Contents
Introduction Introduction .......................... ........................................ ........................... .......................... ........................... ........................... .......................... ....................... .......... 2 Condensation Condensation of mixtures.............................. ........................................... .......................... ........................... ........................... ......................... ............3 Multi-component Multi-component condenser design: .......................... ....................................... ........................... ........................... ......................... ............ 7 Desuperheating Desuperheating and sub-cooling ......................... ....................................... ........................... .......................... .......................... ................... ...... 8 Desuperheating Desuperheating........................... ......................................... ........................... .......................... .......................... ........................... ........................... ............... 8 Sub-cooling Sub-cooling of condensate ......................... ...................................... .......................... ........................... ........................... ......................... ............ 8 Temperature Temperature profile: .......................... ........................................ ........................... ........................... ........................... .......................... ....................... .......... 9 Differential Differential condensation ........................... ........................................ .......................... ........................... ........................... ......................... ............ 9 Integral condensation .......................... ....................................... ........................... ........................... .......................... .......................... ................. .... 10 The model and its assumptions.......................... ........................................ ........................... .......................... .......................... ................... ...... 18 Dew and bubble point temperature........................... ............................... .... Error! Bookmark not defined. Heat transfer area ...................... .................................... ........................... ...................... ......... Error! Bookmark not defined. Condenser flowsheet.................... flowsheet................................. ........................... .................... ...... Error! Bookmark not defined. Experimental Experimental procedure............................... ............................................ ................. .... Error! Bookmark not defined. Optimal design of condenser ............................... ............................................. ........................... .......................... .......................... ................. .... 11 Mathematical modeling of condenser .......................... .......................... Error! Bookmark not defined. Literature review.......................... ....................................... ........................... ........................... .......................... .......................... ........................... ................ 12 Computer Aided Design (CAD) of a Multi-component Multi-component Condenser( 2008): ............ ............ 12 D.R. Webb (2002) ........................ ...................................... ........................... .......................... ........................... ........................... ....................... .......... 12 R. C. CAIRNS (1997) ..................... .................................. .......................... ............. Error! Bookmark not defined. D. R. WEBB AND R. G. SARDESAI ........................... ........................................ .......................... ........................... ................. ... 13 J. BANDROWSKI BANDROWSKI ......................... ....................................... ........................... ........................... ........................... .......................... ..................... ........ 14 Nomenclature Nomenclature.......................... ........................................ ........................... ........................ ........... Error! Bookmark not defined. Objective Objective of the project ............................... ............................................ ................. .... Error! Bookmark not defined. References: ......................... ....................................... ........................... .......................... .......................... ........................... ........................... ....................... .......... 14
Introduction 1.1 General
Condensation is the process of changing vapor into liquid. In so doing, the latent heat is given up by the substance, and will transfer tr ansfer to the condenser coolant. If the temperature of a surface in contact with the vapor is below saturation temperature of vapor mixture, which is able to bring the vapor temperature below saturation temperature, condensation takes place. The liquid which is formed gets sub-cooled by giving more heat to the surface and hence more condensation takes place of this liquid. Thus condensation is always associated with mass transfer. A condenser is a device in which the heat removed in the process of converting a vapor to liquids transferred to a coolant. Condensers are an important class of equipment in process industry. It has equally important role in power generation. In process industry condensation is used to bring the outlet vapor of distillation column, boiling the liquid in a reboiler, removal of liquid from gas phase reactors, separation and process fluid heating applications. Industries such as petrochemicals, food and beverages, biochemical and industrial chemicals use condensers extensively. extensively. In the case of multi-component condensation, the ‘condensing vapour’ contains a mixture of components having different boiling points, which condense over a wide temperature range, either in presence or absence of non-condensing material. The three words ‘multi-component ‘multi-component vapor mixtures ’cover a ’cover a wide range of situations. One limit of this range is one in which all components have boiling points above maximum coolant temperature; in this case the mixture can be totally condensed. The other limit is a mixture in which at least one component in the initial vapor stream has a boiling point lower than the minimum coolant temperature and, also is negligibly soluble in the liquid condensate formed from the other components and hence cannot be condensed at all. Amongst surface condensers, shell and tube type is more popular but the compact types as well as plate type condensers are also making good impact in process industry. Since, in condensers vapor with large specific volume (dependent on temperature) flows, hence effect of buoyancy is considerable. Thus due to buoyancy and venting of non-condensable, orientation (vertical or horizontal) of the condenser is important. important. In vertical as well as in horizontal (because actually actually they are always slightly tilted) the flow direction of vapor is important because under reflux condition ‘flooding’ is an important consideration.
Introduction 1.1 General
Condensation is the process of changing vapor into liquid. In so doing, the latent heat is given up by the substance, and will transfer tr ansfer to the condenser coolant. If the temperature of a surface in contact with the vapor is below saturation temperature of vapor mixture, which is able to bring the vapor temperature below saturation temperature, condensation takes place. The liquid which is formed gets sub-cooled by giving more heat to the surface and hence more condensation takes place of this liquid. Thus condensation is always associated with mass transfer. A condenser is a device in which the heat removed in the process of converting a vapor to liquids transferred to a coolant. Condensers are an important class of equipment in process industry. It has equally important role in power generation. In process industry condensation is used to bring the outlet vapor of distillation column, boiling the liquid in a reboiler, removal of liquid from gas phase reactors, separation and process fluid heating applications. Industries such as petrochemicals, food and beverages, biochemical and industrial chemicals use condensers extensively. extensively. In the case of multi-component condensation, the ‘condensing vapour’ contains a mixture of components having different boiling points, which condense over a wide temperature range, either in presence or absence of non-condensing material. The three words ‘multi-component ‘multi-component vapor mixtures ’cover a ’cover a wide range of situations. One limit of this range is one in which all components have boiling points above maximum coolant temperature; in this case the mixture can be totally condensed. The other limit is a mixture in which at least one component in the initial vapor stream has a boiling point lower than the minimum coolant temperature and, also is negligibly soluble in the liquid condensate formed from the other components and hence cannot be condensed at all. Amongst surface condensers, shell and tube type is more popular but the compact types as well as plate type condensers are also making good impact in process industry. Since, in condensers vapor with large specific volume (dependent on temperature) flows, hence effect of buoyancy is considerable. Thus due to buoyancy and venting of non-condensable, orientation (vertical or horizontal) of the condenser is important. important. In vertical as well as in horizontal (because actually actually they are always slightly tilted) the flow direction of vapor is important because under reflux condition ‘flooding’ is an important consideration.
1.2 technical terms used in the condensation: 1.2.1 dropwise condensation: In dropwise condensation, the drops of liquid form from the vapor on the solid surface. It held mostly on that surfaces which are not strongly wetted b y the liquids. In this type of condensation, high heat transfer coefficient is obtained , but this is not considered good in process industry. 1.2.2 Filmwise condensation: in filmwise condensation, condensation, the drops initially formed quickly coalesce to produce a continous liquid film on the surface through which heat must be transferred to condense more liquid. Filmwise condensation condensation is the ususl mode that occurs in practice and that is i s assumed to exist for condenser design calculations. 1.2.3 Direct contact condensation: in direct contact condensation, the liquid coolant is sprayed directly into the vapor ,which condenses condenses directly onto the surface of the spray spray drops. 1.2.4 superheat : when a vapor is removed upon formation from further contact with a liquid, the addition of heat to the vapor causes superheat. (1.3) Effect of process variables on condenser condenser operation Coolant flow rate: if coolant flow rate is high, less area of condenser is required for specified degree of condensation. Coolant inlet temperature: if it is low, less area of condenser is required required for specified degree of condensation. condensation. Noncondensibles Noncondensibles in vapor mixture: it reduces the efficiency of condenser. (1.4) Flow patterns: there is two type of flow pattern in condensers….. 1.4.1 cocurrent: in this flow pattern coolant , condensate condensate and vapor vapor mixture all have same direction of flow. 1.4.2 countercurrent: countercurrent: in this flow pattern coolant and vapor mixture have have opposite directions of flow. This pattern have better efficiency than previous. (1.5) factors affecting the condensation process: (1.5.1) the temperature of surface: it should be relatively cold so as to create a sit uation where the liquid comes out of the vapor mixture. (1.5.2) type of surface: from the presence of dirt on the surface or the use of a containment results dropwise condensation, smooth surface tends to film wise condensation. condensation.
(1.5.3) flow rate of vapor: if flow rate of vapor is high, large quantity of condensate accumulates. accumulates. Since vapor is flowing due to the mean of a device which is working on vapor. So we should have a good control on that device. (1.6) SELECTION CRITERIA OF A CONDENSER:
It is very difficult to fix on criteria to select a particular condenser for a given duty from the large number of condensers available. generally the following requirements are to be kept in mind, (a) Condensation process (b) Coolant (c) Pressure level and pressure drop (d) fouling and corrosion (e) condensate control (f)venting (1.7) condenser classification: Shell and Tube Condenser: It is comprised of a large number of tubes located in a steel shell, with
coolant flowing inside, and vapor flowing around the tubes. The vapors condense on the exterior surface of the tubes, and drops to the bottom of the condenser. A considerable amount of condensing surface is available in a smaller place. A wide range of condensers under this name, (a) Vertical in tube down flow condenser : the fluids which are more corrosive in vapor state, this type of condenser is preferable. (b) Vertical in tube upflow or reflux condenser : these condensers are used to condensate c ondensate the boiled off vapor coming from an exothermic chemical reactor. (c) Horizontal in tube condenser: for high pressure high velocity vapors this type of condenser is preferred. (d) Horizontal shell side condenser: this is extensively used in petrochemical industry. (e) Vertical shell side condenser: condensation on the shell side is usually carried out when the prime function is not condensing but heating the coolant in applications such as evaporator or thermosyphn reboiler. Compact condensers: the special types are described here;
(a) Plate condenser (b) Plate-fin-condenser (c) Spiral heat exchanger Direct contact condenser: direct contact condensers have high cooling efficiency but
contamination of the fluids is the major concern. (a) Jet condenser : they are mostly used in power plants.
(b) Spray condensers: this is the most popular type of direct contact condenser. It is practically infinite surface area condensation. (c) Pool condensers: they are often used to get desired rise of vapor bubbles. Air cooled condensers: the air cooled condensers are usually compact condensers.
Refrigeration industry uses air cooled condensers extensively.
(1.8) Condensation of mixtures
The design of a condenser for a mixture of vapours is a more difficult task. The term "mixture of vapours" covers three related situations of practical interest:
1. Total condensation of a multicomponent mixture 2. Condensation of only part of a multicomponent vapour mixture 3. Condensation from a non-condensable gas, where the gas is not soluble to any extent in the liquid condensed. The common features, common to all above situations, must be considered in the developing design methods for mixed vapor condensers.
The condensation will not be isothermal as the heavy component condenses out the composition of the vapor, and therefore its dew point, change.
Because the condensation is not isothermal there will be a transfer of sensible heat from the vapor to cool the gas to the dew point. There will also be a transfer of sensible heat from the condensate, as it must be cooled from the temperature at which it condensed to the outlet temperature.
The transfer of sensible heat from the vapor can be particularly significant, as the sensible-heat transfer coefficient will be appreciably lower than the condensation coefficient.
As the composition of the vapour and liquid change throughout the condenser their physical properties vary.
The heavy component must diffuse through the lighter components to reach the condensing surface. The rate of condensation will be governed by the rate of diffusion, as well as the rate of heat transfer.
(1.9) configurations of condensers :
Four condenser configurations are possible: 1. Horizontal, with condensation in the shell, and the cooling medium in the tubes. 2. Horizontal, with condensation in the tubes. 3. Vertical, with condensation in the shell. 4. Vertical, with condensation in the tubes. Horizontal shell-side and vertical tube-side are the most commonly used types of condenser.
Multi-component condenser design:
The physical design of the condenser is a compromise between the desirability of keeping to an entirely standard production design so that measurements of performance are characteristic of real operating conditions and the demands of instrumentation and operational flexibility of a research tool. To design a multi-component condenser, one requires a suitable method to evaluate the overall heat transfer coefficient, which is useful for determining the heat transfer area. Evaluation of the overall heat transfer coefficient needs suitable equations to predict the heat transfer rates i. e. heat transfer coefficients. In this paper, the equilibrium method proposed by Bell and Ghaly was considered for predicting the surface area required for heat transfer because of its robustness, speed, and reliability. Condensation at shell side, in a vertical shell and tube heat exchanger was considered because of its large industrial practices and suitability towards the equilibrium method. For the tube arrangement, square, triangular and rotated square layouts were considered. Multi-component condensation takes place over a wide temperature range – from dew to bubble point. Therefore, it is necessary to determine the dew and bubble points before starting design calculations.
(2.0)SOME DEFINITIONS REGARDING TO CONDENSER
Desuperheating and sub-cooling When the vapour entering the condenser is superheated, and the condensate leaving the condenser is cooled below its boiling point (sub-cooled), the temperature profile will be as shown in Figure
(2.1)Desuperheating Desuperheating
can
be
of
two
types-
drywall
desuperheating
and
wet
wall
desuperheating.when the superheated vapors enter the condenser with a cold wall temperature higher than the saturation temperature, the flow of vapor can be treated as of a pure gas. For superheated vapor entering at a plane where wall temperature is lower than saturated temperature , wet wall desuperheating takes place. here a film is formed at the wall even though vapor is superheated and then desuperheating takes place with condensation at the liquid vapor interface. In wet wall desuperheating it has been found that the heat-transfer coefficient is close to the value for condensation and can be taken as the same. The total heattransfer area required can then be calculated using a mean temperature difference based on the saturation temperature (not the superheat temperature) and the estimated condensate film heat-transfer coefficient.
(2.2)Sub-cooling of condensate Sub-cooling is preferable because without sub-cooling liquid can flash into vapor in valves and lines by partial throttling or cause cavitation in pumps. in the sub-cooled section heat transfer coefficient is small due to low condensate velocity. For more sub-cooling vertical orientation is preferred. Some sub-cooling of the condensate will usually be required to control the net positive suction head at the condensate pump or to cool a product for storage. Where the amount of sub-cooling is large, it is more efficient to sub-cool in a separate exchanger. A small amount of sub-cooling can be obtained in a condenser by controlling the liquid level so that some part of the tube bundle is immersed in the condensate. In a
horizontal shell-side condenser a dam baffle can be used. A vertical condenser can be operated with the liquid level above the bottom tube sheet. The temperature difference in the sub-cooled region will depend on the degree of mixing in the pool of condensate. The limiting conditions are plug flow and complete mixing. The temperature profile for plug flow is that shown in. If the pool is perfectly mixed, the condensate temperature will be constant over the sub-cooling region.
(3.0)Temperature profile in condensers: To evaluate the true temperature difference (driving force) in a mixed vapour condenser a condensation curve (temperature vs. enthalpy diagram) must be calculated; showing the change in vapour temperature versus heat transferred throughout the condenser. The temperature profile will depend on the liquid-flow pattern in the condenser. There are two limiting conditions of condensate-vapor flow:
(3.1)Differential condensation
In which the liquid separates from the vapour from which it has condensed. This process is analogous to differential, or Rayleigh, distillation, and the condensation
curve can be calculated using methods similar to those for determining the change in composition in differential distillation.
(3.2) Integral condensation In which the liquid remains in equilibrium with the uncondensed vapour. The condensation curve can be determined using procedures similar to those for multicomponent flash distillation. This will be a relatively simple calculation for a binary mixture, but complex and tedious for mixtures of more than two components.
(4.0)Optimal design of condenser Optimum heat exchanger problem is one of the most complex yet faced repetitively by a design engineer. Accordingly much literature has been published on this matter which deal with some or the other aspect of the minimization problem but lacks in system integration or generality. The normal mechanism for heat transfer in commercial condensers is film wise condensation. Dropwise condensation will give higher heat-transfer coefficients, but is unpredictable; and is not yet considered a practical proposition for the design of condensers for general purposes. Existing methods for designing heat exchangers to condense multi-component mixtures can broadly be classified into two basic methods: equilibrium methods, such as those proposed by Kern,
and Bell and Ghaly and the differential or non-equilibrium methods that have been
developed following the work of Colburn and Drew Kern proposed a general-purpose design method based on the equilibrium model. He suggested how to employ the nonlinear condensation temperature curve instead of the log mean temperature difference but did not discuss how to handle a multipass coolant quantitatively. Bell and Ghaly proposed an approximate generalized design method based on the equilibrium method for multi-component partial condensers. They compensated the error introduced by neglecting the mass transfer resistance by overestimating the heat transfer resistance. After Bell and Ghaly2 a little work has been done on the equilibrium model. To design a condenser using film theory methods requires calculations of the local heat and mass transfer rates and integrating these local rates over the condenser length using differential mass and energy balances. This was proposed by Krishna and Panch. (5.0) objective of the present work: keeping the above in view, the present investigation has
been planned to carry out modeling and development of an algorithm for simulation of multicomponent condenser , with the following objectives:to formulate the mathematical model of a multicomponent condenser. To develop an algorithm for simulation of this condenser. To analyze the veracity of the model with various inlet operating conditions of condenser. To test and validate the model with available data.
11
Literature review Computer Aided Design (CAD) of a Multi-component Condenser( 2008):
The mathematical design models have been developed based on the equilibrium method. The design algorithm based on Bell and Ghaly’s method was compared with Kern’s method. It has been found that Kern’s method undersizes the condenser because it omits the mass transfer resistance and does not take enough care to handle sensible heat transfer during condensation. The main results associated with this paper was that…….(a) vapor flow rate or vapor inlet temperature increases , overall heat transfer coefficient decreases.(b) if coolant flow rate increases , overall heat transfer coefficient increses and required heat transfer area decreases.(c) if coolant inlet temperature increases , overall heat transfer coefficient decreases. In Bell and Ghaly’s method of condenser design, heat and mass transfer both resistences considered. So it gave more accurate size of condenser than calculated by Kern’s method.
D.R. Webb (2002) This paper makes a direct comparison of the popular silver – bell method, termed as equilibrium method and the film methods due to Colburn and Hougen. the silver approach is more commonly used in design of multicomponent condenser. With unspecified mixtures, where only a cooling curve is available, it must be used. Its advantage is that no further vapour-liquid equilibrium calculations are needed, irrespective of geometry. It has been corrected and improved by use of more physically realistic film model. but it is shown above that substantial discrepancies between the methods can occur, Even when all published correction factors are included. The success of the Silver method in industrial practice must be ascribed to the fact that industrial design is extremely conservative. The two methods are not in agreement at a Lewis number of unity, but at a value somewhat below, typically 0.60-0.80. At Le = 1 the equilibrium method is unsafe in predicting the gas film heat transfer coefficient by up to 50%. As Lewis number increases above unity the equilibrium method is increasingly unsafe.
ANDRZEJ BURGHARDT AND MAREK BEREZOWSKI A mathematical model has been developed which describes quantitatively the phenomena occurring during the condensation of multicomponent mixtures in which all constituents condense to form a homogeneous liquid phase. As a result of the analysis of the model equations two specific modes of the vapour mixture condensation have been defined and described: equilibrium condensation and total local condensation.
12
The methods currently used in the design of heat exchangers in which multicomponent condensation takes place fall into two groups: the equilibrium methods employing the works of Kern , Silver and Bell and Ghaly , and film method those based on the original paper by Colbum and Drew. To describe the phenomena occurring during the condensation, the latter group makes use of the relations defining the mass and energy fluxes both in the vapour phase and in the layer of condensate. The discussion carried out shows that the use of the equilibrium methods in the design of condensers may lead to substantial errors incurred in determining the heat fluxes . In this paper they also developed the model of condenser, which was based on co current flow. Using material balance, heat balance and assuming overall heat transfer coefficient constant along the condenser, they give the variation of total vapor flow rate, temperature variation of coolant and bulk vapor with degree of condensation.
D. R. WEBB AND R. G. SARDESAI: This paper discusses and provides experimental evidence of the applicability of the following theories to multicomponent condensation, The Krishna-Standart method .Toor's linearised theory), An effective diffusivity model based on Colburn & Hougen . It is found that all three models adequately quantify the vapour-side diffusional process for the experimental systems and conditions investigated but that multicomponent diffusional effects can be important. Physical models of the process of multicomponent condensation can be classified into two categories: (1)
Models such as those of Silver and Bell & Ghaly which assume that the multicomponent
condensation process follows the condensation curve, an approach which is extensively used in industrial practice to design multicomponent condensers. The reasons for this widespread use are Simplicity, .rapidity in computation, and no requirement to know intermediate vapor compositions or to obtain diffusivity data. (2)
Models which are more physically realistic, Such models (film, penetration or boundary
layer) lead to design procedures involving calculation of the local heat and mass transfer rates and their integration over the entire condenser area. The film theory of mass transfer forms the basis of the present study. Multicomponent mass transfer has been described by an empirical generalisation of Fick's Law and by the Maxwell-Stefan equations. For isothermal, isobaric conditions of ideal vapours the 13
MS equations are particularly useful. The generalisation of Fick's Law has been applied to film models in the linearised theory of Toor and Stewart & Prober while more recently an exact solution of the Maxwell-Stefan equations has been proposed by Krishna & Standart .The linearised theory and the exact matrix method are commonly referred to as "interactive" models of mass transfer because they allow for "diffusional interactions", where the diffusional behaviour of a constituent depends on al~ independent concentration gradients. A simpler approach to the application of film models in multicomponent mass transfer is by definition of effective diffusion coefficients for constituents with respect to the mixture as a whole, i.e. by assuming independent diffusion of the individual species. In this paper, a comparative study is made of "interactive" and "non interactive" models with experimental data for multicomponent condensation inside a vertical tube. J. BANDROWSKI This paper deals with the analysis of simultaneous heat and mass transfer at the condensation of multicomponent vapour in the presence of inert components. The results of numerical calculations of condensers, based on the solution of the individual versions of process model, resulting from the different description of multicomponent mass transfer, have been compared with the experimental data available. It has been found that best agreement was obtained in the case of variant based on Krishna-Standart method, whereas the shortest computing time was needed for the variant based on Burghardt-Krupiczka method yielding the results differing not significantly from the most accur. The differential equations of energy and mass balances, together with equations determining the interfacial equilibrium, relationships describing the transport of heat and mass as well as with equations of the kinetics of heat and mass transfer, constitute a system of equations which describe the process of simultaneous heat and mass transfer at the condensation of multicomponent vapor in the presence of inerts.
ANDREZJ BURGHARDT AND MAREK BEREZOWSKI: (1996) The changes of flow rates, compositions and temperatures of the phases during condensation are described by the appropriate differential mass and energy balances[I]. The heat exchanged across an infinitesimal surface area of the condenser may be determined from the overall heat balance
14
which, upon introduction of the definition of the enthalpy,takes the form
-∆
+ (1-v)
∑
]
The changes in the cooling medium temperature and in the heat transfer area of the condenser as functions of the degree of condensation are given by the following differential equations:
=
Results of this paper: As the choice of the initial temperature of the coolant, Tco has a direct influence on the magnitude of the total flux of the condensing vapour, N, and thus on the dimensions of the condenser. Interfacial temperature decreases, as degree of condensation increases. it can be seen that the differences in the length of the condenser tubes are insignificant for low values of the coolant temperature according to the two kinetic models (i.e. for the segregated and mixed flows). Therefore, as long as the local total condensation takes place in the condenser the final design is insensitive to the condensate flow model chosen for computations. the most conservative design is obtained by applying the equilibrium segregated flow model. Since in the horizontal condenser the condensate is being separated continuously from the vapour, only the segregated flow model can be employed in the design of this type of condenser. As the coolant temperature is low, final degree of condensation is very high but as the inlet temperature of coolant inceases , final degree of condensation decreases sharply.
15
Andrzej Burghardt, Krystyna Klepacka The process of condensation is governed by two basic physical phenomena, namely the interphase transport of mass and heat. The principal quantities occurring in the mass and energy balances of multicomponent condensation are the mass fluxes of the condensing species and the fluxes of heat transferred between the phases. The assumption of the segregated condensate flow (i.e. infinitely large mass transfer resistance in the layer of condensate) leads to the following relation, which defines the composition of the liquid phase at the vapour-liquid interface:
i = 1,2, ...........n
This paper was based on modelling of condenser for counter current flow. The calculations were done for different temperatures of the cooling medium (from 293 to 390 K), starting from the total condensation to partial condensation to the point when the process stops altogether (i.e. for the case when the interfacial temperature becomes equal to the coolant temperature and the condensation disappears). The variation of the initial coolant temperature, Tco (which has a direct effect on the flux of the condensing vapour and, consequently, on the condenser surface area), enables a comparison to be made between the various mass transfer models over the whole range between the local total condensation and the equilibrium condensation. over a wide range of the coolant temperatures, thus covering the whole region from the local total condensation to the equilibrium condensation. For the cooling medium temperature Tco = 293 K, the process fully corresponds to the local total condensation for all the kinetic models. In this case, the interfacial temperature is constant along the condenser and equal to the boiling point of the liquid of composition xi; the interfacial temperature profiles are then identical for the two kinetic models, independent of the direction of flow of the gas phase relative to the liquid phase (cocurrent or As the coolant temperature increases, the interfacial temperature profiles for the kinetic models rise and approach those corresponding to the equilibrium the final degree of condensation as a function of the cooling medium temperature. The coolant temperature at which the changeover from the total condensation ( ) to the partial condensation ( ) takes place differs by as much as several degrees depending on the model assumed. On the other hand, the coolant temperature at which the condensation stops ( ) is the same for all the models (To, = 390 K). It follows from Figure that the differences in the tube lengths for all the kinetic models are negligibly small at low temperatures of the cooling medium. Therefore, as long as we deal with the local total condensation, the size of the condenser is independent of the kinetic model assumed (segregated flow or ideally mixed flow) or the mode of contacting the phases (cocurrent or countercurrent).
During cocurrent flow of During cocurrent flow of the phases, the most conservative among the kinetic models is the segregated flow model. Since in the majority of condenser designs the flow of condensate is laminar, this model offers the best representation of the actual conditions and should be given preference in design calculations. The ideally mixed flow model may lead to unrealistically low values of the heat transfer area. The kinetic models should have 16
preference in design calculations. The equilibrium models should be used only in rough estimates of the heat transfer area. 395
3.5
390 3
385 e r380 u t a r375 e p 370 m e t l365 a i c a360 f r e t355 n i
2.5 inlet temp. 2 of coolan 1.5 t 1
0.5
350 0
0 0
200
400
0.5
1
1.5
600
length of condenser
degree of condensation
17
DEVELOPMENT OF MATHEMATICAL MODEL :
A mathematical model of multicomponent condenser is nothing but the relationship between the variables of the system. This can be obtained from the equations of material balances, energy balances and heat transfer rate. For simplicity, following are some assumptions taken during formulation of the model for design of multicomponent condenser. The model and its assumptions The basic assumptions of the model of condensation of vapour mixtures are as follows:
(1) The layer of condensate flows down the wall as a laminar film (2) The flow is determined by the equilibrium between the gravitational and viscous forces. (3) The flow of the vapour phase is a plug flow with perfect radial mixing.
(4) According to the film theory, the diffusional and heat resistances are located in suitably thin layers adjacent to the interface and are defined by the mass and heat transfer coefficients.
(5) Thermodynamic equilibrium prevails at the interface.
(6) The wall is cooled from the outside by an appropriate coolant which takes away the heat of condensation.
(7) The possibility of the formation of mist in the vapour phase is not allowed for. It is also assumed that the temperature of the vapour is determined solely by the equilibrium relations from the moment when it reaches the dew point temperature. (8) Steady-state operation (9) Heat conductivity in the direction of flow is negligible. (10)
No chemical reaction is taking place during condensation.
18
(11)Heat transfer by convection between vapor bulk to vapor-condensate interface is proportional to the quantities of each element is present in the bulk vapor. (12)The variation of the velocity profile of the vapour during condensation could not be taken into account since the model applied is one-dimensional.
Total mass balance: change in molar flow rate of vapour-mixture= accumulated condensate
(
-
-
=N.
= -N
For finding N : Heat balance: Heat given by condensing vapour + heat transferred between bulk-vapor and vapour condensate interface = overall heat transfer between interface condensate-vapour to bulk coolant
∑ +
(
) = Uo (
-
)
19
∑ = Uo (
-
)-
(
)
∑ ∑ N=
= -N = -
= π.
.dL
∑––
= - π.
.
=
+
=
+
+
+
Since ho is variable along the length of condenser, so ho =0.725
=
+
+
N=
∑ ) (
UO =
(
)
20
–∑–
= - π.
.
∑ (
= - π.
– – )
.[
]
Mass balance for i th component: For the given cross sectional boundry............
Input –
condensate =
.dA = ( -d )(
dA)
.dA =
dA - d
.dA =
.dA = =
= =
output
+
dA. d
dA - d
dA + d
+
HEAT BALANCE FOR PARTICULAR ELEMENT: Heat given by condensing element + heat transfer due to temp. difference between uncondensed bulk vapor and interface = heat transfer between interface and coolant
+ +
(
(
)=
)=
Uo (
Uo (
-
-
)
21
)
( ) ] ) [ ( =
BULK VAPOR TEMPERATURE VARIATION: Heat given by bulk uncondensed vapour = heat consumed in increasing of temperature of vapour between bulk vapour and interface +heat transferred between vapour bulk and interface
∑ ∑ (
-
)
=
–
=
=
=
∑ ∑
COOLANT TEMPERATURE VARIATION: Total heat transferred to coolant = total heat gained by coolant
22
(
)
Defining: degree of condensation
∫ ∫ ∫ ∫ ∫ ∫
As total mass balance........... =
=
=
N L + p ( integration constant)
BOUNDRY CONDITIONS: At L = 0 ,
=
So p =
NL+
=L
L= L=
TOTAL MASS BALANCE BASED ON DEGREE OF CONDENSATION: =
=
=
23
* + ∑ ∑ ∑ ∑ =
=
=
=
BULK – VAPOR TEMPERATURE VARIATION:
=
=
24
( ∑ )
∑
[
( ∑
)
COOLANT TEMPERATURE VARIATION:
=
25
]
( =
)
∑ ) (
SOLUTION OF MODEL : The numerical integration is performed on the basis of the fol lowing recurrent formulae definig the values of the parameter at the end of each integration step………..
=
+
∆
26
– =
Algorithm for simulation: the flowchart for the developed algorithm is presented in following fi gure. the final results obtained after
27
calculations as per the following steps given below, include variations of different system parameters. Algorithm steps are as follows: (1)Input the values of initial values of vapor flow rate, coolant flow rate and initial compositions. (2) Define the tube wall temperature, operating pressure, heat transfer coefficient of each side. (3) Check whether the condensing vapor temperature is less or more wall temperature. (5) Define the function of variable heat transfer coefficient of condensate film. (5) If it is more than wall temperature, using mass and heat balance find vapor flow rate, mole fraction of each component in vapor phase and liquid phase, variation of coolant temperature along length of condenser. (6) Define degree of condensation. (7) Find variations of the different variables on basis of degree of condensation. (8) Is variations are satisfactory on basis of available data and basic science. (9) if no, go to again on step (5) to repeat till step (7). (10) If yes, find the required results.
Start
Input a, b,xo,yo,h,N
Set m=1 a
xm
yo 28
ym
Compute k1, k2 ,k3 and k4
Xm +h
Xm+1
ym+1/6 (k1 +2k2+2k3+k4)
ym+1
Output Xm+1, ym+1
No Xm+1 ≥ b
Yes End
Start
Input the initial values for system
Define different operating conditions
29
Tw
yes Define variable heat transfer coefficient of condensate film
No Use equations of heat and mass balance
Variations are satisfactory
Yes Define degree of condensation
Variations are satisfactory
No
Yes
Result
End
30
Result
RESULTS AND DISCUSSIONS: For simulation of model equations we have taken vapor mixture of benzene(component 1) , toluene (component 2), xylene(component3) and water as coolant. At present for simulation we have taken system of following properties: y30 = 0.34 # mole fraction of xylene in vapor phase at inlet feed condition 31
y20 = 0.3333 # mole fraction of toluene in vapor phase at inlet feed condition y10 = 0.333 # mole fraction of benzene in vapor phase at inlet feed condition ggo = 2000 # total vapor molar flow rate at inlet condition (moles/second)
ρv= 50 # density of condensate mixture(kg/
)
l(0) = 0.0001 # initial length of condenser(m) l(f) = 100 # final length of condenser(m)
cpc = 75.35 # specific heat capacity for coolant (joule/mole) gc = 1000 # molar flow rate of coolant (mole/second) cp3 =181.7 # specific heat capacity for compound xylene (joule/mole.kelvin) cp2 =155.96 # specific heat capacity for compound toluene(joule/mole.kelvin) cp1 =134.85 # specific heat capacity for compound benzene(joule/mole.kelvin) h3 =35700 # molar enthalpy of evaporation of xylene (joule/mole) h2 =38060 # molar enthalpy of evaporation of toluene (joule/mole) h1 =30720 # molar enthalpy of evaporation of benzene (joule/mole) µ= 2.82*10^-4 # viscosity of condensate (kg/m.s) kf = 0.68 # thermal conductivity of condensate film (w/m.k) hfg = 2454000 # latent heat of condensation of vapor (joule/mole)
g = 9.81 # a physical constant (m/
)
ρ= 960 # density of condensate (kg/
)
k = 370 # thermal conductivity of tube material (w/m.k)
hi = 2100 # heat transfer coefficient inside of coolant pipe (w/ di = 0.015 # inner diameter of inner pipe (m)
.k)
= 1750 # heat transfer coefficient between bulk vapor and interface (w/
do = 0.021 # outer diameter of inner pipe(m) 32
.k)
tc(0) = 290
inlet temperature of coolant (k)
Variation according to length:
(a) Variation of vapor flow rate along length of condenser : it is decreasing as appear in the result of model equation . it should decrease as condensation increases, number of moles in vapor phase decreases. It decreases curvilinear. (b) Variation of mole fraction of benzene in vapor phase: it increases along the length of condenser as appear in the result of model equation . the reason beyond it is that at initial stage of condensation, the rate of condensation of benzene is low and rate of condensation of tolune and xylene is high . so mole fraction of benzene increases in vapor phase. The rate of increase is slow at initial stage , but increases at later stage. (c) Variation of mole fraction of toluene in vapor phase: it decreases along the length of condenser as appear in the result of model equation . the reason beyond it is that at initial stage of condensation, the rate of condensation of toluene is high . . in final stage of condensation , it changes in a complex way. (d) Variation of mole fraction of xylene in vapor phase: it decreases along the length of condenser as appear in the result of model equation . the reason beyond it is that at initial stage of condensation, the rate of condensation of xylene is high. (e) Variation of bulk vapor temperature: it also decreases as the condensation proceeds,
because heat of mixture is transferred from bulk to coolant by the way of heat of condensation and in form of sensible heat. It decreases curvilinear, fastest at initial stage. (f) Variation of coolant temperature: it increases along the length of condenser because along
the whole length it takes heat from vapor through condensate film and tube wall. As seen in graph it appears that it increases linearly, but it increases curvilinear. This is due to lss point taken on graph. (g) Variation of mole fraction of benzene in liquid phase: it increases along the length of
condenser very slowly as appear in the result of model equation . the reason beyond it is that at initial stage of condensation, the rate of condensation of benzene is low and rate of condensation of tolune and xylene is high . so mole fraction of benzene increases very slowly in liquid phase. (h) Variation of mole fraction of tolune in liquid phase: it increases along the length of
condenser as appear in the result of model equation . the reason beyond it is that at initial stage of condensation, the rate of condensation of toluene is high and rate of condensation of benzene is very low . so mole fraction of toluene increases in liquid phase. (i) Variation of mole fraction of xylene in liquid phase: it increases along the length of
condenser as appear in the result of model equation . the reason beyond it is that at initial stage of condensation, the rate of condensation of xylene is high and rate of condensation of benzene is low . so mole fraction of xylene increases in liquid phase. 33
ACCORDING TO THE DEGREE OF CONDENSATION:
(j) Variation of vapor flow rate: it is decreasing as appear in the result of model equation. It should decrease as degree of condensation increases, number of moles in vapor phase decreases. (k) Variation of mole fraction of benzene in vapor phase : it increases as the degree of
condensation increases as appear in the result of model equation. The reason beyond it is that at initial stage of condensation, the rate of condensation of benzene is low and rate of condensation of toluene and xylene is high. So mole fraction of benzene increases in vapor phase. This is also verified by authors ANDREZJ BURGHARDT AND MAREK BEREZOWSKI in reference [1].
(l) Variation of mole fraction of toluene in vapor phase : it decreases as the degree of condensation increases as appear in the result of model equation. The reason beyond it is that at initial stage of condensation, the rate of condensation of toluene is high. Verified in reference [1]. (m) Variation of mole fraction of xylene in vapor phase : it decreases as the degree of condensation increases as appear in the result of model equation. The reason beyond it is that at initial stage of condensation, the rate of condensation of xylene is high. (n) Variation of bulk vapor temperature: it also decreases as the degree of condensation
proceeds, because heat of condensation as well as sensible heat is transferred from bulk to coolant. (o) Variation of mole fraction of benzene in liquid phase: it increases as the degree of
condensation increases very slowly as appear in the result of model equation. The reason beyond it is that at initial stage of condensation, the rate of condensation of benzene is low and rate of condensation of toluene and xylene is high. So mole fraction of benzene increases very slowly in liquid phase. Verified in reference [1]. (p) Variation of mole fraction of toluene in liquid phase: it increases as the degree of
condensation increases as appear in the result of model equation. The reason beyond it is that at initial stage of condensation, the rate of condensation of toluene is high and rate of condensation of benzene is very low . So mole fraction of toluene increases in liquid phase. (q) Variation of mole fraction of xylene in liquid phase: it increases as the degree of
condensation increases as appear in the result of model equation. The reason beyond it is that at initial stage of condensation, the rate of condensation of xylene is high and rate of condensation of benzene is low. So mole fraction of xylene increases in liquid phase. (r) Variation of coolant temperature: it increases as the degree of condensation increases
because the coolant absorbs more heat as condensation increases. 34
120 100 e t 80 a r
w o l f 60 r o p a 40 v
20 0 0
20
40
60
80
length of condenser
35
100
120
0.45
r o p 0.4 a v k l 0.35 u b 0.3 n i e n 0.25 e z n 0.2 e b f 0.15 o n o 0.1 i t c a r 0.05 f e l 0 o m 0
20
40
60
80
100
120
length of condenser
293.5 293 e r 292.5 u t a r 292 e p m291.5 e t t n 291 a l o o 290.5 c
290 289.5 0
20
40
60 length of condenser
36
80
100
120
35 t n 30 e i c i f f 25 e o c r e 20 f n a r t 15 t a e h l l 10 a r e v 5 o
0 0
20
40
60
80
100
120
length of condenser
0.38
e s h p 0.37 d i u q i 0.36 l n i e n 0.35 e l y x f 0.34 o n o i t 0.33 c a r f e 0.32 l o m
0.31 0
0.2
0.4
0.6
degree of condensation
37
0.8
1
0.35
e s a h 0.3 p r o p 0.25 a v n i e 0.2 n u o l 0.15 o t f o n 0.1 o i t c a r 0.05 f e l o 0 m
0
20
40
60
80
length of condenser
38
100
120
0.4
e s a h 0.35 p r o 0.3 p a v n i 0.25 e n e 0.2 l y x f 0.15 o n o i t 0.1 c a r f 0.05 e l o m 0
0
20
40
60
80
100
120
80
100
120
length of condenser
350 300
e r u t 250 a r e p m200 e t r o 150 p a v k l 100 u b
50 0 0
20
40
60 length of condenser
39
12 10 e t a s 8 n e d n o 6 c f o s e 4 l o m
2 0 0
20
40
60
80
100
120
length of condenser
0.45 r o 0.4 p a v 0.35 n i e 0.3 n e z n e 0.25 e s b a f h o p 0.2 n o i 0.15 t c a r 0.1 f e l o 0.05 m
0 0
0.2
0.4
0.6
degree of condensation
40
0.8
1
0.6
e s a h p 0.5 r o p a v 0.4 n i e n e 0.3 l y x f o n 0.2 o i t c a r 0.1 f e l o m 0
0
0.2
0.4
0.6
0.8
1
0.8
1
degree of condensation
0.334
e s a h 0.332 p r o 0.33 p a v n i 0.328 e n u 0.326 o l o t f 0.324 o n 0.322 o i t c a r 0.32 f e l o 0.318 m
0
0.2
0.4
0.6
degree of condensation
41
350 r 300 o p a v 250 k l u b 200 f o e r 150 u t a r e 100 p m e t
50 0 0
0.2
0.4
0.6
0.8
1
0.8
1
degree of condensation
400 350 e r 300 u t a r 250 e p m200 e t t n 150 a l o o 100 c
50 0 0
0.2
0.4
0.6
degree of condensation
42
0.33
e s a h 0.325 p d i u q i 0.32 l n i e 0.315 n e z n 0.31 e b f o n 0.305 o i t c 0.3 a r f e l o 0.295 m
0
0.2
0.4
0.6
0.8
1
0.8
1
degree of condensation
0.38
e s a h 0.37 p d i u q i 0.36 l n i e 0.35 n e l y x 0.34 f o n 0.33 o i t c a r 0.32 f e l o m0.31
0
0.2
0.4
0.6
degree of condensation
43
0.3355
e s a h p 0.335 d i u q i l 0.3345 n i e n e 0.334 u o t f o 0.3335 n o i t c a r 0.333 f e l o m0.3325
0
0.2
0.4
0.6
0.8
1
degree of condensation
e 0.4 s a h p 0.35 d i u 0.3 q i l n i 0.25 e n e u 0.2 l o t f 0.15 o n o i t 0.1 c a r f 0.05 e l o 0 m
0
20
40
60
80
length of condenser
44
100
120
0.035
e s a h 0.03 p d i u q i 0.025 l n i e 0.02 n e l y x 0.015 f o n 0.01 o i t c a r 0.005 f e l o 0 m
0
20
40
60
80
100
120
100
120
length of condenser
4.00E-02
e s a h 3.50E-02 p d i u 3.00E-02 q i l n i 2.50E-02 e n e 2.00E-02 z n e b 1.50E-02 f o n 1.00E-02 o i t c a r 5.00E-03 f e l o0.00E+00 m
0
20
40
60
80
length of condenser
45
46
47
References:
1. Kern, D. Q., AIChE J. 17(5) (1971) 1037. 2. Bell, K. J., Ghaly, M. A., AIChE Symp. Ser. 131(69) (1973) 72. 3. Colburn, A. P., Drew, T. B., Trans. Am. Inst. Chem. Engnrs. 33 (1937) 197. 4. Colburn, A. P., Hougen, O. A., Ind. Eng. Chem. 26 (1934) 1178. 5. Colburn, A. P., Edison, A. G., Hydrocarbon Processing 33 (1941) 457. 6. Krishna, R., Panchal, C. B., Chem. Eng. Sci. 32 (1977) 742. 7. Heat Exchanger Design Handbook, Hemisphere. 1983 New York 8. Lockhart, Q. W., Martinelli, R. C., Chem. Eng. Prog. 48 (1949) 39. 9. Kutaleladze, S. S., Borishanskii, V. M., Concise Encyclopedia of Heat Transfer, Pergamon Press, Oxford, 1966. 10. Sinnott, R. K., Coulson & Richardson’s Chemical Engineering Vol. 6,ButterworthHeinemann, London, 1996. 11. S. BANDYOPADHYAY et al., Computer Aided Design (CAD) of a Multi-component, Chem. Biochem. Eng. Q. 21 (2) 97 – 103 (2007) 103 12. G. Ackermann, Combined heat and mass transfer in the same field at high temperature and partial pressure differences, Forsch. Ing. Wes. VDI 8 (382) (1937) 1-16. 13. W.W. Akers, M.M. Turner,Condensation of vapours of immiscible liquids, AIChE J. 8 (5) (1962) 587-589. 48
14. J. Taborek, (Including the method of K.J. Bell), Shell and tubeheat exchangers, Heat Exchanger Design Handbook, Ch. 3.3, Hemisphere, Washington DC, 1983. 15. K.J. Bell, M.A. Ghaly, An approximate generalised design method for multi-componentpartial condensers, AIChE Symp. Ser. 69 (131) (1972) 72-79. 16. S.H. Bernhardt, J.J. Sheridan, J.W. Westwater, Condensation of immiscible mixtures, AIChE Symp. Ser. 68 (118) (1972) 21-37. 17. D. Butterworth, Developments in the design of shell and tube condensers, ASME Preprint 77-WA/HT-24, Winter AGM, Atlanta, 1977. 18. T.H. Chilton, A.P. Colburn, Mass transfer coefficients: Prediction from data on heat transfer and fluid friction, Ind. Eng. Chem. 26 (1934) 1183. 19. A.P. Colburn, O.A. Hougen, Design of cooler condensers for mixtures of vapours with non-condensing gases, Ind. Eng. Chem. (1934) 1178-1182. 20. A.P. Colburn, T.B. Drew, The condensation of mixed vapours, Trans. AIChemE 33 (1937) 197-215. 21. F.W. Dittus, L.M.K. Boelter, Engineering 2 (13) (1930) 443-461, as modified in E.N. Sieder, C.E. Tate, Heat transfer and pressure drop of liquids in tubes, Ind. Eng. Chem. 28 (1936) 1429. 22. ESDU, Ba.ed Shell-and-tube Heat Exchangers, No 83038, Engineering Sciences Data Unit, London, 1983. 23. I.D.R. Grant, I. Murray, Pressure drop on the shellside of a segmentally ba.ed shell and tube heat exchanger with vertical two-phase flow, NEL (UK) Report No. 500, 1972. 24. I.D.R. Grant, I. Murray, Pressure drop on the shellside of a segmentally ba.ed shell and tube heat exchanger with horizontal two-phase flow, NEL (UK) Report No. 560, 1974. 25. K. Ishirara, J.W. Palen, J. Taborek, Critical review of correlations for predicting twophase flow pressure drop across tube banks, ASME Paper 77-WA/HT-23, 1977. 26. D.Q. Kern, Mathematical development of tube loading in horizontal condensers, AIChE J. 4 (2) (1958) 157-160. 27. J.S. Kim, Condensation of multicomponent vapours of miscible and immiscible liquids in a condenser of industrial scale, M.Sc. Thesis, University of Manchester, 1988. 28. J.S. Kim, Shell-side condensation of vapours forming miscible and immiscible liquids at atmospheric and reduced pressures, Ph.D. Thesis, University of Manchester, 1988. 49
