TY - JOUR
AU - Inambao, Freddie L
AB - Abstract In this paper, a comprehensive technical review of liquid desiccant (LD) dehumidification and regeneration techniques is presented. The operational features, processes and performance indices of various flow configurations of adiabatic dehumidifier and regenerator are extensively covered. The heat and mass transfer assessment is presented in terms of past experimental and modelling evaluations and procedures. The existing adiabatic dehumidifier/regenerator heat and mass transfer models are categorized into finite difference, effectiveness-number of transfer units and simple empirical correlation models. The respective performance prediction models are critically analysed in details and compared in terms of assumptions, iterative procedures, solution methods, accuracy, computation time, output variables and applications. The solar regenerator models are also highlighted with a focus on the collector module. The ideal settings, formulation procedures, current state-of-the-art and opportunities for improvements are outlined. The review provides meaningful insight into the research status and available opportunities in the LD adiabatic dehumidifier and regenerator modelling and optimization as well as conceptualization of the applicable models. Finally, some very impactful suggestions for improvement and further research are outlined. 1. INTRODUCTION The rising requirements for air-conditioning, predominantly in the hot-humid subtropical climates such as in African and Mediterranean countries, have triggered a substantial intensification in demand for energy sources. Power plants experience highest loads in summer season and frequently hardly accomplish sufficient supply of the total demand. Through appropriate know-how, solar-cooling can relieve and eradicate the problem if utilized because the energy consumption is highest during the periods of high solar radiation. Liquid desiccant air conditioning (LDAC) is one such technology that has the potential of using low-grade solar thermal energy in the process of dehumidification and regeneration under adiabatic conditions. The configuration of the adiabatic dehumidifier and regenerator is such that air–desiccant interactions are by direct contact and net energy, as well as mass transfer rates, are zero. The most common types of dehumidifiers and regenerators are vertical columns filled with packing materials through which air–desiccant contact is enabled or spray towers [1]. In the latter, the misty desiccant liquid is spewed freely on the processed air path. However, the major drawback is the possibility of desiccant carry-over with the process air in addition to the complexity of spray head optimization. The packed-column dehumidifier/regenerator is compact in design and provides prolonged interaction time and minimal carry-over as was proved in a verification study covering modelling and practical investigation [2]. The adiabatic type of dehumidifier is prone to low effectiveness due to escalation of desiccant temperature by the ensuing latent heat. However, a carefully balanced air–desiccant flow rates minimizes the temperature rise and risks of carry-over but care must be taken not to weigh down the coefficient of performance (COP). The theory of liquid desiccant (LD) dehumidification and regeneration is firmly hinged on the intricately coupled heat and mass transfer manifestation. Whereas a temperature gradient spearheads the heat transmission, the mass exchange is caused by the air–desiccant interfacial vapour pressure gradient. In practice, during LD dehumidification and regeneration processes, a substantial amount of heat is produced during the phase alteration and dilution. However, the former is negligibly smaller than the latter and is always ignored in the formulation of heat and mass transfer models [3]. The assessment of heat and mass transfer process is based on interfacial film, penetration and surface renewal theories as pioneered by [4]. The film was defined as the slim still interfacial region where mass exchange resistance is highest. Based on this definition, a simple two-film theory was introduced [5]. However, the two-film approach ignores the convective component of mass exchange besides difficulty in allocating the depth of the sub-layers. Therefore, its application is only limited to steady-state conditions. Considering these and many more limitations in other studies, there is a critical need for thorough scrutiny of the existing theories and principles derived from various studies of LD dehumidification and regeneration. This paper aims to provide meaningful insights into the research status and available opportunities in the adiabatic LD dehumidification and regeneration techniques. To unravel the gaps and provide some very impactful suggestions for improvement and further research, an extensive review of experimental and modelling procedures of heat and mass transfer assessments under varying conditions and configurations has been conducted. 2. DEHUMIDIFIERS The packed bed adiabatic dehumidifiers are often characterized by high heat-mass exchange effectiveness due to its big air–desiccant interfacial area with comparatively modest geometric structure. However, there is a likelihood of high air pressure drop through the packing medium as well as high desiccant temperature in the course of moisture exchange. The high desiccant temperature is undesirable and needs to be regulated for effective moisture control. Internally cooled dehumidifiers (outside the scope of the present study) offer a temporary remedy to the heating problem; however, efficient design with optimized air–desiccant flow rates efficiently eliminates the setback [6]. 2.1. Performance indices The key performance appraisal indices for the packed bed adiabatic dehumidifier and regenerator that are predominantly used are effectiveness and moisture removal rate. The dehumidifier effectiveness is a unitless ratio of humidity ratio differences between inlet, exit and saturation conditions as follows [7]: $$\begin{equation} {\varepsilon}_{deh}=\left(\frac{\omega_i-{\omega}_o}{\omega_i-{\omega}_e}\right), \end{equation}$$(1) where w is the humidity ratio in kg/kgdryair, while subscripts i, o and e are an inlet, outlet and equilibrium conditions, respectively, and |${\omega}_e$| is stated in relation to the inlet desiccant temperature Td and the atmospheric pressure Pa as follows: $$\begin{equation} {\omega}_e=0.622\left\{\frac{0.6107\mathit{\exp}\left(\frac{17.27{T}_d}{T_d-237.3}\right)}{P_a-0.6107\mathit{\exp}\left(\frac{17.27{T}_d}{T_d-237.3}\right)}\right\}.\end{equation}$$(2) Moisture removal rate ϵ is, by definition, directly proportional to the humidity ratio difference at outlet and inlet conditions so long as the mass flow rate m˙ a and m˙ d are constants. This ratio takes care of the latent heat capacity of the conditioned air and can also be mathematically formulated in terms of desiccant c concentration as well. $$\begin{equation} {\xi}_{deh}={\dot{m}}_a\left({\omega}_i-{\omega}_o\right)={\dot{m}}_d\left(\frac{\chi_i}{\chi_o}-1\right)\to{\chi}_i>{\chi}_o,\end{equation}$$(3) where the subscripts a and d represent states of air and desiccant, respectively. The desiccant’s concentration defines the proportion and quantity of vapour expended to or engrossed from the air. 2.2. Permanence optimization Numerous parameters such as air and desiccant inlet temperature, air and desiccant flow rates, concentration, inlet air humidity and the geometrical structure of the packing material influence the dehumidification process. Therefore, to achieve the optimum operational point, there have to be well-balanced proportions of these parameters. The L/G ratio is one such parameter that potentially considers the air and desiccant flow rates. However, the air vapour pressure determines the humidity ratio while that of the desiccant solution depends on the temperature and concentration. An optimization strategy based on flow rate ratio and energy preservation was proposed and implemented comparatively on both the adiabatic and internally cooled dehumidifier in [1]. Li et al. [8] examined various air–desiccant flow rate ratios and determined the optimized theoretical dehumidification performance under flexible scenarios. The lower the desiccant flow rate, the patchy the fluid on the packing surface. On the other hand, too high fluid flow results in very little change in concentration that impacts on the regeneration effectiveness. Therefore, the mass flow rate ratio presents a very significant performance optimization quantity. The correlation depicting the interactions of unitless factors such as Nusselt, Reynolds and Sherwood numbers can be found in [9]. Additionally, using the effectiveness number of transfer units (NTU) model, the relationships for Nusselt and Sherwood numbers can be formulated as functions of mass transfer as well as Reynolds number as a significant determinant of heat transfer [10]. 2.3. Multi-stage LD dehumidifiers The dehumidification process can be staggered in multiple stages to limit the effects of increased desiccant temperature on mass transfer capabilities of the dehumidifier. According to Jiang et al. [11], dehumidification vessels can be connected in series where the air from one stage is passed through subsequent stages. This arrangement increases the effectiveness beyond that of a single stage. The concentration of desiccant varies from stage to stage, starting with the weakest. Since both the less concentrated solution and inlet humid air possess high vapour pressures, the interaction thereof results in decreased dry air with relatively lower vapour pressure. As the process continues to the next stage, more concentrated solution interacts with the air and further reduces the vapour pressure until the last step where the vapour difference is almost at equilibrium. The multiple stages eliminate the irredeemable losses associated with the single-stage processes. A simplified diagram is shown in Figure 1. The inter-stage desiccant solution flow rate is relatively low, but the aggregated cumulative flow becomes large depending on the number of stages prompting increased inlet-to-exit desiccant concentration variation. The variation provides a conducive platform for the implementation of the regeneration process. Figure 1 Open in new tabDownload slide Multi-stage LD dehumidifier recovery systems. Figure 1 Open in new tabDownload slide Multi-stage LD dehumidifier recovery systems. 3. REGENERATORS The regenerator is a very vital part of LDAC system in which the dilute solution is re-concentrated to near initial conditions with the aid of low-grade thermal energy from solar and industrial waste heat. The regenerators can be classified as packed or unpacked. The packed type is similar in construction to the dehumidifier except that the process is reversed. The desiccant liquid is heated externally and then pumped to the packed bed regeneration vessel. The temperature of the less concentrated solution is raised to desirable points where its moisture-holding capacity is weakened. Due to the sporadic and fickle nature of solar radiation and demand-constrained low-grade thermal energy, it is always necessary to include a supplementary heater. In the unpacked regenerator configuration, usually, the solution is heated in the heat exchanger or solar collector plate. 3.1. Performance evaluation The goal of the desiccant regeneration process is to improve its concentration undoubtedly. The degree to which the concentration improves is critical to the effectiveness of the vessel. The effectiveness is defined in terms of the ratio of the difference in air humidity ratios between inlet and exit as follows [7]: $$\begin{equation} {\varepsilon}_{reg}=\left(\frac{\omega_o-{\omega}_i}{\omega_e-{\omega}_i}\right). \end{equation}$$(4) On the other hand, the MRR expression is formulated in terms of the desiccant concentration as follows: $$\begin{equation} {\xi}_{reg}={\dot{m}}_a\left({\omega}_o-{\omega}_i\right)={\dot{m}}_d\left(\frac{\chi_o}{\chi_i}-1\right)\to{\chi}_o>{\chi}_i.\end{equation}$$(5) The outlet desiccant concentration would be higher than the inlet conditions if the regenerators work well. It should, however, be remembered that the desiccant temperature is the underlying cause of concentration change. 3.2. Types of solar collector regenerators The conversion of solar radiation into usable thermal energy for application in desiccant regeneration primarily occurs in a solar thermal collector. This energy becomes available as a substitute of complement to the conventional heat sources. The thermal collector idea where the solution was heated in an open collector was originally introduced by Kakabaev et al. [12]. The solar regenerators can be classified as direct, where the dilute desiccant from the dehumidifier gets heated in the collector or indirect and where an intermediary liquid absorbs heat in the collector and then heats the desiccant via a heat exchanger. The direct type offers a more effective mode of solar energy exploitation as the fluid absorbs the maximum radiation available to the collector leading to higher temperatures. A cautious approach should be to include a complementary heater on the regenerator to cater for any unforeseen variations in solar radiation. The solar regenerators can further be used in open, closed, natural or forced convection modes, as shown in Figure 2. Among these categories, the forced convection mode dominates in application due to its verified high effectiveness. Figure 2 Open in new tabDownload slide The various configurations of solar regenerators. Figure 2 Open in new tabDownload slide The various configurations of solar regenerators. The construction and features of these modes are detailed as follows. 3.2.1. Open-mode In the open mode of the solar regenerator, the dilute desiccant glides on the tilted collector surface exposed to the ambient atmosphere. Due to the higher vapour pressure of the desiccant liquid compared to the atmospheric air, the mass exchange process is triggered. Subsequently, the convective, conductive radiative and evaporative heat exchange occurs, causing the desiccant solution to free water vapour to the atmosphere. The working principle, as well as physical components, have improved over the years, after the rigorous experimental tests [12, 13]. The feasibility of open-cycle solar regeneration and cooling in high humidity environments was explored using computational simulation [14]. Various accurate procedures for determining heat and mass exchange have also been laid out ranging from analytical model [15] and numerical methods [16–18]. Despite the enormous positive gains reported in the literature, there are still challenges associated with energy loss to the atmosphere and high dependability on meteorological conditions, especially with the occurrence of gales and storms. 3.2.2. Closed-mode The closed-mode solar regenerator, as the name suggests, is fully covered so that the liquid being regenerated circulates without contact with the bare atmosphere. The top of the collector is glazed to trap the radiated heat from the sun, which is then absorbed by the desiccant stream flowing uniformly on the absorber surface. The evaporated water vapour condenses on the glazing and then directed towards the exit. The desiccant stream leaves the regenerator with a significant increase in concentration [19]. The temperature rise of the desiccant is indicative of the convective, conductive, radiative and evaporative/condensation thermal energy exchange. Due to lack of deficiency of ventilation, the closed-mode regenerators are often characterized by low effectiveness since the vapour pressure change is minimal. The condensed water on the glazing is likely to increase the desiccant vapour pressure and lower the regeneration capacity. 3.2.3. The natural and forced convection solar collector regenerator The convective solar regenerator more or less the same as the closed-mode with a slight difference at the ends where there is provision for ventilation. There is an open channel for air flow either naturally or under the influence of a fan (forced). For effective operation, the natural convection-mode solar regenerator must be able to provide the flexibility of varying the air channel height and inlet desiccant properties. However, because of the unpredictable and disorderly moving air direction, some stationary air may be trapped in the solution stream and affect the overall regenerative performance of the unit. In addition to the aforementioned natural convection-mode, the forced convection type offers access to the regulation of the inflowing air flow rate with ease. When the air flow is kept uniform and smooth, the pressure drop becomes regulated and ensures effectual regeneration output. In both cases, the solar radiation intensity has a significant influence on the mass exchange and outgoing solution temperature [20]. Another determining factor for heat and mass exchange performance is the regenerator length [21]. The theoretical comparison of the natural and forced convection modes in terms of their vaporization rates with and without glazing was presented in [22]. The forced flow convective mode may be configured to unidirectional or bi-directional where air and desiccant flow in same and opposing directions respectively. The former tends to provide the best mass transfer performance [23, 24]. Several factors contribute to the enhancement and optimization of the regenerator effectiveness. The spacing dimension of the glass cover, inlet solution and air temperatures are critical. The glass cover fixed at 70 mm optimized the mass exchange performance. On the other hand, the air–desiccant temperatures are inversely proportional to the desiccant flow rate [25, 26]. 3.2.4. The indirect solar regenerators The indirect solar regenerator scheme involves a secondary fluid heated by the solar panel, which then comes in to contact with the weak desiccant solution and exchanges heat in a heat exchanger. The weak solution is then transferred to the packed regenerator for ultimate regeneration. Even though the heating effectiveness is low due to losses in the heat exchanger, the overall generation effectiveness is better than the direct counterpart. A simplified graphic illustration of the indirect solar-powered regenerator is shown in Figure 3. Figure 3 Open in new tabDownload slide Solar-powered indirect LD regeneration. Figure 3 Open in new tabDownload slide Solar-powered indirect LD regeneration. 3.2.5. The multi-stage regenerator Taking into account the previously stated benefits of solar collector regenerators, the associated mass exchange optimization challenges still needs urgent attention. As the weak solution flow over the collector, its concentration increases and vapour pressure reduces, further shrinking the air–desiccant vapour pressure difference. Because of the small difference, the regeneration becomes problematic, hence the need for regeneration in multiple phases. The multi-stage regeneration utilizes the low thermal intensity to heat the dilute solution while the somewhat concentrated solution’s temperature is raised by a stronger heating element, thereby achieving a higher energy use ratio. An illustrative diagram of a multi-stage regeneration process is shown in Figure 4. The multi-stage regeneration process combines effortlessly with the solar collector system in an indirect configuration to make use of heated water or air to provide sufficient desiccant regeneration temperature. Figure 4 Open in new tabDownload slide Multi-stage LD regeneration. Figure 4 Open in new tabDownload slide Multi-stage LD regeneration. Figure 5 Open in new tabDownload slide The most common packed dehumidifier and regenerator configuration. Figure 5 Open in new tabDownload slide The most common packed dehumidifier and regenerator configuration. 4. HYBRID AIR CONDITIONING SYSTEMS The performance and energy savings of vapour compression system (VCS) and vapour absorption system (VAS) can immensely be improved by incorporating and LDAC for better air humidity management. A combined heat pump and LD dehumidifier attain enhanced energy-saving capability up to 35% [27, 28]. A combined LDAC-VAS system could improve the overall COP by 50%, while significant electric power savings was achieved by incorporating LDAC and VCS in a single system with reduced size and mass flow rates [29, 30]. For the optimal aggregate performance of the hybrid air conditioning system, the geometrical properties of the dehumidifier/regenerator were investigated in addition to the solar collector configuration and dimensions in [31]. Sick et al. [32] conducted performance analysis of both hybrid VAS and VCS systems based on meteorological seasons and obtained exciting outcomes. Among the two systems when compared, the hybrid VAS required a large quantity of desiccant solution; hence, the solar collector heating load is increased, while the hybrid VCS needs preheating of conditioned air that weighs down on the energy demand. The hybrid conventional and LDAC systems are capable of sufficiently supplying the cooling loads under the independent influence of solar energy or low-grade thermal source. In addition to the VCS and VAS, LD dehumidification and regeneration also combines well with heat pumps and co-generation systems in cooling and heating to form a hybrid system having more exceptional general performance than individual stand-alone systems. 5. FLOW CONFIGURATIONS ADIABATIC DEHUMIDIFIER AND REGENERATOR The packed LD dehumidifiers and regenerators are classified according to the air and desiccant flow directions relative to one another in the vessel. Three distinct categories exist, namely parallel-flow (co-flow), counter-flow and cross-flow as shown in Figure 5. The collection of literature on the development of adiabatic packed bed dehumidifier and regenerator vessels are analysed in terms of experimental, modelling as well as combined strategies. The methods, variables and selected results are systematically provided. 5.1. Co-flow Chen et al. [33] experimented to determine the heat and mass transfer coefficient for a vertical film dehumidifier using CaCl2 desiccant solution. The overall heat and mass transfer coefficient were established as a function of inlet and outlet status in terms of logarithmic temperature difference. However, in comparison to the existing data from the literature, an overestimation and underestimation of mass and heat transfer respectively were realized. Further sensitivity analysis revealed that the mass transfer rate increased with an increase in liquid solution flow rate. Liu et al. [34], with suitable and realistic assumptions, formulated a coupled heat and mass transfer phenomenon model and developed its solution analytically concerning humidity ratio and temperature of air and humidity ratio, temperature and effectiveness of the desiccant in co-flow, cross-flow and counter-flow configurations. As an extension of coupled heat and mass transfer theory, Liu et al. [35] configured LD packed bed dehumidifier/regenerator both in co-flow and counter-flow regimes to study the respective desiccant–air interactions. Further comparison between the two configurations, revealed that the co-flow exhibited lower and higher mass transfer during dehumidification and regeneration, respectively. Rahama et al. [36] developed a numerical model of LD dehumidification/regeneration process using CaCl2 based on the borderline and interfacial states of air and desiccant liquid. The control volume method and iterative algorithm techniques were used to formulate, the finite difference (FD) equations defining the preservation of energy, mass and momentum for both air and desiccant solution were created and solved numerically. Correlations for heat and mass transfer coefficients at dehumidifier and regenerator stages were generated using mean Sherwood and Nusselt numbers and compared with a deviation of 15% with those in the existing literature. However, it was noted that, due to underestimation of some parameters, the processes were time intensive, difficulty and carry-over were not guaranteed. A 2D dynamic model was developed by Diaz et al. [37] to examine the influence of changes in temperature and concentration of LD in a co-flow design dehumidifier. The boundary conditions were prepared for adiabatic and constant temperature scenarios taking into account the wall effects, which were then, implemented in the model. The resulting sets of equations were solved by the implicit FD technique and compared with the experimental results from the literature. The interfacial correlations for Nusselt and Sherwood numbers were also developed. Desiccant concentration, regeneration effectiveness and air-side pressure drops were the subjects of additional experimental study by Longo et al. [38] on 1” pall ring element structured and Mellapack 205Y randomly packed column desiccant regenerators using hygroscopic solution H2O/LiBr in a counter-flow configuration. The measured parameters, fluid properties, formulated correlations and known constants were implemented in a computer code solved by step-by-step iterative technique. In the recent study of Peng et al. [39], the dimensionless heat loss coefficient and total temperature differences were considered as variables in solving mass transfer equations in a solar regenerator for both counter-flow and co-flow configurations. The numerical solution of the model revealed both liner and parabolic relationships between a limited NTU and dimensionless air temperature. Backed by a parametric study on the inlet parameters, a conclusion that counter-flow regeneration configuration exhibited superior performance compared to the co-flow counterpart under similar operating conditions was drawn. Tanda et al. [40], in the study of the dehumidifier, used polyethylene glycol desiccant solution, to experimentally determine the correlation of mass transfer, taking into account the desiccant properties and nozzle dimensions. A couple of correlations was developed for the gas phase mass transfer in which one incorporated physical properties of desiccant nozzle diameter and the other, surface tension. The comparison of predicted and experimental results from literature yielded 18% and 10% variations for the former and latter, respectively. However, much as their conclusion recommended application of these correlations for a wide range of operational parameters, a limitation caveat to units with specific nozzle diameters arose. 5.2. Counter-flow The inception of counter-flow LD dehumidification technology was first conceived in [41] where independent models for heat and mass transfer coefficients under adiabatic conditions were formulated for liquid and gaseous states. In the advancement of this idea, the performance of a packed column cross-flow tower was predicted using an analytical model in [2]. The derived expressions were solved using a combination of iterative and successive substitution procedures, allowing for an initial guess of liquid outlet temperature and obtain the remaining lengthwise nodal temperatures of the column. Better regeneration at higher liquid flow rate but poor at low liquid temperature was achieved. In an attempt to validate their analytical model, Factor et al. [2] experimented with evaluating and comparing the effectiveness of lithium bromide (LiBr) and monoethylene-glycol (MEG) LDs in air dehumidification. Interestingly, MEG tests failed to produce satisfactory results for heat and mass transfer coefficient correlations due to its lower vapour pressure while LiBr provided a promising trend that fits well on the analytical data. Further, optimum mass transfer and drop were proposed to lie between 0.5 and 0.8, respectively. In terms of LD temperatures, 68°C or higher was suggested for the regeneration process while for effective dehumidification, a range 25°C–30°C was considered adequate. Lof et al. [42] expressed and evaluated the rates of heat and mass transfer in terms of ordinary differential equations (ODEs) with various assumptions. An experimental study was also conducted employing LiCl LD to validate the model with regards to the respective heat and mass transfer coefficients at different air flow rates, humidities and temperatures. The results showed an agreement within 10% with those of the theoretical model. Gandhidasan et al. [43] investigated the performance of a counter-flow packed column dehumidifier with ceramic Rasching rings and carbon Berl saddles using CaCl2 LD. Guided by the Treybal model [41], they formulated the interfacial heat and mass transfer coefficients both for the liquid and gas phases. Subsequently, heat and mass transfer coefficients showed higher sensitivity to inlet flow rate and concentration of desiccant solution but an insignificant response to variations in air inlet temperature and flow rate as well as desiccant solution’s inlet temperature. Hence, a highly concentrated solution at low temperature combined with a low flow rate of air was recommended for a highly effective dehumidification process. In a related study, Gandhidasan et al. [44] analysed the regeneration process of CaCl2 LD by an analytical model whose solution predicted mass water evaporation rate. An essential correlation for vapour pressure was developed in addition to ratios of dimensionless vapour pressure and temperature variance. Besides their previous study recommendations, the concept of solution pre-heating was introduced as an enhancing technique for an effective regeneration process regardless of the solution’s flow rate. Ullah et al. [45] evaluated on the effect of air and LD inlet parameters on the dehumidifier performance, applied moisture removal effectiveness to quantify and set the lowest theoretical limit of air outlet humidity ratio with fluid inlet conditions. Similar recommendations were made in concurrence with the earlier findings of Gandhidasan et al. [43] that, for effective dehumidification process, desiccant liquid at high concentration and low temperature together with little air flow rate was recommended. A simplified dehumidifier/regenerator effectiveness model for predicting heat and mass transfer processes for LiBr was developed by Stevens et al. [10] based on the cooling tower model they initially formulated. Weighing their findings against the FD model of [2], an excellent fit was realized, but against experimental data, only enthalpies and temperatures of air and solution matched precisely while remarkable differences were shown especially in humidity ratio and outlet air temperature due to the overestimation of the Lewis number that was assumed to be unit. In comparison to other experimental data from the literature, the effectiveness model varied by between 1% to 23% concerning energy balances. Inter-facial heat and mass transfer in the dehumidification process was studied by Ertas et al. [46] for both CaCl2 and LiCl LDs. The possibility of blending the two solutions at a ratio of 50% LiCl to 50% CaCl2 and studying its performance as a cost-effective liquid desiccant (CELD) was explored. The LiCl exhibited better performance in terms of liquid phase mass transfer coefficient at higher flow rates. CELD showed more promising and realistic prosperities but had negligible alteration of liquid phase heat transfer in comparison to both CaCl2 and LiCl but better mass transfer than CaCl2. Elseyad et al. [47] developed another FD model for predicting progressive lengthwise heat and mass transfer effectiveness of LD dehumidifier/regenerator using CaCl2 solution. The focus was on inlet parameters such as air and solution temperatures, flow rates and concentration to generate the primary expressions that were solved numerically by applying the Runge–Kutta integration scheme combined with Nachtsheim–Swigert iteration technique. The solution demonstrated that the heat and mass transfer effectiveness was improved as the liquid mass flow rate increased at reduced air mass flow rate. An adiabatic dehumidifier with air–desiccant in counter-flow configuration and random packing was studied by Chung et al. [48] applying aqueous LiCl desiccant solution. These parameters affected the overall mass transfer coefficient with a similar trend though less sensitivity was shown towards the desiccant flow rate. In a related study, Chung et al. [49] presented different correlations for various packing materials and mixtures of a couple of desiccants for predicting moisture removal efficiencies. The 40% LiCl and 95% triethylene glycol (TEG) solutions were used for the dehumidification process. Using vapour pressure of pure water as the dehumidification driving force, the Ullah [45] model was modified by neglecting liquid concentration that resulted in a more precise prediction of desiccant solution and column efficiency relationship. This study provided a breakthrough since only a mean discrepancy of 7% was obtained when experimentally validated using different packing materials, liquid properties and column lengths. In addition to their earlier work, Chung et al. [50] performed experiments under adiabatic and thin-film air–liquid interface conditions to determine the dimensionless heat and mass transfer correlations using Buckingham pi theorem. Both structured and random packings were evaluated with LiCl desiccant solution in which total liquid phase and gas phase, heat and mass transfer coefficients were obtained respectively. Impressive overall dimensionless coefficients were obtained and compared to existing experimental data from literature at less than 10% discrepancy. An elaborate experimental work was conducted by on an air–desiccant counter-flow system of both random and structured packing bed column of varying depths [51]. The mass transfer correlations for LiBr desiccant solution were developed. A higher mass transfer coefficient was realized for random packing as opposed to structured counterpart with a lower degeneration rate recorded in the dehumidifier. However, owing to the broader mass transfer area of structured packing, they extrapolated a higher deterministic mass transfer rate of in random packing by a factor of 0.05 above structured packing. Guided by the previous works of [2, 41], Oberg et al. [52] developed an FD model for heat and mass transfer prediction in an air 95% TEG, counter-flow adiabatic dehumidifier. The performance evaluation was based on dehumidification effectiveness and rate, subsequently, empirical correlations were derived from existing literature and implemented in a computer simulation code that revealed a convergence level of 0.05°C and 0.0001 kg TEG/kg solution for inlet desiccant temperature and concentration, respectively. A discrepancy of over 15% was recorded, which amounted to an over prediction of the dehumidifier performance. Lazzarini [53] offered a theoretical assessment of the dehumidification process using CaCl2 and LiBr LDs in a packed column counter-flow configuration that was later validated by experimentation. Basing their formulations on the models by [2, 41, 43, 52], a computer procedure was coded and used to evaluate the performance of the adiabatic counter-flow dehumidifier. An over prediction of reduction in the humidity of above 20% was achieved weighed against experimental data. However, the adiabatic conditions, as assumed, was confirmed to be true since the tower heightwise changes in air-side and solution-side enthalpies were 20%. As expected, better dehumidification was achieved at low temperatures and high concentrations of the solution, specifically for LiBr, a concentration of about 45% and between 20°C and 30°C was recommended. Radhwan et al. [54] presented a solar-powered LD system by mathematical modelling in which fourth-order Runge–Kutta integration scheme and Nachtsheim–Swigert iteration techniques were applied to the concentrated CaCl2 solution to generate unidimensional expressions for the dehumidifier. The crucial system evaluation parameters such as solar utilization factor, system thermal ratio and desiccant replacement factor for both dehumidification and regeneration processes were assessed. A solution air flow rate ratio of 1:2.5 was recommended making the system to be most suitable for highly humid climatic conditions. Martin et al. [55] explored the energy consumed in the adiabatic regeneration process of air using 95% TEG configured in a counter-flow scheme under high flow rate conditions by the experimental procedure. Using similar assumptions as [52], they generated an FD model whose findings agreed well with the investigational figures within 15% discrepancy. Consequently, air flow rate, humidity ratio, desiccant concentration and the temperature had a significant effect on the regenerator performance in addition to the packing elevation. Later on, in related developments, Fumo et al. [56] applied the same principles to evaluate the effectiveness of LiCl dehumidification and regeneration processes with slight modifications in the model to include wetted surface area due to superior surface tension properties over TEG. The uneven spreading of desiccant at the above tower was also taken into consideration in which similar trends of results were recorded. Gandhidasan et al. [7] used the experimental results of [56] to corroborate a modest model of dimensionless temperature and vapour-pressure difference ratios. Apart from showing a decrease in condensation rate as inlet water temperature increases, the results of the model and experiments compared within 10.5% discrepancy. Longo et al. [57] presented an experimental and theoretical study on chemical dehumidification and regeneration of air in a counter-flow random packed column using H2O/KCOOH solution in comparison to conventional hygroscopic solutions H2O/LiCl and H2O/LiBr for typical air conditioning ranges. Basing their theoretical analysis on [41], a consistent reduction in humidity reduction was observed in both cases using the respective hygroscopic salt solutions. CaCl2 was used under low flow conditions to study adiabatic dehumidification and regeneration processes by [58] theoretically. A single dimension numerical model was formulated by establishing boundary expressions for quasi-equilibrium condition using similar assumptions as [2, 43]. Additionally, a numerical solution for the 1D model for heat and mass transfer for real conditions was provided and presented on a standard psychrometric chart. A combination of higher desiccant flow rate at low temperature produced better dehumidification while the high desiccant temperature at high flow rate resulted in active regeneration. As a continuation, Ren et al. [59] went further to formulate a pair of coupled differential equations under similar conditions and provided their analytical solutions. The analytical model proved inaccurate and inconsistent, particularly when a big solution temperature difference is involved in the process due to the assumption of constant change in flow rate and concentration of the solution. In an attempt to establish realistic design parameters for a structured packing LD system using TEG, Elsarrag et al. [60] performed experimental procedures whose results were used to validate an FD model they had earlier created. No significant influence on performance was noted for liquid–air flow rate ratio above 2, while regeneration process showed more sensitivity to desiccant temperature and concentration. Still using the same TEG solution, Elsarrag et al. [61] scrutinized the solution seepage and carry-over into the process air concerning pressure drop. The heat and mass transfer empirical correlations and experimental exponentiations from the study, as mentioned above, were adopted to corroborate the FD model, which showed decent agreement. Similar results were obtained in terms of the dependence of heat transfer effectiveness on high air flow rates and packing elevation. Chen et al. [62] analytically solved the heat and mass transfer model for an adiabatic dehumidifier/regenerator both in parallel and counter-flow configurations. The air–desiccant flow rate ratio went up as the solution temperature increased while keeping concentration low, thus allowing for the natural deduction of optimum values and validation of selected parameters against experimental data from literature presented a deviation of ±10%. The influence of inlet and operational factors was the main objective of the empirical study by [63] about the regeneration and dehumidification using LiCl LD. An extreme value of 7.5 g/m2s, in 20% concentration at a temperature of 77.5°C was obtained. An optimum specific humidity ratio at the inlet was established for maximum tower efficiency that provided maximum dehumidification rate. Jian et al. [64] generated different heat and mass transfer correlations for TEG, LiCl and CaCl2 desiccant solutions and performed parametric analysis on dehumidification effectiveness. They found out that increasing desiccant–air flow ratio with all the desiccants resulted in better dehumidification effectiveness. However, solution concentration and inlet temperature coupled with inlet air temperature and packing height had adverse effects on the dehumidification effectiveness in varying proportions for each desiccant solution used. Liu et al. [65] did extensive work in comparing two different direct contact scenarios, namely air–water and air–desiccant schemes using handling zone dividing method. Due to higher surface tension harboured by LD compared to water, the latter was found to have more spread on the packing compared to water as represented on a psychrometric chart. The counter-flow configuration showed a better mass transfer performance during dehumidification while the co-flow pattern was proper for regeneration. Tu et al. [66] implemented the FD model by [59] on modular computer simulator to study an innovative and less energy demanding LD system utilizing LiCl solution. A high inlet temperature of desiccant range of 80°C–85°C was recommended for the regenerator to gag crystallization. Tretiak et al. [67] constructed and investigated a counter-flow sorption and desorption system utilizing clay and CaCl2 LD. Different models from the literature were compared to the formulated desiccant pressure drop correlation with satisfactory convergence. Keeping equilibrium humidity ratio unaltered, Babakhani [68] made a remarkable contribution by providing a novel analytical solution for heat and mass transfer process. Differential equations for typical constraints were formulated whose results compared correctly with the comprehensive and consistent experimental data from literature on desiccant humidity ratio, temperature and concentration peaking at 5% deviation while the air temperature was at 7%, respectively. Peng et al. [69] developed an analytical model recommended for the design of LD systems capable of evaluating heat and mass transfer occurrence under transient and low flow conditions. The average volumetric approach was used to obtain a non-equilibrium heat and mass transfer coefficients. However, the model showed a weak sensitivity to high flow conditions and could not be used to predict the dehumidifier/regenerator performance under varying or fluctuating loads. In addition to their previous study, Babakhani et al. [70] used similar assumptions and evaluation parameters to develop an analytical mathematical model and presented its solution with regards to the desiccant regeneration process in both random and structured packing. Gandhidasan et al. [71] used an artificial neural network (ANN) analysis technique to study the performance of LiCl dehumidifier with random packing. The dimensionless temperature ratio contributed to better dehumidification rate. The ANN predicted the condensation rate and desiccant concentration with high accuracy against experimental data. Spray towers are known to cost less but have very large carry-over, low dehumidification effectiveness and small air-side pressure drop. In respect of these weaknesses, Kumar [72] performed experimental studies on air dehumidification using CaCl2 in a modified spray tower to achieve a near-zero carry-over. The reduction in droplet velocity and increasing wetting surface significantly contributed to the improved performance and reduced carry-over of desiccant droplets to near zero. 5.3. Cross-flow Al-Farayedhi et al. [73] tested three different desiccant solutions: CaCl2, LiCl and CELD in a cross-flow structured packing column. The heat and mass transfer coefficient correlations for air–liquid phases were also developed and compared the outcomes for each fluid. A tight fit was obtained between theoretical and experimental literature volumetric heat and mass transfer coefficients, suggesting that the correlations reliably predicted the performance of the packed column with extraordinary accuracy. With regards to mass transfer performance, LiCl was preferred while higher heat transfer was exhibited by CaCl2. A numerical model to evaluate the heat and mass transfer phenomenon in a cross-flow dehumidifier packed with honey-comb paper material was developed by [74]. A more significant Nusselt number was observed at the inlet conditions of the liquid, which gave a strong indication of better heat and mass transfer performance process. The results of the dimensionless parameters were further compared to experimental data from literature and obtained good agreement. Liu et al. [75] developed an empirical correlation for predicting the heat and mass transfer process in a cross-flow LiBr LD dehumidifier, which was validated with experimental data with high accuracy and outlining the benefits thereof. In a similar assessment, using LiBr aqueous desiccant solution Liu et al. [76] constructed a testbed for performance analysis of a cross-flow, celdek structured packing regenerator. Correlation for regenerator effectiveness and moisture removal rate predicted performance of 95% of total runs to within ±10% discrepancy and an average of 3.9% with the experimental data. Using the same setup, Liu et al. [77] further formulated a theoretical model for heat and mass transfer characteristics of a cross-flow dehumidifier and regenerator based on the NTU, moisture and enthalpy effectiveness. In comparison to the experimental data, impressive theoretical projection outcomes of enthalpy and moisture effectiveness were observed at deviations of 7.9% and 8.8%, respectively, for dehumidification process while 5.8% and 6.9% were obtained for the regeneration process. Liu et al. [78] using their previous model, formulated an analytical solution for heat and mass transfer occurrence in a cross-flow dehumidifier guided by the analogy of heat exchangers. A comparison of the results of analytical solution with experimental outcomes coupled with numerical solutions from literature employing similar LiBr desiccant solution was done, giving a significant deviation of ±20% for enthalpy and moisture effectiveness, due to their earlier finding of varying Lewis number which in the contrary was taken to be constant in this case. The combined NTU and Lewis number methods were used by [79] to predict the heat and mass transfer in the dehumidification process using LiCl LD. The concept of separative evaluation was used to evaluate combined heat and mass transfer coefficients that were then validated with experimental data in terms of humidity and air–desiccant temperatures showing deviations of 10%, 6% and 12%, respectively. Moon et al. [80] through experimental study, provided mass transfer data of a CaCl2 cross-flow dehumidifier with structured packing. An attempt to compare the results with those of counter-flow in [49] and cross-flow in [75] failed to show good agreement. Given this development, a novel empirical correlation was formulated with regards to dehumidifier effectiveness whose outcomes fitted well within the range of 0.4–0.8 at ±10% discrepancy with the experimental values. Zhang et al. [81] performed experiments on a cross-flow structured packing dehumidifier and regenerator using LiCl aqueous desiccant solution under different operating conditions in summer and winter. However, lower overall mass transfer coefficients were observed at higher liquid temperatures. Correlations for dimensionless mass transfer coefficient for the regenerator and dehumidifier were further developed, which compared within ±20% against predicted values. In another evaluation of the structured packing, using CaCl2, Bansal et al. [82] considered both adiabatic conditions and when subjected to internal cooling and compared the performance indices for the two scenarios. The optimum air–liquid flow rate ratio that gave peak dehumidifier effectiveness was established. The internally cooled set up was shown to provide superior performance in terms of efficacy and moisture removal rate compared to the adiabatic system. In addition to their earlier study, Liu et al. [83] compared the performance LiBr and LiCl desiccant solutions in air dehumidification and individual regenerative evaluation through experimental procedures. Correlations were derived for volumetric mass transfer coefficient and moisture removal rate under identical temperature and vapour pressure ranges. The LiCl was found to perform better than LiBr subjected to same mass flow rates in the dehumidification process while LiBr outperforms LiCl in the regeneration process, especially under same volumetric flow rates. Pineda et al. [84] considered the possibility of incorporating a heat exchanger within a dehumidifier to enhance performance in freezing environments. Using CaCl2 desiccant solution, subjected to almost freezing state, they derived 3D numerical model for a cross-flow dehumidifier. The expression for heat exchanger effectiveness was derived upon which sensitivity analysis on humidity ratio, the outlet temperature of air and desiccant concentration were based. Structured packing dehumidifier/regenerator employing CaCl2 desiccant solution in a cross-flow orientation was also experimentally investigated in [85]. Higher inlet solution temperatures enhanced moisture removal rate and mass transfer coefficient but grossly inhibited the regenerator efficiency. On dehumidification vessel, this high desiccant temperature significantly lowered the mass transfer coefficient as well as moisture removal rate but improved productivity. On the life cycle cost evaluation, it was established that the system had a probable payback period of 11 months and contributed to 31% annual cost savings. In the work of Gao et al. [86], lithium chloride (LiCl) desiccant solution was used to experimentally study the performance of a cross-flow, celdek structured packing air dehumidifier based on stepwise regression analysis technique. Enthalpy and moisture efficiencies were their main parameters characterization on which the influence of desiccant/air inlet parameters and structure/size of packing were assessed, leading to fascinating outcomes. In comparison to the predicted values of moisture and enthalpy efficiencies, 91.2% of the total experimental runs showed a discrepancy of within ±10% with an average of 4.2%. In a more recent development, Bakhtiar et al. [87] introduced the COP as the cooling capacity per energy input for computation of the real system’s performance efficiency. The experimental set up for analysing the total energy consumption in a room versus energy change indicated that dehumidification effectiveness and COP were better at low airspeeds. Yonggao et al. [63] in their experimental study on dehumidification and regeneration of LD in a cooling air conditioning system outlined the effects of temperatures (of heating source, desiccant and air), humidity and desiccant concentration on the dehumidification and regeneration rates. They generated mass transfer coefficients based on experimental results obtained and formulated empirical correlations between regeneration mass transfer coefficients, heating temperature and desiccant. From the above literature, it is evident that counter-flow configuration has received more attention than the others because of its high effectiveness and moisture absorption and desorption rates. 6. THEORETICAL MODELS FOR ADIABATIC DEHUMIDIFIER AND REGENERATOR The performance of adiabatic dehumidifier and regenerator is influenced by the rate of coupled heat and mass exchange. Thus, the effectiveness of the dehumidifier/regenerator is a function of the quantity of water vapour absorbed or expelled at the air–desiccant interface. Significant progress in the theoretical analysis has been detailed leading to predictive modelling of adiabatic dehumidifier/regenerators. From the information gathered in existing literature, the available modelling strategies are reliably summed up as the FD, effectiveness-NTU (e-NTU) and simplified algebraic correlation models [88]. The first two models are a bit complex, involving the solution of collective steady-state and momentum expressions to determine the velocity spectrum within the packed column followed by temperature and concentration dispersal by heat and mass equilibrium equalities. Such burdensome solution procedures are time consuming and take up large computer memory; hence, their popularity is waning compared to the simplified correlation-based counterparts. The simplified models have everyday use in prediction of long-term aggregate characteristic outputs of dehumidifier/regenerator systems [21]. 6.1. FD model The FD model is more popular due to its precision and unambiguous computational connotation. The formulation of the FD model is based on the segregation of the dehumidifier/regenerator into regions and considering an elemental air–desiccant interfacial area, as shown in Figure 6a. Treybal [41] founded the FD technique of predictive analysis of adiabatic dehumidification process and later modified by [2] to characterize the counter-flow adiabatic dehumidifier. Figure 6 Open in new tabDownload slide The air–desiccant interfacial differential elements [88]. Figure 6 Open in new tabDownload slide The air–desiccant interfacial differential elements [88]. For simplicity, some assumptions were made, which informed the formulation of fundamental control equations. Taking the mass balance in the elemental volume: $$\begin{equation} d{m}_d={m}_a d\omega, \end{equation}$$(6) where subscripts d, a and w represent desiccant, air and water vapour states, respectively, m is the specific mass flowrate in kg/m2s and ω is the air humidity ratio. The change in air humidity is obtained in terms of the interfacial heat and mass exchange rates and the respective partial pressure P as follows: $$\begin{equation} \frac{d\omega}{d z}=-\frac{\beta^{\prime }{M}_wA}{m_a}\mathit{\ln}\ \left\{\frac{1-{P}_d/{P}_i}{1-{P}_a/{P}_i}\right\}, \end{equation}$$(7) where M is the molar mass in g/mole, A is the specific surface area per unit volume in m2/m3 and b is the mass transfer coefficient in kg/m2s. The change in temperature T is obtained in terms of interfacial air–desiccant useful heat transmission and the air-side energy balance expressed as: $$\begin{equation}\hskip-75pt \frac{d{T}_a}{dz}=-\frac{\gamma_a^{\prime }A\left({T}_a-{T}_s\right)}{G_a{Cp}_a} \end{equation}$$(8) $$\begin{equation} {\gamma}_a^{\prime }A=-\frac{m_a{Cp}_w\left(\frac{d\omega}{d z}\right)}{1-\exp \left[{m}_a{Cp}_w\left( d\omega / dz\right)/{\gamma}_aA\right]}, \end{equation}$$(9) where |${\gamma}_aA$|and |${\gamma}_a^{\prime }A$| represent the actual (sensible) and corrected air-side heat transmission coefficient. The correction considers the influence of mass exchange on temperature achieved by Ackermann method. Therefore, the solution bounds can be defined as z = 0; Td = Td, i; md = md,i; χ = χi; z = H; Ta = Ta;i; ma = ma;i; ω = ωi. The derived complex differential expressions can only be solved by numerical integration using a combination of iterative and successive substitution procedures, allowing for an initial guess of liquid outlet temperature and obtain the remaining column heightwise nodal temperatures. Gandhidasan et al. [89] used the FD model to establish how specific properties such as pressure drop, heat and mass transfer coefficients vary along the packed tower. Similarly, the experimental data of [52, 56] were verified using FD model and later on some modifications were made to the packing exterior to take care of the insufficient wetting of packed bed by incorporating a correction factor. However, Khan et al. [90] assumed that the combined heat and mass exchange was steered by air phase, and hence the interfacial temperature was equivalent to that of the solution. The rate of heat transmitted across the interface was also equivalent to the inlet air, thus: $$\begin{equation} {m}_a{Cp}_ad{T}_a={\gamma}_aA\left({T}_d-{T}_a\right) dz. \end{equation}$$(10) Likewise, the interfacial mass exchange was equivalent to the humidity change: $$\begin{equation} {m}_a d\omega ={\beta}_aA\left({\omega}_e-\omega \right) dz. \end{equation}$$(11) The change in specific air enthalpy becomes: $$\begin{equation} {dh}_a={Cp}_ad{T}_a+ d\omega \left[{Cp}_w\left({T}_a-{T}_r\right)+\lambda \right]. \end{equation}$$(12) Combining the Equations 10, 11 and 12, a simplified expression of change in air enthalpy h is obtained: $$\begin{equation} \frac{dh_a}{dz}=\frac{NTU. Le}{H}\left\{\left({h}_e-{h}_a\right)+\lambda \left(\frac{1}{Le}-1\right)\left({\omega}_e-\omega \right)\right\}, \end{equation}$$(13) where Le and NTU are the Lewis number and number of thermal units, respectively, defined as: $$\begin{equation}\hskip10pt Le=\frac{\gamma }{\beta{Cp}_a} \end{equation}$$(14) $$\begin{equation} NTU=\frac{\beta AV}{m_a}. \end{equation}$$(15) These relationships in Equations 13, 14 and 15 showed that heat and mass exchange were combined and should be considered together. The FD model has also found extensive use in cross-flow configurations of dehumidifier and regenerator in [91, 92]. Of interest is the FD model developed in [76] for heat and mass exchange based on Figure 6b from which the main energy balance, humidity and concentrations equations are expressed as follows: $$\begin{equation} \frac{m{\prime}_a}{H}.\frac{d{h}_a}{dz}+\frac{1}{L}.\frac{\partial \left(m{\prime}_d{h}_d\right)}{\partial x}=0 \end{equation}$$(16) $$\begin{equation}\hskip13pt \frac{m{\prime}_a}{H}.\frac{d\omega}{d z}+\frac{1}{L}.\frac{\partial \left(m{\prime}_d\right)}{\partial x}=0 \end{equation}$$(17) $$\begin{equation}\hskip73pt d\left({m}_d^{\prime}\chi \right)=0, \end{equation}$$(18) where |${m}^{\prime }$| is the mass flow rate in kg/s. The air–desiccant interfacial thermal and mass exchange was the same as Equation 13 and the change in humidity in the z-plane was: $$\begin{equation} \frac{d\omega}{d z}=\frac{NTU}{L}\ \left({\omega}_e-\omega \right). \end{equation}$$(19) The values of NTU varied according to the corresponding experimental data. Based on the same principle, a 2D heat and mass exchange numerical FD model that was precisely validated with experimental data was proposed [93, 94]. Due to the complex nature of heat and mass transmission process in the packed bed dehumidifier/regenerator, the solution of FD models often rely heavily on experimental correlations. For instance, the fractional vapour pressure, interfacial mass exchange constants and area are such parameters. However, since the assumption of equivalent heat-mass exchange and packing specific areas ignores the desiccant solution surface tension, an insufficient surface wetting is often experienced. Therefore, to avoid minimizing the heat-mass exchange area, a correlation ratio that incorporated the surface tension of the fluid was formulated as follows [56]: $$\begin{align} \frac{a_w}{a_t}=&\ 1-\mathit{\exp}\left\{-1.45{\left(\frac{\sigma_c}{\sigma_d}\right)}^{0.75}{\left(\frac{L}{a_i{\mu}_d}\right)}^{0.1}\right.\nonumber\\ &\qquad\qquad\times\left.{\left(\frac{L^2{a}_t\ }{{\rho_d}^2g}\right)}^{-0.05}{\left(\frac{L^2\ }{\rho_d{\sigma}_d{a}_t}\right)}^{0.2}\right\}, \end{align}$$(20) where aw and at are the wetted and actual total packing surface areas, respectively, σ is the fluid surface tension and L is the length of the packing. Additionally, Longo et al. [57] developed an extended FD model that also estimated the pressure drop along the column height. In summary, the majority of the models in the literature only show the reliance of dehumidification/regeneration process on operating conditions but largely ambiguous when it comes to the solution of film flow mass exchange. The FD model is best suited for investigative assessment of performance parameters of LD dehumidifier/regenerator with in-depth and precise outcomes. 6.2. Effectiveness ε-NTU model The ε-NTU model assumes that the temperature and equilibrium enthalpy is directly proportional and that for effective heat-mass exchange, solution balance is devoid of vapour infiltration. Coupled with the presumptions of FD, a simple computational ε-NTU was developed by Stevens et al. [10] for LD heat-mass exchange. Similar basic governing equations as FD are used: $$\begin{equation} {m}_a{dh}_a={m}_d{dh}_d+{h}_a{dh}_{ad}. \end{equation}$$(21) The differential mass balance is: $$\begin{equation} {d m}_d={m}_a{d\omega}_a. \end{equation}$$(22) The air-side enthalpy-mass balance is obtained as: $$\begin{equation} {m}_a{d h}_a={Cp}_a{m}_a{d\omega}_e+{A}_w dV\Big\{\gamma \left({T}_d-{T}_a\right)+\beta\ \left({\omega}_e-{\omega}_a\right). \end{equation}$$(23) The Le and NTU are computed by Equations 15 and 14. However, assuming negligible change in solution flow rate, the Le becomes unity and therefore the fundamental equations modifies to: $$\begin{equation}\hskip2pt \frac{d\omega}{d V}=\frac{NTU}{V}\ \left({\omega}_e-{\omega}_a\right) \end{equation}$$(24) $$\begin{equation} \frac{d{T}_d}{dV}=\frac{NTU\left({h}_e-{h}_a\right)\ }{V{Cp}_d{m}_d}. \end{equation}$$(25) The dehumidifier/regenerator effectiveness in a counter-flow configuration is then computed in combination with the NTU and the conventional heat-exchanger capacitance ratio m* as follows: $$\begin{equation} \varepsilon =\frac{1-{e}^{- NTU\left(1-{m}^{\ast}\right)}}{1-{m}^{\ast }{e}^{- NTU\left(1-{m}^{\ast}\right)}} \end{equation}$$(26) The capacitance ratio is simplified as follows: $$\begin{equation} {m}^{\ast }=\frac{m{\prime}_a{Cp}_{sat}}{m{\prime}_{d,i}{Cp}_d}, \end{equation}$$(27) where Cpsat is the equilibrium specific heat capacity = (dhe = dTd). The exit air and saturation enthalpies are obtained by: $$\begin{equation}\hskip-14pt {h}_{a,o}={h}_{a,i}+\varepsilon \left({h}_e-{h}_{a,i}\right) \end{equation}$$(28) $$\begin{equation} {h}_e={h}_{a,i}+\frac{\left({h}_{a,o}-{h}_{a,i}\ \right)}{1-{e}^{- NTU}}. \end{equation}$$(29) And the air outlet humidity ratio is computed by: $$\begin{equation} {\omega}_o={\omega}_e+\left({\omega}_i-{\omega}_e\right){e}^{- NTU}. \end{equation}$$(30) However, in circumstances where the fluid flow rate is lower than the air flow rate, the Stevens’ NTU model becomes inappropriate, hence, the ma in Equation 15 is replaced with the least flow rate. Alternatively, a disconcertion method in [95] can be used to correct the ε-NTU model accordingly to account for non-linear relationships between ωa and he,d, Cpd and vaporization heat. Tao et al. [96] proposed a 2D numerical ε-NTU model to predict the performance of the system resulting in a realization of low regeneration temperature of 55°C, which is easily obtainable from solar energy or waste exhaust heat. The ensuing formulations are illustrated in Equations 31 to 34 whose results were well in agreement with the experimental data. $$\begin{equation}\hskip-146pt \frac{d{t}_w}{dz}=\frac{NTU_h}{L}\ \left({t}_w-{t}_s\right) \end{equation}$$(31) $$\begin{equation} \frac{dh_a}{dz}=\frac{NTU_h. Le}{H}\left\{\left({h}_e-{h}_a\right)+r\left(\frac{1}{Le}-1\right)\left({\omega}_e-{\omega}_a\right)\right\} \end{equation}$$(32) $$\begin{equation}\hskip-140pt \frac{{d\omega}_a}{d z}=\frac{NTU_m}{L}\left({\omega}_e-{\omega}_a\right) \end{equation}$$(33) $$\begin{equation}\hskip-62pt {NTU}_h=\frac{\beta A}{Cp_w{m}_w};{NTU}_m=\frac{\alpha_mA}{m_a}; Le=\frac{\gamma }{\beta{Cp}_m}. \end{equation}$$(34) In the latest experiments, the Le has been proved to be ~1.2 for practicality, instead of unity as previously assumed. Subsequently, the non-unity Le can be infused in the modified NTU* distinctly accounted for in by the NTU-Le product. By revisiting the model in [90], a simplified analytical solution was provided under adiabatic conditions for a packed bed dehumidification and regeneration chamber by [62]. However, the assumption of constant solution concentration throughout the vessel negated the applicability of the model in low flow states. Lui et al. [77] used the ε-NTU model to evaluate the operational effectiveness of a cross-flow dehumidifier by considering the air humidity ratio and temperature variations coaxial to the desiccant flow and desiccant temperature variations being in line with the airflow direction. 6.3. The simplified empirical correlation models Based on the information gathered from literature, the FD and ε-NTU are both numerically complex and requires iterative computations making them unsuitable for hourly performance assessment. This drawback has resulted in the formulation of more hourly friendly correlations based on empirical and fitted-parametrized numerical data. Khan et al. [90] analysed thousands of data categories using FD model and formulated a simple empirical model connecting the outlet humidity ratio to air and desiccant temperatures deduced as follows: $$\begin{equation}\hskip-15pt {\omega}_o={\omega}_i+{n}_1{\omega}_i+{n}_2{T}_{d,i}+{n}_3{T^2}_{d,i} \end{equation}$$(35) $$\begin{equation} {\omega}_o={m}_o+{m}_1{\omega}_i+{m}_2{T}_{a,o}+{m}_3{T^2}_{a,o}, \end{equation}$$(36) where n and m are constants established by least square technique. These equations were particularly derived and fitted for explicit concentration conditions and flow rate ratios that may not be universally applicable. Therefore, more reliable empirical correlations for adiabatic dehumidifier/regenerator configured in counter-flow and cross-flow were formulated for enthalpy-moisture effectiveness and moisture removal rate in [7, 44, 75], respectively. Thus, temperature gradient and water vapour were formulated as dimensionless ratio as follows: $$\begin{equation} {Cp}_a\overline{T}\left({T}_{a,i}-{T}_{d,i}\right)+\frac{M_w}{M_a}.\frac{\lambda }{P_i}P\left({P}_{a,i}-\!{P}_{d,i}\right)\!=\!\frac{m_s}{m_a}{Cp}_d\left({T}_{a,i}-{T}_{d,i}\right), \end{equation}$$(37) where the partial vapour pressure is related to the moisture removal rate e as: $$\begin{equation} {P}_{d,i}={P}_{a,i}-\frac{\varepsilon{P}_i{M}_a}{m_a-{M}_v} \end{equation}$$(38) And the exiting solution temperature being: $$\begin{equation} {T}_{d,o}=\frac{T_{d,i}-{\varepsilon T}_{c,i}}{\left(1-\varepsilon \right)}. \end{equation}$$(39) Therefore, the moisture removal rate becomes $$\begin{equation} \xi =\frac{1}{\lambda}\left[\frac{m_d^{\prime }{Cp}_e\varepsilon }{\left(1-\varepsilon \right)}\left({T}_{d,i}-{T}_{c,i}\right)-{m}_a^{\prime }{Cp}_e\overline{T}\left({T}_{a,i}-{T}_{d,i}\right)\right], \end{equation}$$(40) where |$\overline{T\ }$|and |$\overline{P\ }$| are the dimensionless temperature and pressure difference ratios, λ is the latent heat of vaporization, ε is the heat exchanger effectiveness and c represents the critical conditions. This method assumed different inlet air–desiccant temperatures and no heat losses between the dehumidifier and the adjacent heat exchanger. Clen et al. [62] formulated an analytical model for both co- and counter-flow dehumidifier configurations founded on the FD technique of [90]. The following correlation constants were presented and conveniently used to simplify the correlation. $$\begin{equation}\hskip-6pt {K}_a= Le.{Cp}_a{T}_a+\lambda \omega \end{equation}$$(41) $$\begin{equation} {K}_d= Le.{Cp}_d{T}_d+\lambda{\omega}_e \end{equation}$$(42) A combination of thermal mass conservation and transmission equations resulted in the flow-wise variation of Ke formulated and solved to obtain the values of air moisture content and temperature as follows: $$\begin{equation} \frac{dK_e}{dz}\!=\!{m}^{\ast }\ \frac{NTU}{H}\!\left\{{h}_{a,i}+\!\frac{1}{m^{\ast }}\left({K}_e-{\!K}_{e,o}\right)+\left({L}_e-\!1\right){Cp}_a{T}_a-{K}_e\right\}\!. \end{equation}$$(43) Another analytical exposition of a unidimensional model of [59] resulted in two linked ODEs whose solutions were deduced in the form of $$\begin{equation}\hskip-30pt \Delta{\omega}_M={C}_1{e}^{\lambda_2{NTU}_z}+{C}_2{e}^{\lambda_1{NTU}_z} \end{equation}$$(44) $$\begin{equation} \Delta \vartheta ={K}_1{C}_1{e}^{\lambda_2{NTU}_z}+{K}_2{C}_2{e}^{\lambda_2{NTU}_z}. \end{equation}$$(45) However, the correlations were based on the assumption that the solution saturation humidity ratio was singularly hinged on the solution temperature. Hence, the method only applicable to very low variations in desiccant concentration and flow rate. A simplified analytical model for adiabatic dehumidifier and regenerator was developed by [68, 70] based on moisture temperature gradients and mass balance differential Equations 6, 7 and 8. The integral solutions of these equations gave rise to the following correlations whose solutions enabled the determination of air–desiccant outlet conditions: $$\begin{equation}\hskip-85pt \omega ={\omega}_{int}-\left({\omega}_i-{\omega}_{int}\right)\exp \left(-\gamma \overline{M}{NTU}_z\right) \end{equation}$$(46) $$\begin{equation} {T}_a={C}_1+{C}_2\exp \left(-\theta{NTU}_z\right)-\frac{\beta }{{\left(\gamma \overline{M}\right)}^2-\gamma \overline{M}\theta}\exp \left(-\gamma \overline{M}{NTU}_z\right) \end{equation}$$(47) $$\begin{align} {T}_a=&\ \frac{1}{R_c Le}\Bigg[-{C}_2\exp \left(-\theta{NTU}_z\right)\nonumber\\ &\qquad\qquad\qquad+\frac{\gamma \overline{M}\beta }{{\left(\gamma \overline{M}\right)}^2-\gamma \overline{M}\theta}\exp \left(-\gamma \overline{M}{NTU}_z\right)\Bigg]+{T}_a \end{align}$$(48) $$\begin{equation}\hskip-65pt \ln \chi =-{R}_m\left({\omega}_i-{\omega}_{int}\right)\exp \left(-\gamma \overline{M}{NTU}_z\right)+{C}_3 \end{equation}$$(49) $$\begin{equation}\hskip-65pt {\mathrm{m}}_s={m}_a\left({\omega}_i-{\omega}_{int}\right)\exp \left(-\gamma \overline{M}{NTU}_z\right)+{C}_4. \end{equation}$$(50) Based on the earlier numerical model of [77], a simplified analytical model was conceptualized by [35] assuming constant solution concentration and flow rate. Sets of predictive correlations for moisture and enthalpy effectiveness of cross-flow dehumidifier were formulated as follows: $$\begin{equation}\hskip5pt {\eta}_h={C}_o{\left(\Delta{h}_i\right)}^{C_1-1}.{\left({\omega}_i\right)}^{C_2}.{\left({m}_a\right)}^{C_3}.{\left({\dot{m}}_{zi}\right)}^{C_4} \end{equation}$$(51) $$\begin{equation} {\eta}_w={b}_o{\left(\Delta{h}_i\right)}^{b_1}.{\left({\omega}_i\right)}^{b_2-1}.{\left({\dot{m}}_a\right)}^{b_3}.{\left({\dot{m}}_{zi}\right)}^{b_4}. \end{equation}$$(52) An improved analytical model applicable to precise prediction of real-time optimized performance with the aid of Levenberg–Marquardt method parameter identification and correlations for effectiveness of various packings using LiCl and TEG solutions were proposed considering air–desiccant flow rates and temperature, packing geometry and interfacial saturation states [50, 97]. The humidity ratios were correlated thus $$\begin{equation} \frac{\omega_o}{\omega_i}=\frac{C_1\exp \left({C}_2\left({T}_{a,i/}{T}_{d,i}\right)\right)}{\xi_i{C}_3} \end{equation}$$(53) $$\begin{equation}\hskip-20pt {\omega}_e=\frac{C_4\exp \left({C}_{5/}{T}_{d,i}\right)}{\xi_i{C}_6}. \end{equation}$$(54) Yonggao et al. [63] generated mass transfer coefficients based on experimental results and formulated empirical correlations between regeneration mass transfer coefficients, heating temperature and desiccant concentrations as shown in Equation 56. While correlations between dehumidification rates with respect to inlet air humidity dry bulb temperature as shown in Equations 57 and 58, respectively. $$\begin{equation} \varepsilon =\frac{1-\left({\omega}_o/{\omega}_i\right)}{1-\left({\omega}_e/{\omega}_i\right)}. \end{equation}$$(55) Yonggao et al. [63] generated mass transfer coefficients based on experimental results and formulated empirical correlations between regeneration mass transfer coefficients, heating temperature and desiccant concentrations as shown in Equation 56. While correlations between dehumidification rate with respect to inlet air humidity dry bulb temperature as shown in Equations 57 and 58, respectively: $$\begin{equation} {\alpha}_{reg}=-341.5314+16.1876{T}_h-0.2552{T_h}^2\ \left(\chi =20\%\right) \end{equation}$$(56) $$\begin{equation} {m}_d=111.5157-22.9969{\omega}_{a,i}+1.5379{\omega_{a,i}}^2-0.0329{\omega_{a,i}}^3 \end{equation}$$(57) $$\begin{equation} \dot{m_d}=11.0939+1.0912{T}_{a,i}-0.0352{T_{a,i}}^2+3.7641x{10}^3{T_{a,i}}^3. \end{equation}$$(58) In summary, the three major categories of predictive models applicable to packed bed adiabatic dehumidifiers and regenerators have been covered in terms of assumptions, formulations and applications. The FD takes the lead in accuracy and suitability for design optimization but takes much memory due to the iterative nature of its solution procedure. Because of the unidimensional nature of FD models, they are best suited for counter-flow configurations. The ε-NTU can be formulated in 2D and mostly applicable to cross-flow dehumidifier/regenerators. Less memory space and time during the solution process is one strong point of this kind of model. However, it is less accurate compared to the FD model, which justifies why less research is reported in the literature on ε-NTU models. Both the FD and ε-NTU models are conditioned for specific circumstances, hence lacking the universality of use. For improved accuracy, simplicity and universal applications, some additional assumptions and modifications have been introduced guided by the experimental data to mimic the exact conditions. The ensuing models are simple and highly efficient in long-term predictions since no iterative procedures are required in their solutions. The details of the model comparison are presented in Table 1. Table 1 Comparison of models for packed bed adiabatic dehumidifier and regenerator. Model category . Assumptions . Iterations . Solution . Accuracy . FD - Minimal - Expansive - Numerical - Most ε –NTU - More - Vast - Minimal none - Numerical/analytical - Analytical - Good - Poor Model category Computation Outputs Application Finite different Long - All variables - Output variations - Parts design - Sensitivity analysis - Performance prediction - System optimization ε − NTU Short - Selected variables - Outlet conditions - System design - Sensitivity analysis - Annual performance prediction Simple correlation Short - Performance indices - Outlet conditions Annual performance assessment Model category . Assumptions . Iterations . Solution . Accuracy . FD - Minimal - Expansive - Numerical - Most ε –NTU - More - Vast - Minimal none - Numerical/analytical - Analytical - Good - Poor Model category Computation Outputs Application Finite different Long - All variables - Output variations - Parts design - Sensitivity analysis - Performance prediction - System optimization ε − NTU Short - Selected variables - Outlet conditions - System design - Sensitivity analysis - Annual performance prediction Simple correlation Short - Performance indices - Outlet conditions Annual performance assessment Open in new tab Table 1 Comparison of models for packed bed adiabatic dehumidifier and regenerator. Model category . Assumptions . Iterations . Solution . Accuracy . FD - Minimal - Expansive - Numerical - Most ε –NTU - More - Vast - Minimal none - Numerical/analytical - Analytical - Good - Poor Model category Computation Outputs Application Finite different Long - All variables - Output variations - Parts design - Sensitivity analysis - Performance prediction - System optimization ε − NTU Short - Selected variables - Outlet conditions - System design - Sensitivity analysis - Annual performance prediction Simple correlation Short - Performance indices - Outlet conditions Annual performance assessment Model category . Assumptions . Iterations . Solution . Accuracy . FD - Minimal - Expansive - Numerical - Most ε –NTU - More - Vast - Minimal none - Numerical/analytical - Analytical - Good - Poor Model category Computation Outputs Application Finite different Long - All variables - Output variations - Parts design - Sensitivity analysis - Performance prediction - System optimization ε − NTU Short - Selected variables - Outlet conditions - System design - Sensitivity analysis - Annual performance prediction Simple correlation Short - Performance indices - Outlet conditions Annual performance assessment Open in new tab 6.4. The solar regenerator models Due to the simplicity in construction, the solar collector/regenerator presents more avenues for analysis than packed bed types. The solar collector/regenerator models are majorly built on the elemental control volume fundamental equations. These equations are formulated in terms of momentum, energy and concentration balances and variations that enable the velocity contour, temperature and concentrations to be profiled [21]. An analytical process of computing the quantity of water vapour evaporated from the dilute desiccant solution under the influence of climatic variables as well as inlet conditions of the solution was introduced in [98]. Both fixed and adjustable fluid stream breadth to assess the performance of solar regenerator with various simplification assumptions were used. The control volume fundamental equations were formulated as follows. Considering the fluid stream: $$\begin{equation} {\gamma}_d\frac{\partial^2{u}_d}{\partial{y}^2}+{\rho}_dg=0 \end{equation}$$(59) $$\begin{equation} {u}_d\frac{\partial^2{T}_d}{\partial x}={\delta}_d\frac{\partial^2{T}_d}{\partial{y}^2} \end{equation}$$(60) $$\begin{equation} {u}_d\frac{\partial^2{C}_d}{\partial x}+{D}_d\frac{\partial^2{C}_d}{\partial{y}^2}. \end{equation}$$(61) Considering the air stream: $$\begin{equation} \frac{\partial P}{\partial x}={\mu}_d\frac{\partial^2{\nu}_d}{\partial{y}^2} \end{equation}$$(62) $$\begin{equation} {u}_a\frac{\partial^2{T}_a}{\partial x}={\delta}_a\frac{\partial^2{T}_a}{\partial{y}^2} \end{equation}$$(63) $$\begin{equation} {u}_a\frac{\partial^2{C}_a}{\partial x}+{D}_a\frac{\partial^2{C}_a}{\partial{y}^2}. \end{equation}$$(64) And the interfacial mass balance equation is: $$\begin{equation} {k}_d\frac{\partial^2{T}_a}{\partial y}={k}_a\frac{\partial^2{Ct}_a}{\partial y}+{\rho}_a{D}_a{h}_{fg}\frac{\partial^2{C}_a}{\partial y} \end{equation}$$(65) $$\begin{equation}\hskip-70pt {\rho}_d{D}_d\frac{\partial^2{C}_d}{\partial y}={\rho}_a{D}_a\frac{\partial^2{C}_a}{\partial y}. \end{equation}$$(66) For varying fluid stream breadth: $$\begin{equation} {\rho}_d=\sqrt[3]{\frac{3{m}_d{\gamma}_d}{\rho_dg}}, \end{equation}$$(67) where ρd is the stream thickness. For improved accuracy of solar regeneration collector, a wide-ranging data from experimental assessment of LD solar regeneration upon which the correlations of moisture removal rates were based were generated [14, 21]. In other experimental analysis, the heat and mass exchange occurrence is correlated in form of Nusselt number, and the Chilton–Colbarn correlation is widely used. $$\begin{equation} \frac{\gamma_a}{\beta_a}={\rho}_a{Cp}_a\sqrt[3]{{\left(\frac{\alpha_a}{D_a}\right)}^2} \end{equation}$$(68) 6.5. Common assumptions in coupled heat and mass exchange model formulations In summary, for convenience, unambiguity and simplification of the models, numerous fundamental postulations have to be made from which an interesting trend has emerged. Table 2 shows the most commonly used assumptions in coupled heat and mass transfer prediction model formulations, classified according to accuracy, practicability and variability. Table 2 Summary of heat and mass transfer modelling assumptions in LDDR systems. Accuracy . Assumptions . Up to ±10% (1) Adiabatic conditions (2) Unidirectional heat and mass transfer (3) Insignificant thermal resistance in liquid phase (4) Uniform heat and mass transfer areas (5) Air-solution interfacial thermal saturation (6) Uniform desiccant interfacial temperature (7) Insignificant desiccant evaporation desiccant vaporization (8) Unequal and varying air and desiccant inlet temperatures Up to ±20% (over-estimation) (9) Unidimensional heat and mass exchange in the air–desiccant flow direction (10) Confined thermal and mass exchange constants in the module (11) Even dispensation of desiccant within the packing material Not true (in practice) (12) Completely established inlet velocity contour (13) Laminar flow (14) Uniform thermophysical air and desiccant characteristics (15) Insignificant water absorption/desorption rates with respect to fluid flow (16) Uniform film breadth (17) Uniform wall temperature (18) Uniform desiccant latent heat of condensation (19) Constant and steady air velocity Constant (20) Air and desiccant characteristics (21) Temperature borderline states (22) Desiccant concentration and flow rate inside the column Negligible (23) Solution energy-balance water losses (24) Liquid phase heat resistance (25) Absorption compared to latent heat (26) Vapour condensation rate in comparison to the solution flow rate (27) Heat energy during air–desiccant mixing (28) Pumps and air blowers power consumption (29) Water vapour diffusion (30) Heat loss within the column Accuracy . Assumptions . Up to ±10% (1) Adiabatic conditions (2) Unidirectional heat and mass transfer (3) Insignificant thermal resistance in liquid phase (4) Uniform heat and mass transfer areas (5) Air-solution interfacial thermal saturation (6) Uniform desiccant interfacial temperature (7) Insignificant desiccant evaporation desiccant vaporization (8) Unequal and varying air and desiccant inlet temperatures Up to ±20% (over-estimation) (9) Unidimensional heat and mass exchange in the air–desiccant flow direction (10) Confined thermal and mass exchange constants in the module (11) Even dispensation of desiccant within the packing material Not true (in practice) (12) Completely established inlet velocity contour (13) Laminar flow (14) Uniform thermophysical air and desiccant characteristics (15) Insignificant water absorption/desorption rates with respect to fluid flow (16) Uniform film breadth (17) Uniform wall temperature (18) Uniform desiccant latent heat of condensation (19) Constant and steady air velocity Constant (20) Air and desiccant characteristics (21) Temperature borderline states (22) Desiccant concentration and flow rate inside the column Negligible (23) Solution energy-balance water losses (24) Liquid phase heat resistance (25) Absorption compared to latent heat (26) Vapour condensation rate in comparison to the solution flow rate (27) Heat energy during air–desiccant mixing (28) Pumps and air blowers power consumption (29) Water vapour diffusion (30) Heat loss within the column Open in new tab Table 2 Summary of heat and mass transfer modelling assumptions in LDDR systems. Accuracy . Assumptions . Up to ±10% (1) Adiabatic conditions (2) Unidirectional heat and mass transfer (3) Insignificant thermal resistance in liquid phase (4) Uniform heat and mass transfer areas (5) Air-solution interfacial thermal saturation (6) Uniform desiccant interfacial temperature (7) Insignificant desiccant evaporation desiccant vaporization (8) Unequal and varying air and desiccant inlet temperatures Up to ±20% (over-estimation) (9) Unidimensional heat and mass exchange in the air–desiccant flow direction (10) Confined thermal and mass exchange constants in the module (11) Even dispensation of desiccant within the packing material Not true (in practice) (12) Completely established inlet velocity contour (13) Laminar flow (14) Uniform thermophysical air and desiccant characteristics (15) Insignificant water absorption/desorption rates with respect to fluid flow (16) Uniform film breadth (17) Uniform wall temperature (18) Uniform desiccant latent heat of condensation (19) Constant and steady air velocity Constant (20) Air and desiccant characteristics (21) Temperature borderline states (22) Desiccant concentration and flow rate inside the column Negligible (23) Solution energy-balance water losses (24) Liquid phase heat resistance (25) Absorption compared to latent heat (26) Vapour condensation rate in comparison to the solution flow rate (27) Heat energy during air–desiccant mixing (28) Pumps and air blowers power consumption (29) Water vapour diffusion (30) Heat loss within the column Accuracy . Assumptions . Up to ±10% (1) Adiabatic conditions (2) Unidirectional heat and mass transfer (3) Insignificant thermal resistance in liquid phase (4) Uniform heat and mass transfer areas (5) Air-solution interfacial thermal saturation (6) Uniform desiccant interfacial temperature (7) Insignificant desiccant evaporation desiccant vaporization (8) Unequal and varying air and desiccant inlet temperatures Up to ±20% (over-estimation) (9) Unidimensional heat and mass exchange in the air–desiccant flow direction (10) Confined thermal and mass exchange constants in the module (11) Even dispensation of desiccant within the packing material Not true (in practice) (12) Completely established inlet velocity contour (13) Laminar flow (14) Uniform thermophysical air and desiccant characteristics (15) Insignificant water absorption/desorption rates with respect to fluid flow (16) Uniform film breadth (17) Uniform wall temperature (18) Uniform desiccant latent heat of condensation (19) Constant and steady air velocity Constant (20) Air and desiccant characteristics (21) Temperature borderline states (22) Desiccant concentration and flow rate inside the column Negligible (23) Solution energy-balance water losses (24) Liquid phase heat resistance (25) Absorption compared to latent heat (26) Vapour condensation rate in comparison to the solution flow rate (27) Heat energy during air–desiccant mixing (28) Pumps and air blowers power consumption (29) Water vapour diffusion (30) Heat loss within the column Open in new tab 7. Conclusions Given the above-reviewed literature, LDACS have been advanced as energy efficient in comparison to the conventional VCS with recommendations for the possible use of low-grade waste heat and renewable energy such as solar for dehumidification and regeneration processes. Various scholarly works have been brought forth dating back to 1969. However, with technological advancement and knowledge evolution, new technologies and improvements have emerged with regards to system design and configurations. Of more importance is the fact that various theoretical (numerical and analytical) models for heat and mass transfer process analysis in dehumidification and regeneration processes raises the LDACS technology to a different level. Flow configurations and patterns have also been extensively investigated. In this regard, the counter-flow arrangement is viewed to be more effective in terms of heat and mass transfer compared to the co-flow and cross-flow counterparts. For validation of the theoretical models, various experimentations have also been carried out using different single and combinations of desiccant solutions to investigate the effects of inlet air/desiccant conditions on the performance output. However, uncertainties still exist to date concerning optimum air desiccant flow ratios, heat and mass transfer area relationships and wetting ratios due to inconsistencies in assumptions used during modelling and analysis. These uncertainties arise from the use of unidimensional and 2D models that do not present realistic scenarios; therefore: More accurate 3D models need to be considered with a view of improving the performance. More experimental and analytical studies are still needed to broaden the conceptualization and improve the existing systems’ overall performance, predictability, use and cost. Most of the critical variables and thermophysical properties of the desiccant solution are assumed to be constant in theory while in practical essence, they are varying. These assumptions oversimplify the models to the extent of underestimating the dehumidifier and regenerator performance characteristics and should be treated as variables. Most of the existing thermal and mass exchange mathematical models consider steady states of dehumidifier/regenerator performances, and hence, there is a need for more advanced transient theories for dynamic operations. Majority of the work has been focused on the outlet conditions of various parameters. However, the heat and mass exchange modelling within the dehumidifier and regenerator is still limited and needs some renewed interest. 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TI - A review of coupled heat and mass transfer in adiabatic liquid desiccant dehumidification and regeneration systems; advances and opportunities
JF - International Journal of Low-Carbon Technologies
DO - 10.1093/ijlct/ctaa031
DA - 2020-05-25
UR - https://www.deepdyve.com/lp/oxford-university-press/a-review-of-coupled-heat-and-mass-transfer-in-adiabatic-liquid-4GdWk08G3r
SP - 1
EP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -