I. TECHNICAL FIELD

This invention relates generally to heat pumps and more particularly to heat pumps which use beds of solid adsorbent to drive the heat pump loop in response to the heating and cooling of beds.

II. BACKGROUND ART

Heat driven heat pumps which use solid adsorbent beds to adsorb and desorb a refrigerant are known in the art. These solid adsorbent beds exhibit the phenomena of adsorbing and desorbing refrigerant vapor in response to the changes in the temperature of the adsorbent. One common example of such" solid adsorbent ^' material is molecular sieves, commonly known as zeolite. Other mat- erials which exhibit this phenomena are silica gel, alumina and activate charcoal. Most any liquid which can be vaporized can be used as the refrigerant. Water is commonly used as a refrigerant with -zeolite.

Because such beds desorb refrigerant vapor when heated and adsorb refrigerant vapor when cooled, they can be used to drive the refrigerant around a heat pump loop to heat or cool a desired space. In the heat pump loop the refrigerant is desorbed from the beds as it is heated to drive refrigerant out of the bed to a conden- ser to condense the vapor. The condensed refrigerant is then expanded through an expansion valve and passes to an evaporator where the refrigerant is again vaporized. When the bed is cooled, refrigerant vapor from the con¬ denser is adsorbed into the bed to complete the cycle. Because a bed cannot readily adsorb and desorb refrig¬ erant at the same time, two solid adsorbent beds are typically used with one being heated while the other is cooled. The heating and cooling steps are reversed when the beds are heated and cooled to the desired tempera- ture limits during a cycle.

A number of different arrangements have been pro¬ posed for heating and cooling the beds of solid adsor¬ bent. One common technique uses a heat transfer fluid with a heat exchange arrangement between the fluid and each solid adsorbent bed so that heat is exchanged bet¬ ween the heat transfer fluid and the bed as the heat transfer fluid is circulated through the heat transfer arrangement. The heat transfer fluid is also connected to an external cooling heat exchanger to cool the fluid and an external heater to heat the fluid. The heat transfer loop may be operated in two different ways. One way is to circulate part of the heat transfer fluid heated by the heater through the bed to be heated and then directly back to the heater for reheating while circulating another part of the heat transfer fluid cooled by the cooling heat exchanger through the bed to be cooled and then .directly back to the cooling heat ex¬ changer. Another way is to circulate the heated heat transfer fluid from the heater through the bed being heated, then through the cooling heat exchanger to finish cooling the heat transfer fluid, then through the bed being cooled, and finally back to the heater to finish heating the heat transfer fluid. Such an arrangement is illustrated in U. S. Patent No. 4,183,227 issued January 15, 1980 to J. Bouvin et al. None of these prior art systems suggested any particular method of operation therefor except that the beds are simply heated or cooled until the entire bed has reached the end temperature limits of the cycle step. Good engineering practice suggests that the average heat transfer rate between the heat transfer fluid and the bed are kept as high as possible. This suggests that heat should be transferred between the fluid and bed at all times while the fluid and bed are in a heat transfer relationship with each other. As a

result, temperature gradients lengthwise of the bed are to be avoided. Using this criteria, the heating co¬ efficient of performance (COP) is typically on the order of 1-1.5 while the cooling COP is typically on the order of 0.1-0.5. The system performance based on this operation has not been able to economically com¬ pete with mechanical compressor heat pump systems. III. SUMMARY OF THE INVENTION

These and other problems and disadvantages associ- ated with the prior art are overcome by the invention disclosed herein by providing a method of operating a solid adsorbent, heat driven heat pump system so that the coefficient of performance (COP) thereof is greatly increased over prior art operating methods so as to economically compete with mechanical compressor heat pump systems. The method of the invention operates contra to good engineering practice in that a tempera- 'ture gradient is established lengthwise of the solid adsorbent bed to establish a thermal wave in the bed moving axially thereof. Preferably, substantially all the heat is transferred at the wave front rather than along the entire length of the bed. Using this criteria, heating coefficient of performances (COP) on the order of 2.5-3.0 and cooling COP on the order of 1.5-2.0 are achieved.

During operation, one of the solid adsorbent beds is being cooled while the other bed is being heated with the heating and cooling cycle steps being reversed so that both beds are heated and then cooled during a cycle. The heat exchange arrangement includes a heat exchanger associated with each bed that allows the heat transfer fluid to move generally axially through the solid adsor¬ bent bed in a single pass. The cooling heat exchanger is connected between one end of the bed heat exchangers while the heater is connected between the other ends of

the bed heat exchangers. A reversible pumping means circulates the heat transfer fluid in either direc¬ tion around the circuit. Thus, the heat transfer fluid always flows serially from the heater through one of the bed heat exchangers to heat that bed while cooling the heat transfer fluid, then through the cooling heat exchanger to further cool the heat trans¬ fer fluid, then through the other bed heat exchanger to coo-I that bed while heating the heat transfer fluid, and finally back to the heater to be heated- back to the initial temperature. This cycles both beds between the upper and lower operating tempera¬ tures selected for the system. The heat transfer fluid flow rate and bed heat exchanger design are selected to establish the thermal waves in the beds. The heater heats the heat transfer fluid to the upper operating temperature while the cooling heat exchanger cools the heat transfer fluid to the lower operating temperature. As the hot heat transfer fluid passes through the cooler bed heat exchanger, it is cooled to the bed temperature well before it reaches the exit end of the bed so that the exiting heat transfer fluid is at the initial cool bed temperature. As the ther¬ mal wave moves lengthwise of the bed, the temperature of the heat transfer fluid exiting the bed remains at the initial cool bed temperature until the thermal wave reaches the exit end of the bed. The cooling heat exchanger then cools the already cooled heat transfer fluid down to the lower operating temperature for the system. As the cold heat transfer fluid passes through the hotter bed heat exchanger, it is heated to the bed temperature well before it reaches the exit end of the bed so that the exiting heat transfer fluid is at the initial hot bed temperature. As the thermal wave moves lengthwise of the bed, the temperature of

the heat transfer fluid exiting the bed remains at the initial hot bed temperature until the thermal wave reaches the exit end of the bed. The heater then re¬ heats the heat transfer fluid back to the upper operating temperature for recycling. When the thermal waves reach the exit ends of the beds, the flow of the heat transfer fluid is reversed so that the heated bed is cooled and the cooled bed is heated.

To achieve a thermal wave, it is necessary that the desired bed temperature differential along its length be achieved within a distance less than the bed length. Preferably, the wavelength should be as short as possible. It has been determined that the key corre¬ lating parameter for wave length is the fluid Peclet number divided by one plus the bed/fluid thermal con¬ ductance ratio. Further, it has been found that a thermal wave will be produced when this wavelength parameter is greater than one but less than the bed Biot number. The optimum value of this wavelength parameter which produces the shortest thermal wavelegnth has been found to be the square root of the bed Biot number.

IV. BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1. is a schematic drawing illustrating the apparatus of the invention;

Fig. 2 is a chart illustrating the solid adsor- bent operating cycle;

Fig. 3 is a diagram illustrating thermal wave¬ length;

Figs. 4A-4D illustrate the temperature profiles during operating of the apparatus of Fig. 1; Fig. 5 is a chart correlating wavelength with the key correlating wavelength parameter; and

Fig. 6 is a chart correlating the maximum per¬ missible key correlating wavelength parameter with Biot number.

V. DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Referring to Fig. 1 it will be seen that the apparatus for practicing the invention includes a heat pump loop 10 and a heat transfer loop 11. The heat pump loop 10 includes a pair of solid adsorbent beds 12 and 14, a condenser 15 connected to both of the beds 12 and 14 in parallel through check valves 16 that allow refrigerant vapor to flow only from the beds 12 and 14 to the condenser, an evaporator 18 connected to both of the beds 12 and 14 through check valves 19 that allow refrigerant vapor to flow only from the evaporator into the beds, and an expansion valve 20 connecting the condenser and evaporator to allow the refrigerant to flow from the condenser to the evaporator. While one of the beds 12 and 14 is heated, the other is cooled so that refrigerant vapor desorbed from the bed- being heated flows to the con-, denser 15 while refrigerant vapor from the evaporator 18 flows to the bed being cooled to be adsorbed therein.

The heat transfer loop 11 includes a pair of bed heat exchangers 21 and 22 respectively associated with the beds 12 and 14 to place a he.at transfer fluid in a heat exchange relation with the beds 12 and 14. A heater 24 connects the heat exchangers 21 and 22 bet¬ ween one end of the beds 12 and 14 while a cooling heat exchanger 25 connects the heat exchangers 21 and 22 between the other ends of the beds. One or more pumps 26 are provided for pumping the heat transfer fluid around the heat transfer loop in either direction. _' A modulating bypass valve 28 connects the common point in loop 11 between the bed heat exchanger 21 and the cooling heat exchanger 25 with the common point bet¬ ween the heater 24 and- the bed heat exchanger 22. A similar modulating bypass valve 29 connects the common

point in loop 11 between the bed heat exchanger 22 and cooling heat exchanger 25 with the common point between heater 24 and the bed heat exchanger 21. A controller 20 is provided for operating pumps 26 and valves 28 and 29. The controller 30 has temperature pickups at the opposite ends of the beds 12 and 14 to monitor the fluid temperature of the heat transfer fluid as it exits the beds. As will become more apparent, the controller 30 controls the pumps 26 and the valves 28 and 29 in response to the exit fluid temperature to reverse the flow of heat tranfer fluid around the heat transfer loop 11 and to control the amount of heat transfer fluid that will bypass one of the beds. The solid adsorbent material used in the beds 12 and 14 may be any such material which adsorbs and de- sorbs -a refrigerant vapor. One material commonly used is natural or synthetic zeolite or molecular sieves and will be used in the example disclosed herein. Any liquid which vaporizes over the pressure and tempera¬ ture range available in the system may be used as the refrigerant. A convenient liquid is water and will be used as the refrigerant in the example disclosed here¬ in. The specific solid adsorbent and refrigerant dis- closed, however, is not meant to be limiting.

Fig. 2 is a chart showing the water adsorption characteristics of a commercially available zeolite from Union Carbide designated as "Molecular Sieve Type 5A". Other zeolites would have similar characteristics. The loading curves shown in Fig. 2 are expressed in terms of pounds of adsorbed water vapor per one hundred pounds of zeolite. Using a typical condensing tempera¬ ture of about 100°F. and evaporating temperature of about 40°F., it will be seen that the zeolite wll ab- sorb about 18 pounds of water vapor/100 pounds of

zeolite when the zeolite is cooled to about 100°F. and will desorb the vapor down to about 2 pounds water vapor/100 pounds zeolite when the zeolite is heated to about 600"F. These temperatures are selected for the system operating example disclosed herein but are not meant to be limiting. The operating cycle of the bulk of each adsorbent bed 12 and 14 has been super¬ imposed on the loading curves of Fig. 2. As the bed is cooled from about 550°F. to 100°F. at evaporator pressure the water vapor loading is increased from about 1.5 pounds to about 17.5 pounds. When the bed is adiabatically pressurized until condenser pressure is reached, the water vapor loading is initially in¬ creased to about 18.5 pounds. As the bed is heated from about 150°F. to 500°F. at condenser pressure, water vapor loading is decreased from about 18.5 pounds to about 2.5 pounds. As the bed is adiabatically de- pressurized until- evaporator pressure is reached, the water vapor loading is reduced to about 1.5 pounds. The cycle is then repeated. Thus, it will be seen that each bed will be cooled to adsorb water vapor at constant evaporator pressure and temperature; then pressurized to condenser pressure; then heated to desorb water vapor at constant condenser pressure and temperature; and finally depressurized back to evap¬ orator pressure.

Heat is transferred into the heat transfer fluid by the heater 24 and is transferred out of the heat transfer fluid by the cooling heat exchanger 25 with a low coefficient of performance. On the other hand, heat is transferred by the condenser 15 and evapora¬ tor 18 with a high coefficient of performance. There¬ fore, minimizing the heat transferred by the heater 24 and heat exchanger 25 and maximizing the heat transferred by the condenser 15 and evaporator 18

serves to maximize the overall COP of the system. The method of the invention disclosed herein minimizes the temperature drop across both the cooling heat exchan¬ ger 25 and the temperature rise across heater 24 while still being able to cycle the beds between the upper and lower temperatures required to operate the system.

As was explained, one of the beds 12 or 14 is being heated while the other bed 12 or 14 is being cooled. After one bed has been heated and the other bed cooled, the fluid flow is reversed so that the heated bed is cooled and the cooled bed is heated. Each is heated to the desired upper operating temp¬ erature at condenser pressure and is cooled to the desired lower operating temperature at evaporator pressure. As will become more apparent, reversing the fluid flow serves to initially adiabatically de- pressurize the bulk of the hot bed down to evapora¬ tor pressure and adiabatically pressurize the bulk of the cool bed up to condenser pressure. This re- suits in the temperature of the bulk of the hot bed being lowered to an intermediate upper temperature during this initial depressurization while the temp¬ erature of the bulk of the cool bed is raised to an intermediate lower temperature during this initial pressurization. Thus, in the example illustrated in Fig. 2, the upper temperature of 600°F, at con¬ denser pressure is lowered to an intermediate upper temperature of about 550°F. at evaporator pressure while the lower temperature of 100°F. at evaporator pressure is raised to an intermediate lower tempera¬ ture of about 150°F. at condenser pressure when the cycle is reversed.

From the foregoing, it will be seen that the fluid temperature entering the bed being heated must be at least as high as the desired upper operating

temperature and that the fluid temperature entering the bed being cooled must be at least as low as the desired lower operating temperature. The method of the invention maintains the minimum temperature drop across the cooling heat exchanger 25 by keeping the temperature of the fluid entering same from the bed being heated at the intermediate lower temperature while maintaining the minimum temperature rise across the heater 24 by keeping the temperature of the fluid entering same from the bed being cooled at the intermediate upper temperature.

To keep the temperature of the heat transfer fluid exiting the bed being heated at the inter¬ mediate lower temperature and the temperature of the heat transfer fluid exiting the bed being cooled at the intermediate upper temperature, a thermal wave is established within each bed which travels lengthwise of the' bed as it i-s heated or cooled. The thermal wave in the bed being heated has a temperature differential thereacross from the upper temperature to the intermediate lower temp¬ erature while the thermal wave in the bed being cooled has a temperature differential thereacross from the lower temperature to the intermediate upper temperature. This, of course, requires that the beds 12 or 14 be capable of having a large temperature differential lengthwise of the bed. In order to develop a thermal wave moving lengthwise of the beds 12 and 14, the heat exchan- gers 21 and 22 placing the heat transfer fluid in a heat exchange relationship with the beds ove _^ the heat transfer fluid in a single direction along the length of the bed. Typically the heat exchangers 21 and 22 are constructed of one or more tubes through which the heat transfer fluid passes and

around which the solid adsorbent is held by a hous¬ ing shell to transfer heat between the fluid and ad¬ sorbent.

To keep the temperature of the heat transfer fluid exiting the bed at the desired temperature, it is necessary to reverse the heating or cooling step when this temperature starts to raise above or drop below this desired temperature by a prescribed amount. To achieve a cycle time of any duration, it will be seen that the thermal wave must have a wavelength shorter than the length of the bed. As will become more apparent, some portion of each end of the bed will effectively not be utilized. The portions of the bed not being utilized will be mini¬ mized when the thermal wavelength is minimzed. Fig. 3 illustrates the thermal wavelength tw as used herein as being the ^* axial bed distance between the point where dimensionless fluid temperature Tr=0.9 to the point where T.p=0.1 and where:

t, =bed temperature at a selected axial position t. ^=: initial bed temperature at start of cycle t =fluid temperature entering bed

Operation

The overall operating cycle of the system can be divided into four distinct process steps, Steps A-D. Step A is a heating/cooling step where one bed is being heated while the other bed is being cooled. Step B is a pressurization/depressuriza- tion step following Step A where the hot bed is de- pressurized to evaporator pressure while the cool bed is pressurized to condenser pressure. Step C follows Step B and is the reverse of Step A in that the bed which was heated in Step A is cooled and the bed that was cooled in Step A is heated. Step A follows Step C and is the reverse of Step B in that the bed pressurized in Step B is depressur- ized back to evaporator pressure and the bed de- pressurized in Step B is repressurized back to condenser pressure. These steps allow the cycle to be repeated between the upper and lower desired operating temperatures. It will also be appreci- ated that the driving force for carrying out the operating cycle is provided simply by heating and cooling the heat transfer fluid and controlling its circulation.

In the following discussion of the operating cycle, the refrigerant is water while the beds 12 and 14 are made of the zeolite described in Fig. 2 by way of example. It will be appreciated that similar operating cycles can be -achieved using the different solid adsorbents and also using different refrigerants. For convenience, the following ex¬ ample of the operating cycle uses a lower tempera¬ ture of 100°F. and an upper temperature of 600°F. between which the beds are cycled, however, it is to be understood that different temperature ranges can just as easily be used. Since one of the beds

ust be heated and the other bed cooled at the be¬ ginning of an operating cycle, the bed 12 has been selected as being initially cool and at condenser pressure while the bed 14 is selected to be initi- ally hot and at evaporator pressure. Also, for simplicity, the cycle is described after the system has been operating sufficiently to reach steady state conditions.

In Step A, the bed 12 is to be heated while the bed 14 is to be cooled. The pump 26 is opera¬ ted to force the heat transfer fluid around the heat transfer loop 11 in a clockwise direction as seen in Fig. 1 so that the heat transfer fluid flows from the heater 24 through the bed 12, then through the cooling heat exchanger 25, then through the bed 14 and finally back to the heater 24. The heater 24 always heats the heat transfer .fluid to the upper operating temperature for the system. in the particular example, this temperature is 600°F. The cooling heat exchanger 25 always cools the heat transfer fluid to the lower temperature at which the system is to be operated. In the example, this lower temperature is 100°F.

Fig. 4A-1 illustrates the temperature profile. in the cool bed 12 and Fig. 4A-2 illustrates the temperature profile in the hot bed 14 during Step A in the operating cycle. This temperature profile at-the beginning of the cycle is illustrated in a solid line in Figs. 4A-1 and 4A-2 while the tempera- • ture profile in the bed at the end of the cycle is illustrated in dashed lines in the figures. As was indicated above, the temperature profile at the be¬ ginning of the cycle assumes that the system has been operating until steady state conditions have been achieved. It will be noted that the tempera-

ture profile along the length of the bed will vary so that a thermal wave is left in the bed from the last cycle. The thermal wave will be located at that end of the particular bed from which the heat transfer fluid exited the bed during the last heat¬ ing or cooling of the bed in the last cycle. In this example, the thermal wave is located in the left end of both of the beds 12 and 14 as seen in Figs. 1 and 4A at the beginning of Step A. Pre- ferably, the heat transfer fluid will flow into the bed from that end at which the thermal wave is lo¬ cated at the beginning of the pro-cess step. Thus, the heat transfer fluid flows into the left end of both of the beds 12 and 14 during Step A. As the pump 26 pumps the heat transfer fluid from the heater 24 through the heat exchanger 21 in bed 12, the hot heat transfer fluid entering the left end of bed 12 as seen in Fig. 1 starts heating the bed up to 600°F. from its left end. As will become more apparent, the system operating parameters are selected so that the heat transfer fluid passing through bed 12 will be cooled down to the initial bed temperature of about 150°F. well before the heat transfer fluid reaches the opposite end of the bed. The cooled heat transfer fluid at about 150°F. then flows through the heat transfer coil 25 where it is cooled down to the lower opera¬ ting temperature of about 100°F. The cold heat transfer fluid enters the left end of the bed 14 through its heat exchanger 22 as seen in Fig. 1 to start cooling the bed 14 down to about 100°F. from its left end. The system operating parameters are such that the heat -transfer fluid passing through bed 14 will be heated up to the initial bed temp- erature of about 550°F. well before it reaches the

opposite end of the bed. The reheated heat transfer fluid then flows back to heater 24 where it is re¬ heated back to the upper operating temperature of about 600°F. and recirculated around the heat trans- 5 fer loop.

As pump 26 continues to circulate the heat transfer fluid around loop 11 in the clockwise dir¬ ection as seen in Fig. 1, the thermal wave in the temperature profile moves lengthwise of the beds 0 12 and 14 from the fluid inlet end toward the fluid exit end of the beds. In Fig. 1 these thermal waves move from the left to the right along the beds. As best seen in Fig. 4A-1, that portion of the bed 12 on the left side of the .thermal wave 5 therein is about 600°F. while that portion of bed 12 on the right side of the thermal wave is at about 150°F. From Fig. 4A-2, that portion of the bed 14 on the left side of the thermal ^' wave there¬ in is at about 100°F. while that portion of bed 14

20 on the right side of the thermal wave is at about 550°F.

Since the bed 12 is at uniform condenser pressure during Step A, that portion of the bed 12 across which the thermal wave temperature difference

25 is being imposed desorbs the refrigerant vapor from its initial high loading of about 18.5 pounds water vapor/100 pounds adsorbent at about 150°F. down to the lower loading of about 2.5 pounds of water vapor/100 pounds of adsorbent at about 600°F. That ^'"

3.0 portion of the bed 12 on the right hand side of the thermal wave remains at the high loading while that portion of the bed on the left hand side of the thermal wave is at" the lower loading. Thus, more and more of the water vapor in the bed 12 is de-

35 sorbed as the thermal wave moves to the right and

is expelled into the condenser.

Since the bed 14 is at uniform evaporator pressure during Step A, that portion of the bed 14 across which the thermal wave temperature difference is being imposed adsorbs the refriger¬ ant vapor from its initial low loading of about 1.5 pounds water vapor/100 pounds adsorbent at about 550°F. up to the higher loading of about 17.5 pounds water vapor/100 pounds adsorbent at about 100°F. That portion of the bed 14 on the right hand side of the thermal wave remains at the low loading while that portion of the bed on the left hand side of the thermal wave is at the higher loading. Thus, more and more water vapor from the evaporator 18 is adsorbed in the bed 14 as the thermal wave moves to the right.

The pump 26 continues to circulate the heat transfer fluid clockwise around ^* the heat transfer loop 11 until the thermal waves in beds 12 and 14 reach the right hand ends thereof as shown by the dashed line temperature profiles in Figs. 4A-1 and 4A-2. This is usually detected by monitoring the temperature of the heat transfer fluid passing out of bed 12 and out of bed 14. The pump 26 is stopped when the fluid temperature at the right hand end of bed 12 rises a prescribed amount above the initial bed temperature of about 150°F. or when the fluid temperature at the right hand end o ^' f bed 14 drops a prescribed amount below the initial bed tempera- - ture of about 550°F. This completes the process Step A leaving the major portion of bed 12 at the lower loading of about 2.5 pounds water vapor/100 pounds solid adsorbent and the major portion of bed 14 at the higher loading of about 17.5 pounds water vapor/100 pounds solid adsorbent.

To initiate the process Step B, the pump 26 is operated to circulate the heat transfer fluid in a counter-clockwise direction as seen in Fig. 1. The heater 24 continues to heat the heat transfer fluid to 600°F. while the heat exchanger 25 continues to cool the heat transfer fluid to about 100°F. Be¬ cause the fluid circulates in the reverse direction, the hot heat transfer fluid from heater 24 enters the right hand end of the bed 14 while the cold heat transfer fluid from the heat exchanger 25 enters the right hand end of the bed 12. At the initia¬ tion of process Step B, the bed 12 is at condenser pressure while the bed 14 is at evaporator pressure. The hot heat transfer fluid from heater 24 to bed 14 starts heating the right hand end of this bed to start desorbing water vapor from the solid adsorbent at that end of the bed. Because no water vapor flows from the bed 14 to evaporator 18 due to check valve 19 or to condenser 15 due to the pressure differential, the water vapor being desorbed from the end of the bed serves to pressurize the entire bed 14. It will be appreciated that the bed 14 to the left of the thermal wave is adiabatically pressurized. As the pressure in the bed 14 is in- creased, the adsorbent material in the bed 14 to the left of the thermal wave tends to adsorb more re¬ frigerant vapor throughout the bed and this adsorp¬ tion releases the heat-of-adsorption from the ad¬ sorbed refrigerant to raise the temperature of that portion of the bed 14. By the time the bed 14 is pressurized to condenser pressure, the released heat-of-adsorption will have raised the temperature of that portion of the bed 14 to the left of the thermal wave in the temperature profile of bed 14 as seen in Fig. 4B-2 from 100°F. as shown by solid

line to 150°F. as shown by dashed line. This increase in pressure will also cause an increase in refrigerant vapor loading from the 17.5 pounds water vapor/100 pounds solid adsorbent at 100°F. to about 18.5 pounds water vapor/100 pounds solid adsorbent at 15Q°F. The solid line in Fig. 4B-2 shows the profile at the be¬ ginning of Step B while the dashed line shows the pro¬ file at the end of Step B.

The heat transfer fluid passing through bed 14 is cooled to the temperature of the bed to the left of the thermal wave and thus passes out of the bed 14 to the heat exchanger 25 at this lower temperature. The heat exchanger 25 cools the heat transfer fluid down to about 100°F. The cold heat transfer fluid entering the right hand end of bed 12 as seen in Fig. 1 starts cooling the right hand end of the bed causing it to adsorb re¬ frigerant vapor. Because no water vapor flows into bed 12 from condenser 15 due to check valve 19 or from evaporator 18 due to pressure differential, the water vapor being adsorbed in the end of the bed serves to depressurize the entire bed 12. It will be appre¬ ciated that the bed 12 to the left of the thermal wave is adiabatically depressurized. This depressurization causes that portion of bed 12 to the left of the ther¬ mal wave to tend to desorb some of the refrigerant vapor and the heat-of-desorption therefor cools that portion of the bed to the left of the thermal wave. By the time the bed 12 is depressurized to ^" evaporator pressure, the heat-of-desorption has cooled that por¬ tion of the bed 12 to the left of the wave in the temperature profile of bed 12 as seen in Fig. 4B-1 from about 600°F. as shown by solid line to about 550°F. as shown by dashed line. This decrease in pressure causes a decrease in refrigerant vapor load-

ing from about 2.5 pounds water vapor/100 pounds solid adsorbent at 600°F. to about 1.5 pounds water vapor/ 100 pounds solid adsorbent at 550°F. The solid line in Fig. 4B-1 shows the temperature profile at the be- ginning of Step B while the dashed line shows the profile at the end of Step B.

At the end of process Step B, the hot bed 12 will be at evaporator pressure and with the thermal wave located at the right hand end of the bed. That por- tion of the bed 12 to the left of the thermal wave will be at the intermediate lower temperature of 550°F. The cool bed 14 will be at evaporator pressure with the thermal wave located at the right hand end of the bed. That portion of the bed to the left of the thermal wave will be at the lower intermediate temper¬ ature of 150°F.

. In process Step C, the pump 26 is operated to continue to circulate the heat transfer fluid in a counter-clockwise direction about the heat transfer loop 11 as seen in Fig. 1. .As the hot heat transfer fluid from heater 24 enters the right end of the bed, it starts heating the bed 14 up to 600°F. from that right end. The hot heat transfer fluid passing through the bed 14 will be cooled down to the initial bed temperature of about 150°F. well before the heat transfer fluid reaches the opposite end of the bed. The cooled heat transfer fluid at about 150°F. then flows through the cooling heat exchanger 25 where it is cooled down to the lower operating temperature of about 100°F. The cold heat transfer fluid enters the right end of the bed 12 through its heat exchanger 21 as seen in Fig. 1 to start cooling the bed 12 down to about 100°F. from its right end. The heat transfer fluid passing through the bed 12 will be heated up to the initial bed temperature of about 550°F. well

before it reaches the opposite end of the bed. The reheated heat transfer fluid then flows back to the heater 24 where it is reheated back to the upper operating temperature of about 600°F. and recircu- lated around the heat transfer loop. As the pump 26 continues to circulate heat transfer fluid around the loop 11 in a counter-clockwise direction as seen in Fig. 1, the wave in the temperature profile moves lengthwise of the beds 12 and 14 from the right end thereof toward the left end. That portion of the bed 14 on the right side of the thermal wave is at about 600°F. while that portion of the bed 12 on the left side of the thermal wave is at about 150°F.. as best seen in Fig. 4C-2. From Fig. 4C-1, that portion of the bed 12 o-n the right side of the thermal wave is at about 100°F. while that portion of the bed 12 on the left-'side of the thermal wave is about 550°F.

Since the bed 14 is at uniform condenser pressure during Step C, that portion of the bed 14 across which the thermal wave temperature difference is be¬ ing imposed desorbs the refrigerant vapor from its initial high loading of about 18.5 pounds water vapor/ 100 pounds solid adsorbent at about 150°F. down to the lower loading of about 2.5 pounds water vapor/100 pounds solid adsorbent at about 600°F. That portion of the bed 14 on the left hand side of the thermal wave remains at the high loading while that portion of the bed on the right -hand side of the thermal wave is at the lower loading. Thus, more and more of the 'water vapor in the bed 14 is desorbed as the thermal wave moves to the left and is expelled into the con¬ denser.

Since the bed 12 is at uniform evapora ^' tor pressure during Step C, that portion of the bed 12 across which the thermal wave temperature difference

is being imposed adsorbs the refrigerant vapor from its initial loading of about 1.5 pounds water vapor/ 100 pounds solid adsorbent at about 550°F. up to the higher loading of about 17.5 pounds water vapor/100 pounds solid adsorbent at about 100°F. That portion of the bed 12 on the left hand side of the thermal wave remains at the low loading while that portion of the bed on the right hand side of the thermal wave is at the high loading. Thus, more and more water vapor from the evaporator 18 is adsorbed in the bed 12 as the thermal wave moves to the left.

The pump 26 continues to circulate the transfer fluid counter-clockwise around the heat transfer loop 11 until the thermal waves in the beds 12 and 14 reach the left hand ends thereof as shown by the dashed line temperature profiles in Figs. 4C-1 and 4C-2. This is usually detected by monitoring the temperature of the heat transfer fluid passing out of the beds 12 and 14. The pump 26 is stopped when the fluid temperature at the left hand end of the bed 14 rises a prescribed amount above the initial bed temperature of about 150°F. or when the fluid temp- ^• erature at the left hand end of the bed 12 drops a prescribed amount below the initial bed temperature of about 550°F. This completes the process Step C leaving the major portion of the bed 14 ^' at the lower loading of about 2.5 pounds ^* ater vapor/100 pounds solid adsorbent and the major portion of the bed 12 at the higher loading of about 17.5 pounds water vapor/100 pounds solid adsorbent.

Process Step D is initiated by operating the pump 26 to again circulate the heat transfer fluid in a clockwise direction as seen in Fig. 1. The heater 24 continues to heat the heat transfer fluid up to about 600°F. while the heat exchanger 25 con-

tinues to cool the bed transfer fluid down to about 100°F. Thus, the hot heat transfer fluid from heater 24 once again enters the left hand end of the bed 12 while the cold heat transfer fluid from the heat ex- changer 25 again enters the left hand end of the bed 14. At the initiation of the process Step D, the bed 12 is normally at evaporator pressure while the bed 14 is at condenser pressure.

The hot heat transfer fluid from heater 24 to bed 12 starts heating the left hand end of this bed to start desorbing water vapor from the solid adsor¬ bent at that end of the bed. Because no water vapor flows from the bed 12 to evaporator 18 due to check valve 19 or to condenser 15 due to the pressure differential, the water vapor being desorbed serves to pressurize the entire bed 12. That portion of bed 12 to the right of the thermal wave is adiabati¬ cally pressurized. As the pressure in the bed 12 is increased, the adsorbent material in that portion of the bed 12 to the right of the thermal wave tends to adsorb more refrigerant vapor and this adsorption releases the heat-of-adsorption in the adsorbed re¬ frigerant to raise the temperature of that portion of the bed 12 to the right of the thermal wave. By the time the bed 12 is pressurized to condenser pressure, the released heat-of-adsorption will have raised the temperature of that portion of the bed 12 to the right of the wave in the temperature profile of bed 12 as seen in Fig. 4D-1 from 100°F. as shown by solid line to 150°F. as shown by dashed line.

This increase in pressure will also cause an increase in refrigerant vapor loading from the 17.5 pounds water vapor/100 pounds solid adsorbent at 100°F. to about 18.5 pounds water vapor/100 pounds solid ad- sorbent at 150°F. The heat transfer fluid passing

through bed 12 is cooled to a temperature of the bed to the right of the thermal wave and thus passes out of the bed 12 to the heat exchanger 25 at this lower temperature. The heat exchanger 25 cools the heat transfer fluid down to about 100°F.

The cold heat transfer fluid entering the left end of bed 14 as seen in Fig. 1 starts cooling the left hand end of the bed causing it to adsorb re¬ frigerant vapor. Because no water vapor flows into the bed 14 from condenser 15 due to check valve 19 or from evaporator 18 due to pressure differential, the water vapor being adsorbed in the end of the bed serves to depressurizethe entire bed 14. That por¬ tion of the bed 14 to the right of the thermal wave is adiabatically depressurized. This depressuriza- tion causes that portion of the bed 14 to the right of the thermal wave to tend to desorb some of the - refrigerant vapor and the heat-of-desorption there¬ for cools that portion of the bed to the right of the thermal wave. By the. time the bed 14 is de¬ pressurized to evaporator pressure, the heat-of- desorption has cooled that portion of the bed 14 to the right of the thermal wave in the temperature pro¬ file of bed 14 as seen in Fig. 4D-2 from about 600°F. as shown- by solid line to about 550°F. as shown by dashed line. This decrease in pressure causes a de¬ crease in refrigerant vapor loading from about 2.5 pounds water vapor/100 pounds solid adsorbent at 550°F. This completes the operation cycle of the system. As this time, the operation cycle is simply repeated.

The controller 30 monitors the heat transfer fluid temperature exiting both beds and reverses the fluid flow when the exit temperature of the heat transfer fluid shifts away from the initial bed

temperature at the beginning of the process step by a prescribed amount. The exit temperature of the fluid from either bed may be used by the controller 30 to reverse the flow of the heat transfer fluid. The particular exit temperature selected will depend on the particular system operating parameters and design. The particular amount that the fluid exit temperature is allowed to shift from the initial bed temperature may be varied to suit design con- siderations. ypically, a value is selected which permits the bed to continue to be heated or cooled with a thermal wave effect over an extended number of cycles while at the same time maximizing the sys¬ tem coefficient of performance. It has been found that the thermal wave will have a positive effect on the COP with a shift in the dimensionless fluid temp¬ erature Tr _, from its initial value at the beginning of the process step by as much as 0.5. A shift- of about 0.1-0.2 in the temperature T^ is typical. When operating according to the above cycle, it is preferable that the thermal waves in both beds reach the end of the beds at the same time in pro¬ cess Steps A and C. If the flow of heat transfer fluid through the beds is the same, however, the traveling thermal waves may not reach the fluid exit ends of both beds at the same time. The modu¬ lating bypass valves 28 and 29 are used to indivi¬ dually adjust the-flow of the heat transfer fluid through the beds so that the thermal waves arrive at the exit ends of the beds at about the same time. Since the amount that the exit temperature of the heat transfer fluid out of a bed has shifted with respect to the initial exit temperature at the be¬ ginning of the process step is representative of the position of the thermal wave in the bed, the

controller 30 uses these values to control the valves 28 and 29. The controller 30 detects the initial exit temperatures of the heat transfer fluid out of both of the beds at the beginning of process Step A. The controller 30 also detects the exit tempera¬ tures of the heat transfer fluid out of both of the beds at the end of process Step A and compares the initial and ending exit fluid temperatures for each bed 12 and 14 at the end of Step A. If the exit fluid temperature for one of the beds has shifted substantially more than that of the other bed, then the controller 30 adjusts the modulating bypass valves to change the heat transfer fluid flow rate through one of the beds during the following Step C to compensate for this difference. This process is repeated after Step C to adjust the fluid flow through the following Step A. The controller 30 con- tinues this adjustment process until the controller 30 causes the bypass valve adjustment to home in on the proper bypass flow of the heat transfer fluid to achieve equal times for the heating and cooling waves to traverse their respective beds. If the thermal wave arrives -first at the end of the bed being cooled, then the modulating bypass valves 28 and 29 are adjusted so that more fluid flows through the bed being heated in the next process step by bypassing a portion of the fluid from the inlet of the heater 24. If the thermal wave arrives first at the end of the bed heated, then the modulating bypass valves 28 and 29 are adjusted so that more fluid flows through the bed being cooled by bypass¬ ing a portion of the fluid.from the inlet of the heater 24 to the inlet of heat exchanger 25.

It will also be noted that the direction of flow of the heat transfer fluid through each bed is

reversed between Steps A and C. When the thermal wave is left in the exit end of the beds at the end of Steps A and C, this reversal of fluid flows through the bed permits the ends of the beds out- board of the thermal waves at the end of Steps A and C to cycle between evaporator and condenser pressures without cycling through the full temp¬ erature differential across the thermal wave. As a result, the amount of heat that is rejected by the heat exchanger 25 and added by heater 24 is minimized thus enhancing the COP of the system.

The above operating cycle description is given after the system has reached steady state opera¬ tion. It will be appreciated that the first cycle in any operation will typically find the beds with a different initial temperature profile. After the initial start up cycle, however, the thermal waves should be fully developed.

Using the above criteria, a theoretical heat- ing COP of about 3 and a theoretical cooling COP of about 2 is available. These theoretical values are based on the net heat input by the heater 24. Where the heater 24 uses a burner, the input energy to operate the system must also include the energy loss in the vented flue gasses.

Design Considerations

The creation of a thermal wave in the tempera¬ ture profile in a heat exchanging device is contra to normal engineering practice where temperature gradients are minimized and typically on the order of 10°F. in the device. In the invention of this application, the thermal wave in the temperature profile in the beds 12 and 14 is maximized.

From the foregoing, it will be seen that the thermal wavelength tw must be such that a thermal wave is in fact generated in the bed. Also, the shorter the wavelength, the longer the bed can be heated or cooled without having to reverse the flow of the heat transfer fluid through the bed and the greater volume of the bed that can be cycled bet¬ ween the upper and lower temperatures and the less be ^' d volume -required at the ends which is not com¬ pletely cycled through the temperatures.

It will also be understood that a thermal wave will be generated in both the hot transfer fluid passing through the bed and in the bed itself. While it is desirable. that the two wavelengths co¬ incide as much as possible and move axially along the length of the bed in registration with each other, the reversal of the flow of heat transfer fluid through the bed is normally based on the arrival of the thermal wave in the heat transfer fluid at the exit end of the bed in order to maxi¬ mize COP. The arrival of the thermal wave is det- ected by monitoring the temperature of the fluid at the exit end of the bed. The fluid flow is reversed when the exit fluid temperature shifts from the initial bed temperature by the above men¬ tioned prescribed amount. Using conservation of energy and Fourier heat

transfer laws, it has been found that the tempera¬ ture profile along the bed is a function of the bed Biot number Bi, the fluid Peclet number Pe, the thermal diffusivity ratio DR between the bed and fluid and the thermal conductance ratio KA between the bed and fluid. This nomenclature is set forth in more detail in Table A at the end of the speci¬ fication.- Since the temperature profile is a func¬ tion of these parameters, it follows that the'ther- mal wavelength tw is also a function of these para¬ meters. Since there is no closed form equation solution available for the temperature profile, it must be determined by numerical analysis (finite difference methods) requiring numerical values for the four non-dimensional parameters before wave¬ length can be found. These parameters can be further combined in a correlating parameter CP for the thermal wavelength where: ^cp ' T-TΠCA

The thermal wavelength tw can be expressed as non- dimensional wavelength TW where:

TW = -p (3)

The wavelength is also affected by the bed Biot number Bi. Fig. 5 is a graph showing the relation¬ ship between the dimensionless thermal wavelength TW for the thermal wave in the heat transfer fluid and the correlating parameter CP at different Biot numbers. In Fig. 5, the thermal conductance ratio KA was selected at 1,000 and the thermal diffusivity ratio, was selected at 100 as representative. Plots for other values of the ratios KA and DR show curves qualitatively and quantitatively similar to those shown. Fig. 5 shows wavelength curves for Biot numbers of 1,000; 100,000 and 10,000,000. The oper¬ ational efficiency of the system is affected when

the dimensionless wavelength TW is 0.9 or less. From Fig. 5, it will be seen that the lower limit¬ ing value for the correlating parameter CP is one regardless of Biot number value. Fig. 5 also shows that the operating parameter CP has an upper limit¬ ing value for each Biot number where the wavelength TW is 0.9. Fig. 6 is a graph showing the relation¬ ship between Biot number Bi and correlating para¬ meter CP at the upper limiting value of parameter CP for each Biot number. It will be seen that the upper limit of the correlating parameter CP is the Biot number value. From the foregoing, it will be seen that a thermal wave is established when the correlating parameter CP is greater than one but less than the Biot number which can be expressed as:

1 < CP < Bi (4)

Reference to Fig. 5 shows, that there is also an optimum value for the correlating parameter CP at each value of Biot number which produces the shortest dimensionless thermal wavelength. This optimum value of the parameter CP has been found to be the square root of the Biot number being used. Fig. 5 also demonstrates that the minimum dimension¬ less thermal wavelength TW which can be achieved decreases with increasing values of Biot number.

Therefore, the Biot number should be maximized for each design.

In the actual system design, it will be seen that the nondimension parameters Bi, Pe, DR and KA are effected by the refrigerant and adsorbent sel¬ ected, the bed heat exchanger design and the velocity of the heat transfer fluid through the bed heat ex- changer. Typically, the refrigerant and adsorbent are first selected and then the fluid velocity and heat exchanger design generated to meet the design

criteria. While different heat exchanger designs and fluid velocities can be used for any selected refrigerant and adsorbent, the following example sets out one heat exchanger design and fluid vel- ocity which falls in the system design criteria for a selected adsorbent and refrigerant.

This example incorporates a shell and tube type heat exchanger design for the bed heat ex¬ changers 21 and 22 where the heat transfer fluid passes through the tubes. Using water as the re¬ frigerant and zeolite as the adsorbent, the follow¬ ing design variables were selected: Bed length L = 6 feet Tube material = stainless steel Tube diameter = 0.25 inch

Tube wall thickness = 0.01 inch Distance between adjacent tubes = 0.15 inch - Heat transfer fluid flow rate - 0.3 gpm This selection produces the following values for the nondimensional parameters: Bi = 56,882 Pe = 56,416 DR = 6.7 ^* KA = 27.56 The correlating parameter CP thus is calculated to be about 1,992. This dimensionless thermal wave¬ length TW is calculated to be about 0.46 and thus allows a thermal wave to be generated in the opera¬ ting system. To operate the system so that the fluid flow through the beds is reversed as soon as the heat transfer fluid exit temperature out of the bed being heated starts rising significantly above the initial bed temperature gives a system cycle time of about 1.4 hours. Where the number of tubes in the bed heat ex-

changer is selected at 300, the bed mass is 129 pounds adsorbent/bed, the upper operating temp¬ erature is 600°F. , the lower operating temperature is 100°F., the condenser temperature of 100°F. , the evaporator temperature is 40°F. and the air temperature at the evaporator is 70°F. , the oper¬ ating COP can be calculated. The heating COP is calculated at about 2.6 while the cooling COP is about 1.6. This is assuming that the heat trans- fer fluid flow in the beds will be reversed as indicated above.

TABLE A Definit ions

n _f c _f LV P ^k .

KA ^k b ^A z k _f A _f

10 h = fluid to tube convective heat transfer coeffi¬ cient in bed heat exchanger P = inside wetter perimeter of cross-section of tube in bed heat exchanger ,.. L = bed length k, = effective axial thermal conductivity of bed in¬ cluding bed heat exchanger

Az= cross-sectional area of adsorbent to which single bed heat exchanger tube exposed _2n d = effective thermal diffusivity of bed including bed heat exchanger fluid thermal diffusivity fluid density C = fluid specific heat capacity

25 V = fluid velocity in tubes of heat exchanger fluid thermal conductivity cross-sectional area of fluid in tube in bed heat exchanger