 −  ∗ + V˙ T [j − 1]/V˙ s [j − 1]



/ V˙ T [j]/(Am Qn+1 ) + (ph

 ∗ /(1 −  ∗

+ (V˙ T [j − 1]/V˙ S [j − 1]))) + pl

2.1.3. Countercurrent configuration The mathematical modeling of the countercurrent configuration is discussed in this section. It is subdivided into the discussion of the crossflow initial guess and actual computation methodology describing mass balance from one cell to the subsequent cell that progresses in a countercurrent flow fashion. Fig. 8(a) shows the schematic representation of the countercurrent hollow fiber membrane module with the feed introduced through the shell side used for mathematical modeling (Rautenbach and Albrecht, 1989). The feed flows axially along the hollow fibers until the retentate end to be collected at the retentate outlet. The permeate stream into the fibers flows in the opposite direction with respect to the feed. The end of the fiber bundle near the feed gas is the tube sheet to enable the permeate stream to exit the membrane module, while the end of the fiber bundle near the retentate end is sealed. In addition, Fig. 8(b) shows the diagram of the one dimension succession of states approach to characterize the mass balance of the countercurrent hollow fiber membrane module. 2.1.3.1. Crossflow initial guess. The complexity associated to mathematical modeling of the countercurrent hollow fiber membrane module arises because the permeation at the stage where the feed gas enters the module is dependent upon the composition of the gas that permeated. This information is initially not known. Therefore, the composition and flow rates of each cell have to be obtained using crossflow results as initial guesses, such as that proposed in Fig. 9. Similar approach has been employed by Coker et al. (1998) to initiate the mass balance computation associated to the countercurrent flow. Similar to the cocurrent flow configuration, the module is divided into many finite cells in only the axial direction. Each cell is a disk similar to the cocurrent configuration, in which the volume, V, and the membrane area for permeation, Am , are computed from (26) and (27) respectively. Solution procedure outlined in Section 2.1.1.2.1 has been employed for computation of the initial guesses



(38)

2.1.3.2. Succession of states in countercurrent configuration. Using the crossflow solution obtained in previous section as an initial guess, improved estimates of xS,n [j] and yT,n [j] are obtained from (39) and (40) respectively, which followed from the mass balance of each cell. xS,n(old) [j − 1]V˙ S(old) [j − 1] + Am Qn pl yT,n(old) [j]

xS,n(new) [j] =

V˙ S(old) [j] + Am Qn ph

yT,n(new) [j] =

yT,n(old) [j + 1]V˙ T (old) [j + 1] + Am Qn ph xS,n(old) [j] V˙ T (old) [j] + Am Qn pl

(39)

(40)

The improved estimates of xS,n(new) [j] and yT,n(new) [j] are employed to calculate the shell and tube sides flow rate, starting from the cell at the feed end to a series of cells until the retentate end, adapting Eqs. (41)–(44) respectively, as depicted below: V˙ (new) =

N 

Qn Am (ph xS,n,(new) [j] − pl yT,n(new) [j])

(41)

n=1

V˙ n(new) = Qn Am (ph xS,n(new) [j] − pl yT,n(new) [j]), n = 1, 2, . . ., N

(42)

V˙ S(new) [j] = V˙ S(new) [j − 1] − V˙ (new)

(43)

V˙ T (new) [j] = V˙ T (new) [j + 1] + V˙ (new)

(44)

Similarly, for the cell in direct contact with the feed side, the index [j − 1] is replaced with the feed condition, e.g. V˙ F and zF,n . The above procedures are iterated until the changes in the component permeate and retentate flow rates are within a defined tolerance limit, ∈. Similarly, to minimize the percentage error, ∈ is determined to be a small value (e.g. ∈ = 0.0001). The criteria for

Fig. 8. Schematic representation of (a) countercurrent hollow fiber membrane module, adapted from Rautenbach and Albrecht (1989) and (b) cells within the one dimension succession of states methodology for mathematical modeling.

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123

Fig. 9. Schematic representation of crossflow module for x number of cells as initial guesses for countercurrent flow simulation.

together with the Aspen HYSYS package during the initial installation process.

Fig. 10. Unit operation extension in Aspen HYSYS.

convergence of the countercurrent hollow fiber membrane module solution procedure are depicted in (45) and (46).

   yT,n(new) [1]V˙ T (new) [1] − yT,n(old) [1]V˙ T (old) [1]    <∈   yT,n(old) [1]V˙ T (old) [1]    xS,n(new) [x]V˙ S(new) [x] − xS,n(old) [x]V˙ S(old) [x]    <∈   x [x]V˙ [x] S,n(old)

(45)

(46)

S(old)

2.2. Simulation method The simulation method adapted in current work is discussed in this section, whereby it is divided into simulation approach within Aspen HYSYS and methodology to compare the radial crossflow, countercurrent and cocurrent configurations of the hollow fiber membrane for CO2 capture from natural gas. 2.2.1. Simulation in Aspen HYSYS The hollow fiber membrane unit operation extension is comprised of two independent constituents, namely the ActiveX Server dynamic link library (DLL) and extension definition file (EDF), as demonstrated in Fig. 10 (HYSYS, 2010). The DLL file is constituted by the actual computer coding to characterize the mathematical model as discussed in Section 2.1 (HYSYS, 2010). The DLL file is compiled adapting the Visual Basic programming language since it provides the most convenient environment to create the unit operation extension. The proprietary information contained within the DLL file is hidden, making it an ideal procedure for commercial application in industry for natural gas purification plant. It requires merely simple registration procedure in order to be adapted in the Aspen HYSYS working environment for various design simulations of the CO2 /natural gas separation process. The EDF is the second component vital to the creation of the unit operation extension by working as the interface view within Aspen HYSYS. In addition, it also works as the point for input variables declaration and storage that are essentially required to pass the arguments to the DLL file for mathematical computation. The EDF is compiled using the Extension View Editor, which is included

2.2.2. Simulation to compare different flow configuration performance In order to evaluate the performance of the radial crossflow, countercurrent and cocurrent flow mechanism, the design configuration has to be consistent throughout for ease of comparison amongst the flow mechanisms. It has been proposed in our previous works that the most economical design among all process configurations that include recycle streams and multiple stages is the two stages membrane with permeate stream recycle (Ahmad et al., 2012, 2013). Therefore, in the simulation method, the mentioned design configuration has been extended by simulating the performance of the two staged membrane module system under different flow configurations: radial crossflow, countercurrent and cocurrent, such as that provided in Fig. 11. The separation of carbon dioxide from a natural gas mixture consisting of methane, ethane, propane and nitrogen is simulated for these flow patterns. The study of design variables adapting a different membrane selectivity and CO2 feed composition is presented. The former is done by altering the permeance of CO2 while keeping the permeance of other components constant. The permeance of CO2 is increased so that the selectivity of CO2 /CH4 falls within the range of 10–40, which are typical selectivities reported for polymeric membrane (Stookey, 2001; Teplyakov et al., 1996). The material of fabrication of the membrane is assumed to be the commonly used cellulose triacetate for CO2 capture application (Coker et al., 1998; Kundu et al., 2012). The effect of the CO2 concentration in the feed gas is evaluated by altering the composition from 10% to 60%. The wide range of CO2 feed composition is presented to represent different applications of CO2 removal process, with the low CO2 feed concentration corresponding to the sweetening of natural gas with low quantities of acid gas, and the high CO2 feed concentration study analogous to the natural gas processing in enriched oil recovery with high CO2 concentration (Thundyil and Koros, 1997). The input parameters used for the simulation condition are summarized in Table 2 (Baker, 2012; Coker et al., 1998; Hao et al., 2002, 2008; Kundu et al., 2012; Lock et al., 2015; Stookey, 2001; Teplyakov et al., 1996; Thundyil and Koros, 1997; Zhai et al., 2013). As demonstrated in Table 2, the feed composition of 10% CO2 has been adapted as the basis when varying the membrane selectivity values since the main objective of the analysis is to study the effect and trend of selectivity to the performance of different flow configurations, while that of higher composition is merely an amplification of the values and differences obtained at lower CO2 content (Thundyil and Koros, 1997). As for the effect of CO2 feed composition to the efficiency of various flow configurations, the membrane selectivity has been kept constant at 20 since it is typical membrane characteristic adapted for industrial scale application (Baker, 2002). From the aspect of process economics, in order to determine the flow configuration that is the most economical to the CO2 capture membrane system, the gas processing cost (GPC) is calculated according to the procedure adapted from Hussain and Hag and Hao et al. studies associated to their respective membrane system (Hao et al., 2002, 2008; Hussain and Hagg, 2010). The GPC computation is

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Fig. 11. The schematic representation of the process flow diagram in Aspen HYSYS to study the effect of flow configuration on the performance and economics of the double staged membrane with permeate recycle for CO2 separation from natural gas. Table 2 Input parameters used for simulation of case studies within Aspen HYSYS. Simulation parameter Membrane characteristic (Coker et al., 1998; Kundu et al., 2012)

Feed gas characteristic

Output gas characteristic Membrane module characteristic

Value Permeance of CO2 (GPU)

Permeance of CH4 (GPU) Permeance of C2 H6 (GPU) Permeance of C3 H8 (GPU) Permeance of N2 (GPU) Feed composition

Feed pressure (bar) Feed flow rate (MMSCF) Permeate pressure (bar) Residue CO2 composition Outer and inner diameter of hollow fibers (␮m) Porosity Diameter of membrane module

28.6–114.4 (by ranging ˛CO2 /CH4 between 10 and 40) (Stookey, 2001; Teplyakov et al., 1996)

*If not specified, value used for base case study is 60. 2.86 2 1.89 3.57 Z F, CO2 (range between 0.1–0.6 with remaining as Z F, CH4 ). Z F, C2 H6 = 0.05 Z F, C3 H8 = 0.05 Z F, N2 = 0.1 * If not specified, value used for base case study is Z F, CO2 = 0.1. 40 (typical offshore natural gas processing pressure) (Baker, 2012; Zhai et al., 2013) 20 (medium size plant) (Lock et al., 2014a,b) 1 (analogous to atmospheric pressure) <2% to meet pipeline specification (Baker and Lokhandwala, 2008; Hao et al., 2002, 2008) 250/100 (Thundyil and Koros, 1997) 0.5 (Thundyil and Koros, 1997) 15 in (Baker and Lokhandwala, 2008)

adapted from the published literature since it is comprehensive to include the capital related cost (CRC) associated to the installation and fabrication of equipments, the variable operating and maintenance cost (VOM) and the cost of hydrocarbon lost in the permeate

stream (CH4 LS) when implementing the solution procedure. The cost of cooling system is included together with the compressor cost (CC) while a total payout period of 5 years is considered to calculate the capital cost (Hao et al., 2002, 2008). The gas processing

Table 3 Economic parameters and assumptions for computation of GPC (Hao et al., 2002, 2008; Hussain and Hagg, 2010). Total plant investment (TPI)

TPI = TFI + SC

Membrane module cost (MC)

$5/ft2

Installed compressor cost (CC)

$8650 ×

 Wcp 0.82 ncp

Wcp (HP) = 1.341RTQcp ln Fixed cost (FC) Base plant cost (BPC) Project contingency (PC) Start up cost (SC) Annual capital related cost (CRC) Annual variable operating and maintenance cost (VOM) Contract and material maintenance cost (CMC) Local taxes and insurance (LTI) Direct labor cost (DL) Labor overhead cost (LOC) Membrane replacement cost (MRC) Utility cost (UC) Annual cost of hydrocarbon lost (CH4 LS) Annual natural gas lost (NGLS) Gas processing cost (GPC) Membrane life Wellhead price of crude natural gas (NWP) Heating value of natural gas (NHV) On stream factor (OSF) Compressor efficiency (ncp )

 ph  pl

FC = MC + CC 1.12 × FC (includes home office cost: 0.12 FC) 0.2 × BPC 0.1 × VOM 0.2 × TPI (based on 5 years payout) VOM = CMC + LTI + DL + LOC + MRC + UC 0.05 × TFI 0.015 × TFI $15/h 1.15 × DL $3/ft2 $0.07 kWh−1 CH4 LS = NGLS × NHV × NWP NGLS = 365 × OSF ×V˙ F × ZF (hydrocarbon) × yT (hydrocarbon) GPC = (CRC + CH4 LS + VOM)/[365 × OSF ×V˙ F × (1 − SCE) × 1000] 4 years $ 2/MMBTU 1066.8 MMBTU/MMSCF 96% 0.8

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Table 4 Input parameters adapted from Pan (1986) experiment data for model validation. Input parameter

Value

Membrane characteristic

Permeance of H2 (GPU)

84.8

Permeance of N2 (GPU) Permeance of CH4 (GPU) Permeance of Ar (GPU)

0.882 0.848 2.30

Feed composition

zF,H2 = 0.5178 zF,N2 = 0.2469 zF,CH4 = 0.1957 zF,Ar = 0.0396 6,964,000

Feed gas characteristic

Feed pressure (Pa) Membrane module characteristic

Active length of fiber bundle (cm) Radius of fiber bundle (mm) Outer and inner diameter of hollow fibers (␮m) Porosity Pressure ratio

15 1.05 200/80 0.8186 6.20

Table 5 Input parameters adapted from Makaruk and Harasek (2009) experiment data for model validation. Input parameter Membrane characteristic

Feed gas characteristic

Value Permeance of CH4 (GPU)

2.0921

Permeance of CO2 (GPU) Permeance of O2 (GPU)

77.7632 17.8947

Feed composition

zF,CH4 = 0.645 zF,CO2 = 0.345 zF,O2 = 0.01 900,000

Feed pressure (Pa) Membrane module characteristic

Active length of fiber bundle (cm) Radius of fiber bundle (mm) Outer and inner diameter of hollow fibers (␮m) Porosity Pressure ratio

38

Fig. 12. Model validation with published literature by Pan (1986) of N2 (), CH4 () and H2 () permeate composition for (a) countercurrent and (b) cocurrent flow (   Experiment — Simulation model ----- Pan’s crossflow model).

0.80 397.8874/160 0.5 8.1818

cost (GPC) is calculated according to the procedure and fundamental assumptions outlined in Table 3 and the data obtained from process simulation. 3. Results and discussion 3.1. Model validation To demonstrate the accuracy of the simulation model, it has been validated using published experimental data by Pan (1986) and Makaruk and Harasek (2009) for their respective multicomponent gas separation system. The published results by Pan (1986) has been adapted to demonstrate the applicably of current mathematical model that considers the effect of bulk flow configuration through comparison with Pan’s original crossflow assumption model. On the other hand, the published experimental data by Makaruk and Harasek (2009) has been adapted to demonstrate the accuracy of the simulation model to predict CO2 related gas separation, which enables further application in CO2 capture study from natural gas provided in the subsequent sections. The variables used as input parameters for computation of the simulation model to validate Pan (1986) and Makaruk and Harasek (2009) data are presented in Tables 4 and 5 respectively. Fig. 12(a) provides the model validation with published literature by Pan for countercurrent flow while Fig. 12(b) provides the model validation for the cocurrent flow. As illustrated in

Fig. 12, the suggested simulation model gives good approximation to the published experiment data within acceptable mean absolute percentage error (MAPE) limit. The higher percentage error contributed by the N2 and CH4 is attributed to their small constituents in the gas mixture, whereby a small deviation is expected to amplify the percentage error. In addition, it can be noticed that for lower stage cuts, the developed simulation model fits well with the experimental data as comparable to Pan (1986) crossflow assumption model. However, at higher stage cuts, the values predicted by the simulation model give closer prediction than the crossflow model proposed by Pan (1986). As suggested by Makaruk and Harasek (2009), gas separation becomes similar regardless of the flow configuration at low stage cuts. This explains the observation that both models provide similar prediction to the experimental data since flow configuration is not substantial at the point. Nevertheless, at higher stage cut, the performance of the asymmetric hollow fiber is highly affected by the bulk flow due to back diffusion along the pore path at extreme conditions, which renders y (local permeate composition at the boundary of active membrane and porous backing surface in the crossflow asymmetric membrane) to be similar to yT (local tube side composition of the bulk flow in current model) (Makaruk and Harasek, 2009; Pan, 1986). The back diffusion causes the permeate flux at the bulk flow to mix with the local permeate composition at the boundary to resemble the characteristic of the hollow fiber membrane with consideration of bulk flow composition more likely in comparison to the simplified crossflow model. The explanation clarifies the better prediction at higher stage cut in this work as compared to the original model prediction by Pan and also demonstrates that the assumption of negligible bulk flow might

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15500

Total Membrane Area (m2)

13500 Countercurrent Radial Crossflow Cocurrent

11500 9500 7500 5500 3500 10

15

20

25 Selectivity

30

35

40

Fig. 14. Effect of membrane selectivity to the required membrane area for different flow configuration with minimum requirement of 2% CO2 residue composition (CO2 feed composition = 10%).

3.2. Comparison of different flow configurations

Fig. 13. Model validation with published data by Makaruk and Harasek (2009) for (a) countercurrent retentate composition versus stage cut, (b) cocurrent retentate composition versus stage cut and (c) methane composition versus methane recovery of both countercurrent and cocurrent flow.

be unnecessary especially under high permeation flux condition (Sidhoum et al., 1988). The proposed simulation model has been further validated with published literature by Makaruk and Harasek (2009) for CO2 separation as depicted in Fig. 13. It is demonstrated that the modeled simulation result is in good agreement with the published experimental data within small MAPE from the aspect of components composition as demonstrated in Fig. 13(a) and (b), and flow rate result as illustrated in Fig. 13(c). The close agreement ensures high accuracy of the simulation model in application of CO2 capture study from natural gas.

As provided in Section 2.2, the simulation conditions are used to evaluate the performance of the radial crossflow, countercurrent and cocurrent flow. For each flow configuration, the performance is evaluated based on several criterions, such as: the required membrane area for separation, the permeate pressure profile, the compressor power, the composition of CO2 in the residue stream, the hydrocarbon lost and the GPC. In all cases, the membrane area is altered by varying the length of the membrane module, while keeping the other membrane specifications constant as provided in Table 2. In addition, the area ratio (ratio of the membrane area in the 1st stage to the area in the 2nd stage) of the cocurrent configuration is minimized to provide the basis for comparison with other flow regimes by altering the length of the 2nd stage membrane as compared to the cocurrent flow. This is important for consistency to evaluate the performance of the different flow configurations since the area ratio is an important parameter that has tremendous impact to the separation efficiency of the membrane system. Two conditions of the membrane unit are investigated, which are as followed: (1) to alter the membrane area in order to achieve the minimal requirement of 2% CO2 composition in the residue stream. (2) To provide the same membrane area for all flow configurations while ensuring the CO2 composition in the residue stream is less than 2%. The first case study is conducted to compare the separation efficiency of the different flow configurations since the higher efficiency flow pattern is expected to reach the designated composition at smaller membrane area. The same membrane area is plotted for the different flow configurations in the second case study to analyze the efficiency of the flow pattern in terms of residue concentration and hydrocarbon lost. In addition, the second case study is typical operation conducted in industry to compare the performance of different design configurations with predetermined membrane area. 3.2.1. Compliance of CO2 pipeline with variable membrane specification 3.2.1.1. Total membrane area. The effect of the membrane selectivity and feed composition to the total membrane area required to achieve the designated separation is investigated for the radial crossflow, countercurrent and cocurrent configuration. Fig. 14 shows the influence of membrane selectivity to the total membrane area. It is shown that increasing the selectivity decreases the total membrane area in order to achieve the requirement of 2% CO2 in the residue stream. This is due to the higher permeation of the CO2

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with increment in the selectivity of the membrane, which decreases the composition of the acid gases for a certain membrane area. It is also observed from Fig. 14 that the total membrane area required to achieve the desired CO2 retentate composition is the smallest for the countercurrent flow, followed by the radial crossflow, and the cocurrent flow. The cocurrent flow configuration is predicted to give the least performance as compared to the radial crossflow and countercurrent. The superiority of the radial crossflow in comparison to the cocurrent flow is attributed to the availability of higher effective membrane area for separation in both the axial and radial direction (Thundyil and Koros, 1997). The availability of more effective membrane area allows for efficient contact of the gas with the membrane, and therefore higher permeation of the CO2 into the hollow fibers. The superiority of the countercurrent flow is attributed to the partial pressure driving force distribution. The opposite flow of the tube and shell sides contributes to the slowly declining pressure gradient that enables the pressure driving force to be maximized along the module length as demonstrated later in Section 3.2.1.2 (Ho and Sirkar, 1992). Therefore higher permeation is achieved for the countercurrent flow in comparison to the cocurrent and radial crossflow pattern. The effect of the feed composition to the total membrane area required for separation is studied by varying the flow configurations. Fig. 15 shows the effect of the CO2 feed composition in which the total membrane area increases with increment in the feed composition until it reaches a maximum point. Then, further increment is demonstrated to lead to the decrease on the total membrane area requirement. This is consistent with the observation by previous published literature, in which the high CO2 feed composition increases the driving force for permeation substantially to the extent of decreasing the membrane area required (Clarizia and Drioli, 2003; Zhang et al., 2012). Similarly, it is also observed from Fig. 15 that the countercurrent flow configuration

requires the smallest membrane area for permeation, followed by the radial crossflow and the cocurrent for all CO2 feed composition due to the higher driving force distribution as explained. It is also apparent from Fig. 15 that the effect of flow configurations on the required membrane area is less substantial at the lower CO2 feed condition. However, at higher CO2 feed condition, the impact of the flow configurations is demonstrated to be more significant, especially by the cocurrent flow pattern, by exhibiting the trend of much bigger membrane area requirement as compared to the countercurrent and the radial crossflow. This is attributed to the more pronounced impact of the CO2 flux permeation with more driving force when the CO2 feed composition is increased, which further increases the superiority of the countercurrent and the radial crossflow in comparison to the cocurrent configuration. 3.2.1.2. Permeate pressure drop. In this section, the effect of the membrane selectivity and feed composition to the permeate pressure drop required to achieve the designated separation is investigated for the radial crossflow, countercurrent and cocurrent configuration. The permeate pressure profile is evaluated since it characterizes the driving force for permeation, whereby the smaller the pressure buildup within the bore of the hollow fibers, the higher the driving force for separation to occur. In addition, the pressure buildup within the fiber bore is also significant to be considered to ensure the fiber is capable of withstanding the transmembrane pressure difference (Thundyil and Koros, 1997). The major difference to be noted when discussing the permeate pressure profile between the radial crossflow and the longitudinal flow configuration (co- and countercurrent) permeators is that while the pressure drop in the bore of the longitudinal permeator is similar radially, the pressure drop within the radial crossflow permeation inherits pressure variation along the radial direction since the flow rate and composition varies radially. Hence, for the radial crossflow configuration, the permeate pressure drops are graphed at three positions,

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which are (1) at the top of the membrane in direct contact with the feed gas (referred later as 0% depth of the fiber bundle), (2) at 50% depth of the fiber bundle and (3) at the bottom of the membrane in contact with the center perforated pipe (referred later as 100% depth of the fiber bundle). Fig. 16 depicts the effect of membrane selectivity to the permeate pressure drop by comparing the pressure profile of membrane with selectivity 10 and 40 through Fig. 16(a) and (b) respectively. It is demonstrated that the permeate pressure buildup is more substantial in the lower selectivity membrane attributed to the fact that it requires a higher membrane area requirement and hence a longer fiber specification to achieve the designated separation, which further contributes to higher pressure buildup in comparison to its counterpart. It is also observed that the smaller length requirement in the higher membrane selectivity case study causes the difference of pressure buildup profile amongst varying flow configurations to be less apparent as compared to the lower selectivity membrane. The effect of CO2 feed composition to the permeate pressure drop is evaluated by comparing the profile of feed composition with 10% and 60% CO2 in Fig. 17(a) and (b). It is demonstrated from Fig. 17 that the permeate pressure drop within the hollow fiber bore of feed gas with higher CO2 composition is also higher. In addition, it is noticeable that there is little difference between the pressure profiles of varying flow configurations at low CO2 content. Nonetheless, the difference become increasingly more substantial with increment in the CO2 feed composition. The reason underlying these observations is attributed to the higher membrane area or fiber length requirement to remove the higher CO2 in the feed gas to the designated content. In addition, the higher impact of pressure drops at higher feed concentration is also intuitively obvious since the pressure buildup within the membrane bore is dependent upon

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Fig. 17. Effect of (a) CO2 feed composition = 10% and (b) CO2 feed composition = 60% to the permeate pressure for different flow configuration with minimum requirement of 2% CO2 residue composition (membrane selectivity = 20).

the flow rate of the tube side permeate stream, which increases at higher feed concentration with more permeation. From Figs. 16 and 17, it is demonstrated that the pressure drop profile is the highest for the cocurrent, followed by the radial crossflow at 0% depth, radial crossflow at 50% depth, countercurrent and radial crossflow at 100%. The higher pressure buildup of the cocurrent as compared to the countercurrent and radial crossflow is due to the higher length requirement to achieve the required separation as discussed in the previous section. The countercurrent flow has a lower permeate pressure drop as compared to the cocurrent, and most part of the radial crossflow permeator. In addition to the smaller length requirement, the opposite flow of the tube and shell sides in the countercurrent permeator causes a lower pressure buildup profile since the sealed end of the fiber bore is exposed to the lowest shell side flow rate, which experiences the least permeation to the fiber bore. The radial crossflow configuration exhibits a higher pressure drop at the outer membrane bundle ascribed to the higher shell side flow rate that contributes to more permeation, and slowly decreases when approaching the bundle center. 3.2.1.3. Compressor power. The effect of feed composition and membrane selectivity to the compressor power requirement has been investigated for the proposed double staged design under varying flow configurations. Fig. 18 shows that the compressor power decreases with the increment in the selectivity of the membrane. The decrease in the compressor power implies decreasing flow rate of the permeate stream that is recycled back to the system, which is due to the characteristics of the specific feed, operating condition and arrangement of the membrane under investigation. With 10% CO2 in the feed, majority of the acid gases have permeated through the hollow fiber membrane module in the first stage with high selectivity of CO2 , while the retentate with smaller capacity

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Fig. 21. Effect of the CO2 feed composition to the gas processing cost for different flow configuration with minimum requirement of 2% CO2 residue composition (membrane selectivity = 20).

is passed on to the second stage for subsequent permeation. This condition further reduces the flow rate of the recycled permeate stream and the compressor power. Fig. 19 shows that the compressor power increases with increment in the CO2 feed composition until it reaches a maximum point, whereby the requirement decreases with further increment in the CO2 feed composition. The increase in the compressor power is ascribed to the higher permeate flow rate due to more permeation since there are higher CO2 content to be removed. Nonetheless, the compressor power requirement decreases with further increment in the CO2 feed composition due to the reduction in the membrane area requirement as mentioned in Section 3.2.1.1. The smaller membrane area results in reduction in the recycled permeate stream flow rate, and therefore lower compressor power requirement. In both case studies, the countercurrent flow configuration is found to give the least compressor power requirement followed by the radial crossflow and the cocurrent flow when provided the same membrane characteristic or feed condition for separation. The countercurrent flow requires the smallest membrane area for CO2 permeation to achieve the designated retentate quality due to the higher partial pressure driving force, which results in smaller recycled permeate flow rate and therefore lower compressor power

requirement in comparison to the radial crossflow and the cocurrent flow. 3.2.1.4. Gas processing cost. In order to determine the optimal design configuration, the gas processing cost (GPC) must be minimal subjected to the operating conditions, membrane material and specification. Fig. 20 shows the effect of membrane selectivity to the GPC for different flow configurations. It is depicted from Fig. 20 that the GPC decreases when the membrane selectivity increases since the higher selectivity membrane is more efficient by allowing more permeation of CO2 at a smaller membrane area and compressor power requirement to achieve the designated separation. The effect of CO2 feed composition to the GPC requirement for the different flow patterns is provided in Fig. 21. It is shown from Fig. 21 that the GPC increases with the increment in the CO2 feed composition until a certain optimum point. This is due to the higher membrane area and auxiliary equipments requirement to remove the excessive CO2 in the feed to the designated composition. However, further increment of the CO2 content in the feed has been shown to decrease the GPC. This is ascribed to the decline in the membrane area, compressor power and utility cost requirement when the CO2 composition increases the driving force for permeation to occur at higher

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Fig. 23. Effect of (a) CO2 feed composition = 10% and (b) CO2 feed composition = 60% to the permeate pressure for different flow configuration with the same membrane area (membrane selectivity = 20).

concentration as discussed previously in Section 3.2.1.1 (Clarizia and Drioli, 2003; Zhang et al., 2012). It is also observed from Figs. 20 and 21 that the GPC requirement for the countercurrent and the radial crossflow configuration is almost similar, with the GPC of the countercurrent flow slightly lower than that of the radial crossflow, while both being the more economical configuration in comparison to the cocurrent at all membrane selectivities and CO2 feed composition. From Figs. 20 and 21, the difference is especially substantial at higher selectivity membrane and higher concentration of CO2 . The difference among the flow configurations is attributed to the membrane area and compressor power requirement, which are especially vital at higher selectivity membrane and CO2 feed concentration operating conditions by producing higher partial pressure driving force for separation.

has been adapted as benchmark for comparison with the other flow configurations. Fig. 22(a) depicts the effect of membrane with selectivity 10 and 40 to the permeate pressure drop of different flow configurations when provided the same membrane area for permeation. The permeate pressure is higher in the lower selectivity membrane ascribed to the higher membrane area requirement to reduce the CO2 composition to the required content. It is also demonstrated that for lower selectivity membrane, the differences among the pressure profiles of the different flow configurations are not apparent but further amplified when the membrane selectivity increases. This is because when the feed gas is processed with a better membrane material of higher selectivity, the molar flow rate within the fiber bore increases, which causes the effect to the pressure buildup profile to be more substantial. On the other hand, the effect of CO2 feed composition to the permeate pressure drop of varying flow configuration is evaluated by comparing the profile of feed gas with 10% and 60% CO2 in Fig. 23(a) and (b) respectively. It is demonstrated from Fig. 23 that the permeate pressure drop within the hollow fiber bore is higher when the CO2 feed composition is higher attributed to the longer fiber length to remove the excessive CO2 , which further contributes to higher permeation in the tube side. Moreover, it is noticeable that the effect of CO2 composition to the difference among pressure drops of different flow configurations is especially substantial at higher CO2 feed composition. Similarly, the more significant effect is caused by the higher flow rate to the bore side of the fiber, which further alters the pressure buildup of varying flow mechanisms. From Figs. 22 and 23, it is shown that the pressure drop is the highest for the radial crossflow at 0% depth, followed by the cocurrent, radial crossflow at 50% depth, countercurrent and radial

3.2.2. Compliance of CO2 pipeline with predefined membrane specification 3.2.2.1. Permeate pressure drop. In this section, the effect of membrane selectivity and feed composition to the permeate pressure drop for the cocurrent, radial crossflow and countercurrent configuration under the same membrane area is investigated as provided in Figs. 22 and 23 respectively. In both figures, it is depicted that the pressure drops of all flow configurations with the exception of cocurrent flow is higher than that of the previous case study with minimum area requirement to achieve the designated residue composition in Section 3.2.1.2. This is because they are provided a larger membrane specification as the cocurrent flow, which causes higher pressure drop with longer length and higher permeation to the tube side, while the cocurrent having the same pressure profile since it

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crossflow at 100%. The radial crossflow at 0% depth experiences the highest pressure drop attributed to the highest permeation near the outside of the bundle with exposure to the feed gas. This is followed by the cocurrent flow that experiences a higher pressure drop than majority of the radial crossflow since the inner bundle of the radial crossflow mechanism has exposure to the slowly declining shell side flow rate for permeation, which further decreases the pressure drop profile when approaching the center of the fiber bundle. The countercurrent flow has a lower permeate pressure drop as compared to the cocurrent, and most part of the radial crossflow permeator attributed to the opposite flow of the tube and shell sides that constitutes a lower pressure buildup profile as discussed earlier. 3.2.2.2. Percentage hydrocarbon lost and CO2 residue composition. Figs. 24 and 25 describe the effect of membrane selectivity and feed composition to the CO2 residue composition and the hydrocarbon percentage lost respectively. The percentage hydrocarbon lost is defined as the amount of hydrocarbon (methane, ethane and propane) that permeates through the membrane to the permeate stream over the total hydrocarbon in the feed. It is shown from Fig. 24 that the hydrocarbon lost decreases when the membrane selectivity increases since the higher

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selectivity membrane is effective in allowing the permeation of more CO2 while retaining the hydrocarbon in the residue stream. From Fig. 25, it is shown that the hydrocarbon lost increases with the CO2 feed composition. This is due to the requirement of more membrane area to remove the increased CO2 content that also enables permeation of more hydrocarbons to the permeate stream. Fig. 24 shows that the percentage hydrocarbon lost is almost similar within the lower membrane selectivity range for all flow configurations. Nonetheless, the distinction becomes apparent for the higher selectivity membrane with the radial crossflow demonstrating the lowest hydrocarbon lost, followed by the countercurrent and the cocurrent fashion. Similarly, for the study of CO2 feed composition effect to the hydrocarbon lost as depicted in Fig. 25, the performance of the different flow configurations based on the hydrocarbon lost is the most effective for the radial crossflow, followed by the countercurrent and cocurrent. The higher hydrocarbon lost of the cocurrent pattern is attributed to the lower separation performance of the configuration by permeating less CO2 and more hydrocarbons when provided the same membrane area for separation. The countercurrent flow experiences higher hydrocarbon lost as compared to the radial crossflow configuration due to availability of more excessive membrane area, which further results in permeability of more hydrocarbons to the permeate stream. Viewing from the aspect of CO2 composition in the retentate as depicted Fig. 24, it is observed to be decreasing with increment in the membrane selectivity since the higher selectivity membrane allows more permeation of the CO2 to the permeate stream. The effect of the feed composition to the CO2 composition in the residue stream is provided in Fig. 25. It is observed that the CO2 concentration in the residue is decreasing with increment in the CO2 feed composition. The decline in the CO2 residue composition is ascribed to the availability of more excessive membrane area among the flow configurations when more driving force for separation is available due to increment in the CO2 feed composition. It is depicted from Figs. 24 and 25 that the performance of the different flow configurations based on removal of CO2 is the most efficient for the countercurrent, followed by the radial crossflow and cocurrent pattern by exhibiting lower CO2 retentate composition at the same membrane area. The higher efficiency of the countercurrent configuration in this context is ascribed to its optimum partial pressure driving force distribution as discussed earlier in Section 3.2.2.1. 3.2.2.3. Compressor power. Figs. 26 and 27 show the effect of the membrane selectivity and CO2 feed composition to the compressor power of the radial crossflow, countercurrent and cocurrent flow configuration when provided the same membrane area for permeation. It is depicted from Fig. 26 that the compressor power decreases since the permeate flow rate or stage cut decreases when the membrane selectivity increases. This is because the higher selectivity membrane allows more permeation of the CO2 under a smaller membrane area requirement that results in a lower permeating flux. On the other hand, from Fig. 27, it is shown that the compressor power increases until a maximum point, while further increment in the CO2 content leads to reduction, which is explained by trend of the membrane area requirement as discussed in Section 3.2.1.1. For both analyses, which are the study on effect of membrane selectivity and CO2 content to the different flow configurations, it is shown that the compressor power requirement is the lowest for the cocurrent fashion, followed by the radial crossflow and the countercurrent. This is attributed to the higher permeation of the countercurrent flow when provided the same membrane area in comparison to the radial crossflow and cocurrent, which

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further increases the duty and power requirement of the auxiliary equipment. 3.2.2.4. Gas processing cost. Figs. 28 and 29 show the effect of the membrane selectivity and CO2 feed concentration to the GPC for the different flow configurations when provided the same membrane area for permeation. Fig. 28 shows that the GPC decreases with increment in the membrane selectivity due to lower hydrocarbon lost, requirement in the compressor power and membrane area. On the other hand, Fig. 29 demonstrates the GPC for analyses of different CO2 feed composition under varying flow configurations. It is depicted from Fig. 29 that the GPC increases with the CO2 feed content until an optimum point, and lead to reduction after reaching that point when the CO2 feed composition is further increased. Similarly, this is ascribed to the trend of the membrane area and the compressor power requirement at different CO2 feed concentration. In both situations, it is depicted from Figs. 28 and 29 that the GPC difference among the radial crossflow, countercurrent and the cocurrent is not that substantial at the lower selectivity and lower CO2 feed composition range. However, the distinction becomes apparent when the membrane selectivity and CO2 feed content increases. The GPC of the radial crossflow configuration is demonstrated to be the lowest, followed by the countercurrent and the

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cocurrent. The countercurrent flow configuration has a higher GPC in comparison to the radial crossflow due to the availability of excessive membrane area that increases the load of the auxiliary equipments and further contributing to more hydrocarbons lost. The cocurrent pattern demonstrates the highest GPC attributed to the lower efficiency in separation by allowing the least permeation of CO2 while retaining the hydrocarbons as compared to the radial crossflow and countercurrent fashion. 4. Conclusion A succession of states coupled with Newton bisection solution algorithm has been established to characterize the separation performance of the hollow fiber membrane module under three different flow configurations: radial crossflow, countercurrent and cocurrent, and later incorporated within the Aspen HYSYS process simulator. The accuracy of the simulated model has been validated with published experimental results, in which the simulated data exhibit good agreement with the laboratory observation. Moreover, the simulation model provides better prediction than previous work that has adapted the simplified crossflow assumption, which is especially apparent at higher stage cuts. The findings highlighted the importance of incorporating the effect of bulk flow configurations in hollow fiber membrane studies particularly under higher permeation flux. The performance of the radial crossflow,

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countercurrent and cocurrent membrane module fashion has been evaluated with consideration of process economics to simulate CO2 separation from natural gas with different membrane selectivity and feed composition. From the analysis, it is predicted that theoretically the countercurrent flow exhibits a slightly higher separative performance in comparison to the radial crossflow, while both being superior to the cocurrent fashion. However, it is found that the flow configuration with the most effective separative performance is not always the most economical configuration since excessive permeation can lead to extra membrane area requirement, compressor load, and unnecessary hydrocarbon lost that increases the gas processing cost. Nevertheless, it is essential to realize that in reality there is no unique flow configuration that is always optimum to the membrane selectivity and CO2 feed composition as presented in the case study since the analysis is limited to the specific operating condition range. In addition, fluctuation of the values, e.g. natural gas price and membrane module cost, used as the basis for calculation of the process economics is predicted to affect the GPC. Nevertheless, the main objective of this analysis is to demonstrate that in addition to the arrangement and design configuration of the membranes that has been demonstrated to be substantial in published literature, the flow configuration is also another important factor to be given consideration. The flow configuration affects the membrane area, hydrocarbon recovery and auxiliary equipment power substantially, which highlights the significance of determining a tradeoff among these parameters to minimize the GPC of the CO2/ natural gas separation plant. In addition, pressure, temperature and composition dependence of permeability coefficients are expected to further amplify the difference among performance of the flow configurations since they would inherently exhibit varying profiles along various locations within the hollow fiber membrane module. Therefore, incorporation of the non-ideal effects to characterize the performance of different flow configurations is of particular interest and will be focus of future treatment. Acknowledgement This work is done with the financial support from Universiti Teknologi PETRONAS. References Ahmad, A.L., Lau, K.K., 2007. Modeling, simulation and experimental validation for aqueous solutions flowing in nanofiltration membrane channel. Ind. Eng. Chem. Res. 46 (4), 1316–1325. Ahmad, F., Lau, K.K., Shariff, A.M., Murshid, G., 2012. Process simulation and optimal design of membrane separation system for CO2 capture from natural gas. Comput. Chem. Eng. 36, 119–128. Ahmad, F., Lau, K.K., Shariff, A.M., Yeong, Y.F., 2013. Temperature and pressure dependence of membrane permeance and its effect on process economics of hollow fiber gas separation system. J. Membr. Sci. 430 (1), 44–55. Antonson, C.R., Gardner, R.J., King, C.F., Ko, D.Y., 1977. Analysis of gas separation by permeation in hollow fibers. Ind. Eng. Chem. Process Des. Dev. 16 (4), 463–469. Baker, R.W., 2002. Future directions of membrane gas separation technology. Ind. Eng. Chem. Res. 41, 1393–1411. Baker, R.W., 2012. Membrane Technology and Applications, 3rd ed. John Wiley and Sons Ltd, Chicester, United Kingdom. Baker, R.W., Lokhandwala, K., 2008. Natural gas processing with membranes: an overview. Ind. Eng. Chem. Res. 47 (7), 2109–2112. Barrer, R.M., Barrie, J.A., Raman, N.K., 1962. Solution and diffusion in silicone rubber: I. A comparison with natural rubber. Polymer 3, 595–603. Chen, H., Jiang, G., Xu, R., 1994. An approximate solution for countercurrent gas permeation separating multicomponent mixtures. J. Membr. Sci. 95 (1), 11–19. Chern, R.T., Koros, M.J., Fedkiw, P.S., 1985. Simulation of hollow-fiber gas separator: the effects of process and design variables. Ind. Eng. Chem. Process Des. Dev. 24 (4), 1015–1022. Chowdhury, M., Feng, X., Douglas, P., Croiset, E., 2005. A new numerical approach for a detailed multicomponent gas separation membrane model and AspenPlus simulation. Chem. Eng. Technol. 28 (7), 773–782. Clarizia, G., Drioli, E., 2003. CO2 separation by membranes in natural gas processing. In: Derouane, V.P.E.G. (Ed.), Nato Advanced study Institute on Sustainable

133

Strategies for the Upgrading of Natural Gas: Fundamentals, Challenges and Opportunities. Springer, pp. 286–292. Coker, D.T., Freeman, B.D., Fleming, G.K., 1998. Modeling multi-component gas separation using hollow-fiber membrane contactor. AIChE J. 44 (6), 1289–1302. Dana, R.A., Yepez-Garcia, J., 2012. Mitigating Vulnerability to High and Volative Oil Prices. The Work Bank, Washington. Davis, R.A., 2002. Simple gas permeation and pervaporation membrane unit operation models for process simulators. Chem. Eng. Technol. 25 (7), 717–722. Donatelli, A.A., 1991. Mathematical and experimental analysis of gas separation by hollow fiber membranes. Ind. Eng. Chem. Res. 30, 1239–1248. Feng, X., Ixory, J., Rajan, V.S., 1999. Air separation by integrally asymmetric hollow fiber membranes. AIChE J. 45, 2142–2152. Ghosal, K., Freeman, B.D., 1994. Gas separation using polymer membranes: an overview. Polym. Adv. Technol. 5 (11), 673–697. Giglia, S., Bikson, B., Perrin, J.E., Donatelli, A.A., 1991. Mathematical and experimental analysis of gas separation by hollow fiber membranes. Ind. Eng. Chem. Res. 30 (6), 1239–1248. Gnanendran, A., Hart, N., 2009. Cryogenic CO2 capture in natural gas. Energy Procedia 1 (1), 697–706. Graham, T., 1866. On the absoprtion and dialytic separation of gases by colloid septa: action of a septum of caoutchouc. Philos. Mag. 32, 399–439. Hao, J., Rice, P.A., Stern, S.A., 2002. Upgrading low-quality natural gas with H2 Sand CO2 -selective polymer membranes: Part I. Process design and economics of membrane stages without recycle streams. J. Membr. Sci. 209 (1), 177–206. Hao, J., Rice, P.A., Stern, S.A., 2008. Upgrading low quality natural gas with H2 Sand CO2 -selective polymer membranes: Part II. Process design, economics and sensitivity study of membrane stages with recycle streams. J. Membr. Sci. 320 (1–2), 108–122. He, X., Hagg, M.B., 2014. Hybrid FSC membrane for CO2 removal from natural gas: experimental. process simulation, and economic feasibility analysis. AIChE J. 60, 4174–4184. He, X., Lie, J.A., Sheridan, E., Hagg, M., 2009. CO2 capture by hollow fibre carbon membranes: experiments and process simulations. Energy Procedia 1, 261–268. Ho, W.S., Sirkar, K.K., 1992. Membrane Handbook, vol. 1. Springer Science and Business, New York. Hussain, A., Hagg, M.B., 2010. A feasibility study of CO2 capture from flue gas by a facilitated transport membrane. J. Membr. Sci. 359 (1–2), 140–148. HYSYS, 2010. Aspen HYSYS Customization Guide. Aspen Technology, Inc., Burlington. Hyun, J.J., Sang, H.H., Young, M.L., Yeong, K.Y., 2011. Modeling and simulation of hollow fiber CO2 separation modules. Korean J. Chem. Eng. 28 (7), 1497–1504. Katoh, T., Tokumura, M., Yoshikawa, H., Kawase, Y., 2011. Dynamic simulation of multi-component gas separation by hollow fiber membrane module: non ideal mixing flows in permeate and residue using the tanks in series model. Sep. Purif. Technol. 76 (3), 362–372. Kundu, P.K., Chakma, A., Feng, X., 2012. Modeling of multi-component gas separation with asymmetric hollow fiber membranes – methane enrichment from biogas. Can. J. Chem. Eng. 91 (6), 1–11. Li, D., Wang, R., Chung, T.S., 2004. Fabrication of lab-scale hollow fiber membrane modules with high packing density. Sep. Purif. Technol. 40 (1), 15–30. Lock, S.S., Lau, K.K., Shariff, A.M., 2015. Effect of recycle ratio on the cost of natural gas processing in countercurrent hollow fiber membrane system. J. Ind. Eng. Chem. 21, 542–551. Lock, S.S., Lau, K.K., Shariff, A.M., 2014b. Mathematical modeling of the radial crossflow hollow fiber membrane module for multi-component gas separation. Appl. Mech. Mater. 625, 726–729. Makaruk, A., Harasek, M., 2009. Numerical algorithm for modeling multicomponent multipermeator systems. J. Membr. Sci. 344 (1–2), 258–265. Marriot, J., Sorensen, E., 2003. A general approach to modelling membrane modules. Chem. Eng. Sci. 58 (22), 4975–4990. Narinsky, A.G., 1991. Applicability conditions of idealized flow models for gas separation by asymmetric membrane. J. Membr. Sci. 35, 333–347. Noble, R., Stern, S., 1996. Membrane Science and Technology Series 2: Membrane Separations Technology Principle and Applications. Elsevier Science, Amsterdam. Pan, C.Y., 1986. Gas separation by high-flux, asymmetric hollow fiber membrane. AIChE J. 32 (12), 2020–2027. Pan, C.Y., Habgood, H.W., 1974. An analysis of the single-stage gaseous permeation process. Ind. Eng. Chem. Fundam. 13 (4), 323–331. Peters, L., Hussain, A., Follmann, M., Melin, T., Hagg, M.B., 2011. CO2 removal from natural gas by employing amine absorption and membrane technology – a technical and economical analysis. Chem. Eng. J. 172 (2–3), 952–960. Pettersen, T., Lien, K.M., 1999. A new robust design model for gas separating membrane modules, based on anology with countercurrent heat exchangers. Comput. Chem. Eng. 18 (5), 427–439. Rautenbach, R., 1990. Process design and optimization. In: Handbook of Industrial Membrane Technology. M.C. Porter, New Jersey, pp. 349–400. Rautenbach, R., Albrecht, R., 1989. Membrane Processes. Wiley & Sons, Chicester. Rautenbach, R., Knauf, R., Struck, A., Vier, J., 1996. Simulation and design of membrane plants with AspenPlus. Chem. Eng. Technol. 19 (5), 391–397. Reid, R.C., Prausnitz, J.M., Sherwood, T.K., 1977. The Properties of Gases and Liquids, 3rd ed. McGraw-Hill, New York. Rezaei, M., Ismail, A.F., Hashemifard, S.A., Bakeri, G., Matsuura, T., 2014. Experimental study on the performance and long-term stability of PVDF/montmorillonite hollow fiber mixed matrix membranes for CO2 separation process. Int. J. Greenh. Gas Control 26, 147–157.

134

S.S.M. Lock et al. / International Journal of Greenhouse Gas Control 36 (2015) 114–134

Sengupta, A., Sirkar, K.K., 1987. Ternary gas mixture separation in two-membrane permeators. AIChE J. 33, 529–539. Shao, P., Huang, R.Y., 2006. An anlytical approach to the gas pressure drop in hollow fiber membranes. J. Membr. Sci. 271, 69–76. Sidhoum, M., Sengupta, A., Sirkar, A.A., 1988. Asymmetric cellulose acetate hollow fibers: studies in gas permeation. AIChE J. 34 (3), 417–425. Soni, V., Abildskov, J., Jonsson, G., Gani, R., 2009. A general model for membrane-based separation processes. Comput. Chem. Eng. 33 (3), 659–664. Sridhar, S., Veerapur, R.S., Patil, M.B., Gudasi, K.B., Aminabhavi, T.M., 2006. Matrimid polyimide membranes for the separation of carbon dioxide from methane. J. Appl. Polym. Sci. 106, 1585–1594. Stern, S.A., Walawender, W.P., 1969. Analysis of membrane separation parameters. Sep. Sci. 4 (2), 129–159. Stookey, D.J., 2001. Gas separation membrane technology. In: Nunes, K.P.S.P. (Ed.), Membrane Technology in the Chemical Industry, vol. 5. Wiley-VCH, New York, pp. 95–123. Teplyakov, V., Sostina, E., Beckman, I., Netrusov, A., 1996. Integrated membrane systems for gas separation in biotechnology: potential and prospect. World J. Microbiol. Biotechnol. 12 (5), 477–485.

Tessendorf, S., Gani, R., Michelsen, M.L., 1996. Aspects of modeling, design and operation of membrane-based separation processes for gaseous mixtures. Comput. Chem. Eng. 20 (1), S653–S658. Thundyil, M.J., Koros, W.J., 1997. Mathematical modeling of gas separation permeators – for radial crossflow, countercurrent and cocurrent hollow fiber membrane modules. J. Membr. Sci. 125 (2), 275–291. United-States-Energy-Information-Administration, 2013. International Energy Outlook. Wijmans, J.G., Baker, R.W., 1995. The solution-diffusion model: a review. J. Membr. Sci. 107 (1–2), 1–21. Woodford, C., Philips, C., 1997. Numerical Methods with Worked Examples, 1st ed. Chapman & Hall, London, United Kingdom. Zhai, S., Foster, J., Ward, S., & Harrison, M. (2013, October 10). Patent No. EP2376374 B1. United States of America. Zhang, Y.T., Dai, X.G., Xu, G.H., Zhang, L., Zhang, H.Q., Liu, J.D., et al., 2012. Modeling of CO2 mass transport across a hollow fiber membrane reactor filled with with immobilized enzyme. AIChE J. 58 (7), 2069–2077. Zhang, Y., Sunarso, J., Liu, S., Wang, R., 2013. Current status and development of membranes for CO2 /CH4 separation: a review. Int. J. Greenh. Gas Control 12, 84–107.