Heat and mass transfer model for diseccant solution

Proyecto Final

Investigación de artículo científico;

Heat and Mass Transfer Model for Desiccant Solution Regeneration Process in Liquid Desiccant Dehumidification System

Fenómenos de Transferencia de Calor y Masa

Adalberto Cortés Ruiz

Instructor: Dr. Miguel Ángel Morales Cabrera

Introducción

Planteamiento del problema

En este artículo de investigación, se desarrolla un modelo para describir el proceso de transferencia

de calor y masa de un regenerador de desecante líquido en columna empacada para la

deshumidificación del aire.

Al relacionar las propiedades termodinámicas de los fluidos y las especificaciones geométricas como

constantes, se desarrollan dos ecuaciones relacionadas con siete parámetros identificados para

predecir la velocidad de transferencia de calor y masa para los procesos de regeneración de la

solución en el regenerador. La información de puesta en marcha y el método de Levenberg-

Marquardt se emplean para determinar los parámetros desconocidos. En comparación con los

modelos anteriores (reportados en literatura), el modelo presentado es simple y preciso y no

requiere cálculos iterativos mientras se aplica en la predicción de la tasa de transferencia de calor y

masa una vez que se determinan los parámetros del modelo propuesto. Los resultados

experimentales demuestran que el modelo actual es eficaz para predecir el rendimiento de la

regeneración del desecante en el regenerador en condiciones de trabajo amplias. El modelo

propuesto promete tener amplia aplicación para monitoreo, optimización y control de desempeño

en tiempo real para la regeneración de desecantes líquidos

Consideraciones en los modelos

Durante el desarrollo de modelos de fenómenos de transporte de masa y calor aplicados a este

proceso, es común despreciar los mecanismos de transporte molecular, debido a que, al ser

comparados con los mecanismos de transporte por convección forzada, estos son muy pequeños.

Conceptos básicos

La deshumidificación consiste en retirar el vapor de agua o humedad, contenida en el aire.

Los desecantes son sustancias que atrapan las moléculas de agua en el ambiente por medio de

procesos de adsorción o absorción, son conocidas como sustancias higroscópicas, (Murphy &

Bradley, 2005). De esa manera, Los sistemas por desecación, se llevan a cabo poniendo en contacto

la corriente de aire húmedo con un desecante, que provoca la migración de la humedad, por

absorción o adsorción, hacia el desecante.

Metodología

Proceso general de la deshumidificación con desecante líquido

En el proceso de deshumidificación con desecante líquido (Figura 1), el aire húmedo se circula a través de un deshumidificador a contracorriente, el cual, consiste en un contenedor con una serie de paredes en zigzag o forma escalonada para la retención del desecante líquido que cae por aspersión, absorbiendo así, la humedad del aire entrante.

En los fondos del deshumidificador, 2, se tiene desecante líquido saturado de humedad. Los fondos se bombean hasta un intercambiador de calor y después se calientan con un sistema de circulación de agua caliente, 3. A partir de ahí, el desecante líquido comienza a desprender humedad debido al calor suministrado. Esta humedad es arrastrada por una corriente de aire, a esta parte del proceso se le conoce como regeneración, y consiste meramente en una columna empacada de la misma forma que el deshumidificador, y se le conoce como regenerador.

Finalmente, los fondos del regenerador, 4, se recirculan hacia el intercambiador de calor en contracorriente con la corriente de desecante líquido saturado, a fin de minimizar la cantidad de energía y tiempo que requerirá el enfriador para disminuir la temperatura del desecante líquido, 1, de tal forma que sea posible la absorción de la humedad en el aire.

Figura 1. Esquema del sistema de deshumidificación del desecante líquido.

Transferencia de Calor y Masa en el Regenerador

Modelo de transferencia de Calor

El empacado en la columna se aplica a menudo en el regenerador para aumentar el área de contacto

de la disolución desecante con el aire, porque se formará una película delgada sobre la superficie

del material de relleno cuando la disolución desecante caiga a lo largo de los canales del empaque

(Figura 2). La disposición escalonada del empaque puede aumentar el efecto convectivo entre el

aire caliente de regeneración ascendente y la disolución desecante descendente. Se produce una

transferencia de calor sensible entre los dos fluidos a través de los canales del empacado. El calor

se transfiere desde la solución desecante caliente en convección hasta la interfase, se realiza a

través de la interfase y finalmente se transfiere al aire de regeneración.

La velocidad de transferencia de calor se expresa con la ley de Newton del enfriamiento:

, ,( )ov s in a inQ h A T T (1)

Donde , ,, , , s in a inQ A T T y ovh son el flujo de calor, el área de transferencia de calor, la temperatura

del desecante en la entrada, la temperatura del aire de regeneración en la entrada y el coeficiente

global de transferencia de calor, respectivamente.

El coeficiente global de transferencia de calor es determinado a partir de la siguiente analogía de

resistencias:

1 1ov

s s m m a a

hh A A h A

(2)

Donde , , , , ,m s a s ah h A A y mA son el espesor de la interfase, la conductividad térmica de la

interfase por conducción, el coeficiente de transferencia de calor local por convección del aire de

regeneración, el coeficiente de transferencia de calor local por convección de la disolución

desecante, el área de transferencia de calor del aire de regeneración, el área de transferencia de

calor del desecante y el área de transferencia de calor de la interfase, respectivamente.

Si se supone las áreas de transferencia de calor son la misma, y la resistencia de la conducción es

muy pequeña, de tal forma que se puede despreciar, el coeficiente global de transferencia de calor

es determinado por:

1

1 1ov

s a

hh h

(3)

El tipo de transferencia de calor entre la disolución desecante y el aire de regeneración puede

considerarse como una transferencia de calor por convección forzada. Para la transferencia de calor

por convección forzada, el coeficiente de transferencia de calor, h , depende del diámetro del paso,

D , la velocidad del fluido, v , y también influye a través de la temperatura media de la película por

la viscosidad del fluido, , calor específico, pc (para la humedad del aire, se utiliza calor húmedo)

y la conductividad térmica , respectivamente. La siguiente ecuación se ha desarrollado después

del análisis dimensional, (método de Buckingham):

f

Nu C Re Pr (4)

Donde / , /Nu hD Re D v y /pPr c son los números adimensionales que se

presentan en la transferencia de calor y dinámica de fluidos, mientras que C y los exponentes y

f son los parámetros constantes que se deben determinar.

Figura 2. Representación esquemática del regenerador para la disolución desecante.

Expresando la Ec. (4) en términos del diámetro de paso y del flujo másico y despejando h :

4f

pcmh C bm

D D

(5)

Siendo 4f

pcb C

D D

Sustituyendo las Eq. (5) en (3)

1

1 11

a as s

ovas s a a

as

s

b R mh

bb m b mR

b

(6)

Donde sm y am son los flujos másicos del desecante líquido y el aire de regeneración,

respectivamente. /as a sR m m es la relación del flujo de aire y la del desecante, sb y ab son dos

constantes que relacionan los coeficientes de la disolución desecante y el aire de regeneración.

Combinando (1) y (6), se obtiene una expresión que define el flujo de calor en la columna empacada

(regenerador) a partir de éste modelo hibrido:

3

3

1 ,

, ,

2 ,1

c

a s s

s in a inc

a s

c R mQ T T

c R

(7)

Donde 1 2 3, / , .a a sc b A c b b c

Modelo de transferencia de Masa

En el proceso de regeneración, se tienen tres resistencias de transferencia de masa para el vapor de

agua que va en la disolución desecante al aire de regeneración: la resistencia en la propia solución

desecante, la que es en la interfase de los dos fluidos y finalmente la resistencia del aire de

regeneración.

La resistencia de la interfase entre los dos fluidos puede ser muy pequeña y se puede despreciar

porque el flujo de la disolución es veloz y se aplica generalmente en el regenerador y la transferencia

de masa entre el aire de regeneración y las soluciones desecantes en la interfase son muy rápidas

comparadas con la transferencia de masa dentro de la disolución desecante o del aire de

regeneración. Además, se puede suponer que existe un estado de equilibrio en la interfase en

términos de transferencia de masa. Consecuentemente, la transferencia de masa con la fuerza

impulsora en términos de la presión de vapor de agua en la fase vapor puede ser descrita para

desarrollar el modelo híbrido en naturaleza empírica:

*

, ,G s in a inN K P P (8)

Donde *

,, , G s inN K P y ,a inP son el flux másico, el coeficiente global de transferencia de masa en el

regenerador, la presión en el equilibrio de la disolución desecante y la presión del vapor de agua en

la entrada del aire de regeneración, respectivamente.

GK puede expresarse con base la ley de Henry y la teoría de la película bajo la analogía de

resistencias,

1

1/ 1/G

a s

Kk Hk

(9)

Donde , a sk k y H son el coeficiente de transferencia de masa por convección en la fase vapor, son

el coeficiente de transferencia de masa por convección en la fase líquida y la constante de Henry,

respectivamente.

Las correlaciones para los coeficientes de transferencia de masa para las fases vapor y líquida en la

columna empacada del aire de regeneración y la disolución desecante están dadas por (Onda,

Takeuchi, & Okumoto, 1968):

1 1

1

1 2

4e f

ga H a t a

a t p

t a a a

m Dk a D

D D RT

(10)

2 2 2

2

2 2

4e f j

gs s s

s t p

w s s s s

mk a D

D D g

(11)

w es el área húmeda superficial específica, t es el área superficial específica, y pD es el tamaño

nominal del material del empaque, que se determina por la geometría del relleno y permanece

constante para un cierto tipos de materiales, aD , H , a y sD , s , s son la difusividad, el

volumen de humedad o la densidad y la viscosidad del aire de regeneración y la disolución

desecante, respectivamente. Suponiendo que no hay variaciones bruscas en la temperatura, se

reducen a:

1

3

,

1e

a a

a in

k b mT

(12)

2

4

e

s sk b m (13)

Donde 3b y

4b agrupan todos los términos constantes de las Ecs. (10) y (11), respectivamente.

Sustituyendo todas estas ecuaciones en la Ec. (8) y reduciendo términos, se obtiene la expresión

final que determina el flux másico en la columna empacada.

6

6 7

4 *

, ,

5 ,1

c

s

s in a inc c

a in s a

c mN P P

c T m m

(14)

La presión ,a inP se determina a partir de la definición de la humedad relativa:

, , ,a in a in a satP P (15)

La presión *

,s inP se determina por aproximación por medio de una expresión polinomial que está

en función de la temperatura de la fase líquida en la entrada.

Validación experimental de los modelos

La validación se hizo a escala piloto

, ,a a out a inN m Y Y (16)

, ,a a out a in wQ m H H N (17)

Donde ,a outY , ,a inY , ,a outH y ,a inH son la humedad absoluta y la entalpía del aire de regeneración

en la salida y en la entrada, respectivamente. Estos parámetros se determinan experimentalmente

de manera indirecta, es decir, a través de la temperatura, humedad relativa y flujos másicos.

Tomando como datos reales, se tiene una desviación tipo error porcentual máximo aceptable del

10%, lo que quiere decir que el modelo del flujo de calor puede tener validez hasta 1.6 kW, mientras

que para el modelo para el flux másico es de 0.016 kg/(m2s)

Figura 3.Predicción del modelo para el flujo de calor y el flux másico.

Conclusiones

Artículo

Se presentó un modelo híbrido simple que es adecuado para el monitoreo del desempeño,

optimización y control de regeneradores desecantes líquidos operativos. El rendimiento de los

procesos de transferencia de calor y masa en el regenerador de desecante líquido puede ser

predicho por el modelo híbrido desarrollado con sólo siete parámetros característicos.

A diferencia de otros modelos anteriores, sólo participan en este modelo variables relacionadas con

la entrada con el regenerador, de manera que se puede evitar el cálculo iterativo cuando se aplica

el modelo propuesto en la predicción de rendimiento para el regenerador de desecante líquido.

Además, los parámetros complejos como las propiedades termodinámicas de los fluidos, las

especificaciones geométricas de empaque y los números termodinámicos (Reynolds, Nusselt y

Prandtl) se consideran parámetros agrupados y pueden identificarse mediante datos operativos. De

acuerdo con los resultados de la validación, el modelo de regenerador actual es lo suficientemente

preciso para la predicción del desempeño y el monitoreo

En una amplia gama de funcionamiento: velocidad de transferencia de calor de 0,6 a 1,6 kW y flujo

de masa de 0,002 a 0,016 kg / m2s. El modelo actual, con sólo siete parámetros implicados, es

simple, flexible, relativamente preciso y fácil para aplicaciones de ingeniería en comparación con los

modelos anteriores del regenerador.

Personal

Los de sistemas de deshumidificación tienen distinto tipo de aplicaciones, son sistemas simples y

efectivos para combatir los problemas de humedad ambiental, retardar la corrosión por humedad

y mantener intactas las características de equipos y productos almacenados. Por ejemplo, en ciertos

productos de la industria alimenticia, se deben mantener a cierto nivel de humedad relativa, por lo

que un ambiente seco previene que estos productos vayan incrementando su nivel de humedad

relativa, manteniendo así, el nivel estándar de humedad que debe contener.

Desde el punto de los fenómenos de transporte y del proceso, disponer de un modelo simple para

la estimación del flux másico y el de calor es importante a la hora de llevar a cabo el control de un

proceso en el que su eficiencia dependerá principalmente de la transferencia de masa y de la

temperatura (calor).

En el artículo se abordan conceptos vistos en clase como:

Ley de Newton del enfriamiento

Analogía de resistencias

Difusión por convección (forzada)

Condiciones de frontera (equilibrio: Ley de Henry)

Conceptos de la teoría de la película

Además de que se aplica el método de Buckingham para la determinación de parámetros constantes

que resultarían difícil de calcular por medio del uso de balances y leyes, ya que se podrían involucrar

un mayor número de variables.

Referencias

Murphy, J., & Bradley, B. (2005). Advances in desiccant-based dehumidification. Trane Engineers

Newsletter, 34(4).

Onda, K., Takeuchi, H., & Okumoto, Y. (1968). Mass transfer coeffients between gas and liquid

phases in packed columns. J. Chem. Eng. Jpn, 56-62.

Artículo citado

Wang, X., Cai, W., Lu, J., & Ding, X. (2014). Heat and Mass Transfer Model for Desiccant Solution

Regeneration Process in Liquid Desiccant Dehumidification System. Industrial &

Engeneering Chemistry Research, 10.

Heat and Mass Transfer Model for Desiccant Solution RegenerationProcess in Liquid Desiccant Dehumidification SystemXinli Wang,†,‡ Wenjian Cai,*,‡ Jiangang Lu,† Youxian Sun,† and Xudong Ding‡

†State Key Laboratory of Industrial Control Technology, Department of Control Science and Engineering Zhejiang University,Hangzhou 310027, China‡EXQUISITUS, Centre for E-City, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore639798

ABSTRACT: In this paper, a simple model, but with high accuracy for a packed column liquid desiccant regenerator, to describethe heat and mass transfer process is developed. By lumping fluids’ thermodynamic properties and the geometric specifications asconstants, two equations related with seven identified parameters are developed to predict the heat and mass transfer rate forsolution regeneration processes in the regenerator. Commissioning information and the Levenberg−Marquardt method areemployed to determine the unknown parameters. Compared with previous models, the presented model is simply constructedand accurate and requires no iterative computations while applied in predicting the heat and mass transfer rate once theparameters of the proposed model are determined. Experimental results demonstrate that the current model is effective to predictthe performance of desiccant regeneration in the regenerator over wide working conditions. The proposed model promises tohave wide application for real-time performance monitoring, optimization, and control for liquid desiccant regeneration.

1. INTRODUCTION

During the past several decades, the liquid desiccantdehumidification system (LDDS) has achieved a steady risefor air dehumidification in comfort conditioning of buildings.Compared with the conventional cooling-based dehumidifica-tion method by cooling air below the dew point, the LDDSshows excellent performance characteristics with the possibilityof energy conservation through turning the energy usage awayfrom electric power to low grade and renewable energyforinstance solar energy, industrial waste heat, etc.;1withflexibility in operation of independent air humidity andtemperature control; and with the advantage of employingthe environment-friendly hygroscopic salt solutions as workingfluids which do not deplete the ozone layer.2

The study on liquid desiccant air dehumidification can betraced back to 1955 when the first open-cycle air-conditioningsystem operating with triethylene glycol as the liquid desiccantwas designed by Lof.3 Since then a large number of studies havebeen made on system design,4,5 experimental investigation6,7

and performance evaluation.8−10 Among these, the develop-ment of the heat- and mass-transfer models in LDDS isessential for all of these studies. So far, three kinds of modelshave been developed, namely: finite difference model,effectiveness number of transfer units (NTU) model, andempirical model.11 In the finite model, the packed column isdivided into small control volumes, and the energy and materialbalances are solved in each control volume. Wide investigationhas been carried out on the finite difference model to predictthe performance of LDDS due to the high accuracy.Gandhidasan et al.12 and Factor and Grossman13 proposedtheoretical models for the LDDS to analyze the hea- and mass-transfer processes in both dehumidifier and regenerator undervarious operating conditions, and good agreement was achievedbetween the experiments and the theoretical model. Oberg and

Goswami14 carried out investigations on coupled heat- andmass-transfer processes of a liquid desiccant dehumidifier byexperimental investigation and proposed a finite differencemodel. Fumo and Goawami15 and Yin et al.16 made somemodifications based on the model proposed by Oberg andGoswami to discuss the performance of a random-packingLDDS with lithium chloride as desiccant solution. Theanalytical solution of the modified finite difference model isdeveloped by employing some linear approximations, andoutlet conditions can be estimated more accurately through thismethod.17 Babakhani and Soleymani18 presented a finitedifference model to describe heat and mass transfer processfor the packed liquid desiccant regenerator and the analyticalsolution of the model war also given. However, it is quitecomplex to develop and solve the finite difference models anditerative calculation is essential since outlet states of fluids aregeneral unknown, therefore the finite model is not suitable tobe utilized in real-time performance evaluation and optimiza-tion of the LDDS.19

For the NTU and empirical approaches, Chen et al.19

presented NTU models for both counter-flow and parallel-flowconfigurations in a packed-type LDDS. The solution of theproposed models has satisfactory accuracy when compared tothe data available from the literature. Liu et al.20 developed atheoretical model using NTU as input parameter correlatedwith the corresponding experimental data to simulate the heatand mass transfer process in a cross-flow dehumidifier andregenerator. Further, the authors showed that the analyticalsolutions which can be utilized in optimization design of the

Received: September 18, 2013Revised: January 11, 2014Accepted: January 29, 2014Published: January 29, 2014

Article

pubs.acs.org/IECR

© 2014 American Chemical Society 2820 dx.doi.org/10.1021/ie403102x | Ind. Eng. Chem. Res. 2014, 53, 2820−2829

pubs.acs.org/IECR

LDDS based on the available NTU model.21 Sensitivity analysisof the heat- and mass-transfer process were carried out by Khanand Ball22,23 conducted in a packed-type liquid desiccantsystem to determine the dehumidifier and regeneratorperformance by using methods of an empirical nature. Thoughthe empirical models are easy to develop, some crucialparameters related to the performance of the system shouldbe obtained in advance which is very difficult in practicalapplications. Furthermore, accuracy will be reduced if it isextended over a wider operating region.The finite difference models can give predictions with good

accuracy, but the solving process is time-consuming andrequires iterative computing. The NTU model and theempirical model are simplified but with low accuracy whenthey are expanded. These models are unsuitable for real-timeperformance monitoring and optimization and control of aliquid desiccant regenerator for which accurate operating dataand heat/mass transfer prediction in real-time are required.In this report, a hybrid modeling approach based on an

empirical nature and system operating data to develop simplemodels,24−26 for real-time applications of performancemonitoring and optimization and control of the regenerator,is presented. By lumping dimensionless and thermodynamicparameters into seven characteristic parameters, the heat- andmass-transfer process in the regenerator can be described bytwo simple nonlinear equations. An experiment is carried out todetermine the related parameters by using the Levenberg−Marquardt method, and the identified model is then varified bythe operating data collected from the experiment in real-time.Also, the comparison between the presented model andprevious studies are made.

2. THE ANALYSIS OF OPERATING LDDS

The dehumidifier and the regenerator are the two maincomponents in the liquid desiccant dehumidification system(LDDS), as shown in Figure 1. The dehumidifier dehumidifiesthe process air, and the regenerator regenerates the diluteddesiccant solution to an acceptable concentration from thediluted solutions in the dehumidifier. Figure 2 describes watervapor pressure changes of the desiccant solution in operating

the LDDS. The cool, strong desiccant solution (state 1) isdistributed into the dehumidifier on the top, and the process airis blown into the dehumidifier at the bottom, making contactwith the falling desiccant solution in a counterflow config-uration. Water vapor pressure in the process air is greater thanthat in the cool, strong desiccant solution; hence, the watervapor in the process air can be absorbed by the desiccantsolution. The difference in the water vapor pressure betweenthe process air and the desiccant solution acts as the mass-transfer driving force. This process is described by lines 1−2 inFigure 2. The moisture that transfers from the process air leadsto a dilution of the desiccant, resulting in a reducing of theability to absorb water vapor. To reuse the desiccant solution, aheater is employed to heat the diluted desiccant solution (2−3), and the heated solution will be pumped to be concentratedby regenerating the air in the regenerator. Mass transfer in thedirection opposite to that which happens in the dehumidifiertakes places in the regenerator since the hot, diluted desiccantsolution has greater water vapor pressure than that of theregenerating air, and thus, the absorbed moisture during thedehumidification process can be transferred from the desiccant

Figure 1. Scheme of a packed liquid desiccant dehumidification system.

Figure 2. Water vapor pressure changes of desiccant solution duringthe cycle.

Industrial & Engineering Chemistry Research Article

dx.doi.org/10.1021/ie403102x | Ind. Eng. Chem. Res. 2014, 53, 2820−28292821

solution to the regenerating air, shown by 3−4. Although thedesiccant solution is regenerated, the surface vapor pressure isstill high due to the high temperature. Therefore, the desiccantsolution should be cooled down until state 1 where thedesiccant solution can be reached to complete the cycle.In the LDDS, the regenerator consumes a large amount of

thermal energy. To regulate the fan and pump so thatmaximum energy efficiency can be obtained in the regenerator,a simple yet efficient model is necessary for real-timeperformance monitoring, optimization, and control. Themodeling of a regenerator can be developed by a hybridapproach from physical principles of heat and mass transfer inthe regenerator which is illustrated in Figure 3 schematically. Inorder to simplify the derivation process in the followingsections, some reasonable assumptions are made:

1. Heat loss to the surroundings is negligible.2. Desiccant vaporization is neglected in the regenerator.3. There is steady state for the heat and mass transfer.4. Mass variations of regenerating air and desiccant solution

are negligible in the regenerator.5. The properties of the desiccant with respect to a small

range of temperature variations are constant.

3. MODEL OF HEAT TRANSFERPacking material is often applied in the regenerator to increasethe air−desiccant contact area because a thin film will form onthe packing material surface when the desiccant solution fallsdown along channels of the packing (shown in Figure 3). Thestaggered arrangement of the packing can enhance theconvective effect between the rising regenerating hot air andthe falling desiccant solution. Sensible heat transfer occursbetween the two fluids through the channels of packingmaterial. The heat is transferred from the hot desiccant solutionin convection to the interface, conducted through the interface,and then finally transferred into the regenerating air. The heattransfer rate is generally expressed by multiplying the heat

transfer coefficient with the heat transfer area and thetemperature difference. By employing the above form, wedevelop the hybrid model as follows:

= −Q h A T T( )ov s in a in, , (1)

where Q, A, Ts,in, Ta,in, and hov are the heat transfer rate, the heattransfer area, the inlet desiccant solution temperature, the inletregenerating air temperature, and the overall heat transfercoefficient, respectively. The overall heat transfer coefficient canbe expressed in terms of heat transfer resistance:

δλ

= + +h A h A A h A

1 1 1

ov s s m m a a (2)

where δ, λm, hs, ha, As, Aa, and Am are the thickness of theinterface, the thermal conductivity of the interface, local heattransfer coefficient regenerating air convection, the local heattransfer coefficient of desiccant solution convection, heattransfer area of desiccant solution convection, the heat transferarea of regenerating air convection, and the heat transfer area ofthe interface, respectively.However, the heat resistance of interface conduction is small

enough to be neglected as the interface between the two fluidsis very thin, and in the packed column, the heat transfer areas indifferent fluids and the interface are the same. Therefore, theoverall heat transfer coefficient can be simplified as:

=+

hh h

11/ 1/ov

s a (3)

It is the characters of the interface and the moving fluid, thegeometry of the packed column, and the velocity of fluid overthe interface as well as the temperature differences thatdetermine the heat transfer rate between the interface and thefluid moving over it. In the regenerator, the pump and fan areused to drive the desiccant solution and regenerating air,respectively. The type of heat transfer between the desiccantsolution and the regenerating air can be considered as forcedconvection heat transfer. For the forced convection heattransfer, the heat transfer coefficient, h, depends on the passagediameter, D, the velocity of fluid, v, and is also influencedthrough the mean film temperature by the fluid’s viscosity, μ,specific heat, cp (for air humidity, humid heat is used), andthermal conductivity λ, respectively. The following equation hasbeen developed after dimensional analysis:27

=Nu C Re Pr( ) ( )e f(4)

where Nu = hD/λ, Re = Dρv/μ and Pr = cpμ/λ are the well-known dimensionless numbers in heat transfer and fluiddynamics, namely Nusselt number, Reynolds number, andPrandtl number, while C and the exponents e and f are theconstant parameters that need to be determined, respectively.It can be assumed that both the volume flow rate V and the

fluid density ρ remain constant for steady flow. Then theproduct of ρV (the mass flow rate m) is unchanged accordingly.Moreover, μ and λ are approximately unchanged if thetemperature variation is not too big (less than 10% changefor desiccant solution and air according to previousstudies27−29). Thus, eq 4 can be expressed as follows:

πμ

μ

λλ= = ⎜ ⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝

⎞⎠h C

mD

c

Dbm

4e

pf

e

(5)

where b = C(4/πμD)e(cpμ/λ)f λ/D.

Figure 3. Schematic of a packed regenerator for desiccant solutionregeneration.



The overall heat transfer coefficient of the packing columncan be written as:

= +

=

+h

b m b mb R m

R

11/ 1/

( )

1 ( )ov

s se

a ae

a as se

bb as

ea

s (6)

where ms and ma are the flow rates of the desiccant solution andregenerating air, respectively. Ra,s = ma/ms is the ratio of theregenerating air flow rate to the desiccant solution flow rate, bsand ba are the two constant coefficients related to the desiccantsolution and the regenerating air. By combining eqs 1 with eq 6,the heat transfer rate in the packing column regenerator for thishybrid model in empirical nature is derived as:

=

+−Q

c R m

c RT T

( )

1 ( )( )a s s

c

a sc s in a in

1 ,

2 ,, ,

3

3 (7)

where c1 = baA, c2 = ba/bs, c3 = e.

4. MODEL OF MASS TRANSFERIn the regenerating process, three mass transfer resistances haveto be overcome for water vapor on its way from the desiccantsolution to the regenerating air: the resistance in desiccantsolution itself, that at the interface of the two fluids, and finallythe resistance of the regenerating air. The resistance of theinterface between the two fluids can be very small and can beneglected because the high solution flow rate is generallyapplied in the regenerator and the mass transfer between theregenerating air and the desiccant solutions at the interface isvery fast when compared to the mass transfer within either thedesiccant solution or the regenerating air. Moreover, anassumption can be made that an equilibrium state exists atthe interface in terms of mass transfer. Consequently, masstransfer with the driving force in terms of water vapor pressurein the gas phase can be described to develop the hybrid modelin empirical nature:

= * −N K p p( )G s in a in, , (8)

where N, KG, ps,in* , and pa,in are the mass flux, overall masstransfer coefficient in the regenerator, the equilibrium watervapor pressure of the desiccant solution, and the water vaporpressure of the inlet of regenerating air, respectively, and KGcan be expressed as follows, based on Henry’s law and the masstransfer two-film theory,28

=+

Kk Hk

11/ 1/G

a s (9)

where ka, ks, and H are the gas phase mass transfer coefficient inconvection, the liquid phase mass transfer coefficient inconvection, and Henry’s law constant, respectively.The correlations of the mass transfer coefficients for both gas

and liquid phases in the packed column between regeneratingair and desiccant solution were respectively presented byOnda29,30 as follows:

α μ πμ

αα

=⎛

⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜

⎞⎠⎟k a

mD

v

DD

DRT

4( )a

a

t a

eH a

a

f

t pg t a

a1 2

1 1

1

(10)

α μπμ

ρα

ρμ

=

ω

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟k a

mD D

Dg

4( )s

s

s

es

s s

f

t pg s

s

j

2 2

2 2

2

2

(11)

where aω is the wetted specific surface area, αt is the specificsurface area, and Dp is the packing material nominal size, whichis determined by the packing geometry and remains constantfor a certain type of packing material, Da, vH, μa, and Ds,ρs,μs arethe diffusivity, humid volume or density, and viscosity ofregenerating air and desiccant solution, respectively. μa, vH,DaμsρsDs can be assumed not to change when the temperaturevariations between regenerating air and desiccant solution aresmall (less than 25 °C for regenerating air and 10 °C fordesiccant solution). The correlations mentioned above cantherefore be simplified below:

= k b mT

( )1

a ae

a in3

,

1

(12)

and

= k b m( )s se

42 (13)

where b3 = a1(4/αtμaπD2)e1 (vH μa/Da)

f1 (αtDp)g1 αtDa/R, b4 =

a2(4/αωμsπD2)e2 (μs/ ρsDs)

f 2 (αtDp)g2 (ρs/μsg)

j2.Substituting eqs 11 and 12 into eq 8,

=+

=

+

−K

Hb m

T H m m

1 ( )

1 ( ) ( )G T

b m Hb m

se

a inbb s

ea

e( )

1( )

4

,a in

ae

se

,

31

42

2

4

3

2 1

(14)

=

+ K

c mc T m m

( )1 ( ) ( )G

sc

a in sc

ac

4

5 ,

6

6 7 (15)

where c4 = Hb4, c5 = Hb4/b3, c6 = e2,c7 = −e1. Thus, the masstransfer flux in the regenerator can be finally presented as:

=

+ * −N

c mc T m m

p p( )

1 ( ) ( )( )s

c

a in sc

ac s in a in

4

5 ,, ,

6

6 7 (16)

where the regenerating air water vapor pressure at the inlet ofthe regenerator, pa,in, can be determined from the definition ofrelative humidity:

φ=p pa in a in a sat, , , (17)

where φa,in is the relative humidity of inlet regenerating air, andpa,sat is the saturated water vapor pressure, influenced only bythe air temperature, and can be fitted in terms of temperatureby the data available:31

γ γ γ= + +p T Ta sat a in a in, 0 ,2

1 , 2 (18)

For temperatures between 30 to 55 °C, the constants are: γ0 =13.099, γ1 = −688.46, γ2 = 14009. For the temperature ofdesiccant solution ranges from 50 to 60 °C and theconcentration ranges from 27% to 35% in regenerator, thethermodynamic properties of the lithium chloride solutionshave been discussed by Conde,32 and the surface of the watervapor for the desiccant solution can be described by algebraicfitting:

β β β ω β β ω β ω* = + + + + +p T T Ts in s in s s in s s in s, 0 1 , 2 3 ,2

42

5 ,

(19)

where ωs is the desiccant solution concentration and the fittedparameters are: β0 = −2.6434273, β1 = 0.20955349, β2 =5.2451548, β3 = 0.0054591075, β4 = 61.771904, β5 =−1.5411157.Thus, eqs 7 and 16 together with only seven parameters (c1−

c7) present the heat and mass transfer process in the



regenerator. Compared with previous models, the proposedmodel is characterized by fewer parameters than can beidentified through the Levenberg−Marquardt method by real-time operating data (see Appendix A for details).

5. MODEL VALIDATION AND DISCUSSION

In order to validate the present regenerator model, theexperiment is conducted on a liquid desiccant dehumidificationsystem operating with aqueous lithium chloride as the desiccant(illustrated in Figure 4). The regeneration capacity of theexperimental rig is as follows:

• Regenerating air flow 500 m3/h• Heater capacity 3.0 kW• Regeneration rate 5 kg/h

which can supply enough concentrated desiccant solution tothe dehumidifier which can cover the sensible and latent loadfrom a 100 m2 room in Singapore. The polypropylene column,which is made of anticorrosive material, is 1 m in height.Structured packing material with face dimensions 300 mm × 00mm × 450 mm is filled in the packed column. To obtain a gooddistribution of desiccant solution, a distributor is installed onthe top of column, and a wire mesh made of stainless steel isequipped to remove desiccant droplets carried by the high-speed regenerating air. All motors (fans, pumps) are installedwith variable speed drive (VSD) to adjust the air and solutionflow rates during different conditions. A humidity/temperaturetransmitter with probe type and a blade airflow meter are

installed in the outlet of the regenerator column (refer to 6 and4 in Figure 4) to measure the outlet conditions of regeneratingair and the air flow rate. Solution temperature and flow rate arerespectively measured by a PT100 temperature sensor and amagnetic flow meter located in the desiccant conduit (refer to 7and 5 in Figure 4). The concentration of desiccant solution isdetermined by the temperature and density,27 the density ismeasured by a glass hydrometer. Table 1 lists the specifications

of the installed sensors. By using the sensors, the heat transferrate and mass flux in the regenerator can be calculated by thereal-time operating data based on the energy and mass balances,

= −N m Y Y( )a a out a in, , (20)

λ= − −Q m H H N( )a a out a in w, , (21)

where Ya,out, Ya,in, Ha,out, and Ha,in are the absolute humidity andenthalpy of regenerating air at the outlet and inlet sides,respectively. The absolute humidity and enthalpy can bedetermined by the temperature and relative humidity which aremeasured and recorded by the data acquisition system. λw is thelatent heat of water vaporization.In order to show the effectiveness of the model, two error

indexes, relative error (RE) and root-mean-square of relativeerror (RMSRE), are proposed:

=| − |

×RED D

D100%real calc

real (22)

=∑ =

−( )RMSRE

M

iM D D

D1

2real calc

real

(23)

Experimental data with 100 sets from a wide operating rangeof the regenerator is acquired to determine the modelparameters through the Levenberg−Marquardt method.Ambient air is utilized as the regenerating air, and its conditionscannot be controlled; thus, only inlet desiccant solutionconditions and air flow rate are changed in the experiment.After identification, the parameters are determined as c1 =4.9895, c2 = 4.2247, c3 = 1.0113 in eq 7 and c4 = 0.0104, c5 =0.4660, c6 = 0.5455 and c7 = −0.5313 in eq 16. To show theeffectiveness of the proposed model in system performanceprediction and monitoring, 270 points which can cover 10−90% of the designed capacity tested and the heat transfer ratefrom 0.6 to 1.6 kW and mass flux from 0.002 to 0.016 kg/m2s,respectively. Table 2 gives the description of the identificationand validation data in the experiment, while predicted values ofheat transfer rate together with the experimental values aregiven in Figure 5 and the RE is shown in Figure 6, accordingly.It can be deduced that for most of the data points, the RE is less

Figure 4. Photo of regenerator: 1 - regenerator (packed column); 2 -heater; 3 - pump; 4 - airflow meter; 5 - solution flow meter; 6 -humidity/temperature transmitter; 7 - solution temperature sensor.

Table 1. Specification of the Sensors

sensors type accuracy range

humidity/temperaturetransmitter

probe 0.5%,0.1 °C

0−100%, 0−60 °C

solution temperaturesensor

PT100, 3-wire 0.15 °C 0−100 °C

solution flow meter magnetic flowmeter

±0.5% 0−25L/min

airflow meter blade ±0.5% 0−600m3/hdensity meter glass

hydrometer1 kg/m3 1100−1300 kg/m3



than 10% with the average RE of 3.84% and RMSRE of 0.0473.While the comparison results of the mass flux in theregenerator predicted by the proposed model with the collectedexperimental data and the RE are shown in Figure 7 and Figure8, respectively, 94% of the 270 data points are within the RE of±10% with the average RE of 5.02% and RMSRE of 0.0623.The conclusion can be drawn from the results that theproposed model shows satifactory agreements with theexperimental data (RE < 10%) and that validating the modelingapproach is effective and accurate enough for real-timeapplications in performance monitoring, optimization, andcontrol for the regenerator in the liquid desiccant dehumidi-fication system.Some experimental data sets have been selected to study the

influence of the variables on regenerator performance, heat

transfer rate, and regeneration rate. Flow rate and temperatureof the desiccant solution are the two variables that have themost significant effect on the performance of the regenerator.Figures 9−12 show the experimental data for regenerationtogether with the model predicting results with the liquiddesiccant flow rate varying from 2.86 to 7.12 kg/min and liquiddesiccant temperature from 53.6 to 61 °C. Uncertainties of the

Table 2. Data Description in the Experiment

desiccant solutionregenerating

air

data sets Ts (°C) ωs (%)ms

(kg/min) ma(kg/min)

identification data 52.8−60.3 29.7−38.5 3.6−7.08 1.5−3.18testing data 52.4−61.5 29.5−39.1 3.0−7.08 1.62−3.0

Figure 5. Model prediction for heat transfer.

Figure 6. Relative error for heat transfer.

Figure 7. Model prediction for mass transfer.

Figure 8. Relative error for mass transfer.

Figure 9. Experimental data and predicted results by the proposedmodel for influence of the desiccant flow rate on the heat transfer rate.



experimental data are calculated, and the error bars are alsogiven in the figures. It turns out once again that the currentmodel has good accuracy and the calculated heat and masstransfer rates show good agreement with the experimental data.From Figure 9 and Figure 10, the heat transfer rate increaseswith the increase of desiccant flow rate and inlet desiccanttemperature. It can be explained that a higher desiccant flow

rate can enhance the heat transfer process by increasing theconvective heat transfer coefficient and a higher inlet desiccanttemperature can give bigger convective heat transfer coefficientand temperature difference and consequently gives the increaseof heat transfer. For the regeneration rate is enhanced with theincrease of the desiccant flow rate and desiccant inlettemperature, as shown in Figure 11 and Figure 12. It happensbecause a higher desiccant flow rate will maintain a higherregeneration rate with less desiccant temperature reduction,and a higher desiccant inlet temperature means a higher watervapor pressure and higher potential for heat and mass transfersince the vapor pressure of the desiccant is highly dependent onthe temperature.Moreover, in order to illustrate the effectiveness of the

proposed model in different systems, reliable sets ofexperimental data in the study of Fumo and Goswami15 areused to identify the model, and comparisons are made betweenthe predicting values from the proposed model and that fromthe study of Babakhani and Soleymani18 which also refers to thesame data. The regeneration rate is taken as the predictingvariable to be compared because it is the key factor to show theperformance of the regenerator. Figure 13 gives the comparison

of predicting regeneration rates presented in the current studyand those obtained by Fumo and Goswami15 and Babakhaniand Soleymani.18 The relative error comparison between theproposed model and models presented in refs 15 and 18 isshown in Figure 14. It should be pointed out that theregeneration rates predicted by Fumo and Goswami15 areconsistently a little smaller than the experiment data and withhigher relative errors, as shown in Figure 13 and Figure 14.Babakhani and Soleymani18 and the proposed model can obtainmore accurate predictions of the regeneration rates, and therelative errors are less than 10%. However, complex parameterssuch as thermodynamic properties of the fluids, geometricspecifications of the packing materials, and the heat and masstransfer coefficients are needed in both the models of Fumoand Goswami15 and Babakhani and Soleymani.18 Theseparameters can hardly be obtained in practical applicationswhich limit its applications in real-time performance monitor-ing, optimization, and control. While only the input variables ofthe regenerator such as desiccant solution temperature, flowrate, concentration, and the air temperature, flow rate, relative

Figure 10. Experimental data and predicted results by the proposedmodel for influence of the desiccant inlet temperature on the heattransfer rate.

Figure 11. Experimental data and predicted results by the proposedmodel for influence of the desiccant flow rate on the regeneration rate.

Figure 12. Experimental data and predicted results by the proposedmodel for influence of the desiccant inlet temperature on theregeneration rate.

Figure 13. Comparison between the predicted regeneration rates indifferent models and the experimental data from Fumo andGoswami.16



humidity are involved in the current model which is developedbased on a hybrid method. Real-time predicting can beobtained because of all the input variables involved in themodel can be measured directly by the sensors and transducersinstalled in the system. Moreover, in the studies of Fumo andGoswami15 and Babakhani and Soleymani,18 the heat and masstransfer process was described by basic differential equations,and solving these equations is time-consuming and complexbecause the outlet conditions of the regenerator must beinitially guessed, and iterative computations are required untilthe results converge to the known inlet conditions. In thecurrent model, the complex parameters are processed bylumping parameters and the lumped parameters can bedetermined by the operating data; no iterative computing isneeded while the identified model is applied in real-timeperformance monitoring, optimization, and control for theregenerator. Therefore, in comparison with the existing models,the present model is simple, accurate, able to be expanded, andsuitable for real-time performance monitoring, optimization,and control. Table 3 illustrates the comparison between theexisting regenerator models and the current model.

6. CONCLUSIONSA simple hybrid model which is suitable for performancemonitoring, optimization, and control of operating liquiddesiccant regenerators was presented in this paper. Theperformance of the heat and mass transfer processes in theliquid desiccant regenerator can be predicted by the developedhybrid model with only seven characteristic parameters.Different from other previous models, only inlet-related

variables with the regenerator are involved in this model sothat iterative computation can be avoided when the proposedmodel is applied in performance prediction for the liquiddesiccant regenerator. Furthermore, complex parameters suchas the thermodynamic properties of the fluids, packinggeometric specifications, and thermodynamic numbers (Rey-nolds, Nusselt, and Prandtl) are considered as lumpedparameters and can be identified by operating data. Accordingto the validation results, the current regenerator model isaccurate enough for performance prediction and monitoringover a wide operating range: heat transfer rate from 0.6 to 1.6kW and mass flux from 0.002 to 0.016 kg/m2s. The presentmodel, with only seven parameters involved, is simple, flexible,relatively accurate, and easy for engineering applicationscompared with the previous models of the regenerator. Afteridentification of the operating data collected from a specificsystem, the proposed model can be used to monitor, optimize,and control the performance of the regenerator by predictingthe heat- and mass-transfer processes with the inlet conditions,such as flow rate, concentration, and temperature of thedesiccant solution and flow rate, relative humidity, andtemperature of regenerating air. It should be pointed out,however, that the model parameters may vary after a longperiod of operating time and should be updated periodically topredict the regenerator performance accurately. The perform-ance optimization by using the proposed model is under studycurrently, and the results will be discussed later.

■ APPENDIX AIn order to identify the seven unknown parameters, thenonlinear least-squares method is employed as follows:take M samples for the variables Ta,in, Ts,in, ma, ms, ϕa,in, ωs, Q,

and N, and define two objective functions as the sum of theresidual squares between the evaluated data and experimentaldata in order to determine the empirical parameters.

∑ ∑= =

+− −

= =

⎛⎝⎜⎜

⎞⎠⎟⎟f u r u

c R m

c RT T Q( ) ( )

( )

1 ( )( )

i

M

ii

Ma s i s in

c

a s ic s in i a in i i1 1

11,2

11

1 , , ,

2 , ,, , , ,

23

3

(A.1)

∑

∑

=

=

+ * − −

=

=

⎛⎝⎜⎜

⎞⎠⎟⎟

f u r u

c m

c T m mp p N

( ) ( )

( )

1 ( ) ( )( )

i

M

i

i

Ms i

c

a in i s ic

a ic s in i a in i i

2 21

2,2

2

1

4 ,

5 , , , ,, , , ,

26

6 7

(A.2)

where f1(u1),f 2(u2),r1(u1),r2(u2), u1 = [c1 c2 c3]T and u2 = [c4 c5

c6 c7]T are the heat transfer objective function, mass transfer

objective function, residuals between the evaluated data andexperimental data for heat transfer objective function, residualsbetween the evaluated data and experimental data for masstransfer objective function, parameter vector in heat transferequation and parameter vector in mass transfer equation,respectively.Employing the Levenberg−Marquardt method to find the

nonlinear unconstraint optimization solution, its searchdirection of between the steepest descent and the Gauss−Newton can be obtained by solving the following equations:

λ+ = −J u J u I d J u R u( ( ) ( ) ) ( ) ( )k T k k k k1( )

1 1( )

1 1( )

1( )

1( )

1 1 1 (A.3)

λ+ = −J u J u I d J u R u( ( ) ( ) ) ( ) ( )k T k k k k2( )

2 2( )

2 2( )

2( )

2( )

2 2 2 (A.4)

Figure 14. Comparison of relative errors for predicting theregeneration rate in different models.

Table 3. Comparison of Different Regenerator Models

model geometriciterative

computationmodelingtechnique model application

finitedifference

yes yes physical design andsimulation

empiricalmodel

no no empirical design andcontrol

NTU yes yes physical design andcontrol

presentmodel

no no hybrid control andoptimization



where λ(k) ≥ 0 is a scalar, and I is the 3rd order identity matrixfor the particular heat transfer model with three parameters andof order 4 for the particular mass transfer model which has fourparameters , = ···R u r u r u r u( ) [ ( ) ( ) ( )]M

T1 1 1,1 1 1,2 1 1, 1 and

= ···R u r u r u r u( ) [ ( ) ( ) ( )]MT

2 2 2,1 2 2,2 2 2, 2 , and the Jacobianmatrixes are defined as:

=

∂∂

∂∂⋮

∂∂

∂∂

∂∂⋮

∂∂

∂∂

∂∂

⋮∂∂

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

J u

r

c

r

c

r

c

r

c

r

c

r

c

r

c

r

c

r

c

( )

M M M

1 1

1,1

1

1,2

1

1,

1

1,1

2

1,2

2

1,

2

1,1

3

1,2

3

1,

3 (A.5)

=

∂∂

∂∂

⋮∂∂

∂∂

∂∂

⋮∂∂

∂∂

∂∂⋮

∂∂

∂∂

∂∂

⋮∂∂

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

J u

r

c

r

c

r

c

r

c

r

c

r

c

r

c

r

c

r

c

r

c

r

c

r

c

( )

M M M M

2 2

2,1

4

2,2

4

2,

4

2,1

5

2,2

5

2,

5

2,1

6

2,2

6

2,

6

2,1

7

2,2

7

2,

7 (A.6)

For sufficiently large values of λ1(k) and λ2

(k), the matrixes of J1(k)

(u1)T J1

(k) (u1) + λ1(k)I and J2

(k) (u2)T J2

(k) (u2) + λ2(k)I are positive

definite matrixes, and thus, d1(k) and d2

(k) are in a descentdirection. Therefore, proper values should be assigned to λ1

(k)

and λ2(k) during the process of iteration. For λ1

(0) = 0.01, λ2(0) =

0.01 and v = 10, it is specific as:

λλ

λ=

<

>+

+

+

⎧⎨⎪⎩⎪

v iff c f c

v iff c f c

/ ( ) ( )

( ) ( )

kk k k

k k k1( 1) 1

( )1( 1)

1 1( )

1

1( )

1( 1)

1 1( )

1 (A.7)

λλ

λ=

<

>+

+

+

⎧⎨⎪⎩⎪

v iff c f c

v iff c f c

/ ( ) ( )

( ) ( )

kk k k

k k k2( 1) 2

( )2( 1)

2 2( )

2

2( )

2( 1)

2 2( )

2 (A.8)

and

= ++u u dk k k1( 1)

1( )

1( )

(A.9)

= ++u u dk k k2( 1)

2( )

2( )

(A.10)

where u1k is the value of c1−c3 in the kth iteration and u2

k is thevalue of c4−c7 in the kth iteration. The iteration ends if |u1

(k + 1)

− u1k| < δ1, |u2

(k + 1) − u2k| < δ2, where δ1 and δ2 are predetermined

positive numbers (generally from the range of 1 × 10−6−1 ×10−5).

■ AUTHOR INFORMATIONCorresponding Author*Tel: +65 6790 6862. Fax: +65 6793 3318. E-mail: [email protected] authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This work was supported by National Research Foundation ofSingapore under the grant NRF2011 NRF-CRP001-090, theNational Natural Science Foundation of China (NSFC) (No.21076179), and the National Basic Research Program of China(973 Program: 2012CB720500).

■ MODEL NOMENCLATURE

A heat transfer area (m2)Aa heat transfer area of regenerating air convection (m2)Am heat transfer area of the interface (m2)As heat transfer area of desiccant solution convection (m2)b constant [W/m2 °C(kg/s)−e]b1−b4 constant [W/m2 °C(kg/s)−e]C constant (dimensionless)c1−c3 heat transfer model parametersc4−c7 mass transfer model parameterscp specific heat capacity of fluids [J/(kg °C)]D the structured packing diameter (m)Da regenerating air diffusivity (m2/s)Dcalc calculated dataDp packing material nominal size (m)Dreal experimental dataDs desiccant solution diffusivity (m2/s)g gravitational acceleration (m/s2)h heat transfer coefficient [W/(m2 °C)]H Henry’s law constant (Pa)Ha,in enthalpy of inlet regenerating air (kJ/kgdray air)Ha,out enthalpy of outlet regenerating air (kJ/kgdray air)ha air convection heat transfer coefficient [W/(m2 °C)]hov overall heat transfer coefficient in the regenerator [W/

(m2 °C)]hs desiccant solution convection heat transfer coefficient

[W/(m2 °C)]k convection mass transfer coefficient [kg/(m2 s Pa)]ka gas phase convection mass transfer coefficient in the

regenerator [kg/(m2 s Pa)]KG overall mass transfer coefficient in the regenerator [kg/

(m2 s Pa)]ks liquid phase convection mass transfer coefficient in the

regenerator [kg/(m2sPa)]m fluid mass flow rate (kg/s)ma regenerating air mass flow rate (kg/s)ms desiccant solution mass flow rate (kg/s)N mass flux in the regenerator (kg/m2 s)pa,in regenerating air water vapor pressure at inlet of the

regenerator (Pa)pa,sat saturated water vapor pressure (Pa)ps,in* equilibrium water vapor pressure of desiccant solution

at inlet of the regenerator (Pa)Q heat transfer rate in the regenerator (W)R ideal gas constant [J/(mol °C)]Ras mass flow rate ratio between the regenerating air and

the desiccant solution (dimensionless)Ta,in regenerating air temperature at inlet of the regenerator

(°C)Ts,in desiccant solution temperature at inlet of the regener-

ator (°C)u1k value of c1−c3in the kth iterationu2k value of c4−c7in the kth iterationV fluid volume flow rate (m3/s)v fluid velocity (m/s)



mailto:[email protected]

mailto:[email protected]

vH humid volume of regenerating air (m3/kg)

Ya,inabsolute humidity of inlet regenerating air (kgwater/kgdry air)

Ya,out absolute humidity of outlet regenerating air (kgwater/kgdry air)

αt specific surface area (m2/m3)αω wetted specific surface area (m2/m3)δ thickness of the interface (m)λ thermal conductivity [W/(m°C)]λm thermal conductivity of the interface [W/(m°C) ]λw latent heat of water vaporization (kJ/kg)μ fluid viscosity (Pa)μa regenerating air viscosity (Pa)μs desiccant solution viscosity (Pa)ρs desiccant solution density (kg/m3)ϕa regenerating air relative humidity (%)ωs desiccant solution concentration (%)

Subscriptsa regenerating airG gas phasein inletm interfaceout outlets desiccant solutionsat saturated

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Heat and mass transfer model for diseccant solution

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