Regenerative adsorption process and multi-reactor regenerative adsorption chiller

Abstract

A regenerative adsorption process and a multi-reactor regenerative adsorption chiller assembly including a condenser adapted to receive a coolant from a source; an evaporator connected to the condenser to provide a refrigerant circuit; a plurality of reactors, each being able to operate in adsorption and desorption modes and having a coolant inlet to directly or indirectly receive coolant when operating in adsorption mode before, after or simultaneous with the condenser, and a waste heat inlet for directly or indirectly receiving waste heat from a waste heat source when operating in desorption mode; and control means for controlling said plurality of reactors such that each reactor alternately operates in adsorption and desorption modes for substantially identical time intervals, and such that each reactor has an equal chance of being the first reactor to receive the coolant when operating in adsorption mode, and the waste heat from the waste heat source when operating in desorption mode.

Description

FIELD OF THE INVENTION

[0001] This invention relates to a regenerative adsorption process and an adsorption chiller designed for utilising waste heat typically having a temperature of below about 150° C. for useful cooling.

BACKGROUND OF THE INVENTION

[0002] Two-reactor adsorption chillers have already been successfully commercialised in Japan [1,2]. By making use of a silica gel-water working pair, such chillers have managed to economically harness the potential of low-grade waste heat for useful cooling before it is discharged into the environment. Insofar as adsorption chillers are concerned, some methods have been devised to improve the conversion efficiency of the potential waste heat to useful cooling. For example, schemes have been proposed where such waste heat is used serially in a string of adsorption chillers before it is finally discharged. As another example, a scheme has previously been proposed where the desorption temperature is significantly reduced by means of multi-stage thermal compression of the refrigerant vapour [3]. This enables waste heat to be further utilized before it is finally purged to the environment. From the trend of development of the prior art, it would be desirable to further improve the conversion efficiency so that maximum cooling capacity can be derived from a given hardware investment, waste heat and coolant flow rate.

[0003] Of equal importance is the need for a stable chilled water outlet temperature. Based on experimental measurement on a commercially available 10 kW two-reactor adsorption chiller, under a typical dynamic steady state operation, the chilled water outlet temperature generally fluctuates by ±1.5° C. [4]. While such fluctuation may be acceptable for sensible cooling and rough process cooling requirements, it begins to pose a problem in dehumidification, and other stringent cooling applications. In the latter field of usage, vapour compression or absorption cooling devices have been employed downstream to attenuate the temperature oscillation. It would therefore be desirable to provide a smoother chilled water outlet temperature so that downstream temperature smoothening devices could be downsized or even eliminated.

[0004] Sato et al. [5-6] have proposed a multi-reactor strategy involving cooling the adsorber with refrigerant emanating from one or more evaporators. It may be desirable and more practical to have the evaporator devoted to cooling the chilled water, with the evaporated refrigerant being superheated at the adsorbers. Master-and-slave configuration is commonly found in these references for the arrangement of the reactors. Such master-and-slave configurations for the string of reactors may represent an under-utilization of downstream reactors. It would therefore be attractive to eliminate such rigid configuration.

[0005] Many other designs [7-14] employ re-circulating fluid to boost the chiller's coefficient of performance. These arrangements are designed for use with a high temperature heat source, which is usually economically valuable; they are done at the expense of a lower firing temperature for the desorber and a higher cooling temperature for the adsorber. In the case of low temperature (typically 150° C. or below) waste heat application, such a strategy may not be feasible. In this case, the objective would then be to maximise the cooling throughput of the chiller.

[0006] The present invention advantageously improves the recovery efficiency of waste heat to useful cooling. Recognizing that cooling water for the adsorber and condenser is a scarce resource, the invention aspires to achieve maximum cooling capacity for a given flow rate of waste heat and cooling stream. This advantageously also ensures maximum conversion efficiency of waste heat to useful cooling and reduces piping material for a given cooling capacity.

[0007] Advantageously, the invention also makes it possible to downsize or even eliminate the need for downstream temperature smoothening devices by providing a more stable chilled water outlet temperature.

[0008] Further, the invention advantageously reduces the risk of ice formation by providing for a sequential start-up of the reactor or reactors when the chiller is activated.

SUMMARY OF THE INVENTION

[0009] According to one aspect of the invention there is provided a regenerative adsorption process for application in an adsorption assembly comprising a condenser, an evaporator and a plurality of reactors each alternately operating in adsorption and desorption modes, said process comprising:

[0010] passing a coolant through the condenser;

[0011] passing the coolant emanating from the condenser through reactors operating in adsorption mode; and

[0012] passing waste heat from a waste heat source through reactors operating in desorption mode; wherein said plurality of reactors are scheduled such that each reactor alternately operates in adsorption and desorption modes for substantially identical time intervals, and such that each reactor has an equal chance of being the first reactor to receive the coolant emanating from the condenser when operating in adsorption mode, and the waste heat from the waste heat source when operating in desorption mode.

[0013] According to another aspect of the invention there is provided a multi-reactor regenerative adsorption chiller assembly comprising:

[0014] a condenser adapted to receive a coolant from a source;

[0015] an evaporator connected to said condenser to provide a refrigerant circuit;

[0016] a plurality of reactors, each being able to operate in adsorption and desorption modes and having a coolant inlet to directly or indirectly receive coolant emitted from said condenser when operating in adsorption mode, and a waste heat inlet for directly or indirectly receiving waste heat from a waste heat source when operating in desorption mode; and control means for controlling said plurality of reactors such that each reactor alternately operates in adsorption and desorption modes for substantially identical time intervals, and such that each reactor has an equal chance of being the first reactor to receive the coolant emanating from the condenser when operating in adsorption mode, and the waste heat from the waste heat source when operating in desorption mode.

[0017] The reactors operating in adsorption mode may be arranged in series and/or in parallel depending upon the particular operation, and also depending on the total number of reactors being used. However, the reactors operating in desorption mode are arranged in series.

[0018] In a preferred embodiment, the plurality of reactors comprises an even number of reactors, wherein at substantially any instant during the process, half of the plurality of reactors operate in adsorption mode and the other half of the plurality of reactors operate in desorption mode. Most preferably, the plurality of reactors comprises at least four reactors.

[0019] The flow rate of coolant and waste heat through the plurality of reactors operating in adsorption and desorption modes respectively maybe any suitable flow rate depending on the particular size of chiller assembly and design of heat exchangers. Preferably, the coolant is flowed through the reactors operating in adsorption mode at a suitable flow rate. A suitable flow rate is preferably any flow rate that result in a transition or turbulent flow regime in the channel of a heat exchanger, be it the chilled water, coolant and/or heat source. When the plurality of reactors comprises four or more reactors, the flow rate of coolant through reactors operating in adsorption mode is preferably at the suitable flow rate, irrespective of whether the reactors operating in adsorption mode are arranged in series or in parallel. Sizing and flow rates can be determined by those who are skilled in the art.

[0020] The waste heat is preferably flowed through the reactors operating in desorption mode at a suitable flow rate. More preferably, where the plurality of reactors comprises four or more reactors, the flow rate of waste heat through reactors operating in desorption mode is also sized at the suitable flow rate.

[0021] Similarly, the flow rate of coolant through the condenser may be determined for a specific application of the invention. It will be recognised that the flow rate of coolant through the reactors operating in adsorption mode will be somewhat dependent on the flow rate of coolant through the condenser. In a preferred embodiment, the flow rate of coolant through the condenser is at a suitable flow rate as described above.

[0022] As discussed above, the adsorption assembly comprises a condenser, an evaporator and a plurality of reactors, each of which alternatively operates in adsorption and desorption modes. In a preferred embodiment, the plurality of reactors are arranged in series such that, in use, reactors operating in adsorption mode constitute a first sub-series of reactors connected in series and/or in parallel to receive coolant from the condenser and reactors operating in desorption mode constitute a second sub-series of reactors connected in series to receive waste heat from the waste heat source.

[0023] Each reactor is preferably composed of heat exchanging material and contains adsorbents. The adsorbent could be any material, such as silica gel, that is able to adsorb, either by physisorption and/or chemisorption refrigerant, for example water vapour, ammonia, or methanol at a typical cooling tower temperature and desorb refrigerant at moderately low temperature (typically 150° C. or below). The coolant from a cooling tower is first passed through the condenser and subsequently to each of the reactors operating in adsorption mode either in series or in parallel. The waste heat source is passed serially from one reactor operating in desorption mode to another reactor in the same mode. After passing through the last reactor operating in desorption mode, the waste heat is purged from the system.

[0024] The reactors are scheduled such that each reactor alternately operates in adsorption and desorption mode for substantially the same time interval, and that each reactor has equal chance of being the first reactor to either receive the coolant emanating from the condenser or the waste heat. Such a schedule ensures that maximum smoothening of chilled water outlet temperature is achieved. This arrangement also facilitates maximum extraction of energy from the waste heat to maximise cooling capacity. Cooling the condenser first and then the reactors operating in adsorption mode ensures that minimum coolant flow rate is used.

BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawing which is incorporated into and constitutes apart of the description of the invention, illustrates an embodiment of the invention and serves to explain the principles of the invention. It is to be understood, however, that the drawing is designed for purposes of illustration only, and not as a definition of the limits of the invention.

[0026] FIG. 1 is a schematic of one embodiment of an adsorption chiller constructed according to the present invention showing the operation of the multi-reactor regenerative strategy. Fluid flow between reactors has been depicted as top-down. 1 refers to waste heat stream inlet, 2 refers to coolant inlet, 2a refers to coolant inlet to the reactor, 3 refers to waste heat stream outlet, 4 refers to coolant outlet, and 5 refers to the outflow of excess coolant. The bold lines depict the refrigerant circuit, while the thin lines depict the coolant and heat source circuit. indicates either a manual or elect

[0027] FIG. 2 illustrates the relation of recovery efficiency, η, as a function of dimensionless cycle time, ω for two-, four-, and six-bed adsorption chillers.

[0028] FIG. 3 illustrates the dimensionless outlet temperature, {overscore (T)} profiles for the chilled water, condenser coolant, adsorber coolant, and waste heat stream for two-, four-, and six-bed adsorption chillers under dynamic-steady-state condition. Due to the choice of non-dimensionalising the temperature, the chilled water outlet dimensionless temperature turns out to be negative, a direct reflection that the system is operating as a chiller.

DESCRIPTION OF THE EMBODIMENTS OF THE INVENTION

[0029] In detail now and referring to the drawings, FIG. 1 illustrates one embodiment of the multi-reactor regenerative adsorption chiller assembly of the present invention. The N-reactor regenerative adsorption chiller consists of N reactors, where N is even to achieve optimal chilled water outlet temperature smoothening, a condenser and an evaporator.

[0030] In general, N/2 reactors operate under adsorption mode, while the other N/2 reactors operate under desorption mode at any instant of use of the adsorption chiller. Coolant from a cooling source enters the condenser at location 2 and travels through the condenser. Subsequently, the coolant enters one or more reactors operating under adsorption mode through valve(s) 2a, depending on whether the reactors are arranged in parallel or in series. A rated amount of coolant flows through the reactors operating under adsorption mode, and is eventually purged from port(s) 4. Excess coolant from the condenser is removed from port 5.

[0031] Heat source is introduced at any one port 1 and flows serially through all the N/2 reactors operating under desorption mode and is purged from a port 3. The reactors are scheduled such that each reactor alternately operates in adsorption and desorption mode for the same half-cycle time interval, and that each reactor has equal chance of being the first reactor to either receive the coolant emanating from the condenser through port 2a or the waste heat through valve 1. The energy schedules may be best understood by referring to the following tables:

TABLE 1
The following table illustrates the general schedule for a series-cooled
4-reactor system. Energy utilization schedule for a 4-reactor chiller
Reactor	sw	ads (2)	ads (1)	sw	des (2)	des (1)
1
Reactor	des (1)	sw	ads (2)	ads (1)	sw	des (2)
2
Reactor	sw	des (2)	des (1)	sw	ads (2)	ads (1)
3
Reactor	ads (1)	sw	des (2)	des (1)	sw	ads (2)
4
Legend:
ads: reactor operating in adsorption mode (adsorber)
des: reactor operating in desorption mode (desorber)
sw: switching from adsorber to desorber, and receiving heating stream from des(1) or switching from desorber to adsorber, and receiving cooling stream from ads(1)
(1): this refers to the situation when the reactor receives either cooling stream from the condenser or heating stream directly from the heat source.
(2): this refers to the situation when the reactor receives either cooling stream from ads(1) or heating stream from des(1).
Note:
The width of each box is an indication of the relative time duration over one cycle.

[0032] The responding schedule for a parallel-cooled, 4-reactor system can be inferred from the table.

TABLE 2
The following table illustrates the general schedule for a series- or and parallel-cooled 6-
reactor system.
Two possible energy utilization schedules for a six-reactor chiller
Reactor	sw	ads(3)	ads(2)	ads(1)	sw	des(3)	des(2)	des(1)
1
Reactor	des(1)	sw	ads(3)	ads(2)	ads(1)	sw	des(3)	des(2)
2
Reactor	des(2)	des(1)	sw	ads(3)	ads(2)	ads(1)	sw	des(3)
3
Reactor	sw	des(3)	des(2)	des(1)	sw	ads(3)	ads(2)	ads(1)
4
Reactor	ads(1)	sw	des(3)	des(2)	des(1)	sw	ads(3)	ads(2)
5
Reactor	ads(2)	ads(1)	sw	des(3)	des(2)	des(1)	sw	ads(3)
6
Legend:
ads: reactor operating in adsorption mode (adsorber)
des: reactor operating in desorption mode (desorber)
sw: switching from adsorber to desorber, and receiving heating stream from des(2). Or switching from desorber to adsorber, and receiving coolant from the condenser if it is a parallel cooling scheme, or receiving coolant from the ads(2) if it is a series cooling scheme.
(1): this refers to the situation when the reactor receives either cooling stream from the condenser or heating stream directly from the heat source.
(2): this refers to the situation when the reactor receives either cooling stream from ads(1) or heating stream from des(1).
(3): this refers to the situation when the reactor receives heating stream from des(2); and if it is a parallel cooling scheme, the reactor receives cooling stream directly from the condenser, whereas if it is a series cooling scheme, the reactor receives cooling stream from ads(2).
Note:
The width of each box is an indication of the relative time duration over one cycle.

[0033] As discussed above, parallel cooling of one or more of the reactors operating under adsorption mode may be possible. This will generally depend on the coolant flow rate through the condenser. Typically, parallel cooling of one or more of the reactors operating under adsorption mode is more practical for a system with six or more reactors.

TABLE 3
Bed 1	sw	ads (N/2)	ads(N/2-1)	1	sw	des (N/2)	des(N/2-1)	2	des(2)	des(1)
Bed 2	des(1)	sw	ads	3	ads(1)	sw	des (N/2)	4	des(3)	des(2)
5	6	7	8	9	10	11
Bed N/2 + 1	sw	des (N/2)	des(N/2-1)	12	sw	ads (N/2)	ads(N/2-1)	13	ads(2)	ads(1)
Bed N/2 + 2	ads(1)	sw	des (N/2)	14	des(1)	sw	ads (N/2)	15	ads(3)	ads(2)
16	17	18	19	20	21	22
Bed N-1	ads(N/2-2)	ads(N/2-3)	23	des(N/2-2)	des(N/2-3)	24	sw	ads (N/s)	ads(N/2-1)
Bed N	ads(N/2-1)	ads(N/2-2)	25	des(N/2-1)	des(N/2-2)	26	des(1)	sw	ads (N/2)
Legend:
ads: reactor operating in adsorption mode (adsorber)
des: reactor operating in desorption mode (desorber)
sw: switching from adsorber to desorber, and receiving heating stream from des(N/2-1). Or switching from desorber to adsorber, and receiving coolant from the condenser if it is a special parallel cooling scheme, or receiving coolant from the ads(N/2-1)
# if it is a series cooling scheme.
(1): this refers to the situation when the reactor receives either cooling stream from the condenser or heating stream directly from the heat source.
(I): where I < I < N/2, this refers to the situation when the reactor receives either cooling stream from ads(1-1) or heating stream from des(1-1).
(N/2): this refers to the situation when the reactor receives heating stream from des(N/2-1); and if it is a special parallel cooling scheme, the reactor receives cooling stream directly from the condenser, whereas if it is a series cooling scheme,
# the reactor receives cooling stream from ads(N/2-1).
Other than the special parallel cooling scheme mentioned above, a general parallel cooling scheme exists, where the cooling stream from the condenser separately services ads(1) to ads(J), where 1 < J < N/2, and ads(J + 1) to ads(K) where
# J < K ≦ N/2, and so on.
Note:
The width of each box is an indication of the relative time duration over one cycle.

[0034] In general, the schedule for an N-reactor chiller, where N is even, is shown in Table 1. In principle N could be odd, but this would not lead to optimal temperature smoothening of the outlet chilled water. The N-reactor system is advantageously devised to start-up sequentially. Specifically, during start-up, reactors operating under adsorption mode and reactors operating under desorption mode are preferably activated one at a time so that a sudden depression of the evaporator temperature is prevented thus reducing the risk of ice formation in the evaporator.

[0035] The following technical analysis is provided only to demonstrate the efficacy of the invention. This analysis has made use of certain specific technical specifications so as to quantatively demonstrate the advantages of the invention. It is emphasised that other similar analyses based on different technical specifications and even different formalisms are possible. Hence, the associated specifications of the present analysis should not, in any way, be construed as restrictive on the present invention.

[0036] Specifics of the analysis:

[0037] linear driving force (LDF) kinetic equation, equation (1),

[0038] silicagel-water binary system, equation (2),

[0039] lumped-parameter treatment for the reactors, evaporator and condenser,

[0040] specifications as delineated in Table 4.

[0041] The performance prediction of the proposed multi-bed regenerative strategy is based on an extension of the verified design code for the commercial two-bed chiller [15-16]. The structure of the original formalism is essentially unchanged, except that the energy balances for the condenser and evaporator have to be augmented to account for interaction with more than one bed. Heat and mass balance equations must similarly be augmented; they must also handle the additional bed transients. The rate of adsorption or desorption is governed by the linear driving force kinetic equation: 1$\begin{array}{cc}\frac{dq}{d\tau }=\frac{15t_{\mathrm{cycle}}{D}_{\mathrm{s0}}\exp \left[-E_a/\left(\mathrm{RT}\right)\right]}{R_p^2}\left[q^{*}\left(P,T\right)-q\right]& \left(1\right)\end{array}$

[0042] The coefficients of which were determined by Chihara and Suzuki [17] and q* is given by the following empirical isotherm equation [19] which is based on the manufacturer's proprietary data [19]: 2$\begin{array}{cc}{q}^{*}={A\left(T_{\mathrm{sg}}\right)\left[\frac{P_{\mathrm{sat}}\left(T_{\mathrm{ref}}\right)}{P_{\mathrm{sat}}\left(T_{\mathrm{sg}}\right)}\right]}^{B\left(T_{\mathrm{sg}}\right)}& \left(2\right)\end{array}$

[0043] The energy balance for bed I, ignoring heat losses, during its interaction with the evaporator can be written as 3$\begin{array}{cc}\left(1+{\alpha }_{\mathrm{Hex}}\right)\frac{d{\stackrel{\_}{T}}_{\mathrm{bed},I}}{d\tau }+q_{\mathrm{bed},I}\frac{d{\stackrel{\_}{h}}_{\mathrm{ads}}}{d\tau }=\frac{d{q}_{\mathrm{bed},I}}{d\tau }\left\{{\delta }_I\left[{\stackrel{\_}{h}}_g\left(T_{\mathrm{evap}}\right)-{\stackrel{\_}{h}}_{\mathrm{ads}}\left(P_{\mathrm{evap}},T_{\mathrm{bed},I}\right)\right]-\left(1-{\delta }_I\right){\stackrel{\_}{\Delta H}}_{\mathrm{ads}}\right\}-{\mathrm{NTU}}_{\mathrm{cooling}}\omega c_{c,i}\sum _{i=1}^N\left({\stackrel{\_}{T}}_{\mathrm{bed},I}-{\stackrel{\_}{T}}_i\right).& \text{(3a)}\end{array}$

[0044] The energy balance for the coolant can be expressed as 4$\begin{array}{cc}{\alpha }_{\mathrm{bed\_tube},i}\frac{d{\stackrel{\_}{T}}_i}{d\tau }=\omega \left[{\stackrel{\_}{h}}_f\left(T_{i-1}\right)-{\stackrel{\_}{h}}_f\left(T_i\right)+{\mathrm{NTU}}_{\mathrm{cooling}}{c}_{c,i}\left({\stackrel{\_}{T}}_{\mathrm{bed},I}-{\stackrel{\_}{T}}_i\right)\right]\mathrm{for}i=1\mathrm{to}N.{\stackrel{\_}{T}}_i\left(0\right)={\stackrel{\_}{T}}_{\mathrm{bedi}}\left(0\right)=0.{\stackrel{\_}{T}}_i\left(\tau \right)={\stackrel{\_}{T}}_{N_2}\left(\tau \right){❘}_{\mathrm{cond}}& \text{(3b)}\end{array}$

[0045] when bed I is being cooled directly by the coolant from the condenser, and {overscore (T)}1(τ)={overscore (T)}N(τ)|bed, I−1 when it is being cooled by the coolant from bed I−1. qbed,I(0)=q*(Pevap(0),Tbed,I(0)). It has been assumed that the relation {overscore (h)}ads (P, T)={overscore (h)}g(P, T)−{overscore (ΔH)}ads holds at all time, so that the transient isosteric heat of adsorption is insensitive to the instantaneous adsorbate concentration. The isosteric heat of adsorption has been obtained from the work of Sakoda and Suzuki [20].

[0046] When the bed J is interacting with the condenser, its energy balance can be written as 5$\begin{array}{cc}\left(1+{\alpha }_{\mathrm{Hex}}\right)\frac{d{\stackrel{\_}{T}}_{\mathrm{bed},J}}{d\tau }+q_{\mathrm{bed},I}\frac{d{\stackrel{\_}{h}}_{\mathrm{ads}}}{d\tau }={\theta }_J\frac{d{q}_{\mathrm{bed},J}}{d\tau }{\stackrel{\_}{\Delta H}}_{\mathrm{ads}}-{\mathrm{NTU}}_{\mathrm{heating}}\omega {\stackrel{\_}{\stackrel{.}{m}}}_{\mathrm{heating}}{c}_{h,i}\sum _{i=1}^N\left({\stackrel{\_}{T}}_{\mathrm{bed},J}-{\stackrel{\_}{T}}_i\right).& \text{(4a)}\end{array}$

[0047] The energy balance for the coolant can be expressed as 6$\begin{array}{cc}{\alpha }_{\mathrm{bed\_tube},i}\frac{d{\stackrel{\_}{T}}_i}{d\tau }=\omega {\stackrel{\_}{\stackrel{.}{m}}}_{\mathrm{heating}}\left[{\stackrel{\_}{h}}_f\left(T_{i-1}\right)-{\stackrel{\_}{h}}_f\left(T_i\right)+{\mathrm{NTU}}_{\mathrm{heating}}{c}_{c,i}\left({\stackrel{\_}{T}}_{\mathrm{bed},J}-{\stackrel{\_}{T}}_i\right)\right]& \text{(4b)}\end{array}$

[0048] for i=1 to N. {overscore (T)}i(0)={overscore (T)}bed,J (0)=1. {overscore (T)}i(τ) when bed J is being heated directly by the waste heat source, and {overscore (T)}1(τ)={overscore (T)}N(τ)|bed,J−1 when it is being regenerated by the heating stream from bed J-1. qbed,J(0)=q*(Pcond(0), Tbed,J(0)). The condenser has been assumed, relative to the beds and evaporator, to be retaining negligible amount of refrigeration. However, since the condenser heat exchanging tube has been designed to be corrugated by the manufacturer, the enhanced surfaces will inevitably retain a thin film of condensate on the surface. This will ensure that the condenser is always maintained at the refrigerant saturated vapour pressure. Consequently, if dqbed,J/dt>0, θJ=0.

[0049] During bed switching, the bed pressure changes in tandem with the bed temperature. Hence, in the current formalism, such operation has been assumed to be isosteric (i.e. dq/dτ=0). This phase of operation could still be described by the above equations, and the pressure prescribed by the isotherm equation.

[0050] The evaporator is, in general, interacting with N/2 beds at any time, its energy balance can be expressed as 7$\begin{array}{cc}\left({\alpha }_{\mathrm{ref}}+{\alpha }_{\mathrm{evap}}\right)\frac{d{\stackrel{\_}{T}}_{\mathrm{evap}}}{d\tau }+{\stackrel{\_}{h}}_f\left(T_{\mathrm{evap}}\right)\frac{d{q}_{\mathrm{ref}}}{d\tau }=-{\stackrel{\_}{h}}_f\left(T_{\mathrm{cond}}\right)\sum _{J=1}^{n/2}{\theta }_J\frac{d{q}_{\mathrm{bed},J}}{d\tau }-{\mathrm{NTU}}_{\mathrm{chilled}}\omega {\stackrel{\_}{\stackrel{.}{m}}}_{\mathrm{chilled}}\sum _{i=1}^{N_1}\left({\stackrel{\_}{T}}_{\mathrm{evap}}-{\stackrel{\_}{T}}_i\right)-\sum _{I=1}^{n/2}\left[{\delta }_I{\stackrel{\_}{h}}_g\left(T_{\mathrm{evap}}\right)+\left(1-{\delta }_I\right){\stackrel{\_}{h}}_g\left(P_{\mathrm{evap},}{T}_{\mathrm{bed},I}\right)\right]\frac{d{q}_{\mathrm{bed},I}}{d\tau }& \text{(5a)}\end{array}$

[0051] The rate of change of liquid refrigerant mass is given by 8$\begin{array}{cc}\frac{d{q}_{\mathrm{ref}}}{d\tau }=-\sum _{k=1}^n{\theta }_k\frac{d{q}_{\mathrm{bed},k}}{d\tau }.& \text{(5b)}\end{array}$

[0052] If bed k is interacting with the evaporator, θk=1, and if it is interacting with the condenser, θk=1 when dqbed,k/dt<0 and θk=0 when dqbed/dt>0.

[0053] The energy balance for the chilled water can be expressed as 9$\begin{array}{cc}{\alpha }_{\mathrm{evap\_tube},i}\frac{d{\stackrel{\_}{T}}_i}{d\tau }=\omega {\stackrel{\_}{\stackrel{.}{m}}}_{\mathrm{chilled}}\left[{\stackrel{\_}{h}}_f\left(T_{i-1}\right)-{\stackrel{\_}{h}}_f\left(T_i\right)+{\mathrm{NTU}}_{\mathrm{chilled}}{c}_{\mathrm{chilled},i}\left({\stackrel{\_}{T}}_{\mathrm{evap}}-{\stackrel{\_}{T}}_i\right)\right]\mathrm{for}i=1\mathrm{to}{N}_1.{\stackrel{\_}{T}}_i\left(0\right)={\stackrel{\_}{T}}_{\mathrm{evap}}\left(0\right)={\stackrel{\_}{T}}_1\left(\tau \right)=\frac{T_{\mathrm{chilled},i}-T_{c,i}}{T_{h,i}-T_{c,i}},\mathrm{and}{q}_{\mathrm{ref}}\left(0\right)=q_{\mathrm{ref}}^{\mathrm{ini}}.& \text{(5c)}\end{array}$

[0054] Finally, the energy balance for the condenser which is interacting with N/2 beds in general and that of its coolant can be respectively expressed as 10$\begin{array}{cc}{\alpha }_{\mathrm{cond}}\frac{d{\stackrel{\_}{T}}_{\mathrm{cond}}}{d\tau }=-\sum _{J=1}^{n/2}{\theta }_J\left[{\stackrel{\_}{h}}_g\left(P_{\mathrm{cond}},T_{\mathrm{bed},J}\right)-{\stackrel{\_}{h}}_f\left(T_{\mathrm{cond}}\right)\right]\frac{d{q}_{\mathrm{bed},J}}{d\tau }-{\mathrm{NTU}}_{\mathrm{cond}}\omega {\stackrel{\_}{\stackrel{.}{m}}}_{\mathrm{cond}}\sum _{i=1}^{N_2}\left({\stackrel{\_}{T}}_{\mathrm{cond}}-{\stackrel{\_}{T}}_1\right),\mathrm{and}& \text{(6a)}\\ {\alpha }_{\mathrm{cond\_tube},i}\frac{d{\stackrel{\_}{T}}_i}{d\tau }=\omega {\stackrel{\_}{\stackrel{.}{m}}}_{\mathrm{cond}}\left[{\stackrel{\_}{h}}_f\left(T_{i-1}\right)-{\stackrel{\_}{h}}_f\left(T_i\right)+{\mathrm{NTU}}_{\mathrm{cond}}{c}_{c,i}\left({\stackrel{\_}{T}}_{\mathrm{cond}}-{\stackrel{\_}{T}}_i\right)\right]\mathrm{for}i=1\mathrm{to}{N}_2.{\stackrel{\_}{T}}_i\left(0\right)={\stackrel{\_}{T}}_{\mathrm{cond}}\left(0\right)={\stackrel{\_}{T}}_1\left(\tau \right)=0.& \text{(6b)}\end{array}$

[0055] It is intuitively clear that, during the dynamic-steady-state operation of an N-bed chiller, where all the beds are operating symmetrically, the optimal phase difference between the beds would be 2ω/N and that N has to be an even number. This would ensure that the condenser and evaporator have minimum temperature fluctuation.

[0056] The above mentioned set of coupled equations is solved by the Adams-Moulton method found in the DWVPAG subroutine of the IMSL Fortran library subroutines. The tolerance has been set to 1IE-8. Once the initial conditions are prescribed, the chiller is allowed to operate from transient to dynamic steady state. On a Pentium 233 MHz, 64 MB personal computer, it takes about 110 min to calculate a six-bed chiller operation.

[0057] The non-dimensional cycle averaged cooling power is defined as 11$\begin{array}{cc}{\stackrel{\_}{Q}}_{evap}=\omega {\stackrel{\_}{\stackrel{.}{m}}}_{chilled}{c}_{chilled,i}{\int }_0^1\left({\stackrel{\_}{T}}_{chilled,i}-{\stackrel{\_}{T}}_{chilled,o}\right)d\tau & \left(7\right)\end{array}$

[0058] As mentioned earlier, since the invention focuses on the utilization of waste heat before it is ultimately purged to the environment, its enthalpy relative to that of the environment can be viewed as being a fixed energy input to a system. Consequently, maximising cooling capacity rather than the conventional coefficient of performance may be more pertinent. Thus, the following conversion efficiency is accordingly defined: 12$\begin{array}{cc}\eta =\frac{{\stackrel{\_}{\stackrel{.}{m}}}_{chilled}{c}_{chilled,i}}{{\stackrel{\_}{\stackrel{.}{m}}}_{heating}{c}_{h,i}}{\int }_0^1\left({\stackrel{\_}{T}}_{chilled,i}-{\stackrel{\_}{T}}_{chilled,o}\right)d\tau .& \left(8\right)\end{array}$

[0059] The environment temperature has been selected to be Tc,i.

[0060] Performance Comparison of Two-, Four-, and Six-Bed Chillers

[0061] In order to effect a fair evaluation, the performances of the four- and six-bed chillers operating at an optimal phase difference are compared against the result of a commercial two-bed chiller.

[0062] The parameters of the commercial two-bed chiller and those of the multi-bed chillers are collated in table 4. It is emphasised that the total mass of adsorbent, refrigerant inventory and heat exchanging material have been held fixed. In this description, there are presented various cases when the adsorbers are cooled by the rated flow rate as delineated in Table 4. This will ensure that heat exchange is undertaken in the transition flow region, so that pumping power is kept to a minimum. One could always pipe all the coolant into the adsorbers. The improved heat exchange will be at the expense of pumping power.

[0063] This comparison is meant solely as an example to demonstrate the virtues of the present invention. In no way should the specific numbers provided for the various parameters be construed as restrictive on the present invention.

TABLE 4
Comparison of two-bed and multi-bed chillers specifications
	6-bed
				Parallel
Parameters	2-bed	4-bed	Series cooling	cooling
Total coolant	2.89		1.37
flowrate (kg/s)
Total adsorber	1.52 (fresh	0.760 (piped	0.507 (piped	1.01 (piped
coolant	stream from	from	from	from
flowrate (kg/s)	cooling tower)	condenser)	condenser)	condenser)
{dot over (m)}heating	1.28	0.64	0.427
{dot over (m)}chilled	0.71
{dot over (m)}cond	1.37
Ucooling	1602.56
Uheating	1724.14
Uchilled	2557.54
Ucond	4115.23
Abed	2.46	1.23	0.820
Aevap	1.91
Acond	3.73
Msg	47.0	23.5	15.7
cp,HexMHex	77719.4 × 103	38859.7 × 103	25906.5 × 103
cp,evapMevap	4805.7 × 103
cp,condMcond	9372.08 × 103
Vbed	1.778 × 10−2	8.89 × 10−3	5.93 × 10−3
Vevap	6.916 × 10−3
Vcond	1.349 × 10−2

[0064] The cost of construction necessarily goes up with the number of beds. But depending on the prevailing economic conditions, the performance improvement of a multi-bed chiller over a two-bed chiller could outweigh the increase in capital investment. Structure wise, there should not be a drastic increase in cost. The expensive leak-proof outer shell of the two-bed chiller need not be changed significantly. One only needs to weld partitions and, of course, additional insulated piping in each of the two beds to create a multi-bed system. The four large-bore-size, vacuum-rated solenoid on-off valves of a two-bed system are replaced, in general, by 2N similar but smaller valves for an N-bed system. It is imperative to mention that, just as in a two-bed chiller, these on-off valves and the associated piping have to be designed such that the pressure drop between the bed and the evaporator/condenser is minimised. In general, each additional bed requires five normal duty solenoid gate valves for flow control.

[0065] FIG. 2 shows the recovery efficiency, ρ of the various multi-bed schemes as a function of dimensionless cycle time, ω. The recovery efficiency of a two-bed chiller at a standard rated ω of 14.55 (corresponding to a cycle time of 450s) is 0.0478. It can be appreciated that, from two to four beds, the recovery efficiency is boosted by about 70%, whereas from four to six beds, the recovery efficiency is increased by another 40%. The six-bed-parallel configuration can be observed to be marginally better than its series counterpart, but one has to pay the price for added complexities. Specifically, flow metering has to be done carefully during design and commissioning so that there is sufficient flow from the condenser to the two beds in series and the one bed in parallel. One could anticipate that the recovery efficiency improves with the number of beds, but this has to be balanced with the cost of construction. It is worth mentioning that all these schemes have been operated at optimal switching time, ωsw for maximum peak chilled water outlet temperature suppression. Since the speed of operation reduces with the number of beds, the optimal switching time tends to increase correspondingly. ωsw for the two-bed, four-bed, six-bed parallel, and six-bed series are 1.13, 1.29, 1.46, and 1.78 respectively.

[0066] FIG. 3 illustrates the dimensionless outlet temperatures for the coolants, waste heat stream and chilled water during dynamic steady state. The trend for the 6-bed-parallel configuration has been omitted for clarity. One observes that the waste heat outlet temperature generally decreases with the number of beds, representing a better utilization of the waste heat before it is purged. The condenser coolant peak temperature for the two-bed is significantly slashed, rendering it suitable for subsequent cooling of the adsorbers. In the case of multi-bed chillers, chilled water outlet temperature tends to be smoothened. This may lead to the elimination of downstream cooling devices for demanding process cooling and dehumidification. With the same amount of resource commitment, chilled water outlet temperature and cycle average cooling capacity necessarily drop but at a rate slower than the reduction in heat source and coolant flowrate, resulting in an improved recovery efficiency. In fact heat rejection and input at the various components drop with an increase in the number of beds. Coupled with the fact that there is a better match in temperature between the bed and the coolant/waste heat stream and that the rate of change of temperature in the beds are slower, the entire chiller is working more reversibly. This result in a mitigation of the various irreversibilities identified and quantified in previous references [16].

[0067] The proposed multi-bed configuration also advantageously reduces the risk of ice formation in the evaporation upon the initial pull-down. It is customary to purge the beds of any non-condensibles before the inception. In a two-bed chiller, this leads to a vigorous boiling in the evaporator and a sudden temperature depression, increasing the risk of ice formation. Whereas in a multi-bed scheme, the N/2 adsorbers and desorbers start one at a time. Such a soft-start ensures that the evaporator approaches the targeted temperature in a gradual manner. This further implies that the total refrigerant inventory in the system can be reduced.

[0068] The present invention advantageously makes it possible to improve the recovery efficiency of low grade waste heat via a multi-bed regenerative scheme. This ensures that the enthalpy of waste stream relative to the environment is better utilized before being purged eventually. The same scheme can also suppress the chilled water outlet temperature fluctuation. This suggests that downstream temperature smoothening device may be downsized or eliminated for those applications involving demanding process cooling or dehumidification. It is also advantageously able to reduce the oscillation in the condenser coolant outlet temperature, making it possible to pipe the condenser coolant to further cool the adsorbers before finally returning to the cooling tower. For the same cooling capacity, the waste heat and coolant flowrates are reduced, resulting in an economy of piping material. By a better match between beds and streams temperatures, it has also advantageously been possible to mitigate the heat transfer bottleneck identified and quantified in previous references [16]. The reduction in the speed of chiller also reduces the rate of entropy generation.

[0069] It has further been quantified that, compared with a two-bed scheme, a four-bed scheme improves the recovery efficiency by about 70%. Whereas from a four- to a six-bed scheme, the margin of improvement is about 40%. With a reduction in chiller's speed, optimal switching time also tends to increase with the number of beds so as to achieve maximum peak chilled water temperature suppression. Finally, a multi-bed scheme makes it possible to start the beds one at a time. This prevents a sudden temperature drop in the evaporator, reducing the risk of ice formation.

TABLE 5
Cyclic-steady-state dimensionless outlet temperature profiles for two-, four-, and six-bed chillers
0	6	62	2700	6	85.0742	80.61085	34.91316	38.02287	10.63948	33.02395	38.02287	80.61085	0.125414	0.896936	−0.370662	0.034854
0.002222	7	1	2701	6.002222	85.10871	80.63467	34.95692	38.00587	10.64399	33.00034	85.10871	34.95692	0.978419	0.069872	−0.37058	0.034426
0.004444	7	2	2702	6.004444	85.12186	80.65738	35.01326	37.98815	10.65137	32.97133	85.12186	35.01326	0.978657	0.070892	−0.370446	0.033901
0.006667	7	3	2703	6.006667	84.91622	80.68008	35.12224	37.96302	10.66104	32.9433	84.91622	35.12224	0.974931	0.072867	−0.370271	0.033393
0.008889	7	4	2704	6.008889	82.7542	80.71429	35.68107	37.86722	10.67252	32.91687	82.7542	35.68107	0.935764	0.08299	−0.370063	0.032914
0.011111	7	5	2705	6.011111	76.27895	80.798	38.09131	37.60416	10.68539	32.8923	76.27895	38.09131	0.818459	0.126654	−0.36983	0.032469
0.022222	7	6	2710	6.022222	56.84923	81.39016	58.54128	36.73256	10.75873	32.79927	56.84923	58.54128	0.466472	0.497125	−0.368501	0.030784
0.033333	7	7	2715	6.033333	54.2324	81.5192	61.4383	36.57665	10.82822	32.73744	54.2324	61.4383	0.419065	0.549607	−0.367242	0.029664
0.044444	7	8	2720	6.044444	52.23825	81.63665	63.60561	36.46012	10.88829	32.68497	52.23825	63.60561	0.382939	0.58887	−0.366154	0.028713
0.055556	7	9	2725	6.055556	50.47681	81.75319	65.51993	36.36281	10.94148	32.63601	50.47681	65.51993	0.351029	0.623549	−0.36519	10.027826
0.066667	7	10	2730	6.066667	48.90493	81.86878	67.24673	36.27588	10.98993	32.58932	48.90493	67.24673	0.322553	0.654832	−0.364313	0.02698
0.077778	7	11	2735	6.077778	47.49868	81.9832	68.80579	36.1955	11.03505	32.54444	47.49868	68.80579	0.297077	0.683076	−0.363495	0.026167
0.088889	7	12	2740	6.088889	46.23895	82.09624	70.21434	36.11956	11.07771	32.5011	46.23895	70.21434	0.274256	0.708593	−0.362723	0.025382
0.093333	7	13	2742	6.093333	45.74963	82.14103	70.73914	36.09043	11.1032	32.48415	45.74963	70.73914	0.265392	0.7181	−0.362261	0.025075
0.097778	7	14	2744	6.097778	45.26072	82.18557	71.24326	36.06293	11.13486	32.4674	45.26072	71.24326	0.256535	0.727233	−0.361687	0.024772
0.102222	7	15	2746	6.102222	44.80102	82.22985	71.72758	36.03694	11.16192	32.45085	44.80102	71.72758	0.248207	0.736007	−0.361197	0.024472
0.106667	7	16	2748	6.106667	44.39201	82.27385	72.19292	36.01142	11.17914	32.43448	44.39201	72.19292	0.240797	0.744437	−0.360885	0.024175
0.111111	7	17	2750	6.111111	44.03634	82.31764	72.63973	35.98506	11.18448	32.42172	44.03634	72.63973	0.234354	0.752531	−0.360788	0.023944
0.115556	7	18	2752	6.115556	43.72504	82.36585	73.05415	35.95699	11.17843	32.46803	43.72504	73.05415	0.228715	0.760039	−0.360898	0.024783
0.12	7	19	2754	6.12	43.4491	82.42748	73.41611	35.92747	11.16306	32.56832	43.4491	73.41611	0.223716	0.766596	−0.361176	0.0266
0.124444	7	20	2756	6.124444	43.20138	82.50546	73.7208	35.90635	11.14073	32.69564	43.20138	73.7208	0.219228	0.772116	−0.361581	0.028907
0.128889	7	21	2758	6.128889	42.97646	82.59728	73.97658	35.91141	11.1135	32.83169	42.97646	73.97658	0.215153	0.77675	−0.362074	0.031371
0.133333	7	22	2760	6.133333	42.77189	82.69706	74.19966	35.94124	11.08299	32.96486	42.77189	74.19966	0.211447	0.780791	−0.362627	0.033784
0.177778	7	23	2780	6.177778	41.67746	83.54111	75.84822	36.26883	10.76971	33.77629	41.67746	75.84822	0.191621	0.810656	−0.368302	0.048483
0.222222	7	24	2800	6.222222	40.97296	84.01023	76.89669	36.23703	10.58274	33.9854	40.97296	76.89669	0.178858	0.82965	−0.371689	0.052272
0.266667	7	25	2820	6.266667	40.3516	84.29919	77.66962	36.05828	10.50025	33.94428	40.3516	77.66962	0.167601	0.843653	−0.373184	0.051527
0.311111	7	26	2840	6.311111	39.79843	84.50554	78.32023	35.83459	10.47795	33.8029	39.79843	78.32023	0.15758	0.855439	−0.373588	0.048966
0.355556	7	27	2860	6.355556	39.3061	84.67041	78.91069	35.60375	10.49031	33.62437	39.3061	78.91069	0.148661	0.866136	−0.373364	0.045731
0.4	7	28	2880	6.4	38.86565	84.81153	79.46536	35.37899	10.52337	33.43536	38.86565	79.46536	0.140682	0.876184	−0.372765	0.042307
0.444444	7	29	2900	6.444444	38.46852	84.93683	79.99309	35.16446	10.5691	33.24735	38.46852	79.99309	0.133488	0.885744	−0.371937	0.038901
0.488889	7	30	2920	6.488889	38.10737	85.05023	80.49646	34.96099	10.62262	33.06543	38.10737	80.49646	0.126945	0.894863	−0.370967	0.035606
0.5	7	31	2925	6.5	38.02201	85.07699	80.61854	34.91185	10.63683	33.02123	38.02201	80.61854	0.125399	0.897075	−0.37071	0.034805
0.502222	7	32	2926	6.502222	38.00502	85.11141	80.64234	34.95565	10.64134	32.99766	85.11141	34.95565	0.978468	0.069849	−0.370628	0.034378
0.504444	7	33	2927	6.504444	37.98729	85.12446	80.66503	35.01203	10.64873	32.9687	85.12446	35.01203	0.978704	0.07087	−0.370494	0.033853
0.506667	7	34	2928	6.506667	37.96216	84.9187	80.68772	35.12105	10.65841	32.94072	84.9187	35.12105	0.974976	0.072845	−0.370319	0.033346
0.508889	7	35	2929	6.508889	37.8663	82.75652	80.72189	35.68002	10.66991	32.91433	82.75652	35.68002	0.935807	0.082971	−0.37011	0.032868
0.511111	7	36	2930	6.511111	37.60306	76.28105	80.80544	38.0908	10.68279	32.8898	76.28105	38.0908	0.818497	0.126645	−0.369877	0.032424
0.522222	7	37	2935	6.522222	36.73099	56.85063	81.39644	58.54516	10.75622	32.7969	56.85063	58.54516	0.466497	0.497195	−0.368547	0.030741
0.533333	7	38	2940	6.533333	36.57514	54.23315	81.52537	61.44215	10.82579	32.73513	54.23315	61.44215	0.419079	0.549677	−0.367286	0.029622
0.544444	7	39	2945	6.544444	36.45864	52.23877	81.64274	63.60961	10.88594	32.68271	52.23877	63.60961	0.382949	0.588942	−0.366197	0.028672
0.555556	7	40	2950	6.555556	36.36135	50.47712	81.75918	65.52416	10.93919	32.63379	50.47712	65.52416	0.351035	0.623626	−0.365232	0.027786
0.566667	7	41	2955	6.566667	36.27444	48.90502	81.87469	67.25115	10.98772	32.58715	48.90502	67.25115	0.322555	0.654912	−0.364353	0.026941
0.577778	7	42	2960	6.577778	36.19409	47.4986	81.98902	68.81035	11.0329	32.54232	47.4986	68.81035	0.297076	0.683159	−0.363534	0.026129
0.588889	7	43	2965	6.588889	36.11818	46.23873	82.10196	70.21903	11.07562	32.49902	46.23873	70.21903	0.274252	0.708678	−0.362761	0.025345
0.593333	7	44	2967	6.593333	36.08906	45.74941	82.14672	70.74387	11.10111	32.48208	45.74941	70.74387	0.265388	0.718186	−0.362299	0.025038
0.597778	7	45	2969	6.597778	36.06158	45.26056	82.19122	71.24803	11.13275	32.46535	45.26056	71.24803	0.256532	0.727319	−0.361726	0.024735
0.602222	7	46	2971	6.602222	36.03559	44.80095	82.23545	71.73238	11.15978	32.44882	44.80095	71.73238	0.248206	0.736094	−0.361236	0.024435
0.606667	7	47	2973	6.606667	36.01006	44.39201	82.27942	72.19776	11.17698	32.43247	44.39201	72.19776	0.240797	0.744525	−0.360924	0.024139
0.611111	7	48	2975	6.611111	35.98371	44.03639	82.32318	72.64459	11.1823	32.41971	44.03639	72.64459	0.234355	0.752619	−0.360828	0.023908
0.615556	7	49	2977	6.615556	35.95564	43.72512	82.37134	73.05905	11.17624	32.46601	43.72512	73.05905	0.228716	0.760128	−0.360938	0.024747
0.62	7	50	2979	6.62	35.92612	43.44919	82.43292	73.42105	11.16087	32.56631	43.44919	73.42105	0.223717	0.766686	−0.361216	0.026563
0.624444	7	51	2981	6.624444	35.905	43.20146	82.51085	73.72578	11.13853	32.69363	43.20146	73.72578	0.219229	0.772206	−0.361621	0.02887
0.628889	7	52	2983	6.628889	35.91004	42.97654	82.60262	73.98159	11.11131	32.82969	42.97654	73.98159	0.215155	0.77684	−0.362114	0.031335
0.633333	7	53	2985	6.633333	35.93987	42.77196	82.70235	74.20469	11.08081	32.96288	42.77196	74.20469	0.211448	0.780882	−0.362666	0.033748
0.677778	7	54	3005	6.677778	36.26754	41.6773	83.54593	75.85331	10.76767	33.77446	41.6773	75.85331	0.191618	0.810748	−0.368339	0.04845
0.722222	7	55	3025	6.722222	36.23582	40.97268	84.01459	76.90175	10.58082	33.98364	40.97268	76.90175	0.178853	0.829742	−0.371724	0.05224
0.766667	7	56	3045	6.766667	36.05711	40.35121	84.30311	77.67459	10.49844	33.94258	40.35121	77.67459	0.167594	0.843743	−0.373217	0.051496
0.811111	7	57	3065	6.811111	35.83345	39.798	84.50904	78.3251	10.47625	33.80123	39.798	78.3251	0.157573	0.855527	−0.373619	0.048935
0.855556	7	58	3085	6.855556	35.60263	39.30561	84.67353	78.91543	10.48871	33.62275	39.30561	78.91543	0.148652	0.866222	−0.373393	0.045702
0.9	7	59	3105	6.9	35.37791	38.86513	84.8143	79.46996	10.52186	33.43379	38.86513	79.46996	0.140673	0.876267	−0.372792	0.042279
0.944444	7	60	3125	6.944444	35.1634	38.46795	84.9393	79.99753	10.56767	33.24582	38.46795	79.99753	0.133477	0.885825	−0.371963	0.038874
0.988889	7	61	3145	6.988889	34.95998	38.10683	85.05242	80.50072	10.62126	33.06397	38.10683	80.50072	0.126935	0.894941	−0.370992	0.035579
1	7	62	3150	7	34.91084	38.02145	85.07912	80.62276	10.63549	33.01978	38.02145	80.62276	0.125389	0.897151	−0.370734	0.034779
1.002222	8	1	3151	7.002222	34.95466	38.00446	85.11347	80.64655	10.64001	32.99624	85.11347	34.95466	0.978505	0.069831	−0.370652	0.034352
1.004444	8	2	3152	7.004444	35.01105	37.98673	85.12644	80.66924	10.6474	32.96731	85.12644	35.01105	0.97874	0.070852	−0.370518	0.033828
1.006667	8	3	3153	7.006667	35.12009	37.9616	84.92059	80.69192	10.65709	32.93936	84.92059	35.12009	0.975011	0.072828	−0.370343	0.033322
1.008889	8	4	3154	7.008889	35.67914	37.86572	82.7583	80.72606	10.66859	32.913	82.7583	35.67914	0.935839	0.082955	−0.370134	0.032844
1.011111	8	5	3155	7.011111	38.0902	37.60243	76.28266	80.8095	10.68148	32.8885	76.28266	38.0902	0.818526	0.126634	−0.369901	0.0324
1.022222	8	6	3160	7.022222	58.54696	36.73024	56.85174	81.39963	10.75495	32.79568	56.85174	58.54696	0.466517	0.497228	−0.36857	0.030719
1.033333	8	7	3165	7.033333	61.44387	36.57443	54.23402	81.5285	10.82455	32.73395	54.23402	61.44387	0.419095	0.549708	−0.367309	0.029601
1.044444	8	8	3170	7.044444	63.6114	36.45795	52.23945	81.64583	10.88474	32.68156	52.23945	63.6114	0.382961	0.588975	−0.366219	0.028651
1.055556	8	9	3175	7.055556	65.52608	36.36067	50.47764	81.76223	10.93802	32.63266	50.47764	65.52608	0.351044	0.623661	−0.365253	0.027766
1.066667	8	10	3180	7.066667	67.25319	36.27378	48.90542	81.87769	10.98658	32.58604	48.90542	67.25319	0.322562	0.654949	−0.364374	0.026921
1.077778	8	11	3185	7.077778	68.81249	36.19345	47.49889	81.99197	11.03179	32.54124	47.49889	68.81249	0.297081	0.683197	−0.363555	0.026109
1.088889	8	12	3190	7.088889	70.22125	36.11755	46.2389	82.10487	11.07453	32.49796	46.2389	70.22125	0.274255	0.708718	−0.36278	0.025325
1.093333	8	13	3192	7.093333	70.74611	36.08843	45.74958	82.1496	11.10002	32.48104	45.74958	70.74611	0.265391	0.718227	−0.362318	0.025019
1.097778	8	14	3194	7.097778	71.2503	36.06095	45.26079	82.19408	11.13164	32.46431	45.26079	71.2503	0.256536	0.72736	−0.361746	0.024716
1.102222	8	15	3196	7.102222	71.73467	36.03496	44.80124	82.2383	11.15865	32.44779	44.80124	71.73467	0.248211	0.736135	−0.361256	0.024416
1.106667	8	16	3198	7.106667	72.20007	36.00943	44.39234	82.28225	11.17583	32.43145	44.39234	72.20007	0.240803	0.744566	−0.360945	0.02412
1.111111	8	17	3200	7.111111	72.64692	35.98308	44.03675	82.32598	11.18112	32.41872	44.03675	72.64692	0.234361	0.752662	−0.360849	0.02389
1.115556	8	18	3202	7.115556	73.06137	35.95501	43.72549	82.37414	11.17505	32.4651	43.72549	73.06137	0.228723	0.76017	−0.360959	0.02473
1.12	8	19	3204	7.12	73.42334	35.92548	43.44956	82.43571	11.15967	32.56543	43.44956	73.42334	0.223724	0.766727	−0.361238	0.026548
1.124444	8	20	3206	7.124444	73.72806	35.90437	43.20183	82.51364	11.13734	32.69279	43.20183	73.72806	0.219236	0.772248	−0.361642	0.028855
1.128889	8	21	3208	7.128889	73.98386	35.90945	42.9769	82.60539	11.11011	32.82887	42.9769	73.98386	0.215161	0.776881	−0.362136	0.03132
1.133333	8	22	3210	7.133333	74.20695	35.9393	42.77232	82.70511	11.07962	32.96207	42.77232	74.20695	0.211455	0.780923	−0.362688	0.033733
1.177778	8	23	3230	7.177778	75.85558	36.26703	41.67756	83.54845	10.76653	33.7737	41.67756	75.85558	0.191623	0.810789	−0.36836	0.048437
1.222222	8	24	3250	7.222222	76.90399	36.23533	40.97283	84.01685	10.57976	33.9829	40.97283	76.90399	0.178856	0.829782	−0.371743	0.052226
1.266667	8	25	3270	7.266667	77.67679	36.05663	40.35131	84.30513	10.49744	33.9418	40.35131	77.67679	0.167596	0.843782	−0.373235	0.051483
1.311111	8	26	3290	7.311111	78.32725	35.83299	39.79801	84.51084	10.47531	33.80052	39.79801	78.32725	0.157573	0.855566	−0.373636	0.048922
1.355556	8	27	3310	7.355556	78.91752	35.60219	39.30557	84.67514	10.48782	33.62205	39.30557	78.91752	0.148652	0.866259	−0.373409	0.045689
1.4	8	28	3330	7.4	79.47198	35.37748	38.86508	84.81572	10.52102	33.43311	38.86508	79.47198	0.140672	0.876304	−0.372808	0.042266
1.444444	8	29	3350	7.444444	79.99948	35.16299	38.46789	84.94056	10.56688	33.24516	38.46789	79.99948	0.133476	0.88586	−0.371977	0.038862
1.488889	8	30	3370	7.488889	80.5026	34.95958	38.10673	85.05354	10.62052	33.06334	38.10673	80.5026	0.126934	0.894975	−0.371005	0.035568
1.5	8	31	3375	7.5	80.62461	34.91044	38.02136	85.0802	10.63475	33.01915	38.02136	80.62461	0.125387	0.897185	−0.370747	0.034767
1.502222	8	32	3376	7.502222	80.64841	34.95427	38.00437	85.11452	10.63927	32.99563	85.11452	34.95427	0.978524	0.069824	−0.370665	0.034341
1.504444	8	33	3377	7.504444	80.67109	35.01067	37.98664	85.12744	10.64667	32.96672	85.12744	35.01067	0.978758	0.070845	−0.370531	0.033817
1.506667	8	34	3378	7.506667	80.69377	35.11971	37.96151	84.92155	10.65636	32.93878	84.92155	35.11971	0.975028	0.072821	−0.370356	0.033311
1.508889	8	35	3379	7.508889	80.7279	35.67879	37.86562	82.75921	10.66786	32.91244	82.75921	35.67879	0.935855	0.082949	−0.370147	0.032834
1.511111	8	36	3380	7.511111	80.81128	38.08999	37.6023	76.28351	10.68076	32.88795	76.28351	38.08999	0.818542	0.12663	−0.369914	0.03239
1.522222	8	37	3385	7.522222	81.40097	58.5478	36.73005	56.85242	10.75424	32.79517	56.85242	58.5478	0.466529	0.497243	−0.368583	0.03071
1.533333	8	38	3390	7.533333	81.52981	61.44464	36.57426	54.23456	10.82387	32.73346	54.23456	61.44464	0.419104	0.549722	−0.367321	0.029592
1.544444	8	39	3395	7.544444	81.64712	63.61219	36.45778	52.23992	10.88407	32.68108	52.23992	63.61219	0.38297	0.588989	−0.366231	0.028643
1.555556	8	40	3400	7.555556	81.7635	65.52693	36.3605	50.47804	10.93737	32.63219	50.47804	65.52693	0.351051	0.623676	−0.365265	0.027757
1.566667	8	41	3405	7.566667	81.87894	67.25408	36.27362	48.90574	10.98594	32.58558	48.90574	67.25408	0.322568	0.654965	−0.364385	0.026913
1.577778	8	42	3410	7.577778	81.99321	68.81341	36.19328	47.49917	11.03117	32.54078	47.49917	68.81341	0.297086	0.683214	−0.363566	0.026101
1.588889	8	43	3415	7.588889	82.10608	70.2222	36.11739	46.23913	11.07393	32.49752	46.23913	70.2222	0.27426	0.708735	−0.362791	0.025317
1.593333	8	44	3417	7.593333	82.15081	70.74707	36.08827	45.74981	11.09942	32.4806	45.74981	70.74707	0.265395	0.718244	−0.362329	0.025011
1.597778	8	45	3419	7.597778	82.19528	71.25127	36.06079	45.26102	11.13103	32.46388	45.26102	71.25127	0.25654	0.727378	−0.361757	0.024708
1.602222	8	46	3421	7.602222	82.23949	71.73565	36.0348	44.80149	11.15804	32.44736	44.80149	71.73565	0.248215	0.736153	−0.361267	0.024409
1.606667	8	47	3423	7.606667	82.28343	72.20106	36.00927	44.39261	11.1752	32.43102	44.39261	72.20106	0.240808	0.744584	−0.360956	0.024113
1.611111	8	48	3425	7.611111	82.32716	72.64792	35.98292	44.03704	11.1805	32.41829	44.03704	72.64792	0.234367	0.75268	−0.360861	0.023882
1.615556	8	49	3427	7.615556	82.3753	73.06238	35.95484	43.72578	11.17442	32.46465	43.72578	73.06238	0.228728	0.760188	−0.360971	0.024722
1.62	8	50	3429	7.62	82.43687	73.42437	35.92533	43.44985	11.15904	32.56498	43.44985	73.42437	0.223729	0.766746	−0.361249	0.02654
1.624444	8	51	3431	7.624444	82.51478	73.72909	35.90421	43.20212	11.13671	32.69235	43.20212	73.72909	0.219241	0.772266	−0.361654	0.028847
1.628889	8	52	3433	7.628889	82.60653	73.98489	35.90928	42.97718	11.10948	32.82843	42.97718	73.98489	0.215166	0.7769	−0.362147	0.031312
1.633333	8	53	3435	7.633333	82.70623	74.208	35.93912	42.77258	11.07899	32.96163	42.77258	74.208	0.21146	0.780942	−0.362699	0.033725
1.677778	8	54	3455	7.677778	83.54947	75.85666	36.26685	41.67774	10.76594	33.7733	41.67774	75.85666	0.191626	0.810809	−0.368371	0.048429
1.722222	8	55	3475	7.722222	84.01778	76.90507	36.23516	40.97294	10.5792	33.98252	40.97294	76.90507	0.178858	0.829802	−0.371754	0.05222
1.766667	8	56	3495	7.766667	84.30596	77.67786	36.05647	40.35138	10.49691	33.94148	40.35138	77.67786	0.167597	0.843802	−0.373244	0.051476
1.811111	8	57	3515	7.811111	84.51158	78.32829	35.83283	39.79807	10.4748	33.80016	39.79807	78.32829	0.157574	0.855585	−0.373645	0.048916
1.855556	8	58	3535	7.855556	84.6758	78.91854	35.60203	39.3056	10.48735	33.6217	39.3056	78.91854	0.148652	0.866278	−0.373418	0.045683
1.9	8	59	3555	7.9	84.81631	79.47297	35.37732	38.86508	10.52057	33.43277	38.86508	79.47297	0.140672	0.876322	−0.372816	0.04226
1.944444	8	60	3575	7.944444	84.94109	80.00044	35.16283	38.46789	10.56645	33.24483	38.46789	80.00044	0.133476	0.885878	−0.371985	0.038856
1.988889	8	61	3595	7.988889	85.054	80.50352	34.95942	38.10671	10.62011	33.06302	38.10671	80.50352	0.126933	0.894991	−0.371013	0.035562
2	8	62	3600	8	85.08066	80.62553	34.91029	38.02134	10.63435	33.01884	38.02134	80.62553	0.125387	0.897202	−0.370755	0.034762

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NOMENELATUCE

[0090] A coefficient appearing in the empirical isotherm correlation

[0091] Abed bed heat transfer area (m2)

[0092] Aevap evaporator heat transfer area (m2)

[0093] Acond condenser heat transfer area (m2)

[0094] B index appearing in the empirical isotherm correlation

[0095] cp,evap specific heat capacity of evaporator heat exchanging material (Jkg−1K−1)

[0096] cp,cond specific heat capacity of condenser heat exchanging material (Jkg−1K−1)

[0097] cp,Hex specific heat capacity of heat exchanger tube and fin (Jkg−1H−1)

[0098] cp,ref specific heat capacity of liquid refrigerant (Jkg−1K−1)

[0099] cp,sg specific heat capacity of dry adsorbent (Jkg−1K−1)

[0100] cx,i 13$\frac{c_p\left(T_{x,i}\right)}{c_{p,sg}}$

[0101] q fraction of refrigerant adsorbed by the adsorbent (kg per kg of dry adsorbent)

[0102] q* fraction of refrigerant which can be adsorbed by the adsorbent under conditions of saturation (kg per kg of dry adsorbent)

[0103] qbed,I fraction of refrigerant adsorbed by the adsorbent in bed I (kg per kg of dry adsorbent)

[0104] qref ratio of the mass of liquid refrigerant inventory in the evaporator to that of the dry adsorbent (kg per kg of dry adsorbent)

[0105] qrefini ratio of the initial mass of liquid refrigerant inventory in the evaporator to that of the dry adsorbent (kg per kg of dry adsorbent)

[0106] qcond ratio of the mass of condensed refrigerant in the condenser to that of the dry adsorbent (kg per kg of dry adsorbent)

[0107] Ea activation energy of surface diffusion (Jmol−1)

[0108] Ds0 pre-exponent constant in the kinetics equation (m2s−1)

[0109] hads specific enthalpy of adsorbate (Jkg−1)

[0110] hf saturated fluid specific enthalpy (Jkg−1)

[0111] {overscore (h)} 14$\frac{h}{c_{p,sg}\left(T_{h,i}-T_{c,i}\right)}$

[0112] {dot over (m)}chilled chilled water flowrate (kgs−1)

[0113] {dot over (m)}cond condenser coolant flowrate (kgs−1)

[0114] {dot over (m)}cooling adsorber coolant flowrate (kgs−1)

[0115] {dot over (m)}heating desorber waste heat source flowrate (kgs−1)

[0116] {dot over (m)} 15$\frac{\stackrel{.}{m}}{{\stackrel{.}{m}}_{cooling}}$

[0117] Mcond mass of condenser heat exchanger tube (kg)

[0118] Mevap mass of evaporator heat exchanger tube (kg)

[0119] MHex mass of heat exchanger tube and fin in the bed (kg)

[0120] Msg mass of silica gel mass in one bed (kg)

[0121] n,N1,N2 number of discrete elements in the heat exchanging tubes

[0122] NTUcooling 16$\frac{U_{cooling}{A}_{bed}/N}{{\stackrel{.}{m}}_{cooling}{c}_p\left(T_{c,i}\right)}$$\frac{U_{chilled}{A}_{evap}/N_1}{{\stackrel{.}{m}}_{chilled}{c}_p\left(T_{chilled,i}\right)}$$\frac{U_{cond}{A}_{cond}/N_2}{{\stackrel{.}{m}}_{cond}{c}_p\left(T_{c,i}\right)}$

[0123] NTUchilled

[0124] NYUcond

[0125] NTUheating 17$\frac{U_{heating}{A}_{bed}/N}{{\stackrel{.}{m}}_{heating}{c}_p\left(T_{h,i}\right)}$

[0126] p pressure (pa)

[0127] Pcond condenser pressure (Pa)

[0128] Pevap evaporator pressure (Pa)

[0129] Psat saturated vapour pressure (Pa)

[0130] R universal gas constant (Jmol−1K−1 or Jkg−1K−1)

[0131] Pp average radius of silica gel (m)

[0132] t time (s)

[0133] tcycle cycle time (s)

[0134] tsw switching time (s)

[0135] T temperature (K. or ° C.)

[0136] Tbed,I bed I temperature (K. or ° C.)

[0137] Tc,i coolant water inlet temperature to the condenser (K. or ° C.)

[0138] Tchilled,i chilled water inlet temperature to the evaporator K. or ° C.)

[0139] Tchilled,o chilled water outlet temperature from the evaporator (K. or ° C.)

[0140] Tcond condenser temperature (K. or ° C.)

[0141] Tevap evaporator temperature (K. or ° C.)

[0142] Th,i waste heat supply temperature to the chiller (K. or ° C.)

[0143] Ti temperature of fluid within a discrete element i in the heat exchanging tube (K. or ° C.)

[0144] Tref refrigerant temperature (K. or ° C.)

[0145] Tsg silica gel temperature (K. or ° C.)

[0146] {overscore (T)} 18$\frac{T-T_{c,i}}{T_{h,i}-T_{c,i}}$

[0147] Ucooling adsorber heat transfer coefficient (Wm−2K−1)

[0148] Ubeating desorber heat transfer coefficient (Wm−2K−1)

[0149] Uchilled evaporator heat transfer coefficient (Wm−2K−1)

[0150] Ucond condenser heat transfer coefficient (Wm2K−1)

[0151] Vx—tube volume of fluid within the heat exchanging tube of component x, where x could be the bed, evaporator, or condenser (m3)

[0152] βcond 19$\frac{M_{cond}{c}_{p,cond}}{M_{sg}{c}_{p,sg}}$$\frac{M_{evap}{c}_{p,evap}}{M_{sg}{c}_{p,sg}}$$\frac{M_{Hex}{c}_{p,Hex}}{M_{sg}{c}_{p,sg}}$$\frac{M_{ref}{c}_{p,ref}}{M_{sg}{c}_{p,sg}}$$\frac{\rho \left(T_i\right)V_{\mathrm{x\_tube}}{c}_p\left(T_i\right)/N_x}{M_{sg}{c}_{p,sg}};$

[0153] βevap

[0154] βHex

[0155] βref

[0156] βx—tube,i

[0157] if x refers to the bed, Nx=N, if x refers to the evaporator and condenser, Nx=N1 and Nx=N2 respectively

[0158] δI,θI flags governing the transient operation of bed I

[0159] Δ{overscore (H)}ads isosteric heat of adsorption

[0160] {overscore (ΔH)}ads 20$\frac{\Delta H_{ads}}{c_{p,sg}\left(T_{h,i}-T_{c,i}\right)}$

[0161] η conversion efficiency, ratio of cycle averaged cooling capacity to the enthalpy of waste heat stream relative to the environment

[0162] T 21$\tau t/t_{\mathrm{cycle}}$$\omega \frac{{\stackrel{.}{m}}_{\mathrm{cooling}}{t}_{\mathrm{cycle}}}{M_{\mathrm{sg}}}$${\omega }_{\mathrm{sw}}\frac{{\stackrel{.}{m}}_{\mathrm{cooling}}{t}_{\mathrm{sw}}}{M_{\mathrm{sg}}}$

[0163] ω

[0164] ωs ω

Claims

1. A regenerative adsorption process for application in an adsorption assembly comprising a condenser, an evaporator and a plurality of reactors each alternately operating in adsorption and desorption modes, said process comprising: passing a coolant through the condenser; passing the coolant through reactors operating in adsorption mode before, after or simultaneous with the passing of the coolant through the condenser; and passing waste heat from a waste heat source through reactors operating in desorption mode; wherein said plurality of reactors are scheduled such that each reactor alternately operates in adsorption and desorption modes for substantially identical time intervals, and such that each reactor has an equal chance of being the first reactor to receive the coolant emanating from the condenser when operating in adsorption mode, and the waste heat from the waste heat source when operating in desorption mode.

2. A process according to claim 1, further comprising the step of arranging said reactors operating in adsorption mode in series and/or in parallel.

3. A process according to claim 1, wherein said plurality of reactors comprises an even number of reactors, further comprising the step of operating at substantially any instant during said process half of said plurality of reactors in adsorption mode and the other half of said plurality of reactors in desorption mode.

4. A process according to claim 3, further comprising the step of providing at least four reactors.

5. A process according to claim 4, further comprising the step of providing six reactors.

6. A process according to claim 1, further comprising the step of flowing the coolant through said reactors operating in adsorption mode at a flow rate which provides a transition or turbulent flow regime in the channel of a heat exchanger.

7. A process according to claim 1, flrher comprising the step of flowing the waste heat through said reactors operating in desorption mode at a predetermined flow rate.

8. A process according to claim 1, flrer comprising the step of flowing the coolant through said condenser at a predetermined flow rate.

9. A multi-reactor regenerative adsorption chiller assembly comprising: a condenser adapted to receive a coolant from a source; an evaporator connected to said condenser to provide a refrigerant circuit; a plurality of reactors, each being able to operate in adsorption and desorption modes and having a coolant inlet to directly or indirectly receive coolant when operating in adsorption mode before, after or simultaneous with the condenser, and a waste heat inlet for directly or indirectly receiving waste heat from a waste heat source when operating in desorption mode; and control means for controlling said plurality of reactors such that each reactor alternately operates in adsorption and desorption modes for substantially identical time intervals, and such that each reactor has an equal chance of being the first reactor to receive the coolant when operating in adsorption mode, and the waste heat from the waste heat source when operating in desorption mode.

10. An assembly according to claim 9, wherein said plurality of reactors are arranged in series such that, in use, reactors operating in adsorption mode constitute a first sub-series of reactors connected in series and/or in parallel to receive the coolant, and reactors operating in desorption mode constitute a second sub-series of reactors connected in series to receive waste heat from said waste heat source.

11. An assembly according to claim 9, wherein said plurality of reactors comprises an even number of reactors, and wherein in use at substantially any instant half of said plurality of reactors operate in adsorption mode and the other half of said plurality of reactors operate in desorption mode.

12. An assembly according to claim I 1, wherein said plurality of reactors comprises at least four reactors.

13. An assembly according to claim 9, wherein each of said plurality of reactors is composed of a heat exchanging material and contain an adsorbent, that binds adsorbate byphysi-sorption and/or chemi-sorption.

14. An assembly according to claim 13, wherein said adsorbent comprises silica gel.

15. An assembly according to claim 9, wherein said plurality ofreactors indirectly or directly receive coolant emitted from said condenser.

16. An assembly according to claim 10, wherein said plurality of reactors indirectly or directly receive coolant emitted from said condenser.

17. A process according to claim 1, wherein said step of passing the coolant through the reactors operating in adsorption mode further comprises the step of passing the coolant emanating from the condenser through the reactors operating in adsorption mode.