Recent developments in adsorption heat pumps for heating applications

Working principle

Heat pumps perform an operation of collecting heat from a reduced temperature level and transferring this to a temperature with elevated levels, all while being operated by a tertiary energy supply. ²⁵ The AHPs working principles may be comprehended by considering the comparatively basic situation example of a single bed unit, that involves an adsorbent heat exchanger (AHEx), a collection of valves, an evaporator, and a condenser with an expansion system (V). Figure 3 depicts, there are four stages of the adsorption heating cycle: isobaric adsorption (from 1 to 2), isosteric heating (from 2 to 3), isobaric desorption (from 3 to 4), and isosteric cooling (from 4 to 1).^4,9,26 Figure 3 portrays an optimal period and demonstrates the pressure (P) over four successive cycles.^9,27 Almost every loop works in the following manner.^9,27

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Figure 3.

Schematics of four phases of an adsorption heating cycle with the simple depiction of the fundamental AHP.

As presented in Figure 3, the isobaric adsorption (from 1 to 2) and the evaporator and bed are attached, which gains heat from the atmosphere. If the temperature of the bed drops on the porous adsorbent, the adsorption of vapor occurs, and the device generates heat, which can be employed for various purposes. At pressure P_evap, it can prevail to the point, till maximum (equilibrium) concentration of adsorbent is achieved. Veritably, although this is unlikely to be the case, the phase could be disrupted if the temperature differential among the adsorbent bed and the heat transfer fluid (HTF) is no longer sufficient. ²⁸ The adsorbent bed production in this stage can be estimated using the equation (1)^4,29:

− Q 1 − 2 ≈ ∫ T 1 T 2 [ m s ( C s + X C p , a ) + m bed C bed ] dT − ∫ X min X max m s Δ H ads dX

(1)

Similarly, the heating and bed isolation takes place in the isoteric heating stage (2 → 3), and the bed pressure elevates from P_evap → P_cond, as shown in Figure 3 due to desorption of some part of the adsorbate. The amount of heat emitted during this process is determined as follows (equation (2))^4,29:

Q 2 − 3 ≈ ∫ T 2 T 3 [ m s ( C s + X max C p , a ) + m bed C bed ] dT

(2)

The isobaric desorption (3 → 4) begins, as presented in Figure 3 when the adsorbent bed is exposed to the condenser, and P_cond is attained. At this stage, for the promotion of adsorbent regeneration, heat is needed. The adsorbate desorption (W decreases from W₃ to W₄) occurs when bed temperature elevates (from T₃ to T₄), and adsorbate condenses while releasing the latent heat, that can be used for multiple applications. The heat that really should be delivered to the bed during this process is given by equation (3)^4,29:

Q 3 − 4 ≈ ∫ T 3 T 4 [ m s ( C s + X C p , a ) + m bed C bed ] dT − ∫ X max X min m s Δ H ads dX

(3)

Eventually, in the isosteric cooling stage, the separation and bed cooling occur, that is from 4 to 1 (Figure 3), which results in the decrease of pressure since a vapor gets partly adsorbed; mostly sensible heat is emitted. Similarly, another cycle starts as the bed pressure (P_evap) is reached, by reconnecting the evaporator and the adsorbent bed.^4,9,30 The heat extracted from the bed under isosteric cooling is given as (equation (4 4 ))^4,29:

− Q 4 − 1 ≈ ∫ 4 T 1 [ m s ( C s + X min C p , a ) + m bed C bed ] dT

(4)

The condenser and the evaporator operate according to vapor-liquid equilibrium (VLE) conditions, where the flow rate of HTF and inlet temperature affect the heat exchanger. In practice, each AHP cycle can be considered a two-stage process in which the bed is provided the heat or the bed releases heat. The AHP unit often matches with the isosteric heating’s beginning step, as shown in point 2 of Figure 3. ⁵ The process from 1 to 4 shows the heat supplied and pumped out in every cycle of the AHP unit, with the help of arrows of various colors, representing different temperature ranges of AHPs. Although fuel for the evaporation process is provided during the reduced temperature, regeneration of the adsorbent bed necessitates a heat supply that is at an elevated temperature, and usable heat is emitted at a mid-temperature range. The amount of heat provided at high and low temperatures (for regeneration, bed heating, and evaporation) correlates to the heat emitted at a moderate T stage (by the bed and the condenser through isobaric adsorption and isosteric cooling). ³¹ The greater the cycle’s temperature level ( Δ T cycle = T 4 − T 2 ), the larger the W_cycle, and hence the greater the effect of heat transfer (more heat transfer through evaporator and condenser). ¹¹ The ideal heat pump operation contrasts with the actual heat pump operation in the vapor pressure diagram. The optimal procedure indicates the greatest quantity of water that can be evaporated in the dry zeolite mass over a heat pump cycle.

Δ x max = m w , max m zeo

(5)

Δx_max from equation (5) represents the gap in the maximum water content of zeolite x_max at evaporation pressure and minimum adsorption temperature and the minimum water content x_min at condensation pressure and maximum process temperature. These process points cannot be attained due to the requisite temperature gradient among the adsorber, heating system, and between the gas burner and the desorber. D_x, which is the difference in the water content of zeolite at the end of the adsorption phase x_ads and the end of the desorption phase x_des, describes the quantity of water that can be evaporated under actual scenarios. ³²

In one module throughout the heat pumping cycle, a gas burner supplies heat to the heat transfer circuit of the adsorber/desorber to increase zeolite temperature and vacuum vessel pressure in the desorption phase. Liquification of water in the condenser occurs. The heat emitted causes the condenser temperature to elevate. As the condenser temperature surpasses, the temperature can be transmitted via usable heat (t_heat). This stage is halted as the highest process temperature reaches around 200°C and the burner is turned off. Similarly, a decrease in the temperature starts the adsorption phase – the zeolite and evaporator temperatures and pressure decrease. The ambient heat may be provided in heat pumps when the evaporation temperature stays below ambient temperature (t_cool), the evaporated water is adsorbed onto zeolites, and the heating system can be supplied with the adsorption heat. When all the adsorbate evaporates, the current phase stops, and the next phase starts. ³²

Parameters affecting performance

Adsorption heat pumps are usually tested based on their coefficient of performance (COP) and specific cooling or heating capacity (SCP/SHP). For cooling requirements, COP_c (equation (6)) is defined as the ratio between the heat of evaporation to the heat provided to the bed. For heating, COP_h (equation (7)) is defined as the ratio of the heat of the adsorbent bed released during adsorption phases and isosteric cooling (Q_4–1 + Q_1–2), including the condensation heat Q_c, as well as the heat used for desorption and isosteric heating (Q_2–3 + Q_3–4)^4,29:

CO P c = Q e Q 2 − 3 + Q 3 − 4

(6)

CO P h = Q c + Q 4 − 1 + Q 1 − 2 Q 2 − 3 + Q 3 − 4

(7)

The ratio of proper heat, the cycle time and adsorbent mass gives SHP (equation (8)). The SCP (equation (9)) is computed by the heat of evaporation over the cycle time and adsorbent mass. The specific cooling and heating power is one of the distinguishing features. The specific heating/cooling capacity is a feature that is strongly reliant on the system design, providing analysis of various system configurations and designs^4,29:

SHP = Q c + Q 4 − 1 + Q 1 − 2 m s τ cyc

(8)

SCP = Q e m s τ cyc

(9)

According to Cabeza and Schossig, ³³ a skilled assessment of the efficiency of AHPs for real-world implementations necessitates a consistent specification of key performance indicators (KPIs). It provides a comparative analysis of system efficiencies employing variable energy sources. The primary energy ratio (PER) is the ratio of total useful energy (Q_useful) and the total primary energy inputs. The following formula (equation (10)) can be used to measure PER:

PER = Q useful F f p , fuel + E f p , elect

(10)

where E, F are the electrical energy and the fuel energy inputs, respectively, and the f_p,fuel is the primary energy conversion factor for fuel, and f_p,elect is the primary energy conversion factor for electricity. A thermal COP is often determined excluding electrical energy because this contribution demanded by AHPs may be overlooked (equation (7)). ³¹

Effect of operating conditions on the system performance

The operating conditions which have a substantial impact on the performance of AHPs include temperatures of evaporation (T_evap), condensation (T_cond), minimum bed temperature, and bed regeneration (T₄).^34–36 The T₂ and T_cond depend on the useful heat’s temperature and should be analogous for delivering the condenser and the bed heat at a comparable T level.^14,37,38 The basis of T_evap is the temperature ( T heat source low ), environmental temperature source and is controlled by the refrigerant employed. Besides, a part of T₄ is affected by the available heat source temperature ( T heat source high ) for adsorbent regeneration and the working pair’s thermal stability. The T heat source high can be controlled by the cost, type of HTF, durability issues, and the peak permissible pressure in heating circuits to be used locally. Figure 4 represents the effects of T₄, T_evap, and T_cond on the adsorption heating cycle, where adsorption isotherm of type I is considered, which is the property of microporous and water vapor adsorbents, that is, zeolites X and Y while being broadly used for the study of AHPs.^39,40

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Figure 4.

Impact of increasing: (a and d) T_cond from T_cond,1 to T_cond,3; P_evap from P_evap,1 to P_evap,3; and T₄ from T_4,1 to T_4,3, using (a–c) type I isotherms and (d–f) ideal P versus T plots. The equilibrium adsorption cycles are represented by colored rectangles (case 1: blue; case 2: red, case 3: orange), reproduced from Pinheiro et al. ¹

The effect of minimum bed and condenser temperatures is that with the increase in the condenser and minimum bed temperatures, the adsorption and desorption stages are constrained. As presented in Figure 4(a), a reduction in ΔW_eq from ΔW_eq,1 → ΔW_eq,3 occurs when T_cond is increased from T_cond,1 to T_cond,3 when T₄ and T_evap are kept constant. As the T_cond increases from T_cond,1 to T_cond,3, the adsorption cycles become increasingly constrained (Figure 4(d)) and result in a uniform drop in the performance of AHP. This phenomenon occurs in successive cycles for domestic hot water (DHW) production, such as the setpoint value from ambient air temperature being defined by the consumer.

The bed regeneration temperature and evaporation are associated with each other, as shown in Figure 4(b). The increase in P_evap from P_evap,1 to P_evap,3, when T₄ and T_evap are kept constant, increases the ΔW_eq. Consequently, an increased W_eq was attained after the adsorption phase (Figure 4(b) and (e)). Furthermore, an increase in the ΔW_eq and the adsorbent regeneration occurs when T₄ is increased, as shown in Figure 4(c) and (f).

Adsorption equilibrium

Four equations are widely used related to adsorption equilibrium: Freundlich equation, Dubinin equations (typically Dubinin-Astakhov equation), Toth equation, and Langmuir equation. Hassan et al. ⁴¹ have presented a thorough review through the theory and equations of adsorption equilibrium. Another work on the experimental adsorption data for the AQSOA zeolite-like adsorbent and equation predictions comparison was performed. ⁴² The International Union of Pure and Applied Chemistry (IUPAC) ⁴³ classifies equilibrium isotherms into six forms (I–VI types), depicted in Figure 5. Hysteresis can be observed in Type IV and Type V isotherms represented through the red curve for adsorption and the blue curve for desorption. An S-shaped isotherm is advantageous for AHP applications since a large portion of adsorbate absorption occurs at reduced relative pressures. ⁴⁴ Many other simulation models for adsorption kinetics use the LDF (linear driving force) technique, which is a feasible approach for portraying the growth of adsorption uptake in time.^45,46

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Figure 5.

Classification of adsorption isotherms according to IUPAC. ⁴⁷

Numerical methods and physical models

Lumped parameters models

Some specific assumptions are applied commonly to facilitate the study depending on lumped parameters; (i) there is a uniform temperature within the adsorbent; (ii) uniform adsorption of refrigerant occurs in the adsorber; and (iii) at thermodynamic equilibrium, both solid and gas phases exist. The thermal resistance and mass transfer resistance of the adsorbent are disregarded in these models. One of the features of such models is that the adsorbed phase varies with time generally as a dynamic model. The model generally consists of three main equations: energy equilibrium, mass equilibrium, and the adsorption equilibrium equation. Throughout the desorption process, the generalized statement is presented of an energy balance equation (11) for the adsorbent bed ⁵⁴ :

( m mt c pm + m z c pz + m z q c pa ) d T z dt = m z Δ H dq dt + ϕ w → z

(11)

Consequently, throughout the adsorption process, the energy equation (12) is obtained as:

( m mt c pmt + m z c pz + m z q c pa ) d T z dt = − m z Δ H dq dt + ϕ w → z + m z c pa ( T e − T z ) dq dt

(12)

The mass balance of adsorbate was provided in the model proposed by Sakoda and Suzuki ⁴⁶ as follows (equation (13):

m z dq dt + d m ae dt = 0

(13)

The term on the left-hand side bracket of equations (11) and (12) comprises the sensible heat of the metallic elements of the adsorber, completely regenerated adsorbed bed, and the adsorbed phase. The first right-hand side term of equations (equation (11)) and (equation (12)) is the heat due to desorption and adsorption. The character w → z indicates heat from the heating or refrigerating medium. Owing to the movement of coolant vapor, the third component on the right-hand side of equation (12) is sensible heat, where “m_ae” in equation (13) is the evaporator adsorbate.

Douss and Meunier ⁵⁵ proposed the predictive dynamical model. It employed a primary lumped model parameter and considered that in the adsorber, evaporator, and condenser every component was homogenous in the system. Thus, the model was suitably confined to waterfall heat exchangers and film evaporators. However, there were also certain numerical instabilities, especially in short periods. The two-reactor heat adsorption pump was numerically simulated by Cacciola et al., ⁵⁶ given the heat regeneration. Two critical assumptions were made: to facilitate the analysis (a) each reactor had a uniform temperature and (b) a balanced adsorption operation. The adsorber, condenser, and evaporator’s energy balance equations were constructed based on the efficiency of different components. The equations have been changed and numerically solved to a non-dimensional form. At different times, the convergence of the numerical approach was validated. The model was evaluated using the adsorption pair of zeolites and the technical characteristics available. ⁵⁷ Douss’s findings were consistent with the projected changes of temperatures of the adsorbent bed, condenser, and evaporator. ⁵⁷ It was also experimentally validated, ⁵⁸ and the software was an effective tool for the design of adsorption heat pumps and for the maximum performance to be optimized in component sizes.^54,58

The models presented by Wu et al. ⁵⁹ were similar to what Sami et al. ⁶⁰ have suggested. A new heat exchanger tube and shell-type were used as adsorber in their investigation, but its impacts were not analyzed. Instead, an experimental investigation has been conducted depending on the experimental parameters reproduced by the suggested model. In the simulation, various operating variables were optimized according to experimental data, including cycle duration, the heat source temperature, cooling water, and the adsorber total heat transference coefficient. On the contrary, Sami’s model ⁶⁰ calculated the heat transfer coefficients correspondence for smooth tubes. The findings therefore correlated closely with the computation of dynamic simulation data in the research of Wu et al. ⁵⁹

A double bed silica gel-water adsorption chiller was presented by Saha et al. ⁶¹ as a numerical simulation comparable to that of Sakoda. ⁴⁶ By applying the Freundlich Equation with the experimental data of the supplier, the adsorption balancing equation was achieved. The simulation was carried out to validate the working temperature effect, discharge, and adsorption-desorption cycle periods. It was shown to be the most crucial parameter of COP of the system for the operating temperature associated with water discharge. In addition, it was discovered that cycle times were less quantitatively impactful but still quite essential in terms of quality. Critoph ⁶² developed and patented a novel, ongoing rotational cooling adsorption system. The technology is comparable to the Llobet and Goetz ⁶³ rotary systems. The adsorbent bed within the tube as a closed segment of the module in the rotational system was suggested by Critoph ⁶² which includes a generator and a receptor/condenser/evaporator. The coolant in the module was comparable to the coolant in the heat pipe. A laboratory-sized prototype device was manufactured and validated. As mentioned earlier, the efficiency of the system, comprising of 32 modules, was forecasted by applying basic governing equations. Research development on improving this system has been proposed and uncovering the optimal constraints of the notion utilizing second law analysis.

Heat and mass transfer model

Simulation-based heat transfer and mass transfer are particularly relevant among many models found in the field as they offer an interpretation of the adsorber dynamics. A model for heat and mass transmission was developed, demonstrating that the temperature or weight of adsorbate fluctuates with time and space. For the appropriate/optimal design of adsorption systems, it is therefore vital. The models may be categorized into single, two- and three-dimensional models based on the adsorber geometry. The variations in the simplification of assumptions, the numerical resolution method, the design, and the purpose often exist across different models employed for the adsorption cooling system simulation.

The heat and mass transmission of solid adsorbents to adsorbent beds generally includes four primary governing equations: energy balancing, mass conservation equation, momentum equation, and adsorbent-adsorbate system state equation. Generally, the completeness and nonlinearity of these heat-connected models restrict the feasibility of an analytical approach. Therefore, numerical approaches are ultimately the only possible solution for the modeling of adsorbent bed dynamics. Several approaches employed provide the technique of final differences,^64,65 finite volume, ⁶⁶ and the technique of finite element. ⁶⁷ The finite difference approach is commonly used due to its brevity, effectiveness, and easiness of different start and limiting conditions. Some assumptions have been made that may be divided into four categories to ease numerical analyses, involving heat and mass transfer: (i) thermodynamic condition; (ii) heat and mass transfer; (iii) evaporator, heat source, and condenser; (iv) thermophysical and material characteristics.

To evaluate the heat transmission of a solid, fixed bed adsorbent, Guilleminot et al. ⁶⁴ devised a uniform pressure model. The approach disregards mass diffusion resistances yet incorporates heat diffusion resistance into consideration via two coefficients: the adsorbing bed’s thermal conductivity and the thermal transmission coefficient among the fins and the adsorbent bed. Boubakri et al. ⁶⁸ performed the comparable modification of the Guilleminot et al. ⁶⁴ models to predict the operational efficacy of an adsorbent solar-powered ice system and conducted experimental verification. The classification procedure utilized by Guilleminot et al. ⁶⁴ was employed for three unknown heat transfer coefficients related to condensers, evaporators, and ice tanks. This universal model also determined the ice production limit employing an adsorbent collector-condenser system: daily ice production (D.I.P.) may approach around 115 kg/m² of collector and the COP of around 19%. An expansion of Zheng et al.’s model may be regarded as a standard numerical model^69,70 that Sun et al. ⁶⁹ could first offer. This model was utilized to study several features of heat pumps for thermal wave regeneration. The adsorbers have high-temperature gradients: the energy transmission to the adsorber during the heating phase is considerably greater than that provided by the heat supply. Pons and Feng ⁷⁰ also utilized the previous model to study the influence on the adsorption cooling cycles of the number of transfer units (NTU) and the dimensionless output fluid temperature using thermal regeneration.

Szarzynski et al. ⁷¹ utilized this model to study various internal vapor transfers to study the adsorber to lessen the internal irreversibility of adsorption cycles. Firstly, adiabatic direct pressure recovery with a condenser instead of pressure variations with heat transfer; secondly, adiabatic of inner vapor recovery among adsorbers; thirdly, the division of the adsorber into specific chambers. ⁶⁴ The one-dimensional model of Hajji and Khalloufi ⁷² was nearly similar to Guilleminot et al., ⁶⁴ with some adjustments. By taking on the continuous fluid heating/cooling temperature, researchers have improved the model. The definite difference equations were computed employing an explicit technique and confirmed utilizing the average values of the apparent heat and heat-conductivity comparison of the projected temperature gradient with the analytical formulation.

The parametric study of this two-dimensional model demonstrated that the sorption kinetics might be considerably improved by lowering the distance among the fins and the contact resistance of the metal adsorbent contact. Therefore, thin fins and inexpensive metals have been advocated for minimizing the operating cost and weights. Sward et al. ⁷³ suggested a model wherein heat transfer travels axially and thermal contact with the bed for thermal wave adsorption thermal pumping cycles. The exponential performance was expected to be provided via local balance.

The material balance f(z) for every portion of the bed included an adsorbed phase term, a gas-phase term, and a flow term as follows (equation (14)):

ρ b ∂ n ∂ t + ∂ ( ε t C ) ∂ t + ∂ ( ε b u v C ) ∂ z = f ( z )

(14)

The energy balance comprises the four terms stated earlier, including a heat flow term via the bed walls (J_b).

ρ b ∂ i s ∂ t + ∂ ( ε t i v ) ∂ t + ∂ ( ε b u v h v ) ∂ z = J b + g ( z )

(15)

In which g(z) in equation (15), input and outlet valves represent the energy fluxes from and into the bed. The preceding equations have been transformed into dimensional, differentiated, and inserted in the ordinary differential equations into multiple separate cells of a specified height, and the equation set was numerically included in the Gear’s process using the LSODE software. ⁷³ The findings revealed an influence on the layout of the temperature and loading fronts of the entrance/outflow valve inside the bed.

Adsorbent-adsorbate working pairs

Significant research has been conducted and continues to be carried out to classify and evaluate adsorbent-adsorbate working pairs, usually under standard operating conditions.^{3,4,13,30,74–77} Water is perhaps the most used adsorbate, but ethanol, methanol, and ammonia are also used. Since they have low vaporization temperatures, methanol and ethanol are widely employed for refrigeration applications. ¹³ Since ammonia has high specific heating power during the adsorption phase due to high pressure, thus it is widely employed with activated carbon adsorbents, but it has the disadvantage of being toxic and emits a strong odor accidental leakage. ¹³ Activated carbons, zeolites, zeolite-like AIPOs (aluminophosphates), silica gels, and SAPOs (silico-aluminophosphates) are common adsorbent materials for AHPs. One of the most critical aspects of a durable adsorption heat pump is the adsorbent-adsorbate pair selection. While several experiments on working pairs have been performed, most of them focus solely on the kinetics and outputs of the adsorbate and adsorbent materials, overlooking their practicability for a functional or marketable framework. Numerous working pairs with outstanding adsorption potential are currently being presented; even then, the majority of these have poor hydrothermal stability or exhibit hysteresis due to material maturing through some cycles. One other consideration includes market readiness, and while some adsorbent materials exhibit strong, hydrothermal durability, absorption capability, and prolonged life cycle time.

Heating performances

It is worthwhile considering the variation of SHP and COP values mentioned in the publications for adsorption heating purposes over the last several years. Figures 6 to 9 depict this evolution by differentiating the working pairs, cycle characteristics, and work domain for different cases. For example, commercial AHPs have COPs in the region of 1.30–1.50 when zeolite/water is used or 1.40–1.60 when silica gel/water is used. ³⁸

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Figure 6.

Values of performance indicators of AHPs (for heating applications) in the reported literature for zeolite/water pair:(a) COP^{3,32,49,54,58,94–96} and (b) SHP.^{3,57,58,94,96–98}

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Figure 7.

Values of performance indicators of AHPs (for heating applications) in the reported literature for activated carbon/methanol pair: (a) COP^{14,49,55,58,80,99–104} and (b) SHP.^99,100,105

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Figure 8.

Values of performance indicators of AHPs (for heating applications) in the reported literature for activated carbon/ammonia pair: (a) COP^{79,80,102,106–113} and (b) SHP.^{107,109,111,112,114}

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Figure 9.

Values of performance indicators of AHPs (for heating applications) in the reported literature for activated silica gel/water pair: (a) COP^{3,75,89,98,115–119} and (b) SHP.^3,98,115,118

An investigation by Freni et al. ⁷⁵ stated that the suitable COP for heating pumping applications is >1.55, which was following the suggestion of Shelton et al., ⁵² which was 1.50. The COP values discussed in Figures 6(a), 7(a), 8(a) and 9(a) assist as references. Contrary to this, for the cost advantage of AHPs, the minimum SHP is found to be ca. 1000 W/kg, ¹²⁰ whereas the SHP is 1600 W/kg for Viessmann AHP, which is regarded as a remarkable reference case in the coating technology of adsorbents. The SHP values discussed in Figures 6(b), 7(b), 8(b) and 9(b) assist as references. The difference between the experimental and theoretical values of COP on an average is 18%, where theoretical values outperform experimental values. The highest COPs having the values of 1.30–1.60 reported in experiments are within the market range. ³⁸ In 2016, by employing silicoaluminophosphate SAPO-34/water working pair, the COP of single-bed AHP was 1.40⁸³ whereas, in 2011, AQSOA^® FAM-Z02/water working pair was employed and for single-bed prototype, the reported COP was 1.47. ¹¹⁵

Critoph ¹⁰⁶ in 2007 investigated the COP of a two-bed, activated carbon (AC)/ammonia-based, forced convection AHP prototype, where COP was found to be 1.80. Furthermore, in 2005, another four-bed prototype using a heat recovery cycle was reported with a COP of 1.31 using the activated carbon (AC)/ammonia working pair. ¹⁰⁷ In contrast to AHP industry statistics before 2012, no significant changes in creative COPs have been recorded since that time. Perhaps this is primarily due to the small adsorption ability of the investigated adsorbents. Attempts are being taken to produce new materials with excellent adsorption capacities to increase the efficiency of AHPs. ⁸² The single-bed AHPs, which employ water and novel metal-organic frameworks (MOFs) as adsorbate, have been found to report theoretical COPs greater than 1.55. ³⁸ The analysis of AHPs using COP (Figures 6(a), 7(a), 8(a) and 9(a)) tend to be more discussed in the research than the evaluation using SHP. In theoretical cases, SHP values were on average 35% greater than in practical applications. In advanced cycles, for AC/methanol and silica gel/water pairs, the experimental SHPs of up to 500 W/kg were recorded until 2007, with the adsorbents specifically in a loose grain configuration.^105,115,121

In a study, coatings were presented and found that a single-bed AHP with AQSOA^® FAM-Z02 binder-based coating for water adsorbate obtained a maximum SHP of 2200 W/kg. ¹²² In 2016, SAPO-34 coating was prepared through direct crystallization, where water was used as adsorbate, and the SHP higher than 3200 W/kg was recorded. ¹²³ An impact of adsorbent configuration on experimental SHP was demonstrated by contrasting the (zeolite or zeotype)/water working pairs based on single-bed AHPs, and it was found that: loose grains (240 W/kg (zeolite/water in 2001)) < binder-based coatings (2200 W/kg < directly synthesized coatings (3200 W/kg)). Coatings were found to have a 10-fold rise in SHP as compared to lose grains. Consequently, another research presented that zeolite coating technology has allowed attaining the SHPs in the thousands, which is around 10 times greater than random zeolite pellets among finned tubes. Consequently, transitioning from traditional pellets/grains to novel adsorbent configurations is critical for improving cost-competitiveness and adsorption heat pump’s SHP. Furthermore, improving the efficiency of AHPs requires the production of materials with optimized adsorbent configurations and enhanced adsorption capacities for effective heat transfer.

Adsorbent bed configurations

The adsorber bed configurations vary in their packing techniques, including finned tube, coated tube, spiral plate, plate-finned, fin plate, flat pipe, and tube, elaborated by Li et al. ¹²⁴ Similarly, shell packing was employed by Pinheiro et al. ³ The significant impact of various configurations is the variable metal to adsorbent mass ratios, heat losses to the atmosphere, adsorbent-metal wall contact areas, and the area of adsorbent being exposed to the adsorbate. Consequently, a significant amount of effort must be expended to choose the right adsorber arrangement, which can also vary depending on the physical properties, adsorbent-adsorbate working pair, and adsorber metal thermodynamics. Nonetheless, the HTF travels the adsorbent material within shell configuration, while in the tube configuration, the adsorbent material is wrapped all over the tube, minimizing heat losses so heat could only be transmitted to the adsorbent material from the tube. The finned heat exchangers have a smaller adsorbent-adsorbate contact area and a greater adsorbent-metal contact area and, consequently, a higher mass ratio of adsorbent-metal. The adsorber bed design process should include the following essential factors: a maximum amount of heat transfer should be ensured among the heat transfer fluid and the adsorbent material, adsorbent surface-exposed should be maximum to the adsorbate, the metal-adsorbent mass ratio should be minimized, an excellent thermal interaction among the metal and the adsorbent bed should be assured, and the overall design should be kept straightforward that it can be developed by using the vacuum technology elements. Choosing the correct arrangement and constructing the appropriate adsorber is a complex process that necessitates additional research to achieve the best combination between all these factors. ²⁹

The configurations of the adsorbent bed being commonly employed can be classified into four types: binder-based coatings, consolidated beds, directly synthesized coatings, and loose grains. ¹²⁵ For loose grains, fibers, pellets, powder, and adsorbent grains are inserted in the heat exchanger without any binders. Whereas for consolidated beds, the pore-forming additive and the binder are compacted along with the adsorbent to ensure the formation of a dense compressed layer on the wall of HEx. The preparation of binder-based coatings is performed by combining binder and an adsorbent, and then the composite material can be served on heat exchangers using dip coating or spraying techniques. Directly synthesized coatings are created by depositing adsorbent directly upon the HEx walls. ¹²⁵ Considerable attention (approximately 80% of the published studies) has been received by loose grains configuration, probably owing to its simplicity and being relatively inexpensive. All of the other remaining configurations account for below 10% of the findings. Table 1 presents a quantitative comparison of the four-bed configurations, representing the bed thickness (based explicitly on research for silica gels, zeolites, and zeotypes (i.e. SAPO-34, AQSOA^® FAM-Z02) where water acts as adsorbate), heat transfer coefficient on the adsorbent side (h_ads), the thermal conductivity of the adsorbent bed (λ_ads). It also includes the qualitative comparison based on mechanical resistance, pore structure stability, bed permeability, and industrial factors. Improvements in the AHEx total heat transfer coefficient (U) benefit heating efficiency, for which higher λ_ad and h_ads, and smaller δ are advantageous, conferring to equation (16 16 ) ¹²⁶ as given below:

1 U A fluid = 1 h fluid A fluid + 1 h ads A ads + δ λ ads A ads

(16)

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Table 1.

Comparison of the adsorbent configurations for AHPs in terms of λ_ads, h_ads, δ, bed permeability, stability issues, and industrial application features. ¹

Adsorbent bed configuration	Performance drivers				Stability issues			Industrialapplications			Schematic	References
	λads (W/m K)	has (W/m2 K)	δ ( m )	Bed permeability	Poresocclusion	Outgassing	Mechanicalresistance	Use in complexgeometries	AHEx manufacture	Productioncosts
Loosegrains	0.10–0.20	70 -120	1 × 10−3 to 1.6 × 10−3	Fair	Not critical	Minorproblem	Good	Unrestricted	Simple	Low		Wang et al., 30 Liu and Leong, 34 Schawe, 98 De Boer et al. 127
Consolidatedbeds	4–17	3000	2 × 10−3 to 10 × 10−3	Poor	Critical	Major problem	Good	Limited	–	–		Ge et al., 128 Miyazaki et al. 129
Binder-basedcoatings	0.36	3000	1 × 10−4 to 8 × 10−4	Good	Critical	Majorproblem	Poor	Unrestricted	Normal	Average		Ge et al., 128 Chang et al., 130 Liu et al. 131
Directlysynthesizedcoatings	27	1000	1 × 10-5 to 5 × 10−5	Good	Not critical	Minorproblem	Good	Unrestricted	Complex	High		Ge et al., 128 Wang et al. 132

where A_fluid denotes heat exchanger area on the fluid side, A_ads represents heat exchanger area on the adsorbent side, and h_fluid is the convective heat transfer coefficient on the fluid side. Then, equation (16 16 ) analyses the perceived value of the physical components of the heating device, as well as any heat transfer resistances that might occur.

The λ_ads values for the beds comprised of loose grains/pellets or binder-based coatings, in the tenths of W/m K have been reported, as shown in Table 1. For example, for the equivalent powdered bed, the λ_ads = 0.11 W/m K and AQSOA binder-based coating λ_ads = 0.36 W/m K ¹²⁶ ; for zeolites, zeo-types, and silica gel, λ_ads in the range 0.10–0.20 W/m K.^26,32,120 Restuccia et al. ²⁶ identified a binder-based coating with λ_ads = 0.30 W/m K. λ_ads values for condensed beds and specifically synthesized coatings were nearly two orders of magnitude higher than for binder-based coatings and loose grains/pellets. For loose grains, the values for convective heat transfer coefficients (h_ads) are reported in the range of 70–120 W/m K, ¹³³ but the most commonly used values are 10–50 W/m K. ¹³³ For the other configurations, the convective heat transfer coefficients are greater than 1000 W/m K, such as, for directly synthesized SAPO-34 coatings on aluminum fibers, binder-based coating of silica gel, and consolidated 13X zeolite, the h_ads are >1000 W/m K ¹²⁵ for former, and up to 3000 W/m K^125,134 for the later ones, respectively. Such findings are helpful for improved interaction among the AHEx metal and adsorbent surface while consolidated beds or coatings are used rather than loose grains. In terms of stability, direct synthesis’s loose grains coatings and configuration are typically not a major concern. According to Freni et al., ¹²⁵ direct zeolite crystallization produces enhanced coating stability. The reduced mechanical resistance ¹³⁵ possible compression of pores due to the binder, and the hazard of volatile compound outgassing from natural binders (which impacts pressure and can result in total failure) of binder-based coatings are disadvantages that must still be addressed to obtain sustainable products. ¹²⁵ There can be a negative effect of large quantities of additives or binders on the performance of AHP because they can cause pore occlusion, which further leads to the reduction in the adsorption capacity. ¹²⁵ Contrastingly, in the binder-bed coating, a typically thicker layer is attained, which restrain the mass transfer, and at the interface in coating and the HEX, thermal resistance is exhibited, decreasing the efficiency of heat transfer. Nonetheless, the attained performance for the binder-based technique is indeed very satisfactory, as evidenced by comparative research published in some of the scientific publications,^136,137 wherein the authors performed corresponding experimental studies on both the loose and coated grain configurations, using the identical heat exchanger equipment.

Significant pressure reductions can result in grain beds based on the size of particles. However, the problem is usually not as severe as heat transfer constraints (low λ_ads and h_ads).^125,138 Because of the shortage of information in the literature (Table 1) shows the bed permeability qualitative comparisons. Nevertheless, for the adsorbent beds’ permeability, the favored values are more than 10–12 m^2,123 but the estimates stated in the research are in the range of 10⁻¹⁴ to 10⁻⁸m ² for the beds employing methanol, water, or ammonia as adsorbates. ¹³⁹ The loose grains replacement by directly synthesized coatings allows for an increase in λ_ads and h_ads by 1–2 orders of magnitude and a considerable reduction by a factor of around 100 in δ.

Conversely, it results in a reduced m_ads = m_metal ratio, which reduces COP. ¹²⁵ To make the materials marketable, the industrialization of product features is of utmost importance, and to enable cheaper production, the loose grains beds are inarguably one of the basic configurations. The heat exchanger consists of adsorbent particles wrapped and enclosed with a grid. ¹⁴⁰ However, the adsorbent structure in consolidated layers is limited to basic geometries such as cylindrical and planar, limiting the application in complex and actual HEx. ¹²⁵ Furthermore, directly synthesized coatings may necessitate costly and time-consuming production practices. For example, in SAPOs, the necessary conditions for autoclaves are 200°C and 20 bar.

Consequently, for industrialization, the production of simplified and less expensive preparation procedures is favorable. ¹²⁵ For heat exchanger production complexity and expenses, binder-based coatings fall among directly synthesized coatings and loose grains because they can be manufactured in mild reaction conditions in serial production lines and therefore are simple to scale up and incorporate. ¹²⁵ It was presented by Schicktanz et al. ¹⁴⁰ that dip coating can be employed for the formulation of binder-based coatings, which involves the metal substrate immersion in an organic binder (such as resins) mixed active powder liquid solution or an inorganic binder (such as aluminum hydroxide clays). For the removal of surplus solvent, it is thermally treated. In this way, by adjusting the dipping velocity and liquid solution’s viscosity, the coating thickness can be varied from 1 × 10⁻⁴ to 10 × 10⁻⁴ m. For the consolidated beds, the reduced bed permeability is a significant disadvantage. ¹⁴⁰ It has been observed through current findings that research on configuration for AHPs appears to be mainly concentrated on AC/ammonia working pairs.

Similarly, a parametric study was presented by Kowsari et al. ¹⁴¹ in which using the numerical model, heat exchanger (HEx) was employed as an adsorbent bed, and validation was performed with an experimental setup. Using variable pitches and fin heights, the trapezoidal and rectangular bed geometries were investigated, and then a comparison was made based on metal mass, COPc, VSCP, SCP, and adsorbent mass. While contrasted to a comparable arrangement for the trapezoidal geometry, the rectangular geometry demonstrated impressive SCP.

Earlier studies have shown that higher metal mass results in reduced COP_c and that a strong adsorbent thickness results in a low SCP. Consequently, a dynamic model was presented by Graf et al. ¹⁴² that was experimentally optimized to estimate the COP and SCP of adsorption heat pumps. On a demonstrative adsorber component, gravimetric large temperature jump (G-LTJ) experiments were carried out for the calibration of the adsorber model, which is being used to predict COP and SCP of AHP. The evaluation of the model was made for a minor adsorber component, resulting in a faster analysis of operating and design parameters comprising operating temperatures, fin geometry, and cycle times. San et al. ¹⁴³ and Frazzica et al. ⁷⁷ demonstrated the AHP systems testing, and design based on earlier single. Such methodologies are strictly experimental and offer reliable device features for a provided experimental setting. Conversely, such experimental methods are restricted to the applied configuration, making a parametric study of the whole structure challenging because the whole setup will have to be demolished and rebuilt to adjust specific parameters.

According to the reported literature, it has been found that the binder-based coatings appear to provide reasonable exchange among performance drivers such as h_ads, δ, λ_ads, bed permeability including manufacturing characteristics, and enhancements stability can increase their market value. This configuration has produced a slew of patent literature. Sauer et al. ¹⁴⁴ reported the development of coatings that do not expel gases over the required 15-year period of AHPs and, are constituted of an inorganic colloidal binder such as colloidal aluminum oxides or hydroxides and colloidal silicon oxides for binding the adsorbent particles and thermally conductive inorganic fibers (such as carbon nanotubes, carbon fibers, glass fibers) to provide mechanical stability and elasticity. Nevertheless, experimental work on loose grain beds seems to be that when particles with diameters below 5 × 10⁻⁴ m and more than 1000 m ² /m³ area/volume heat exchangers are used, this configuration can produce adequate efficiency. ¹⁴⁰ The production of coated AHExs that allow for the scaling-up of coating procedures and compact designs continue to be well-known R&D’s main concerns in the AHP field. ¹¹

Adsorbent heat exchanger (AHEx) geometries

The primary purpose has always been to attain relatively portable and lightweight systems by decreasing the weight of the adsorbers, that are the most important determinant from the perspective of dynamic optimization. ¹¹ Adsorbent optimization entails determining the optimal balance between adsorbent material and HEx. Consequently, it is commonly known as the adsorbent HEX (Ad-HEX) optimization issue. ¹⁴⁵ Hybrid systems, operation controlling, bed improvements, and adsorbents, including ADCs, are increasingly the topic of investigation. ¹⁴⁶ Different heat exchangers in conjunction with different adsorbent placement methods result in various bedforms, such as consolidated bed, coated bed, and granular bed. ¹⁴⁶

AHP adsorbent bed geometries are classified into four types: extended surface (including fiber plate and finned plate geometries), tubular (e.g. hairpin, spiral), plate-type (e.g. lamella heat exchangers) both with as well as without fins (annular or longitudinal). The geometrical classification is premised on the broad categorization of heat exchangers based on construction elements given by Shah et al. ¹⁴⁷ ; however, finned tubes are incorporated in a specific area of tubular with fins. Figure 10 depicts the literature research on AHEx geometries and systematically studied pairings, where only works with experimental domains or theoretical and experimental domains were included in computing the percentages presented.

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Figure 10.

Adsorption heat exchanger geometries studied for AHPs (tubular with and without fins), extended surface (e.g. finned plate and fiber plate), plate-type (e.g. lamella heat exchangers), and percentage of works that adopted each geometry, along with information of the respective investigated adsorbent/adsorbate pairs. Again, only research focusing on experimental or theoretical and experimental work was considered to calculate the percentages.

The total heat transfer coefficient (U), heat exchanger size, and the ratio m_ads/m_metal are essential elements in AHEx performance ¹³⁶ (Table 2). The most often used AHEx geometries for adsorbent/water pairings are extended surface heat exchangers and tubular with fins, as shown in Figure 10. Finned tubes have been reported to have heat transfer area per total volume of heat exchanger (or surface area density) values of up to 3300 m ² /m³, whereas finned plate heat exchangers (extended surface type) can potentially reach ca – 5900 m ² /m³, ¹⁴⁷ enabling further efficient configurations. Table 2 depicts average readings of U, m_ads/V_AHEx (an indicator of compatibility), and m_ads/m_metal for the two designs employing loose grains or coating structures: finned tubes/loose grains, ⁹⁴ finned tubes/coatings, ¹²² extended surface/loose grains, ¹³⁶ or extended surface/coatings. ¹⁴⁸ Employing coated finned tubes rather than loose grains raised U by about 4.5 times, nearing 106 W/m²K, resulting in higher h_ads and λ_ads, and lowered δ (Table 1)).

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Table 2.

Average values of U, m_ads/V_AHEx, and m_ads/m_metal for finned tubes/loose grains, ⁹⁴ finned tubes/coatings, ¹²² extended surface/loose grains, ¹³⁶ or extended surface/coatings. ¹⁴⁸

AHEx geometry	Extended surface		Tabular with fins
	Coatings	Loose grains	Coatings	Loose grains
U (W m2 K)	N/A	N/A	106	23
m ads/VAHEx (kg/m3)	167	358	149	310
m ads/mmetal (kg/kg)	0.39	0.63	0.30	0.67

Dawoud et al. ¹⁴⁸ revealed that the SHPs for loose pellets in the finned tube AHEx were smaller than a fourth of the tested utilizing coatings. Thus, when employing loose grains rather than coatings, a more significant amount of adsorbent can be incorporated per unit volume of heat exchanger (m_ads/V_AHEx) regardless of shape (Table 2). The ratio m_ads/V_AHEx for coatings in extended surface, and finned tube AHExs is in the limit of 40–390 kg/m³, ¹⁴⁸ and 100–200 kg/m^{3 149} (the corresponding typical values are 167 and 149 kg/m³). Generally, extended surface heat exchangers have had the greatest mads/VAHEx values; for loose grains, the value is (567 kg/m³) ¹⁵⁰ for finned tubes the value is 315 kg/m³⁹⁸ for coatings, it is 388 kg/m³, ¹⁵¹ and the value for loose grains and coatings is 203 kg/m³, ¹⁴⁹ respectively.

The findings imply that by employing an expanded surface geometry, relatively efficient AHExs may be developed. Consequently, a reasonable balance among the different variables is required to build efficient, small, lightweight, and large surface area AHExs, a research emphasis in the domain of AHP components. ¹¹

Fin-tube heat exchanger

Fin-tube heat exchangers are straightforward designs centered on straight tubes with perpendicular fins. A finned tube has the potential to be utilized as a single straight line linked in parallel, curved into a coil with straight finned components, or formed into a u-tube with fins (Figure 11(a)). Fins can be rectangular or circular. Fin-tube HEX may be converted into an adsorption bed by covering the area between the fins using loose adsorbent granules and mesh enclosing to hold the adsorbent granules in place. It is also feasible to wrap the top of a heat exchanger with a coat composed of adsorbent granules and a binder. Poyelle et al. ¹⁵² used zeolite and fit-tube HEX to evaluate grained and cemented beds. The chiller was indeed a two-bed adsorption chiller, including mass and heat recovery. It was discovered that SCC might rise threefold to 97 W/kg and that mass transfer and heat transfer resistances in bed seemed to impact both COP and SCC substantially. Restuccia et al. ¹⁵³ reported analogous findings during chiller studies using the material SWS-1L as adsorbent. Fins used in this kind of HEX may have varying geometries.

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Figure 11.

Schematic representation of a conventional adsorption heat pump, ¹²⁹ (a) fin-tube heat exchanger, (b) plate fin-tube heat exchanger, (c) finned flat-tube heat exchanger, and (d) modular adsorbent bed.

A thorough examination of the effects of typical geometric characteristics on chiller efficiency was carried out. ¹⁵⁴ Raising fin length necessitates more excellent heat for regeneration, yet it has been shown that the COP value grows simultaneously. Thus, the increased cooling power outnumbers the increased heating needs. According to the findings, utilizing circular fins to improve SCC value is advised, mainly when a low-cost heat source exists. A COP of 0.54 and 73 W/kg_ads of SCC was attained in experimental testing ¹⁴³ of a bed with HEX packed with adsorbent particles wrapped with mesh. These findings can be pretty encouraging, especially given the ease of bed assembly.

In 2015, Sharafian et al. ¹⁵⁵ investigated an identical bed structure specialized to an automobile A/C system. Rectangular plates have been used instead of convectional ribs on a u-tube. This was discovered that when employing loose grains, the fin interval should be more than the adsorbent particle size, while the overall HEX length stays the same. Li et al. ¹³⁴ investigated silica gel in laminated bed designs. Hydroxyethylcellulose (HEC) was chosen among various binders, including bentonite, epoxy resin, and polyvinyl alcohol. Combining binder and powdered silica gel allowed for forming a 0.7 mm width of solid layer on the heat exchanger area while not affecting adsorption capacities. Caglar ¹⁵⁶ exhibited in a numerical simulation, including its effects of fin design specifications on chiller with thermal wave cycle performance, found that increasing fin width will not enhance temperature distribution of adsorbent. The fin spacing (f_s) and fin height (f_h) analyses revealed that an increase in the fin length has a detrimental influence on heat transfer applications in the adsorption bed. Decreasing fin distance has been advantageous. However, it also reduces adsorbent weight, which reduces cooling capacity.