Indian Jornal of Chemical Technology

Vol. 11, November 2004, pp. 820-824

network. It consists of multi-layer hierarchicalstructure, which, apart from input and an output layer,has at least one layer of processing units betweenthem. The layers between the input and output layersare termed "hidden" since they do not converse withthe outside world directly. The nodes between the twosuccessive layers are fully connected by means ofweights. That is output from the input layer are fed tothe hidden layer units, which in turn, feed theiroutputs to the next hidden nodes. The hidden nodepasses the net activation through a non-lineartransformation of a linear function, such as the log,sigmoidal or hyperbolic tangent to complete theiroutputs.

For the training of such a MLP error backpropagation algorithm suggested by Rumelhare ispopular. This is based on a non-linear version of theWindro-Hoff rule known as Generalized Delta Rule(GDR). The schematic of the MLP network with twohidden layer is as shown in Fig. 1.

Various applications of ANN are, an approach tofault diagnosis in chemical processes:', fault diagnosisin complex chemical plants", incipient fault diagnosisof chemical process", leak detection in liquefied gas. 1· 610 + .. f +pipe me', Lor estimation 0 mass transrer

coefficient for fast fluidized bed solids 7, modelling ofdistillation column" detergent formulation", modelling

Modelling of packed column using artificial neural networksS L Pandharipande=" & S A Mandavgane"

"Laxminarayan Institute of Technology, Nagpur University, Nagpur 440010, India.

bDr C V Raman Institute of Technology, Nagpur, India

Received 29 October 2003; revised received J5 May 2004; accepted 8 June 2004Packed column is an established gas liquid contacting device with many industrial applications. Estimation of liquid

hold up and pressure drop as a function of gas and liquid flow rates for single as well as two phase flow are of significancefrom operational as well as design point of view. Various empirical models have been suggested for the same. ArtificialNeural Networks (ANN) are gaining importance in modelling of multivariable, non-linear relationship with high accuracyand even in presence of inadequate data. In present work multi layer perceptron (MLP) ANN with GDR based learning havebeen developed for estimation of liquid hold up and pressure drop for packed column. The ANN models thus developed areobserved to be of good accuracy level, both for training and test data set.

IPC Code: B 0] D 3/26Keywords: Artificial neural networks, ANN, packed column, Ergun's equation,

Columns contammg a packing material such asRasching rings are frequently used as absorbers. Thepacking is used inside the column to effect gas andliquid contact. A gas stream containing thecomponent to be removed is forced up the column bya blower or compressor, while a stream of liquidflows down the column under the influence ofgravity. During this counter current flow, thecomponent in question is absorbed into the liquidphase. An alternative use for a packed column is insystems where the liquid phase contains thecomponent, which is stripped by the gas phase.

Artificial neural networkAn Artificial Neural Network (ANN) is an

information-processing paradigm that is inspired bythe way the biological nervous systems such as thebrain processes information. It is composed of largenumber of highly interconnected processing elements(neurons) working in unison to solve specificproblem'.

The most common for chemical engineeringapplications is MLP, which is a feed-forward neural

*For correspondence(E-mail: slpandharipande@rediffmail.com;Fax: 0712-2561107)

PANDHARIPANDE & MANDA VGANE: MODELLING OF PACKED COLUMN USING NEURAL NETWORKS 821

XI

X,

Fig. 1 - Artificial neural network

of unsteady state heat conduction in semi-infinitesolid II, prediction of mass transfer coefficient indown flow jet loop reactor" and modelling of heatexchanger" etc.

In the present work, artificial neural networks aredeveloped 18 for modelling of packed column forestimation of liquid hold up and pressure drop as afunction of liquid as well as gas flow rates for singlephase and two phase counter current system. Forsingle-phase system Ergun's correlation wasvalidated. The data required for training of thesenetworks has been generated by .using a packedcolumn fabricated for this purpose. The trainednetworks were then used for prediction of theseparameters and comparison has been carried outbetween actual and predicted values.

Experimental ProcedurePacked column details

The packed column fabricated is a glass columnof 750 mm height. The details of the packed columnare presented in Table 1. It is fitted with stationaryheads at both the ends. It is equipped with twonozzles at each end for the entry of liquid and gas.The glass column contains random packing ofRaschig rings. Packed height across manometertapping is 440 mm. Table 2 indicates the details ofpacking. The column was packed with Raschig ringsof II) 6 mm, OD 9.5 mm and length 9 mm. The voidfraction of the packed bed € was 0.68 with specificsurface area of packing (ap) 508. The characterizationfactor of packing for two-phase flow was 1000.

Experimental set-upThe schematic diagram for the experimental set-

up is as shown in Fig. 2.

Water rotameter

Air exit

Manometer

Water tank

Water exit

Com ressed air

Fig. 2 - Experimental set-up for hydrodynamic study of packedcolumn

Table 1 - Packed column details

Sf No. DimensionParts

Column ID 50mm

2 Column height 750mm

3 Packing height 440mm

Table 2 - Details of packing material 13

6mm 9.5 mm 9 mm 0.68 508 1000

Provisions for water to pump into the columnfrom the top as well as compressed air from thebottom were made. The operational range of liquidflow-rate and gas flow-rate are presented in Table 3.U tube water manometer was fitted across the columnwith a distance of 440 mm between the tapings torecord the pressure drop for the corresponding flowrates.Method and data generationSingle phase flow

When a single phase flows through a packedcolumn, the relationship between pressure drop andflow rate is reasonably well correlated by Ergun' sEquationI2

•13

.

822 INDIAN J. CHEM. TECHNOL., NOVEMBER 2004

Table 3 - Operational parameters

SrNo. Parameter Units Value

Liquid flow rate kg/m2.s 1.4-12.0

2 Gas Flow rate kglm2s 0.05-0.55

3 Manometer fluid Water

4 Liquid Water

5 Gas Compressed air

6 Temperature °C 30

M £3dpPg. = 150(1- £) + 1.75Z (1-£)G 2 Re

... (1)

simplified as

f = 150 +1.75Re'

where

... (2)

Re'= dppV.u(l-£)

The term on the left side of Eqs (1) and (2) is afriction factor. The first term on the right hand siderepresents the laminar flow contribution to the frictionfactor, while the second term represents the turbulentflow contribution.

For single-phase flow, for different airflow rates(range between 0.05 kg-0.5 kg/m' s), pressure dropacross the column was noted down. The data thusgenerated experimentally was processed analyticallyby Eq. (1) and compared with the results obtained bythe model developed by ANN.

... (3)

Two phase flow (gas-liquid)

The pressure drop across the packed column isinfluenced by the gas and liquid flow rates. At fixedgas velocity, the gas pressure drop increases withincreased liquid flow rate, principally because of thereduced free cross-section available for flow of gasresulting from the presence of the liquid. For differentwater flow rates, by varying the gas flow rate thepressure drop was recorded at steady state.

In present work, the pressure drop and liquid holdup were recorded as a function of gas and liquid flowrates.

Table 4 - Neural network topology for packed column withsingle-phase flow

Number of neurons Data points

Input Ist IInd IIIrd Output Training Test Learninglayer Hidden Hidden Hidden layer rate

layer layer layer

2 10 0.9510 10 2 13 5

* First momentum factor = 0.75* Second momentum factor = 0.01

Table 5 - Neural network topology for packed column with two-phase flow

Number of neurons Data points

Input 1st IInd IIlrd Output Training Test Learninglayer Hidden Hidden Hidden layer rate

layer layer layer

2 5 6 0.9555 2 24

* First momentum factor = 0.75

* Second momentum factor = 0.01

The data thus generated was divided into twoparts; training data set and test data set. The trainingdata set was used for training of the network whereasthe test data set was used for testing the extent towhich the network was trained. Out of 18 data pointsgenerated in single-phase flow, 13 points were usedas training data points whereas 5 were used as testdata points. Similarly, in two-phase flow the total 30data points generated were divided as 24 training datapoints and 6 test data points.

The topologies of ANN are as shown in Tables 4and 5. These were arrived at after few trials. InTable 4, the two nodes in input layer, for single-phasesystem, denote gas flow rate in kg/m's and modifiedReynold's number where as the two nodes in outputlayer represent pressure drop and friction factor.Similarly, in Table 5 two nodes in input layerrepresents liquid flow rate in kg/m's and gas flow ratein kg/m's whereas two nodes in output layers denotepressure drop and liquid hold-up.

Various ANN architectures were tried fordeveloping model for single-phase and two-phaseflow. The most accurate of these models are presented

. 18here. It was observed that the present software withthree hidden layers could model more complicatedI . I .. . 915 16 dc rerruca engmeenng operations" as compare to

ANN topology with two hidden layers.

PANDHARIPANDE & MANDAVGANE: MODELLING OF PACKED COLUMN USING NEURAL NETWORKS 823

320~--------------------------------,

~ 270e:,~ 220"C

~ 170~a 120~ii 700':

20~~--~------r------'-----'------120 70 170 220 270120

Actual pressure drop (Palm)

Fig. 3 -- Comparison between actual and predicted values forpressure drop. (Training data set)

320~-------------------------------.

~ 270e:,e 220"C

e~ 170~ 120~~ 70'"

70 120 170 220 270Actual pressure drop (Palm)

Fig. 4 -- Comparison between actual and predicted values forpressure drop. (Test data set)

5.2

•... 4.7

~ 4.2.!!

~ 3.7:.s

3.2~'0 2.7~s,

2.2

Calculated Irictlcn factor r

Fig. 5 -- Comparison between actual and predicted values formodified friction factor. (Training data set)

Results and DiscussionThe single phase flow

Figures 3-6 represent comparison between actualand predicted values of pressure drop and modifiedfriction factor. As can be seen from these graphs,predicted values are in close agreement with theactual values. Figs 7 and 8 represent the!' versus Re'graph, for the packed column (single phase) using theexperimental and' the predicted data respectively.Hence, it can be said that the ANN Model developedfor the estimation of pressure drop and modifiedfriction factor as a function of gas flow rates has beensuccessful and has very good accuracy levels.

5.2

4.7•...Co

t 4.2::c

3.70

"'8~ 3.2~'0 2.7..•...'" 2.2

1.71.7 2.2 2.7 3.2

Calculated friction factor rFig. 6 -- Comparison between actual and predicted values for

modified friction factor. (Test data set)

10~----------------------------1

1 +---------.----------,---------110 100 1000 10000

Re'

Fig. 7 -- The modified friction factor as a function of modifiedReynolds number from Ergun's equation. (From actual data)

10.-----------------------------~

1+-------.-------r----~10 100 1000 10000

Re'

Fig. 8 -- The modified friction factor as a function of modifiedReynolds number from Ergun's equation. (From predicted data)

7000...-----------------------------------....,~ 6000e:,!5000

~ 4000~50 300e)1l.;; 2000'e•.. 1000

1000 2000 3000 4000 5000 6000 7000Actual prcssut'c drop (Palm)

Fig. 9 -- Comparison between actual and predicted values forpressure drop across the column (Training data set)

824 INDIAN J. CHEM. TECHNOL., NOVEMBER 2004

2500.--------------------------,~ 2000!1500~[ 1000]'0 500~Ow ---.--.--.---,.,----,..----1

500 1000 1500 2000 2500Actual pressure drop (Palm)

Fig. 10 - Comparison between actual and predicted valuesfor pressure drop across the column (Test data set)

0.4

M0.35E

1 0.3a.:> 0.25'0'0s: 0.2'0

's0.15g

'0

~ 0.1'C

0.05£0

0 0.1 0.2 0.3 0.4

Actual liquid holdup (m3lm3)

Fig. 11 - Comparison between actual and predicted valuesfor liquid hold-up of the column (Training data set)

0.4

M 0.35EM 0.3.§.c. 0.25:>'0'lI 0.2s:

~ 0.15g-e 0.1~ 0.05'¥0.. 0

a 0.05 0.1 0.15 0.2 0.25 0.3 0:35 0.4

Actual liquid holdup (m3/m3)

Fig. 12 - Comparison between actual and predicted valuesfor liquid hold-up of the column (Test data set)

The two-phase flow

Figures 9 and 10 represent actual and predictedvalues pressure drop in two-phase flow for trainingdata set and test data set respectively. SimilarlyFigs 11 and 12 show actual and predicted values ofliquid hold-up for training data set and test data setrespectively.

ConclusionFrom these graphs, it can be concluded that the

ANN models developed for packed column have been

successful and have very high accuracy levels. If pastdata is available related to the packed column, then itcan be used for training of artificial neural networkthat would predict the pressure drop and liquid hold-up as a function of liquid and gas flow rates with highdegree of accuracy.

Nomenclatures

= internal diameter

= outer diameter

E = void fraction of packed bed

ap (m2tm3) = specific surface area of packing (area/volume)

C, = characterization factor of packing, two-phase flow

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