Regenerative adsorption process and multi-reactor regenerative adsorption chiller

FIELD OF THE INVENTION

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

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.

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.

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.

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.

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.

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.

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

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:

passing a coolant through the condenser;

passing the coolant emanating from the condenser through reactors operating in adsorption mode; 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.

According to another aspect of the invention there is provided 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 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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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,

2

a

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 electromagnetic on/off valve.

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.

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

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.

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)

2

a

, 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

.

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

2

a

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.

The cooresponding 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.

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)

sw

des (N/2)

des(N/2-1)

des(2)

des(1)

Bed 2

des(1)

sw

ads

ads(1)

sw

des (N/2)

des(3)

des(2)

Bed N/2 + 1

sw

des (N/2)

des(N/2-1)

sw

ads (N/2)

ads(N/2-I)

ads(2)

ads(1)

Bed N/2 + 2

ads(1)

sw

des (N/2)

des(1)

sw

ads (N/2)

ads(3)

ads(2)

Bed N-1

ads(N/2-2)

ads(N/2-3)

des(N/2-2)

des(N/2-3)

sw

ads (N/2)

ads(N/2-1)

Bed N

ads(N/2-I)

ads(N/2-2)

des(N/2-1)

des(N/2-2)

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(I-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-I); 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.

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.

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.

Specifics of the analysis:

linear driving force (LDF) kinetic equation, equation (1),

silicagel-water binary system, equation (2),

lumped-parameter treatment for the reactors, evaporator and condenser,

specifications as delineated in Table 4.

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:

\begin{matrix} \frac{ⅆ q}{ⅆ τ} = \frac{15 t_{cycle} D_{s0} \exp [- E_{a} / (RT)]}{R_{p}^{2}} [q^{*} (P, T) - q] & (1) \end{matrix}

The coefficients of which were determined by Chihara and Suzuki [17] and q* is given by the following empirical isotherm equation [18] which is based on the manufacturer's proprietary data [19]:

\begin{matrix} q^{*} = {A (T_{sg}) [\frac{P_{sat} (T_{ref})}{P_{sat} (T_{sg})}]}^{B (T_{sg})} & (2) \end{matrix}

The energy balance for bed I, ignoring heat losses, during its interaction with the evaporator can be written as

\begin{matrix} (1 + α_{Hex}) \frac{ⅆ {\overline{T}}_{bed, I}}{ⅆ τ} + q_{bed, I} \frac{ⅆ {\overline{h}}_{ads}}{ⅆ τ} = \frac{ⅆ q_{bed, I}}{ⅆ τ} {δ_{I} [{\overline{h}}_{g} (T_{evap}) - {\overline{h}}_{ads} (P_{evap}, T_{bed, I})] - (1 - δ_{I}) {\overline{Δ H}}_{ads}} - {NTU}_{cooling} ω c_{c, i} \sum_{i = 1}^{N} ({\overline{T}}_{bed, I} - {\overline{T}}_{i}) . & (3a) \end{matrix}

The energy balance for the coolant can be expressed as

\begin{matrix} α_{bed_tube, i} \frac{ⅆ {\overline{T}}_{i}}{ⅆ τ} = ω [{\overline{h}}_{f} (T_{i - 1}) - {\overline{h}}_{f} (T_{i}) + {NTU}_{cooling} c_{c, i} ({\overline{T}}_{bed, I} - {\overline{T}}_{i})] for i = 1 to N . {\overline{T}}_{i} (0) = {\overline{T}}_{bedi} (0) = 0. {\overline{T}}_{i} (τ) = {\overline{T}}_{N_{2}} (τ) ❘_{cond} & (3b) \end{matrix}

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. q

bed,I

(0)=q*(P

evap

(0),T

bed,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].

When the bed J is interacting with the condenser, its energy balance can be written as

\begin{matrix} (1 + α_{Hex}) \frac{ⅆ {\overline{T}}_{bed, J}}{ⅆ τ} + q_{bed, I} \frac{ⅆ {\overline{h}}_{ads}}{ⅆ τ} = θ_{J} \frac{ⅆ q_{bed, J}}{ⅆ τ} {\overline{Δ H}}_{ads} - {NTU}_{heating} ω {\overline{\dot{m}}}_{heating} c_{h, i} \sum_{i = 1}^{N} ({\overline{T}}_{bed, J} - {\overline{T}}_{i}) . & (4a) \end{matrix}

The energy balance for the coolant can be expressed as

\begin{matrix} α_{bed_tube, i} \frac{ⅆ {\overline{T}}_{i}}{ⅆ τ} = ω {\overline{\dot{m}}}_{heating} [{\overline{h}}_{f} (T_{i - 1}) - {\overline{h}}_{f} (T_{i}) + {NTU}_{heating} c_{c, i} ({\overline{T}}_{bed, J} - {\overline{T}}_{i})] & (4b) \end{matrix}

for i=1 to N. {overscore (T)}

i

(0)={overscore (T)}

bed,J

(0)=1. {overscore (T)}

1

(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. q

bed,J

(0)=q*(P

cond

(0), T

bed,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 dq

bed,J

/dt>0, θ

J

=0.

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.

The evaporator is, in general, interacting with N/2 beds at any time, its energy balance can be expressed as

\begin{matrix} (α_{ref} + α_{evap}) \frac{ⅆ {\overline{T}}_{evap}}{ⅆ τ} + {\overline{h}}_{f} (T_{evap}) \frac{ⅆ q_{ref}}{ⅆ τ} = - {\overline{h}}_{f} (T_{cond}) \sum_{J = 1}^{n / 2} θ_{J} \frac{ⅆ q_{bed, J}}{ⅆ τ} - {NTU}_{chilled} ω {\overline{\dot{m}}}_{chilled} \sum_{i = 1}^{N_{1}} ({\overline{T}}_{evap} - {\overline{T}}_{i}) - \sum_{I = 1}^{n / 2} [δ_{I} {\overline{h}}_{g} (T_{evap}) + (1 - δ_{I}) {\overline{h}}_{g} (P_{evap,} T_{bed, I})] \frac{ⅆ q_{bed, I}}{ⅆ τ} & (5a) \end{matrix}

The rate of change of liquid refrigerant mass is given by

\begin{matrix} \frac{ⅆ q_{ref}}{ⅆ τ} = - \sum_{k = 1}^{n} θ_{k} \frac{ⅆ q_{bed, k}}{ⅆ τ} . & (5b) \end{matrix}

If bed k is interacting with the evaporator, θ

k

=1, and if it is interacting with the condenser, θ

k

=1 when dq

bed,k

/dt<0 and θ

k

=0 when dq

bed, k

/dt>0.

The energy balance for the chilled water can be expressed as

\begin{matrix} α_{evap_tube, i} \frac{ⅆ {\overline{T}}_{i}}{ⅆ τ} = ω {\overline{\dot{m}}}_{chilled} [{\overline{h}}_{f} (T_{i - 1}) - {\overline{h}}_{f} (T_{i}) + {NTU}_{chilled} c_{chilled, i} ({\overline{T}}_{evap} - {\overline{T}}_{i})] for i = 1 to N_{1} . {\overline{T}}_{i} (0) = {\overline{T}}_{evap} (0) = {\overline{T}}_{1} (τ) = \frac{T_{chilled, i} - T_{c, i}}{T_{h, i} - T_{c, i}}, and q_{ref} (0) = q_{ref}^{ini} . & (5c) \end{matrix}

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

\begin{matrix} α_{cond} \frac{ⅆ {\overline{T}}_{cond}}{ⅆ τ} = - \sum_{J = 1}^{n / 2} θ_{J} [{\overline{h}}_{g} (P_{cond}, T_{bed, J}) - {\overline{h}}_{f} (T_{cond})] \frac{ⅆ q_{bed, J}}{ⅆ τ} - {NTU}_{cond} ω {\overline{\dot{m}}}_{cond} \sum_{i = 1}^{N_{2}} ({\overline{T}}_{cond} - {\overline{T}}_{1}), and & (6a) \\ α_{cond_tube, i} \frac{ⅆ {\overline{T}}_{i}}{ⅆ τ} = ω {\overline{\dot{m}}}_{cond} [{\overline{h}}_{f} (T_{i - 1}) - {\overline{h}}_{f} (T_{i}) + {NTU}_{cond} c_{c, i} ({\overline{T}}_{cond} - {\overline{T}}_{i})] for i = 1 to N_{2} . {\overline{T}}_{i} (0) = {\overline{T}}_{cond} (0) = {\overline{T}}_{1} (τ) = 0. & (6b) \end{matrix}

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.

The above mentioned set of coupled equations is solved by the Adams-Moulton method found in the DIVPAG subroutine of the IMSL Fortran library subroutines. The tolerance has been set to 1E-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.

The non-dimensional cycle averaged cooling power is defined as

\begin{matrix} {\overline{Q}}_{e v a p} = ω {\overline{\dot{m}}}_{c h i l l e d} c_{c h i l l e d, i} \int_{0}^{1} ({\overline{T}}_{c h i l l e d, i} - {\overline{T}}_{c h i l l e d, o}) ⅆ τ & (7) \end{matrix}

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:

\begin{matrix} η = \frac{{\overline{\dot{m}}}_{c h i l l e d} c_{c h i l l e d, i}}{{\overline{\dot{m}}}_{h e a t i n g} c_{h, i}} \int_{0}^{1} ({\overline{T}}_{c h i l l e d, i} - {\overline{T}}_{c h i l l e d, o}) ⅆ τ . & (8) \end{matrix}

The environment temperature has been selected to be T

c,i

.

Performance Comparison of Two-, Four-, and Six-Bed Chillers

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.

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.

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

U

cooling

1602.56

U

heating

1724.14

U

chilled

2557.54

U

cond

4115.23

A

bed

2.46

1.23

0.820

A

evap

1.91

A

cond

3.73

M

sg

47.0

23.5

15.7

c

p,Hex

M

Hex

77719.4 × 10

3

38859.7 × 10

3

25906.5 × 10

3

c

p,evap

M

evap

4805.7 × 10

3

c

p,cond

M

cond

9372.08 × 10

3

V

bed

1.778 × 10

−2

8.89 × 10

−3

5.93 × 10

−3

V

evap

6.916 × 10

−3

V

cond

1.349 × 10

−2

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.

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, ω

sw

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. ω

sw

for the two-bed, four-bed, six-bed parallel, and six-bed series are 1.13, 1.29, 1.46, and 1.78 respectively.

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].

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.

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.

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

−0.365191

0.027826

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

REFERENCES

[1] Y. Yonezawa, T. Ohnishi, S. Okumura, A. Sakai, H. Nakano, M. Matsushita, A. Morikawa, M. Yoshihara, “Method of operating adsorption refrigerator”, U.S. Pat. No. 5,024,064, (1991).

[2] Y. Yonezawa, M. Matsushita, K. Oku, H. Nakano, S. Okumura, M. Yoshihara, A. Sakai, A. Morikawa, “Adsorption refrigeration system”, U.S. Pat. No. 4,881,376, (1989).

[3] BB Saha, EC Boelman, and T Kashiwagi, “Computational analysis of an advanced adsorption-refrigeration cycle”, Energy, vol. 20, no. 10, pp. 983-994, (1995).

[4] EC Boelman, BB Saha, and T Kashiwagi, “Experimental investigation of a silica gel-water adsorption refrigeration cycle—the influence of operating conditions on cooling output and COP”, ASHRAE Trans: Research, vol. 101, part 2, pp. 358-366, (1995).

[5] H. Sato, S. Honda, S. Inoue, H. Tanaka, T. Terao, “adsorptive type refrigeration apparatus”, U.S. Pat. No. 5,619,866, (1997).

[6] H. Sato, H. Tanaka, S. Honda, K. Fujiwara, S. Inoue, “Adsorptive type refrigeration apparatus”, U.S. Pat. No. 5,775,126, (1998).

[7] D. I. Tchemev, “Heat pump energized by low-grade heat source”, U.S. Pat. No. 5,729,988, (1998).

[8] L. D. Kirol, U. Rockenfeller, “Heat transfer apparatus and methods for solid-vapor sorption systems”, U.S. Pat. No. 5,477,706, (1995).

[9] F. Meunier, “Refrigerating and heating apparatus using a solid sorbent”, U.S. Pat. No. 5,477,705, (1995).

[10] J. A. Jones, “Heat cascading regenerative sorption heat pump”, U.S. Pat. No. 5,463,879, (1995).

[11] S. V. Shelton, “Dual bed heat pump”, U.S. Pat. No. 4,694,659, (1987).

[12] J. A. Jones, “Staged regenerative sorption heat pump opening method”, U.S. Pat. No. 5,386,705, (1995).

[13] J. A. Jones, “Regenerative adsorbent heat pump system with working fluid and adsorbent”, U.S. Pat. No. 5,347,815, (1994).

[14] J. A. Jones, “Heat pump system with sorbent bed compressors”, U.S. Pat. No. 5,046,319, (1991).

[15] HT Chua, KC Ng, A Malek, T Kashiwagi, A Akisawa, and BB Saha, “Modeling the performance of two-bed, silica gel-water adsorption chillers”, Accepted by Int. J. Refrig., (1998).

[16] HT Chua, KC Ng, A Malek, T Kashiwagi, A Akisawa, and BB Saha, “Entropy generation analysis of two-bed, silica gel-water, non-regenerative adsorption chillers”, J. Phys. D: Appl. Phys., vol. 31, no. 12, pp. 1471-1477, (1998).

[17] K Chihara and M Suzuki, “Air drying by pressure swing adsorption”, J. Chem. Eng. Japan, vol. 16, pp. 293-298, (1983).

[18] BB Saha, EC Boelman, and T Kashiwagi, “Computer simulation of a silica gel-water adsorption refrigeration cycle—the influence of operating conditions on cooling output and COP”, ASHRAE Trans.: Res., vol. 101, pp. 348-357, (1995).

[19] NACC, PTX data for the silica gel/water pair, manufacturer's proprietary data, Nishiyodo Air Conditioning Co Ltd, Tokyo, (1992).

[20] A Sakoda and M Suzuki, “Fundamental study on solar powered adsorption cooling system”, J. Chem. Eng. Japan, vol. 17, no. 1, pp. 52-57, (1984).

NOMENELATUCE

A coefficient appearing in the empirical isotherm correlation

A

bed

bed heat transfer area (m

2

)

A

evap

evaporator heat transfer area (m

2

)

A

cond

condenser heat transfer area (m

2

)

B index appearing in the empirical isotherm correlation

c

p,evap

specific heat capacity of evaporator heat exchanging material (Jkg

−1

K

−1

)

c

p,cond

specific heat capacity of condenser heat exchanging material (Jkg

−1

K

−1

)

c

p,Hex

specific heat capacity of heat exchanger tube and fin (Jkg

−1

H

−1

)

c

p,ref

specific heat capacity of liquid refrigerant (Jkg

−1

K

−1

)

c

p,sg

specific heat capacity of dry adsorbent (Jkg

−1

K

−1

)

c

x,i

\frac{c_{p} (T_{x, i})}{c_{p, s g}}

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

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

q

bed,I

fraction of refrigerant adsorbed by the adsorbent in bed I (kg per kg of dry adsorbent)

q

ref

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

q

ref

ini

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

q

cond

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

E

a

activation energy of surface diffusion (Jmol

−1

)

D

s0

pre-exponent constant in the kinetics equation (m

2

s

−1

)

h

ads

specific enthalpy of adsorbate (Jkg

−1

)

h

f

saturated fluid specific enthalpy (Jkg

−1

)

{overscore (h)}

\frac{h}{c_{p, s g} (T_{h, i} - T_{c, i})}

{dot over (m)}

chilled

chilled water flowrate (kgs

−1

)

{dot over (m)}

cond

condenser coolant flowrate (kgs

−1

)

{dot over (m)}

cooling

adsorber coolant flowrate (kgs

−1

)

{dot over (m)}

heating

desorber waste heat source flowrate (kgs

−1

)

{dot over ({overscore (m)})}

\frac{\dot{m}}{{\dot{m}}_{c o o l i n g}}

M

cond

mass of condenser heat exchanger tube (kg)

M

evap

mass of evaporator heat exchanger tube (kg)

M

Hex

mass of heat exchanger tube and fin in the bed (kg)

M

sg

mass of silica gel mass in one bed (kg)

n,N

1

,N

2

number of discrete elements in the heat exchanging tubes

NTU

cooling

\frac{U_{c o o l i n g} A_{b e d} / N}{{\dot{m}}_{c o o l i n g} c_{p} (T_{c, i})}

NTU

chilled

\frac{U_{c h i l l e d} A_{e v a p} / N_{1}}{{\dot{m}}_{c h i l l e d} c_{p} (T_{c h i l l e d, i})}

NYU

cond

\frac{U_{c o n d} A_{c o n d} / N_{2}}{{\dot{m}}_{c o n d} c_{p} (T_{c, i})}

NTU

heating

\frac{U_{h e a t i n g} A_{b e d} / N}{{\dot{m}}_{h e a t i n g} c_{p} (T_{h, i})}

p pressure (Pa)

P

cond

condenser pressure (Pa)

P

evap

evaporator pressure (Pa)

P

sat

saturated vapour pressure (Pa)

R universal gas constant (Jmol

−1

K

−1

or Jkg

−1

K

−1

)

P

p

average radius of silica gel (m)

t time (s)

t

cycle

cycle time (s)

t

sw

switching time (s)

T temperature (K or ° C.)

T

bed,I

bed I temperature (K or ° C.)

T

c,i

coolant water inlet temperature to the condenser (K or ° C.)

T

chilled,i

chilled water inlet temperature to the evaporator K or ° C.)

T

chilled,o

chilled water outlet temperature from the evaporator (K or ° C.)

T

cond

condenser temperature (K or ° C.)

T

evap

evaporator temperature (K or ° C.)

T

h,i

waste heat supply temperature to the chiller (K or ° C.)

T

i

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

T

ref

refrigerant temperature (K or ° C.)

T

sg

silica gel temperature (K or ° C.)

{overscore (T)}

\frac{T - T_{c, i}}{T_{h, i} - T_{c, i}}

U

cooling

adsorber heat transfer coefficient (Wm

−2

K

−1

)

U

beating

desorber heat transfer coefficient (Wm

−2

K

−1

)

U

chilled

evaporator heat transfer coefficient (Wm

−2

K

−1

)

U

cond

condenser heat transfer coefficient (Wm

2K

−1

)

V

x

—tube

volume of fluid within the heat exchanging tube of component x, where x could be the bed, evaporator, or condenser (m

3

)

β

cond

\frac{M_{c o n d} c_{p, c o n d}}{M_{s g} c_{p, s g}}

β

evap

\frac{M_{e v a p} c_{p, e v a p}}{M_{s g} c_{p, s g}}

β

Hex

\frac{M_{H e x} c_{p, H e x}}{M_{s g} c_{p, s g}}

β

ref

\frac{M_{r e f} c_{p, r e f}}{M_{s g} c_{p, s g}}

β

x—tube,i

\frac{ρ (T_{i}) V_{x_tube} c_{p} (T_{i}) / N_{x}}{M_{s g} c_{p, s g}};

if x refers to the bed, N

x

=N, if x refers to the evaporator and condenser, N

x

=N

1

and N

x

=N

2

respectively

δ

I

,θ

I

flags governing the transient operation of bed I

ΔH

ads

isosteric heat of adsorption

{overscore (ΔH)}

ads

\frac{Δ H_{a d s}}{c_{p, s g} (T_{h, i} - T_{c, i})}

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

τ

t / t_{cycle}

\frac{{\dot{m}}_{cooling} t_{cycle}}{M_{sg}}

ω

sw

\frac{{\dot{m}}_{cooling} t_{sw}}{M_{sg}}

Number	Name	Date	Kind
4548046	Brandon et al.	Oct 1985	A
4881376	Yonezawa et al.	Nov 1989	A
5360057	Rockenfeller et al.	Nov 1994	A
5463879	Jones	Nov 1995	A
5664427	Rockenfeller et al.	Sep 1997	A
5823003	Rosser, Jr. et al.	Oct 1998	A
6041617	Sanada et al.	Mar 2000	A

	Number	Date	Country
Parent	PCT/SG99/00136	Dec 1999	US
Child	09/875922		US

Regenerative adsorption process and multi-reactor regenerative adsorption chiller

Information

Patent Number

Date Filed

Date Issued

Inventors

Original Assignees

Examiners

Agents

CPC

US Classifications

Field of Search

US

International Classifications

Abstract

Description

Claims

Parent Case Info

US Referenced Citations (7)

Foreign Referenced Citations (1)

Continuations (1)