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Analysis of Mass Transfer Performance of Monoethanolamine-Based CO2 Absorption in a Packed Column Using Artificial Neural Networks Kaiyun Fu,† Guangying Chen,† Zhiwu Liang,*,† Teerawat Sema,† Raphael Idem,†,‡ and Paitoon Tontiwachwuthikul†,‡ †

Joint International Center for CO2 Capture and Storage (iCCS), College of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082, P.R. China ‡ International Test Centre for CO2 Capture (ITC), Faculty of Engineering and Applied Science, University of Regina, Regina, Saskatchewan, S4S 0A2, Canada ABSTRACT: Exact and reliable estimation of mass transfer performance is very important for the design, simulation, and optimization of CO2 absorption in a packed column. In this study, two types of artificial neural networks (ANNs), namely backpropagation neural network and radial basis function network, were applied to predict the mass-transfer performance of CO2 absorption into aqueous monoethanolamine (MEA) in packed columns (containing Berl saddles, Pall rings, IMTP random packing, and 4A Gempack, Sulzer DX structured packing, respectively) from input variables. These variables were inert gas flow rate, liquid flow rate, solution concentration, liquid CO2 loading, CO2 mole fraction, temperature, and total packing area, which were considered to predict the targeted output mass transfer variables. The predicted results from ANN were validated against experimental data as well as compared with results from well-known correlations in terms of the volumetric mass flux, CO2 mole fraction, and temperature profiles along the height of the packed column. The comparisons between the predicted and experimental results showed that the proposed ANN models performed very well in predicting mass transfer performance of CO2 absorption into aqueous MEA in a packed column. desired amount of CO2 from the flue gas to the amine solution in a packed column, accurate prediction of the mass transfer efficiency is critical. To maximize the design confidence and to provide the best possible scale-up data for the construction of packed column-based CO2 capture plants, a deep understanding of the fundamental concepts of designing and modeling is essentially needed.9 Presently, CO2 absorption into aqueous amines in a packed column is regarded as one of the most intricate systems because of the existence of complex interactions among hydromechanics, mass transfer, heat transfer, thermodynamics, and kinetics of the chemical reaction. Up to now, a number of empirical or semiempirical correlations have been proposed to predict mass transfer in packed columns. However, these correlations vary in accuracy, limitation, and sometimes system specific applicability. Wang et al.10 presented an extensive review of numerous mass transfer correlations and concluded that the limited experimental data and the lack of understanding of the complex transport phenomena occurring in the packed columns make it difficult to use these correlations with a wide application range and a high level of confidence. To improve reliability and accuracy of the predictive models used for design, simulation, and optimization of CO2 absorption in packed column, it becomes essential to explore advanced predictive correlations for mass transfer performance in packed column.

1. INTRODUCTION One of the most serious environmental concerns facing mankind currently is that of an increased dependence on the combustion of fossil fuels (i.e., coal, petroleum, and natural gas) for energy supply, which results in an increased emission of carbon dioxide (CO2). Thus, a question has arisen as to how to reduce CO2 emission in an economical and efficient way. CO2 capture from fossil fuel-fired power plants, which accounts for approximately 80% of CO2 emissions worldwide, is a major option to mitigate CO2 emissions to the atmosphere .1 Presently, an amine-based CO2 absorption technology in a packed column is considered to be the most commercially mature and cost-effective method for separating CO2 from fossil fuel-fired power plants.2 Of all the amines, monoethanolamine (MEA), the most studied chemical solvent for CO2 capture, is considered to be the bench-mark absorbent which has also been employed industrially for over 50 years.3,4 This technology is especially suitable for absorbing large volumes of low-pressure flue gas, and retrofitting to existing power plants without significant changes in the plant configuration. The characteristics of flue gas (i.e., large volume and low pressure) require large and highly efficient separation equipment to achieve a certain capture efficiency, which directly determines the installed equipment and operational costs. Over the past decades, various separators, such as packed, tray, and spray column, and membrane contactors have been intensively studied and have received significant attention for CO2 absorption.5−8 Among them, the packed column has been widely known to possess high hydrodynamic and mass transfer performance characteristics. To accurately estimate the proper size and height of a packed column required for the transfer of the © 2014 American Chemical Society

Received: Revised: Accepted: Published: 4413

October 1, 2013 January 14, 2014 February 24, 2014 February 24, 2014 dx.doi.org/10.1021/ie403259g | Ind. Eng. Chem. Res. 2014, 53, 4413−4423

Industrial & Engineering Chemistry Research

Article

rules to respond to a new set of input data within the range of the training examples to predict the required output.25 In general, ANN is used to settle engineering problems that are difficult for conventional process simulation tools or mechanistic correlation, as it possesses a high self-mapping ability and does not require prior knowledge of the relationships of the process parameters and accurate mathematical models (or correlations). Moreover, the intricate relationships among fitting parameters increase the freedom of the ANN framework, making them more effective to reflect the complexity of the systems, allowing higher generalization ability, and making them more accurate than common mathematical correlations. For these reasons, it is conventional and effective to use the ANN method to analyze and settle complex engineering problems. There are two kinds of ANNs that are very powerful and practical to approximate complex nonlinear systems: backpropagation neural network (BPNN) and radial basis function network (RBFNN). The emphasis of this paper is to apply BPNN and RBFNN to the simulation of CO2 absorption into aqueous MEA in a packed column through the view of engineering. The high accuracy and outstanding performance of BPNN and RBFNN were validated by comparing the predicted results with experimental data and literature correlations.

With the advent of the ever-accelerated pace of computer technology, computer-aided numerical simulation has enjoyed great popularity and applicability in many aspects of science and engineering. In the field of chemical engineering, a number of process simulation tools, such as artificial networks (ANNs), Aspen Plus, Aspen HYSYS, Promax, and ProTreat, have played important roles in modeling process units and/or optimizing process-configurations with the aims of quality improvement and cost reduction.11−14 For the simulation of CO2 absorption with chemical reaction in a packed column, several main approaches have been used to estimate the mass transfer performance in terms of the volumetric mass flux (NCO2av), mass transfer coefficient, and CO2 concentration and temperature distributions along the column. Ji et al.15 formulated an absorption model in terms of NCO2av to describe the system of CO2 absorption into sodium hydroxide solution (NaOH) in a packed column by using a nonlinear least-squares method. Aboudheir et al.16 developed a rigorous computer model for the simulation of the absorption of CO2 in aqueous 2-amino-2-methyl-1-propanol (AMP) solutions in a packed absorption column that took the effects of heat transfer into account. Liu et al.17 introduced a complex model for simulating the chemical absorption of CO2 in aqueous NaOH in a randomly packed column by combining the quasi-single-liquid-phase computational fluid dynamics (CFD) model, the turbulent mass transfer model with the c 2‐ϵc equations (which considered the influence of concentration field in calculating the turbulent diffusivity) for its closure, and the heat balance equation. In addition, Hanley and Chen18 compared correlation predictions with experimental data in terms of height equivalent to a theoretical plate (HETP), CO2 mole fraction and temperature distributions along the column for a number of different chemical systems, packing types performed with Aspen Rate Based Distillation v7.2.2 While these methods can predict the chemical absorption of CO2 in a packed column effectively, they suffer numerous drawbacks in presenting a feasible model, such as the requirements of (i) a high-level understanding of intricate relationships among the parameters, (ii) huge databases within software, (iii) explicitly predefined rules or equations, and (iv) the simulation performing in an ideal way. For example, Aspen plus has been widely used in the modeling of CO2 capture by aqueous MEA solution in a packed column and achieved good prediction results. This is because MEA has been well studied for CO2 capture, and the thermodynamic and kinetics data are adequate for the MEA− CO2−H2O system within an amine package. However, as to new and data-limited solvents and packings, the fundamental data and the underlying relationships in the chemical mass transfer process are either unknown or difficult to determine, thereby making Aspen plus modeling powerless. For more than five decades, especially within the past 15 years, artificial neural networks (ANNs) have found widespread application in diverse fields such as pattern recognition, identification, classification, and controlling systems owing to their powerful ability to deal with the uncertainties of noisy data or linear or nonlinear relationships.19−24 An ANN attempts to mimic human brain activities, mapping from a set of given data (input data) to an associated set of known data (target output), comparing the output of the network to the given data, and then adjusting the internal weights and biases, with the goal of minimizing the error between the network output and the target output. Once the learning (or training) process is satisfactorily completed, the neural network hence generates a set of certain

2. THEORETICAL BASIS OF CO2−MEA−H2O SYSTEM 2.1. Chemical Reactions. According to the generally accepted zwitterion mechanism, which was originally proposed by Caplow26 and reintroduced by Danckwerts27 for primary amine reactions with CO2, MEA interacts with CO2 in a 2:1 ratio; that is, one molecule of MEA absorbs CO2 to form a zwitterion, while another one acts as a base for the deprotonation of a zwitterion. The reaction of CO2 with MEA (RNH2 denotes as MEA): k1, k −1

RNH 2 + H+ ←⎯⎯→ RNH+3 k 2 , k −2

CO2 + RNH 2 ←⎯⎯→ RNH+2 COO−

(1) (2)

Dissociation of dissolved carbon dioxide to carbonic acid: k 3 , k −3

CO2 + H 2O ←⎯⎯→ HCO−3 + H+

(3)

Formation of bicarbonate: k4 , k −4

CO2 + OH− ←⎯⎯→ HCO−3

(4)

Dissociation of bicarbonate: k5 , k −5

HCO−3 ←⎯⎯→ H+ + CO32 −

(5)

Ionization of water: k6 , k −6

H 2O ←⎯⎯→ OH− + H+

(6)

where ki is the second order forward rate coefficient for reaction (i), and k−i is the backward rate coefficient for the reaction (i). Reactions 2 and 4 are considered to be reversible with finite reaction rates, whereas reactions 1, 3, 5, and 6 are considered to be reversible, instantaneous, and at equilibrium, since they involve only proton transfer.28 4414

dx.doi.org/10.1021/ie403259g | Ind. Eng. Chem. Res. 2014, 53, 4413−4423


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2.2. Kinetics Model Based on Zwitterion Mechanism. From the zwitterion mechanism, the general reaction rate of CO2 with MEA is given as follows: rCO2 =

3. MODELING AND OPTIMIZATION METHOD FOR MASS TRANSFER WITH CHEMICAL REACTION The design and scale-up of a packed column for various packings require accurate assessments of mass transfer models such as the volumetric mass flux, the mass transfer coefficients of the gas and liquid phases, and the effective interfacial area. Generally, researchers assess the reliability of the model on the basis of the deviation of the predictions and experimental results. 3.1. Basic Theory of Mass Transfer. The mass flux per unit volume of CO2 (NCO2av) transferring from the gas phase to a liquid bulk at a steady state can be expressed as5

+ k −2 + − ∑ k −b[RNH3 ] [RNH COO ] 2 ∑ k b[B] k2 k −2 1 + k ∑ k [B] k2 2 b

[CO2 ][RNH 2] −

(7)

where rCO2 is the overall CO2 absorption rate, B is a base which could be amine, H2O, or OH−. kb and k−b are the forward and backward second order reaction-rate constant for base B, respectively. In the case of the deprotonation of the zwitterions being very fast, such as in the CO2−MEA reaction, k−2/ k2[RNH+2 COO−]∑k−b[RNH3+]/∑kb[B] is usually considered to be negligible, and hence, the rate of reaction can be reduced to rCO2 =

* ) NCO2a v = K Ga v P(yCO − yCO 2

where NCO2av is the mass flux per unit volume of CO2, KGav is the gas-phase volumetric overall mass transfer coefficient, P is the total pressure, yCO2 and y*CO2 represent the mole fraction of CO2 in the gas phase and in equilibrium with the bulk concentration, respectively. The term y*CO2 can be calculated by

[CO2 ][RNH 2] 1 k2

+

k −2 k 2 ∑ k b[B]

(8)

Moreover, a formation of the zwitterion has been shown to be much slower than the reverse rate to MEA and CO2, and is considered to be the rate determining step, which can be defined as k −2/(k 2 ∑ k b[B]) ≪ 1/k 2

* = yCO 2

(9)

2152 T

2

HeCO2

(13)

HeCO2 1 1 = + K Ga v k Ga v EkLoa v

(10)

(14)

where av is the effective interfacial area, kG is the gas-phase mass transfer coefficient, koL is the physical liquid-phase mass transfer coefficient, and E is the enhancement factor. Substituting eq 14 into eq 12 and rearranging yields:

Hikita et al.29 proposed the following correlation for the k2, which depends on the temperature: k 2 = 10.99 −

PyCO

where yCO2 is the CO2 mole fraction, and HeCO2 represent Henry’s law constant of CO2 in solution. The relationships among the overall volume mass transfer coefficient, the individual-phase coefficients, effective interfacial area, and enhancement factor can be given as follows:5

Hence, the reaction rate in eq 7 can be simplified to the following expression, where the reaction rate appears to be first order with respect to concentration of amine and CO2: rCO2 = k 2[CO2 ][RNH 2]

(12)

2

(11)

NCO2a v =

2.3. Physical and Thermodynamic Properties. The physicochemical properties of the fluids (i.e., solubility, density, viscosity, surface tension, and diffusivity) are necessary for analyzing the CO2 absorption process because of their great influence on the mass transfer performance, especially on the effective interface area and the liquid film coefficient. The density and viscosity of MEA solution were taken from the work of Weiland et al.30 who took CO2 loading into account, and developed empirical equations to describe the density and viscosity of the MEA solution as a function of temperature, concentration, and CO2 loading. However, when the concentration is higher than 40 wt % MEA, the viscosity correlation of Weiland et al.30 becomes inapplicable, and therefore we need to seek a more suitable correlation. Hsu and Li31 developed a Redlich−Kister equation-based correlation for the estimation of the viscosity, which can be used for MEA concentrations higher than 40 wt %. The predicted results of viscosity showed good agreement with experimental data, with an average deviation at about 1.0%. The physical solubility and diffusivity of CO2 can be calculated via the N2O analogy because of the similarity of the molecular weight, chemical configuration, volume, and electronic structure between CO2 and N2O.32−34 In addition, the surface tension of the aqueous MEA solution was obtained from the correlation developed by Vazquez et al.35

a v EkLoP(HeCO2yCO − yCO ) 2

(1 + E HeCO2kLo/k Ga v )

2

(15)

Considering an element of column with height (dZ), the mass balance can also be expressed as follows: NCO2a v = G I

dYCO2 dZ

(16)

where G1 and YCO2 represent molar flow rate of inert gas and mole ratio of CO2 in the gas phase, respectively. 3.2. Numerical Model of Mass-Transfer Correlations. Up to the present, extensive empirical or semiempirical correlations have emerged for various random and structured packings. These correlations are based on a huge number of experimental data and theoretical assumptions and, therefore, their application scope, precision, and stability sometimes vary considerably. Among these correlations, the mass-transfer correlations proposed by Onda et al.36 and Henriques de Brito et al.37 are two widely used models for random and structured packings, respectively.5 The Onda’s correlations, which were developed based on the experiment data of Raschig rings, Berl saddles, Pall ring, Spheres packing, and Rode packing, have been highly recommend by many publications such as Perry’s Handbook5 to apply to various random packings. These 4415



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al.,38 which deviates by less than 3% from the most accurate solution, was therefore adopted here:

correlations were present based on the assumption that the wetted surface on packing pieces is equal to the effective gas− liquid interface. The effective surface area (ae), the physical liquid-side mass transfer coefficient (koL), and the gas phase mass transfer coefficient (kG) in packed columns are shown in eqs 22−24.

E = 1 + {1/[1/(E∞ − 1)1.35 + 1/(E1 − 1)1.35 ]}(1/1.35) (23)

−0.05 0.1 ⎧ ⎛ σc ⎞0.75⎛ L ⎞ ⎛ L2a t ⎞ ⎪ ae ⎟⎟ ⎟⎟ ⎜⎜ = 1 − exp⎨− 1.45⎜ ⎟ ⎜⎜ ⎪ at ⎝ σL ⎠ ⎝ a tμL ⎠ ⎝ ρL 2 g ⎠ ⎩

⎛ L ⎞ ⎜⎜ ⎟⎟ ⎝ ρL σLa t ⎠ 2

0.1⎫

⎪ ⎬ ⎪ ⎭

(24)

E1 =

(25)

Ha /tanh( Ha )

Ha = (k 2DamineCamine)/(kLo)2

(26)

(17)

⎛ ρ ⎞ kLo = 0.0051⎜⎜ L ⎟⎟ ⎝ μL g ⎠

−0.33

⎛ L ⎞ ⎜ ⎟ ⎝ aeDL ⎠

0.67

⎛ μ ⎞ ⎜⎜ L ⎟⎟ ⎝ ρL DL ⎠

where E is the enhancement, E∞ is the enhancement factor for instantaneous reaction, E1 is the enhancement factor of a pseudofirst-order reaction, υAB is the stoichiometry of reactants for absorption reaction, CCO2 is the CO2 concentration in liquid phase, Camine is the concentration of amine solution in the bulk liquid, Damine and DCO2 are the diffusivity of amine and CO2 in liquid, respectively, and Ha is the Hatta number. 3. 4. Artificial Neural Networks Modeling. As is wellknown, artificial neural networks (ANNs) have the powerful ability to recognize underlying linear and nonlinear relationships among input and output data.39 The basic topology structure of an ANN is composed of a number of simple and highly interconnected processing elements called neuron units which are organized within multilayers (i.e., one input layer, one output layer, and at least one hidden layer). Each neuron unit is completely interconnected with neuron units in neighboring layers by means of direct communication linked with associated weights. ANNs work by receiving limited representative samples data, learning complex relationships among these data in certain algorithms, adjusting the weights of the internal connections to minimize errors between the network output and target output, and responding to unseen input data to predict targeted output within the range covered by the training examples. This type of procedure is highly amendable to predicting mass transfer performance of CO2 absorption in an amine solution. The two ANN approaches BPNN and RBFNN were considered for mass transfer performance prediction application. 3.4.1. Back-Propagation Neural Network (BPNN). BPNN, as one of the most classic ANNs,40 is based on the steepest gradient descent method with attempt to minimize the error (normally presented in term of root-mean-square of percentage error, RMSPE) between the input and output values. In a BPNN, a portion of input/output pattern pairs selected from a sample data set are used to train the network, and then the network iteratively adjusts its connection weights and bias values according to the feedback errors, which are calculated between the network output and actual output. After being well trained, the BPNN can then be used to predict the unseen target parameters. Figure 1 shows the general architecture of a three-layer BPNN with multiple input nodes and a single output node. The training procedures of BPNN algorithm can be summarized as follows: (1) Collecting all required data, and selecting a portion of input/output pattern pairs from the sample data set. (2) Normalizing all the data (scaled data between 0 and 1) in the program in order to decrease the sample distribution range. This is one of the most suitable methods for data preprocessing, especially when the values of these input/output variables differ by more than 1 order of magnitude.

−0.5

(a tdP)0.4 (18)

⎛ D ⎞⎛ G k G = 5.23⎜ L ⎟⎜⎜ ⎝ RT ⎠⎝ a tμ

⎞0.7 ⎛ u ⎞0.33 ⎟⎟ ⎜⎜ G ⎟⎟ (a td p)−2.0 ρ D G ⎠ ⎝ G G⎠

(19)

where ae and at are the effective and total surface area of packing, respectively, σc and σL are the critical surface tension of packing material and the surface tension of liquid, respectively, L and G are the liquid and gas phases flow rate, μL and μG are the viscosity of liquid phase and gas phase, respectively, ρL and ρG are the liquid density and gas density, respectively, g is the gravitational constant, DL and DG are the diffusion of the liquid and gas phase, respectively, dp denotes nominal size of packing. The correlations developed by Henriques de Brito et al.37 were proposed for predicting ae, koL, and kG for the Sulzer structured packing Mellapak 125.Y, 250.Y, and 500.Y. under industrial-scale operating conditions. In their model, the effective mass transfer area of the packing can be considerably higher than the defined geometric area of the packing owing to liquid flow instabilities, leading to waves, film detachment, and droplet formation between the sheets. ⎛ ρ uL ⎞0.3 ae = 0.465⎜⎜ L ⎟⎟ at ⎝ a tμL ⎠

kLo =

E∞ = 1 + [(DamineCamine)/υABDCO2CCO2]

(20)

(DL k 2CA,L)0.5 Ha

0.8 0.3 ⎛ DG ⎞⎛ ρG uGdh ⎞ ⎛ μG ⎞ ⎟⎟ ⎜⎜ ⎟⎟ k G = 0.0338P ⎜ ⎟⎜⎜ ⎝ dh ⎠⎝ μG cos 45° ⎠ ⎝ ρG DG ⎠

(21)

(22)

where uL and uG are the superficial velocity of liquid and gas flows, respectively, CA,L is the concentration of solute A in the bulk liquid, Ha is the Hatta number, P is the pressure, and dh is the hydraulic diameter of packing. 3.3. Enhancement Factor. In comparison with pure physical mass transfer, chemical reaction-accompanied mass transfer would greatly enhance the absorption rate beyond pure physical diffusion because the reacting species is consumed within liquid-film very quickly thereby preserving a very great driving force. The enhancement factor (E) refers to the increase in mass transfer due to the chemical reaction relative to purely physical absorption. The explicit equation presented by Wellek et 4416



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ek = −(dk − Ok )f k′

(32)

f k′ = 1

(33)

where ek is the vector of errors for each output neuron unit, dk is the kth desired output value, f ′k is the derivative of the activation function (i.e., purelin function) for output nodes. Then, the hidden layer errors become: n

ej = f h′ (∑ wkjek ) k=1

f h′ = hj(1 − hj)

th

(27) th

n

∑ wijxi + bj i=1

hj = fh (n j) =

1 1 + exp( −n j)

(28)

(29)

where subscripts i and j represent the input and hidden layer nodes, respectively, x is the normalized input, wij is weight linked the ith input node to the jth hidden layer node, and b is the bias between the input and hidden layers, h is the vector of hiddenlayer neurons, f h(nj) is the logistic sigmoid activation function. (4) Transferring the net hidden layer signal to the kth node in the output layer by summing the weights and the biases, and calculating the output of the kth node in the output layer using the purelin transfer function.

nk =

∑ wkjxj + b k j

Ok = fk (nk ) = nk

wkj(t + 1) = wkj(t ) + rek + η(wkj(t ) − wkj(t − 1))

(36)

b k(t + 1) = b k(t ) + rek

(37)

where r is the learning rate, η is the momentum factor, and t is the calculation period. These calculation steps will be repeated constantly to train the model until the output layer errors are acceptable for each pattern and neuron. On the other hand, although overtraining the BPNN model makes training data fit well, it will reduce the generalization ability of the model since the random noise from new data (for testing) will be quite different from that of training data. A common solution is to set a maximum number of iterations to stop the training process early even if setting the training goal is not achieved. Although the BP algorithm is successful in training a feed forward network, it is subjected to some drawbacks of slowly learning convergent rate and easily converging to local minimum. In addition, the selections of step size, learning rate, momentum, and the number of hidden neurons largely depend on trial-anderror and experience. Hornik et al.41 argued that a BP network with only one hidden layer and sufficient neurons can approximate any nonlinear function to an arbitrary degree of accuracy. 3.4.2. Radial Basis Function Neural Network (RBFNN). RBFNN enjoys much praise in recent years due to its remarkable properties of (i) the powerful abilities for generating multivariate nonlinear mapping functions, (ii) structure determination by self-adaptation, and (iii) the independence of output on initial weight.39,42 RBFNN is a feed-forward network with three layers: one input layer, one output layer, and only one hidden layer. Figure 2 shows the structure of a basic RBFNN with multi-input and single output. The input−output mapping undergoes two steps: (i) the mdimensional input vector I1, I2, ..., Im collects the input information and nonlinearly transforms from the input layer to the hidden layer, and (ii) the hidden layer consisted of n hidden nodes linearly transforms information from hidden layer to output layer. The connections between the input and hidden layers and the connection between the hidden layer and output layer are called centers and weights, respectively.

where xi is the i normalized input variable; Ii is the i original input variable; Imax and Imin are the maximum and minimum among all original input variables, respectively. (3) Transferring the net input signal to the jth node in the hidden layer by summing the weight and the bias, and calculating the output of the jth node in the hidden layer. The logistic sigmoid activation function (range between 0 and 1), which is the most popular function in BPNN because of its powerful ability to simulate the nonlinear relations, was used between the inputhidden layers. nj =

(35)

where ej is the vector of errors for each hidden layer neuron unit, f ′h is the derivative of the activation function (i.e., logistic function) for hidden nodes. (6) Adjusting the weights and biases in the output layer:

Figure 1. The general architecture of a three-layer BPNN with multiple inputs and single output, where I1, I2, ..., In and Ok represent the input vector and the output vector, respectively, x1, x2, ..., xn are the normalized input vector, w1j, w2j, ..., wnj’ are weight factors associated with the inputs to the node, and bj is the threshold connecting the hidden and output layers.

I − Imin xi = i Imax − Imin

(34)

(30) (31)

where subscript k represents the output layer, wkj is the weight linked the jth hidden layer node to the kth output layer, and bk is the threshold linked the hidden to output layers. Ok is the output of output-layer neurons. f k (nk) is a linear activation function. (5) Calculating the errors between the calculated and the desired outputs:

K

Ok =

∑ w k θ k (I ) + b k=1

4417

(38)



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values greatly differ from the targeted values, one has to readjust many times the sample data, the configuration parameters, or the network topological structure, until the error between model output and target value is acceptable. Step 4: After being well trained, the RBFNN model can then be used to predict the target parameters. In RBFNN, it is very important to determine the number of neuron in the hidden layer because it affects the complexity and the approximating capability of the network. Too many neurons in the hidden layer may lead to poor generalization or overfitting, while insufficient neurons cannot learn the data adequately. In addition, the position of the centers in the hidden layer also affects the network performance significantly, while the nonlinear transfer functions used by RBFNN have little influence. 3.5. Data collection. The building of a predictive model requires a series of representative data sets that should factually and effectively reflect the nonlinearities, complexities, and intricacies of the targeted system behavior. In this paper, five databases of MEA-based mass transfer results were collected from the work of Tontiwachwuthikul et al.,43 and deMontigny.44,45 The detailed parameters of the packed columns and the operational variables are presented in Table 1. Tontiwachwuthikul et al.43 carried out a number of experiments for the absorption of air-diluted CO2 into aqueous MEA solution. The absorber column was packed with 12.7 mm ceramic Berl saddles with a total packing height of 6.55 and 0.1 m in diameter. DeMontigny44 reported the absorption data of CO2 absorption into ultrahighly concentrated MEA solution over the range of 2.98 kmol/m3 to 9.02 kmol/m3 in a pilot plant absorption column containing 16 mm Pall rings, IMTP#15 random packing, and 4A Gempack structured packing. DeMontigny45 also conducted CO2 absorption by MEA in the absorption column by using the Sulzer DX type packing. The experiments were performed in a small scale pilot-plant absorption column of 2.35 m packing height and 0.028 m in diameter. All these experiments were conducted in a countercurrent mode in order to provide a larger mass transfer force for the gas and liquid phases contacting with each other. Once the steady-state conditions were reached, the CO2 concentrations in the gas phase and solution temperatures were collected along the column height for different gas/liquid ratios, inlet CO2, and solution concentration.

Figure 2. The general architecture of a three-layer RBFNN with multiple inputs and single output, where I1, I2, ..., Im and Ok denote the input and output of the network, θk(I) is the radial basis function, w = (w1, w2, ..., wK) is the connecting weights between the hidden neuron and the output layer, and b is the bias value.

where I1, I2, ..., Im and Ok denote the input and output of the network, m is the number of input variables, w = w1, w2, ..., wK) is the connecting weights between the hidden neuron and the output layer, n is the number of hidden neurons, θk(I) is the radial basis function, b is the bias value. The activation function usually chosen for the hidden node is a Gaussian function: θ k(I ) = exp( −|| I − μ k ||2 /σk2)

(39)

where μk denotes the center vector of the kth hidden neuron, ∥I − μk∥ is the Euclidean distance between I and μk, and σk is the radius or width of the kth hidden neuron. Like BPNN, the forecast by means of RBFNN first determines the structure of the RBF network and the input−output data set based on the practical problems, so as to achieve the corresponding mapping relationships. Within the Matlab program, the training procedures of the RBF algorithm can be summarized as follow: Step 1: Design the input−output pattern, mainly including (i) the selection of key parameters, (ii) the design of input and output variables, and (iii) the preprocessing of sample data. Step 2: Determine the center and width of the radial basis function and the weights information between hidden layer and output layer. Step 3: Call the newrbe function to create the RBFNN, and call the sim function to test the established network. If the output

4. RESULTS AND DISCUSSION For the CO2 absorption with chemical reaction in a packed column with a special packing, 14 factors could have potential impact on the hydromechanics and mass transfer performance. These factors are inert gas flow rate (GI, kmol/(m2·h)), liquid

Table 1. The Parameters of the Columns and the Operational Variables

diameter of the column (mm) hight of packing (m) packing gas phase CO2 concentration (%) inert gas load (kmol/m3h) liquid flow rate (m3/m2h) solvent concentration (kmol/m3) CO2 loading (mol CO2/mol amine) feed temperature (K) pressure (atm)

Tontiwachwuthikul et al.43

deMontigny44

deMontigny45

100 6.15 Berl saddles 11.5−19.2 39.96−53.28 9.5−13.5 2.0−3.8 0−0.237 19.0−20.0 1

100 2.40 Pall ring, IMTP, 4A Gempack 5.3−19.9 31.79−72.58 6.94−23.96 2.98−9.02 0.105−0.228 22.5−28.3 1

28 2.35 Sulzer DX 13.92−14.54 30.7−30.9 5.4−12.8 1.0−3.0 0.030−0.195 17.6−21.7 1

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flow rate (L, m3/(m2·h)), solution concentration (C, kmol/m3), CO2 loading in solution (α, mol/mol), CO2 mole fraction (yCO2), temperature (T, K), reaction kinetics (k2, kmol/(m2·h·kPa)), liquid and gas phase density (ηL and ηG, kg/m3), liquid and gas viscosity (μL and μG, cp), diffusivity of CO2 in liquid and gas phases (DL and DG, m2/h), and liquid surface tension (σL, mN/ m). In the above 14 parameters, only 6 parameters (G, L, C, α, yCO2 and T) are independent, and the remaining eight can be obtained by a combination of the other parameters. By means of BPNN and RBFNN models, this paper focuses on the prediction of MEA-based CO2 absorption in packed columns containing Berl saddles, Pall rings, IMTP#15 random packing, and 4A Gempack, Sulzer DX structured packing, respectively. The predicted results were validated with experimental results as well as compared with numerical correlations from available literature, so as to verify the effectiveness and accuracy of the BPNN and RBFNN models. The simulated data in this work were derived from original experimental results; that is, multiple sample points in each experimental run, along with the value for the packed height in which α, yCO2, and T varied greatly while L, GI, and C were assumed to be constant. Note that those data containing extremely low α and yCO2 were left out of the model prediction to avoid as far as possible misuse of experimental data with high relative error due to almost inevitably operating and systematic errors. The BPNN and RBFNN were developed within the Matlab R2010a program with the neural network toolbox. The mass flux per unit volume per unit interfacial volume (NCO2av, kmol/(m3·h)) is convenient and effective in assessing the mass transfer performance of any solvent and packing in a packed column, and is also a key parameter for designing the packed columns. The design methodology and steps can be found in the work of Liang et al.9 who gave a detailed review of the design and modeling for postcombustion CO2 capture systems using reactive solvents. So, the prophase of this work is to predict the NCO2av of MEA−CO2 absorption. The predicting results were evaluated by average absolute deviation (AAD), root-mean-square of percentage error (RMSPE), and the correlation coefficient (R). These evaluation parameters display how closely the model prediction matched the experimental results. Figure 3 shows a parity plot of the experimental values of NCO2av compared with those predicted values obtained from

BPNN and RBFNN as well as those predicted values obtained from the correlation proposed by Onda et al.36 for the MEA− CO2 absorption in a column packed with Berl Saddles. In this simulation, the AAD, RMSPE, and R for BPNN and RBFNN were found to be 1.8% and 0.7%; 2.7% and 1.7%; 0.996 and 0.999, respectively, which are favorably acceptable for mass transfer study. By contrast, the AAD, RMSPE, and R for the correlations of Onda were 25.9%, 32.3%, and 0.878, respectively. Therefore, these two ANN models were found to greatly outperform the correlations of Onda et al.36 especially in low NCO2av value conditions, in which the relative error for BPNN and RBFNN were much smaller than that of the Onda’s correlations. In addition, the RBFNN performed slightly better than the BPNN, probably due to two reasons: (i) the drawback of BPNN easily converges to a local minimum of the error surface and thus the global minimum is not found; and (ii) to achieve the predicted goal under the same accuracy requirement, RBFNN generally possesses more neurons in the hidden layer than BPNN, thereby increasing the freedom of the network, which helps to reflect the complexity of the system. Similar results were observed in the cases of the Pall ring, IMTP, 4A Gempack, and DX packing in that the predicted results obtained from the present work were found to (i) fit favorably with the experimental results and (ii) be better than those predicted from the correlations proposed by Onda et al.36 as can be seen in Figure 4a−d. Additionally, the RBFNN was observed to perform slightly better than BPNN. The evaluation parameters are presented in Table 2. According to the parity charts as presented in Figures 3 and 4, it can be found that the BPNN and RBFNN have the capacity to predict NCO2av with adequate accuracies for several packings (Berl saddles, Pall ring, IMTP, 4A Gempack, and DX). However, it should be acknowledged that the comparisons presented in Figures 3 and 4 are unfair. This is because the correlations proposed by Onda et al. and Henriques de Brito et al. were developed on the basis of the data of multiple packings, while the ANN models performing in this work were well trained for each type of packing. To further validate the outstanding performance of BPNN and RBFNN, we attempt to develop individually two models for random packings (by combining all data of three random packing) and structured packings (by combining all data of two structured packing) by using BPNNs and RBFNNs. As is well-known, the total packing area at is an important parameter in mass transfer prediction because it will affect the hydromechanics and mass transfer performance greatly. In the modeling of the CO2 absorption into aqueous MEA in packed columns for different packings, besides the six key parameters mentions above (i.e., G, L, C, α, yCO2 and T), at should be considered as another input value for the model designing since it varies from packing to packing. Figure 5 shows the comparisons of predicted NCO2av values from BPNN and RBFNN against experimental values for random and structured packings. As can be seen in Figure 5, the predicted results from BPNN and RBFNN are found to be very close to the experimental values with AAD of 2.9% and 1.7%, respectively for random packings; and 4.8% and 3.6%, respectively for structured packings. Needless to say, the approaches of the ANNs are well suited for application in the estimation of mass flux. In the present work, the AAD values for structured packings were found to be higher than that of random packings. This could be because of the less experimental data (22 runs: 14 runs for 4A Gempack, 8 runs for DX packing) for structured packings to be used for building a

Figure 3. Comparisons between predicted and experimental NCO2av for CO2 into MEA in column containing Berl saddles. 4419



Article

Figure 4. Comparisons between predicted and experimental NCO2av for CO2 into MEA in column containing (A) Pall ring, (B) IMTP, (C) 4A Gempack, and (D) DX packing.

Table 2. Statistical Analysis of Correlations (corr) on the Mass Flux number of data sets data source Tontiwachwuthikul et al.43 deMontigny44

deMontigny45

AAD (%)

R

RMSPE (%)

packing

total

training

testing

corr

BPNN

RBFNN

corr

BPNN

RBFNN

corr

BPNN

RBFNN

Berl saddles

160

120 (75%)

40 (25%)

25.9

1.8

0.7

32.3

2.7

1.7

0.878

0.996

0.999

Pall ring IMTP 4A Gempack DX

196 764 208

147 (75%) 573 (75%) 156 (75%)

49 (25%) 191 (25%) 52 (25%)

18.2 24.1 22.1

2.4 2.6 5.3

0.1 0.2 3.4

25.7 29.5 26.7

4.5 4.0 10.8

0.1 0.6 4.2

0.966 0.916 0.892

0.999 0.998 0.989

1.000 1.000 0.998

68

51 (75%)

17 (25%)

25.4

6.4

4.9

37.1

8.5

7.3

0.854

0.981

0.988

comprehensive neural network to find the relationship among the key parameters, while there are 52 runs (10 runs for Berl saddles, 7 runs for Pall ring, and 35 runs for IMTP) for random packings that can be used. In most cases, the CO2 mole fraction and temperature profiles along the height of the column can reflect the prediction results more directly and effectively. To simulate the CO2 concentration and temperature profiles, only inlet gas/liquid flow conditions are generally known, not the outlet conditions. Thus, the problem of two-point boundary value would then occur. To obtain an output, the shooting method is recommended.16,43,46 In this work, the algorithm of the formulated ANNs model to calculate the CO2 concentration and temperature profiles was done as follows: (i) Build an ANN model based on the experimental data in which at, G, L, C, α, yCO2, and T are considered as input

values, while dyCO2/dZ and dT/dZ are considered as output values. (ii) Assume a CO2 mole fraction in the outlet as yout CO2. (iii) Estimate the first set of y1CO2 and T1 at a certain height of Z1, which should be very close to the column top. In this case, the distance ΔZ1 between Z1 and the column top (Ztop) can be considered as differential height dZ. (iv) Calculate corresponding CO2 loading a1 at a column height of Z1 based on mass balance. 1 1 (v) Put the values of the (y1CO2 + yout CO2)/2, (a + ain)/2, (T + Tin)/2; and the other four factors into the established model, then obtain predicted values of (Δy1CO2/ΔZ1)pre 1 and (ΔT1/ΔZ1)pre, where Δy1CO2 = y1CO2 − yout CO2 and ΔT = T1 − Tin 4420



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Figure 5. Comparisons between predicted and experimental NCO2av for CO2 into MEA in a column containing (A) random packings, (B) structured packings.

Figure 6. Concentration (A) and temperature (B) profiles along the height of the column for CO2 absorption into MEA in a column packed with IMTP random packing (dots are experimental data obtained from deMontigny44 (run B-023), lines are the predicted results obtained in the present work).

(vi) Compare the values of the predicted (y1CO2)pre and (T1)pre with those of the estimated (y1CO2)est and (T1)est, if the differences for both values are acceptable, then proceed; otherwise, go back to Step (ii). (vii) Iteratively calculate until (ynCO2)pre ≅ yinCO2. (viii) End the algorithm. Figures 6 and 7 show comparisons of the CO2 mole fraction and temperature profiles between the predicted results obtained from BPNN and RBFNN and the experimental results (runs B023 and C-003) obtained from the work of deMontigny.44 The AAD values of the CO2 mole fraction and temperature profiles between the simulation results from BPNN and RBFNN; and experimental results for both random and structured packings were found to be in the acceptable range of less than 10% as shown in Figures 6 and 7. This observation clearly shows that the proposed two ANNs models can be effectively used for predicting CO2 concentration and temperature profiles along the height of the column for CO2 absorption, the column packed with randomly packing (Berl saddles, Pall rings, and IMTP) and structured packing (4A Gempack and DX packing).

5. CONCLUSIONS In this work, we employed two artificial neural networks, BPNN and RBFNN, to the simulation of the CO2 absorption into aqueous MEA in a packed column. The predicted results of mass flux obtained from this work via BPNN and RBFNN modeling were compared with the numerical correlations reported in the literature. It was clearly observed that the ANN modeling (BPNN and RBFNN) provided better predicted results. It was also found that the RBFNN modeling performed slightly better than BPNN modeling. In addition, the CO2 concentration and temperature profiles along the height of the column were

Figure 7. Concentration (A) and temperature (B) profiles along the height of the column for CO2 absorption into MEA in a column packed with 4A Gempack structured packing (dots are experimental data obtained from deMontigny44 (run C-003), lines are the predicted results obtained in the present work). 4421



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t = calculation period, s T = temperature, K wij = weights connecting the ith input node to the jth hidden layer node for BPNN wkj = weights connecting the jth hidden node to the kth output layer node for BPNN wk = connecting weights for RBFNN xi = the ith normalized input variable for BPNN yA* = mole fraction of solute A in equilibrium with CA,L yA,G = mole fraction of solute A in the bulk gas-phase yA,i = mole fraction of solute A at the interface YA = mole ratio of component A in gas bulk Z = height, m

successfully predicted using ANN with a satisfactory AAD of less than 10%.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-13618481627. Fax: +86-731-88573033. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The financial supports from the National Natural Science Foundation of China (No. 21276068, No. U1362112 and No. 21376067); National Key Technology R&D Program (No. 2012BAC26B01, No.2014BAC18B04); Innovative Research Team Development Plan-Ministry of Education of China (No. IRT1238); Specialized Research Fund for the Doctoral Program of Higher Education (No. 20130161110025); Innovative Research Program for Graduate Student of Hunan Province, China (No. CX2013B158); and China’s State “Project 985” in Hunan UniversityNovel Technology Research & Development for CO2 Capture are gratefully acknowledged.

Greek Symbols

■

NOMENCLATURE α = liquid CO2 loading, mol CO2/mol amine av = effective interfacial area, m2/m3 at = total packing surface area, m2/m3 b = bias value BPNN = back-propagation neural network C = solution concentration, kmol/m3 CA,i = concentration of component A at the interface, kmol/m3 CA,L = concentration of component A in the bulk liquid, kmol/ m3 dh = hydraulic diameter, m dk = desired output value for BPNN dp = nominal size of packing, m Di = diffusivity of phase i, m2/h ek = vector of errors for BPNN E = enhancement factor E1 = enhancement factor for a pseudo-first-order reaction Ei = enhancement factor for instantaneous reactions GI = inert gas flow rate, kmol/(m2·h) hi = the ith input variable for BPNN Ha = Hatta number He = Henry’s law constant, m3·kPa/kmol Ii = the ith input variable kG = gas side mass transfer coefficient, kmol/(m2·h·kPa) KGav = gas-phase volumetric overall mass transfer coefficient, kmol/(m3·h·kPa) koL = physical liquid-phase mass transfer coefficient, kmol/(m2· h·kPa) ki = second order forward rate coefficient for reaction i, m3/ (kmol·h) k−i = second order reverse rate coefficient for reaction i, m3/ (kmol·h) L = liquid flow rate, m3/(m2·h) NCO2av = CO2 absorption rate per unit area, kmol/(m3·h) Ok = output vector for BPNN P = total system pressure, kPa PCO2 = partial pressure of CO2, kPa r = learning rate RBFNN = radial basis function network

■

θk() = radial basis function f h() = logistic sigmoid activation function from input layer to hidden layer for BPNN f h′ = local slope of the node activation function for hidden nodes for BPNN f k() = purelin transfer function from input layer to hidden layer for BPNN f k′ = local slope of the node activation function for output nodes for BPNN μi = viscosity of phase i, cp μk = center vector of the kth hidden neuron for RBFNN ρi = density of phase i, kg/m3 η = momentum factor σc = critical surface tension of the packing material, mN/m σL = surface tension of liquid phase, mN/m σk = radius or width of the kth hidden neuron for RBFNN

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