Modeling and simulation of direct contact evaporators

MODELING AND SIMULATION OF DIRECT CONTACT EVAPORATORS

F.B.Campos and P.L.C.Lage

Programa de Engenharia Química, COPPE/UFRJ,

C.P.68502, CEP 21945-970, Rio de Janeiro - RJ, Brazil

Phone [phone], Fax [phone]

(Received: April 19, 2001; Accepted: July 31, 2001)

Abstract - A dynamic model of a direct contact evaporator was developed and coupled to a recently developed superheated bubble model. The latter model takes into account heat and mass transfer during the bubble formation and ascension stages and is able to predict gas holdup in nonisothermal systems. The results of the coupled model, which does not have any adjustable parameter, were compared with experimental data. The transient behavior of the liquid-phase temperature and the vaporization rate under quasi-steady-state conditions were in very good agreement with experimental data. The transient behavior of liquid height was only reasonably simulated. In order to explain this partial disagreement, some possible causes were analyzed.

Keywords: heat and mass transfer, direct contact evaporator, modeling and simulation, bubble, bubble column

INTRODUCTION

Direct contact evaporators are devices in which the liquid phase is vaporized by injection of a superheated gas. Several of its applications are reported in the literature (Smith, 1986; Sideman, 1966; Bharathan, 1988). Compared to tube and shell evaporators, direct contact evaporators have lower manufacture and maintenance costs, higher heat transfer rates (there is no additional heat transfer resistance due to tube wall and fouling) and greater efficiency of operation for highly corrosive, fouling and viscous mixtures.

The superheated gas is injected into the liquid phase through submerged orifices of a distribution system. The gas forms bubbles that grow at the orifices until reaching a critical volume, at which point they detach (Kumar and Kuloor, 1970). After the formation stage, the bubbles ascend in the liquid column. Heat and mass transfer occur during both stages. Part of the exchanged energy is used to vaporize the liquid and the other portion is used to heat the liquid phase. The vapor is removed from the system by the bubbles that reach the top of the liquid column.

A direct contact evaporator has two different time scales: one is the time necessary to reach steady-state conditions (typically, several hours) and the other is the bubble residence time (several seconds). Therefore, in the modeling of direct contact evaporators, a scale decomposition can be used (Lage and Hackenberg, 1990; Queiroz and Hackenberg, 1997) to create a dynamic model for the liquid phase using the former time scale and a dynamic model for the superheated bubble using the latter time scale.

The liquid-phase model consists of overall heat and mass balances for the liquid phase in the evaporator. This model needs the transient values for gas holdup, vaporization rate and rate of heat transfer to the liquid by the bubbles. These values are calculated by the superheated bubble model, which consists of the continuity, energy and species conservation equations for a bubble coupled to a bubble dynamics model (Campos and Lage, 2000b). This model assumes that the instantaneous liquid-phase conditions can be considered constant during the formation and ascension of an isolated bubble.

Several superheated bubble models were developed. Some of them took into account heat and mass transfer only during the ascension stage (Queiroz and Hackenberg, 1997), while others analyzed heat and mass transfer only during the formation stage (Pinto and Hackenberg, 1994; Hackenberg and Mezavilla, 1997). However, the above-cited models assumed constant physical properties for the gas and a bubble detachment volume (bubble volume at the end of the formation stage) given by a bubble dynamics model that does not take into account the heat and mass transfer (Davidson and Schüler, 1960). Only recently, Campos and Lage (2000a, 2000b) developed a model that allows variable physical properties for the gas, takes into account variable bubble radius and includes the effects of heat and mass transfer on dynamics of the bubbles during their formation. Using this model, they developed a correction factor for isothermal gas holdup correlations to allow their application to nonisothermal columns. The Campos and Lage (2000b) model predictions agreed well with the experimental data for mass vaporization rate and gas holdup in the quasi-steady state of a direct contact evaporator (Queiroz, 1990).

Lage and Hackenberg (1990) developed a dynamic model for the liquid phase which was coupled to the superheated bubble model developed by Queiroz (1990). The model showed good agreement (Queiroz, 1990; Queiroz and Hackenberg, 1997) only when the experimental gas holdups (Queiroz, 1990) were used as input data.

In this work, a new dynamic model for a direct contact evaporator was developed and coupled to the Campos and Lage (2000b) superheated bubble model, which allows the prediction of gas holdup in nonisothermal systems. For the first time, Queiroz’s experimental data will be compared to a dynamic model of a direct contact evaporator that does not use any experimentally adjustable parameter.

EVAPORATOR MODEL

A scheme of the direct contact evaporator used by Queiroz (1990) is shown in Figure 1. It consists of a vessel with a gas distribution system located close to its bottom. The combustion gases that are fed into the distribution system pass through a central tube that comes from the top of the evaporator. Therefore, the gas-feed system consists of the central tube and the distribution system. Figure 1 also shows the symbols for temperatures, mass fractions, mass flow rates and heat transfer rates necessary to model this kind of direct contact evaporator. For this kind of evaporator, the overall model is obtained by the coupling of the liquid-phase model, the gas-feed model and the superheated bubble model.

Liquid-Phase Model

Due to the high level of agitation in the bubbling process, the liquid phase can be assumed to be well mixed (Queiroz, 1990). Therefore, the direct contact evaporator model was derived from overall balances of liquid mass, solute mass and energy.

where it was assumed that the solid entrainment in the gas flow is negligible and the reference liquid-phase enthalpy was taken at the inlet liquid temperature. Q_b, Q_d and Q_p are, respectively, the heat transfer rates from bubbles to liquid phase, from inlet gas to liquid phase through the gas-feed system and from liquid phase to the surroundings through the evaporator walls.

Using Equation (1), Equation (2) can be written as

Assuming that the mean specific heat of the liquid phase is constant and equal to the pure solvent, C_o = C, and using Equation (1), one can rewrite Equation (3) as

The assumption C_o = C is valid for diluted solution and is perfectly correct for the experiments carried out by Queiroz (1990) with pure water.

The transient behaviors of m_L, Y and T_L are obtained when Equations 1, 4 and 3 (or 5) are coupled to a model for the heat transfer in the gas-feed system and a model for the heat and mass transfer from bubbles to the liquid phase.

Gas-Feed Model

This model determines heat lost with the gas-feed system. Two losses are computed: the heat lost through the central tube to the gas phase that leaves the evaporator (Q_v) and that lost through the central tube and the distribution system to the liquid phase (Q_d). Both values are used to determine temperatures T_gn, T_gd and T_gb in the gas-feed system. T_gb is used in the superheated bubble model. The temperature of the gas phase that leaves the evaporator, T_v, can also be calculated.

The input data for the gas-feed model consists of constant parameters, , T_g, x_g and the dimensions of the evaporator, which were measured or estimated, and some variables that are calculated by the other coupled models, , x_v, T_L, H and T_vn. T_L is determined by the liquid-phase model and , x_v, H and T_vn by the superheated bubble model.

However, a dynamic model for the gas-feed system was not developed in this work. Our main purpose is to simulate Queiroz’s (1990) experimental data using the superheated bubble model developed by Campos and Lage (2000b). Here we used the results of the simplified calculations developed by Queiroz (1990) for the heat transfer through the gas-feed system. The modeling features of these calculations are described below.

Queiroz (1990) developed a pseudo-steady-state model to calculate the heat transfer in the gas-feed system. From the experimental data in semibatch operation, Queiroz (1990) determined the mean values of , , x_g, x_v, T_g, T_L, H and T_vn under quasi-steady-state conditions (T_L approximately constant). These mean values were used to determine Q_v and Q_d and, consequently, T_gn, T_gd and T_gb.

In order to determine Q_v, the following assumptions were made: pseudo-steady-state convective heat transfer inside the central tube, negligible thermal resistance of the central tube and pure radiation heat transfer in the annular region between the external surface of the central tube and the vessel walls, where the gas was assumed to be gray and the internal vessel walls were assumed to be adiabatic. The annular region was considered to have an infinite length so that all the view factors were assumed to be unity. The Gnielinski correlation (Incropera and De Witt, 1990) was used to calculate the convective heat transfer coefficient inside the central tube.

To determine Q_d, the thermal resistance of the submerged part of the central tube of the gas-feed system and the thermal resistance of the liquid phase were neglected. The decrease in gas flow rate due to the bubbling process was taken into account in determining the internal convective heat transfer coefficient in the tubes of the distribution system. The Gnielinski correlation was used again to determine the internal convective heat transfer coefficients for the submerged part of the central tube and for the eight tubes in the distribution system. For the latter case, two values for the gas flow rate were considered in the calculation: the inlet mass flow rate, /8, and the mean mass flow rate within any of the distribution tubes, /16.

In this work, only experiments 1, 3 and 6 by Queiroz (1990) will be analyzed. Table 1 presents the values for T_g, T_gn and T_gb obtained by Queiroz (1990). The value or T_g was determined using a radiation correction for the thermocouple reading. The thermocouple radiative properties were estimated. Since the correction factor is quite dependent on the thermocouple emissivity, T_g can assume several values. The values for T_gb are mean values for the entire distribution system. Using these data, Q_v and Q_d can be determined from

where the mean specific heats at constant pressure must be determined for the different ranges of temperature, as indicated. Knowing Q_v, T_v can be given by

where and T_vn are calculated by the superheated bubble model. The mean values for T_v – T_vn determined by experimental values under quasi-steady-state conditions ( approximately constant) are also shown in Table 1.

Superheated Bubble Model

Direct contact evaporators show low values for gas holdup which usually results in the homogeneous regime. In this case, the process of heat and mass transfer between the gas and liquid phases may be analyzed using a single bubble. Thus, the superheated bubble model is an attempt to represent the simultaneous heat and mass transfer phenomena during bubble formation at a submerged orifice and bubble ascension through the continuous liquid phase.

In this work, we used the superheated bubble model developed by Campos and Lage (2000b) to determine the frequency of bubble formation at one orifice, f, and, for the whole process of bubble formation and ascension along the liquid height, H, the integrated values for the vaporized mass per bubble, m_vb, and the sensible heat exchanged with the liquid phase, Q_vb. With these values and the total number of orifices, one can determine and Q_b as

However, as H is unknown, it should be determined from the mass of liquid and the gas holdup.

From the definition of e_c, we have

Combining, Equations (11) and (12), H may be determined by

According to Queiroz (1990), we can assume that there is no gas under the distribution system (e_h = 0). This assumption agrees with the hypothesis of homogeneous regime, where the liquid circulation is not strong enough to drag bubbles to the region under the distribution system. Thus, H can be calculated from Equation (13) if the gas holdup above the distribution system, e_H, is known.

Campos and Lage (2000a, 2000b) showed that gas holdup in nonisothermal systems can be estimated using a correction factor for isothermal gas holdup correlations (Akita and Yoshida, 1974; Hikita et al., 1980) where the correction factor is based on bubble model results. This procedure was used to determine e_H.

NUMERICAL PROCEDURE

The initial conditions for Equations (1), (4) and (5) were obtained from the initial liquid height before starting the gas injection, H₀, and initial liquid-phase temperature, T_L0, given by Queiroz (1990) for each one of his experiments. The initial liquid mass can be calculated from Equation (13) with e_H = e_h = 0. In the experiments analyzed in this work, the liquid phase was pure water, so Y = 0.

Equations (1), (4) and (5) were integrated from their initial conditions using the DDASPG routine from the IMSL library, which is an implementation of the DASSL routine (Petzold, 1989). The DASSL routine was not used because it is already used in the subroutine that implements the time integration of the superheated bubble model (Campos and Lage, 2000b). During the time integration of the liquid-phase model, the superheated bubble model periodically updates the values of Q_b, and e_H. The last value was obtained by applying the nonisothermal correction factor to the gas holdup correlation of Hikita et al. (1980). The superheated bubble model calculation parameters, such as number of discretized points, time integration tolerance and number of quadrature points in the determination of Q_b and , were varied to assure that convergence was obtained in the results. The results discussed in this work were determined with a degree of accuracy higher than 0.1%.

RESULTS AND DISCUSSIONS

From the group of ten experiments done by Queiroz (1990), we selected those that are representative of the analyzed range of liquid height, corresponding to Queiroz’s (1990) experiment numbers 1, 3 and 6. The simulated results presented below were obtained for the initial conditions given in Table 2 and the following values for the evaporator parameters: d_c = 0.57 m, N = 288, d_or = 1.3 mm, d_t = 2.67 cm, h = 6.8 cm, V_d = 1.12 ´ 10^-3 m³, = 5.4 ´ 10^-3 kg/s, = = 0, Y = 0 and Q_p = 0, and for the combustion gas, y(CO₂) = 0.09, y(H₂O) = 0.12, y(O₂) = 0.05 and y(N₂) = 0.74.

In some simulations, the thermal capacitance of the evaporator ((mC)_m = 3.83 ´ 10⁴ J/K) was added to the liquid-phase thermal capacitance in Equation (5) to take into account, in a simplified manner, the thermal inertia of the evaporator. This analysis assumes that the evaporator is kept at the liquid- phase temperature.

Figures 2, 3 and 4 show the experimental results obtained by Queiroz (1990) for T_L, T_v and H for experiments 1 (Figure 2), 3 (Figure 3) and 6 (Figure 4). These figures also show the simulated results for T_L, T_vn and H using the direct contact evaporator model developed in this work, either with or without the evaporator thermal capacitance. The simulations were carried out under the initial conditions given in Table 2 and the values of T_gn given in Table 1 corresponding to the case where e = 0.3 and /8. Simulations using the other values of T_gn given in Table 1 gave worst results for H and T_L. For this reason, these simulations are not presented here. It is worth pointing out that the experimental data is for T_v and not T_vn, which is simulated by the model. So, it is not possible to compare these values directly.

The values of T_v – T_vn are much greater than the predictions made by Queiroz (1990) and given in Table 1. In fact, the prediction of T_v – T_vn made by Queiroz (1990) for experiment 6, which is 26^oC, is even greater than the measured value of T_v – T_L. Thus, the heat transfer model for the gas-feed system seems to be inadequate to determine the quantity of energy transferred to the gas and vessel walls by radiation. Thus, this model must be improved.

Inclusion of the evaporator thermal capacitance in the simulations, as described above, remarkably improved the agreement between the simulated and experimental data on the transient behavior of T_L. Prediction of the vaporization rate, , under quasi-steady-state conditions, which is experimentally determined by the slope of the H(t) curve, also improved. Thus, the predictions for the transient behavior of T_L and for the values of under quasi-steady-state conditions show a better agreement with the experimental data when the evaporator thermal capacitance was considered in the direct contact evaporator model.

Prediction of liquid height is reasonably good. Our model determined column expansions just after start-up larger than those shown in the experimental data. This can be clearly seen in Figures 2b, 3b and 4b, which show the transient behavior of liquid height, H, for experiments 1, 3 and 6, respectively. However, Queiroz (1990) did not report the initial liquid mass. As previously described in this work, the initial liquid mass was determined using the initial value of H before start-up reported by Queiroz (1990) and shown in Table 2. However, these initial values of H are not always consistent. This can be clearly seen by comparing the experimental values for the initial column expansion in experiment 3 (Figure 3b) with those in experiments 1 and 6 (Figure 2b and 4b). Experiment 3 shows a negligible column liquid expansion, which is quite different from the behavior observed in experiments 1 and 6. It seems possible that the error in the measurement of the initial liquid height was larger than the value reported by Queiroz (1990).

Based on the above discussion, two groups of simulations were performed. For the first group, the liquid mass was 2% lower than the value determined by Equation (13). For the second group of simulations, the initial liquid height was the first experimental point after start-up, calculating liquid mass with Equation (13) using the value of e_H as given by the superheated bubble model. The results for the transient behavior of H are also presented in Figures 2b, 3b and 4b for each experiment. The transient profiles of T_L and T_vn were not significantly affected by these changes, and for this reason, they are not presented.

These two groups of simulations gave transient profiles for H which were very similar in all the experiments. Both changes in the simulation conditions resulted in a decrease in the initial liquid mass. The agreement with experimental data is very good for experiment 1, good for experiment 3 and poor for experiment 6.

The experimental results show that the maximum on the transient profile for H decreases as the initial liquid height increases. This maximum appears because, initially, H increases due to the thermal dilation of the liquid, the condensation of the water vapor present in the inlet combustion gas and the increase in gas holdup due to the reduction of gas contraction as T_L increases. The first effect, the liquid thermal dilation, is unequivocal, but the others depend upon the model and the gas composition, x_g, which was estimated by Queiroz (1990) assuming complete combustion. Furthermore, the values of T_g determined by Queiroz (1990) and used in this work were obtained from the heat transfer model for the gas-feed system under quasi-steady-state conditions. This can affect the transient behavior of gas holdup in the direct contact evaporator, and thus, the liquid height, H.

CONCLUSIONS

The simulated results for the transient behavior of the liquid-phase temperature and for the vaporization rate under quasi-steady-state conditions were in excellent agreement with experimental data. The prediction of the transient behavior of the liquid height was only reasonable. Possible reasons for the observed discrepancy were analyzed.

NOMENCLATURE

C mean specific heat (J/kgK) d diameter (m) e thermocouple emissivity f frequency of bubble formation (s^-1) H liquid height (m) m mass (kg)

mass flow rate (kg/s)

N number of orifices in the distribution system Q heat transfer rate (W) t time (s) T temperature (K) V volume (m³) y molar fraction x mass fraction vector Y solid mass fraction Greek Symbols e gas holdup Subscript 0 initial conditions b related to the bubbling process or the bubble c column d related to the distribution system e inlet liquid in the evaporator g feed gas h height h H height H L liquid phase m evaporator metallic material n at liquid level o pure solvent or orifice p thermal loss v evaporated s outlet flow of liquid from the evaporator t admission gas central tube

REFERENCES

• Akita, K., Yoshida, F., Bubble Interfacial Area and Liquid Phase Mass Transfer Coefficient in Bubble Columns, Ind. Eng. Chem. Proc. Des. Dev., Vol. 13, p. 84 (1974).
• Bharathan, D., Direct Contact Evaporation, In Direct Contact Heat Transfer, Kreith, F. and Boehm, R. F. (eds.) Hemisphere, New York, 203 (1988).
• Campos, F. B. and Lage, P. L. C., Simultaneous Heat and Mass Transfer During the Ascension of Superheated Bubbles, Int. J. Heat Mass Transfer, 43, 179 (2000a).
• Campos, F. B. and Lage, P. L. C., Heat and Mass Transfer Modeling During the Formation and Ascension of Superheated Bubbles, Int. J. Heat Mass Transfer, 43, 2883 (2000b).
• Davidson, J. F. and Schüler, B. O. G., Bubbles Formation at an Orifice in an Inviscid Liquid. Trans. Instn. Chem. Engrs., Vol. 38, p. 335 (1960).
• Hackenberg, C. M., Mezavilla, A. C., Transient Heat and Mass Transfer During the Formation of Superheated Spherical Bubbles. In Transient Convective Heat Transfer ICHMT, Vol. 1, Padet, J. and Arinç, F. (eds.), Begellhouse, New York, p. 409 (1997).
• Hikita, H., Asai, S., Tanigawa, K., Segawa, K., Kitao, M., Gas Hold-up in Bubbles Columns, Chem. Eng. Journal, Vol. 20, p. 59 (1980).
• Incropera, F. P. and De Witt, D. P., Fundamentals of Heat and Mass Transfer, 3^d ed., New York, John Wiley, p. 497 (1990).
• Kumar, R., Kuloor, N. R., The Formation of Bubbles and Drops, Adv. in Chem. Engineering, 8, 255 (1970).
• Lage, P. L. C., Hackenberg, C. M., Simulation and Design of Direct Contact Evaporators. In Multiphase Transport and Particulate Phenomena, Vol. 2, Veziroglu, T. N. (ed.) Hemisphere, New York, p. 577 (1990).
• Petzold, L.R., DASSL code, 1989, L316, Computing and Mathematics Research Division, Lawrence Livermore Nat. Lab., Livermore (1989).
• Pinto, A. D., Hackenberg, C. M., Evaporaçăo Interfacial Durante a Formaçăo de Bolhas Superaquecidas em Orifícios. Anais do V ENCIT, Săo Paulo, SP, 1, 36 (1994).
• Queiroz, E. M., Hackenberg, C. M., On the Transient Heat and Mass Transfer Modelling of Direct Contact Evaporators, In Transient Convective Heat Transfer ICHMT, Vol. 1, Padet, J. and Arinç, F. (eds.) Begellhouse, New York, p. 179 (1997).
• Queiroz, E. M., Transferęncia Simultânea de Calor e Massa em Processos de Borbulhamento. Ph.D. diss., COPPE/UFRJ, Rio de Janeiro, Brazil (1990).
• Sideman, S., Direct-Contact Heat Transfer Between Immiscible Liquids, Advances in Chemical Engineering, 6, 207 (1966).
• Smith, R. A., Vaporisers Selection, Design & Operation. Harlow, Longman Sci. & Tech., 50 (1986).

Publication Dates

• Publication in this collection
  10 Oct 2001
• Date of issue
  Sept 2001

History

• Received
  19 Apr 2001
• Accepted
  31 July 2001