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Ideal Adsorption Isotherm Behavior for Cooling Applications Morteza H. Bagheri, and Scott N Schiffres Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03989 • Publication Date (Web): 02 Jan 2018 Downloaded from http://pubs.acs.org on January 8, 2018
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Langmuir Title: Ideal Adsorption Isotherm Behavior for Cooling Applications Short Title (less than 40 characters): Ideal Adsorption Isotherm Behavior Authors: Morteza H. Bagheri‖, Scott N. Schiffres (ORCiD: 0000-0003-1847-7715)‖ Affiliations: ‖ State University of New York at Binghamton, Department of Mechanical Engineering, 4400 Vestal Pkwy E, Binghamton, NY 13902, United States * Corresponding Author -
[email protected] Abstract Purely heat-driven refrigeration has the potential for high primary-energy efficiency, especially when powered by waste heat or solar thermal sources. This paper presents a novel expression for ideal adsorption step location as a function of operating conditions. This methodology is then applied to a hypothetical stepwise material to evaluate its intrinsic efficiency. This analysis technique is then extended to allow facile efficiency comparisons for any adsorbent-refrigerant pair using an adsorbent’s isotherm and heat of adsorption properties. The work focuses on limitations to efficiency due to the equilibrium thermodynamics. It is found that a stepwise adsorbent can have a single-effect intrinsic efficiency as high as about 85% of Carnot assuming typical adsorbent specific heats and uptake capacity. Using these tools, we analyze the maximum ratio of cooling to heat input (coefficient of performance) for two adsorption pairs, zeolite 13X-water and UiO-66-water, which are found to have maximum coefficient of performances of 0.52 and 0.88 for a cold-side temperature of 10 °C and an ambient temperature of 30 °C. Meanwhile, the maximum fraction of Carnot cooling is 37% for zeolite 13X-water and 67% for UiO-66-water. Moreover, these peak fractions of Carnot occur at much higher regeneration temperatures for 13X (196 °C), than UiO-66 (60 °C). These two materials could be coupled in a two-stage cascading triple effect adsorption cycle that operates with a combined coefficient of performance of 1.50, at a regeneration temperature of 196 °C, a cold-side temperature of 10 °C, and an ambient temperature of 30 °C. Keywords Adsorption heat pump, ideal isotherm, adsorption refrigeration, stepwise isotherm, efficiency, primary coefficient-of-performance Introduction Recent advances in metal-organic frameworks and zeolites have the potential to dramatically improve the efficiency of adsorption technology. 1–12 This paper identifies 1 ACS Paragon Plus Environment
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1) the ideal isotherm shape for a desired cold-side temperature and regeneration temperature, and 2) provides a facile and novel method to plot efficiency for an adsorbent-refrigerant pair based solely on an isotherm and its heat of adsorption. While many experiments have compared the experimental performance of various refrigerantadsorbent pairs, the literature lacks a theoretical description of what adsorption uptake isotherms are ideal for adsorption refrigeration, and how that limits efficiency.13–16 With advances in nanoporous material design, especially metal-organic frameworks and zeolites, stepwise isotherms are feasible.1–12 The research of Meunier et al, Cacciola et al, have investigated optimizing traditional adsorption refrigeration pairs of NaX zeolitewater and activated carbon-methanol.17–19 While Meunier et al identifies step-like isotherm as ideal, this work did not explore where the step should be located as a function of temperature, nor did it explore the maximum potential efficiency of a material with ideal behavior. This work elucidates a simple technique to estimate the limiting performance of adsorbent-refrigerant pairs. This methodology generates a novel visual representation of the intrinsic material-limiting operating efficiency of adsorbent systems, which will help with optimal selection of refrigerant pairs as a function of ambient temperature, heat source temperature, and cold-side temperature. About two-thirds of energy consumed in buildings goes to maintain temperature and humidity-levels with astonishingly low energy efficiency.20 The average air conditioner has a 𝐶𝐶𝐶Cooling (ratio of heat removed to work input) of 3.6 compared to an ideal 𝐶𝐶𝐶Cooling of 11.3 under standard conditions (𝑇Amb = 35 °C, 𝑇Cold = 10 °C).21 To compare work-driven to heat-driven cycles, the heat removed should be normalized by the primary thermal energy required to drive the cycle. The cooling performance can be characterized by the primary coefficient of performance, 𝑃𝑃𝑃𝑃Cooling , which is the ratio of heat removed from the system to the total primary energy consumed. Primary coefficients of performance are less than one for typical air conditioners, hot water heaters, and boilers, assuming current commercial technology and electrical grid. Considering that the electrical energy to drive the compressor was generated at only 40% of Carnot efficiency (as typical for current grid power), the conventional air conditioner has a primary 𝐶𝐶𝐶Cooling that is just 13% of the Carnot limit. Aside from efficiency, it is also important to compare the lifetime average cost of the cooling, the greenhouse gases emitted during operation, and the global warming potential of the refrigerants. Adsorption refrigeration has the advantage of being able to utilize of low-grade heat from rooftop solar thermal or industrial sources, and zero global warming potential refrigerants.22,15,23,13,24,25 Adsorption refrigeration in its simplest single-effect form has two chambers, an adsorbent bed and a refrigerant reservoir. When the adsorbent bed is connected to the refrigerant reservoir, evaporation will cool the refrigerant reservoir and adsorption will heat the adsorbent bed (Figure 1a).26–28 In the summer, evaporative 2 ACS Paragon Plus Environment
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cooling provides building cooling and the heat of adsorption warms the hot water for the building. In the winter, heat released during adsorption and rejected by the condenser warm the building and hot water. The state of the adsorbent goes from state 1 to state 2 along the 𝑇Amb isotherm during adsorption.
After the adsorbent bed saturates, the adsorbent bed needs recharging (i.e., desorbing). Recharging occurs through heating the adsorbent bed (Figure 1b). The released vapor will condense in the condenser. During regeneration, the adsorbent state goes from state 3 to state 4 along the 𝑇Hot isotherm. The minimum uptake achieved during regeneration will be determined by the bed regeneration and condenser temperatures.
Figure 1: Adsorption refrigeration cycle schematic depicts (a) forward operation with cooling provided by the evaporator and heat rejected to the environment by the heat of adsorption. The isotherm behavior during adsorption follows the ambient temperature isotherm (blue) on the uptake versus pressure plot to the right (state 1 to 2). (b) In reverse operation or regeneration heat is input into the adsorbent bed to liberate the adsorbed refrigerant. The refrigerant vapor is condensed in the condenser, releasing the heat of condensation. The thermodynamic state during desorption follows the hot isotherm (red) (state 3 to 4).
Single-bed adsorption refrigerators have two operating states: forward operation and reverse operation. In the forward mode, the adsorbent should have high uptakes when the bed is at the hottest possible outside temperature (𝑇Amb ), and the evaporator is at the required cooling temperature (𝑇Evap ). Meanwhile, the bed should desorb at a minimum 3
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regeneration temperature (𝑇Hot ) even while the condenser is at the hottest possible outside temperature (𝑇Amb ). Optimizing for these two modes of operation requires tradeoffs. An adsorbent that is optimal for one set of operating conditions will operate with reduced efficiency for any other operating conditions (𝑇Hot , 𝑇Evap and 𝑇Amb ). Next, this paper explores optimizing a dual bed system with different adsorbents in each bed, so that the first bed can generate enough heat during adsorption and condensation to regenerate a second bed (two-stage cascading triple effect adsorption refrigeration cycle).26 Finally, we generalize this performance to analyze non-ideal adsorption pairs. Theory of the Ideal Step Location for Adsorption Refrigeration For a set of fixed performance temperatures (𝑇Hot , 𝑇Evap and 𝑇Amb ), the ideal isotherm behavior will be a step function. The optimal stepwise adsorbent (IUPAC adsorbent type 4, 5) will fully desorb at a minimum bed regeneration temperature, while the condenser is near ambient temperature. Meanwhile, the adsorbent must fully adsorb while the bed is at near ambient temperature and the evaporator is at the cold evaporator temperature. We translate these two requirements for adsorption and desorption into a system of equations using the Clausius-Claperyon relationship. The complete adsorption requirement imposes 𝑃Step (𝑇Amb ) < 𝑃Sat �𝑇Evap �,
(Eq 1)
𝑃Step (𝑇Hot ) > 𝑃Sat (𝑇Amb ),
(Eq 2)
where 𝑃Step (𝑇Amb ) is the location of the isotherm step when the bed is at ambient temperature 𝑇Amb . Meanwhile, the desorption requires where 𝑇Hot is the temperature of the bed during regeneration, and the condenser is at 𝑇Amb .
As the temperature of the bed increases, the step will occur at higher absolute pressures. This can be modeled using the Clausius-Clapeyron relation,29,30 𝑃Step (𝑇) = 𝑃Step (𝑇0 )𝑒
ℎAds 1 1 � − � 𝑅 𝑇0 𝑇 ,
(Eq 3)
where 𝑃Step (𝑇0 ) is the pressure of the step at a reference temperature 𝑇0 , ℎAds is the heat of adsorption, and 𝑅 is the universal gas constant.
Meanwhile, the pressure of the evaporator and condenser will also shift with the temperature of evaporator/condenser according to Clausius-Clapeyron relation, 𝑃Sat (𝑇) = 𝑃Sat (𝑇0 )𝑒
ℎfg 𝑅
�
1 1 − � 𝑇0 𝑇
(Eq 4)
,
where ℎfg is the heat of evaporation. 4 ACS Paragon Plus Environment
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We can solve for the coldest possible evaporator temperature by combining equations 1, 3, and 4, to become 𝑇MinEvap
−1
𝑃Step 𝑅 1 ℎAds ℎAds = �− ln � � + �1 − �+ � ℎfg 𝑃Sat 𝑇0 ℎfg ℎfg 𝑇Amb
,
(Eq 5)
where 𝑃Step /𝑃Sat is the ratio of the step pressure to the saturation pressure of the refrigerant (i.e., relative pressure) at 𝑇0 . This equation should use ℎAds /ℎfg and ℎfg evaluated in the middle of the operating temperature range to minimize errors from changing thermodynamic properties with temperature. This equation produces the color map of Figure 2 indicating the coldest temperature achievable as a function of room-temperature relative pressure of the step function, and ℎAds /ℎfg , for a given refrigerant.
Figure 2: Minimum evaporator temperature for an ideal stepwise adsorbent with variable 𝑷𝐒𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂)/𝑷𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂). Ambient temperature is assumed to be 35 °C. Cooler evaporator temperatures are achieved when the room temperature step of the isotherm occurs at as low a relative pressure (𝑷𝐒𝐒𝐒𝐒 /𝑷𝐒𝐒𝐒) as possible, and at as low an 𝒉𝐀𝐀𝐀 /𝒉𝐟𝐟 as possible.
Likewise, we can solve for minimum desorption temperature of the adsorbent as a function of 𝑃Step /𝑃Sat at 𝑇0 by combining equations 2, 3, and 4, for the minimum bed regeneration temperature, 5 ACS Paragon Plus Environment
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𝑇MinReg
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−1
ℎfg ℎfg 𝑃Step 1 =� ln � � + �1 − �+ � ℎAds 𝑃Sat 𝑇0 ℎAds ℎAds 𝑇Amb 𝑅
.
(Eq 6)
The minimum regeneration heat versus minimum required regeneration temperature is plotted in Figure 3.
Figure 3: Minimum regeneration temperature for an ideal stepwise adsorbent with variable 𝑷𝐒𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂)/𝑷𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂). Ambient temperature is assumed to be 35 °C. Lower regeneration temperatures are achieved when the room temperature step of the isotherm occurs at as high a relative pressure (𝑷𝐒𝐒𝐒𝐒 /𝑷𝐒𝐒𝐒) as possible, and at as low an 𝒉𝐀𝐀𝐀 /𝒉𝐟𝐟 as possible.
Figure 2 and 3 shows how the location of the step dictates the minimum evaporator and the minimum regeneration temperature. Colder evaporator temperature requires lower relative pressure step location, and comes at the expense of higher regeneration temperature. Holding the 25 °C step location constant, smaller ℎAds will lead to lower evaporator temperatures and higher regeneration temperatures. This is because the rate at which the isotherm step shifts to higher pressure increases with increasing ℎAds , so smaller ℎAds will desorb at higher temperatures and evaporate refrigerant at lower temperatures. This methodology will be applied later in this paper to calculate the minimum adsorbent uptake and the maximum adsorbent uptake as a function of operating conditions. 6 ACS Paragon Plus Environment
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Stepwise Isotherm Ideal Performance To calculate the theoretical efficiency of a stepwise isotherm adsorption cycle, the thermal inputs and outputs of an adsorption cycle are tracked. These equations were derived using the open system thermodynamic conservation equation, 𝑑𝑑 = 𝑑𝑑 + 𝑑𝑑 + 𝑑𝑚out ℎout − 𝑑𝑚in ℎin ,
(Eq 7)
where 𝑑𝑑 is the heat input to the system, 𝑑𝑑 is the internal energy change of the system, and 𝑑𝑑 is the work done by the system. The mass entering and leaving the control volume are denoted by 𝑑𝑚in and 𝑑𝑚out , and the specific enthalpy of that mass ℎin and ℎout . The cooling load 𝑄Cooling developed by the evaporator is 𝑄Cooling = 𝑚ref . �ℎfg �𝑇Evap , 𝑃Evap � − 𝑐p,l . (𝑇Amb − 𝑇Evap )�,
(Eq 8)
𝑄Regeneration = 𝑚bed 𝑐bed . (𝑇Hot − 𝑇Amb ) + 𝑚ref . �ℎAds (𝑇Amb , 𝑃Cond ) + 𝑐p,v . (𝑇Hot − 𝑇Amb ) �,
(Eq 9)
𝑄RejectCondensor = 𝑚ref . �ℎfg (𝑇Hot , 𝑃Cond ) + 𝑐p,l . (𝑇Hot − 𝑇Amb )�.
(Eq 10)
𝑄RejectBed = 𝑚bed 𝑐bed . (𝑇Hot − 𝑇Amb ) + 𝑚ref . �ℎAds �𝑇Amb , 𝑃Evap � − 𝑐p,v . �𝑇Amb − 𝑇Evap ��.
(Eq 11)
where 𝑚ref is the mass of refrigerant. The average specific heat of liquid refrigerant is 𝑐p,l . The heat input required to desorb the refrigerant is where 𝑚bed and 𝑐bed are the mass and the specific heat of the adsorbent bed, respectively. The average specific heat of vapor refrigerant is 𝑐p,v . Similarly, the expression for heat rejected by the condenser is The heat rejected by the adsorbent bed during forward operation is
The derivations of these equations are provided in the supporting information. The idealized stepwise adsorption chiller has efficiency loss due to specific heat inputs that are not recovered when switching between regeneration and chilling. The efficiency of cooling is measured as the coefficient-of-performance cooling,
𝐶𝐶𝐶Cooling =
𝑄Cooling
𝑄Regeneration
(Eq 12)
.
Non-recoverable thermal losses due to the kinetics of heat and mass transfer reduce the stepwise system efficiency from these isotherm-derived limits, yet these provide a useful method for comparing adsorbent-refrigerant pairs, as the kinetics are a largely function of adsorption bed design, and can be modified by thermal and mass transfer enhancements. 7 ACS Paragon Plus Environment
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A useful way to compare the efficiency of heat-driven refrigerant pairs is to compare the material’s intrinsic 𝐶𝐶𝐶Cooling to the ideal Carnot 𝐶𝐶𝐶Cooling . The limit to heat driven refrigeration is, 𝐶𝐶𝐶Cooling = (𝑇Cold ⁄𝑇Hot )�(𝑇Hot − 𝑇Amb )/(𝑇Amb − 𝑇Cold )� , which is the product of the Carnot heat engine efficiency limit and the Carnot coefficient-ofperformance for a work driven heat pump. By normalizing the 𝐶𝐶𝐶Cooling at different operating conditions to the ideal case, we can see what operating condition has a high fraction of Carnot 𝐶𝐶𝐶Cooling . The theoretical 𝐶𝐶𝐶Cooling and fraction of Carnot 𝐶𝐶𝐶Cooling for adsorption refrigeration is visualized in Figure 4 for 𝑃Step /𝑃Sat at 25 °C of 0.01, 0.05, 0.10, 0.15, and 0.20. The evaporator temperature is fixed at 10 °C. Water is used as the refrigerant and the adsorbent is assumed to have a net 20% mass uptake, and an ℎAds /ℎfg ratio of 1.2. More step-like isotherms can raise the maximum fraction of Carnot to as high as 85%. For these step locations, the highest fraction of Carnot was found for an adsorbent with a 𝑃Step /𝑃Sat equals to 0.20 that is operating at an ambient temperature of 36 °C and with a heat source at 74 °C. This model also assumes specific heats for water and Zeolite 13X, ℎAds /ℎfg ratio of 1.2.
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Figure 4: Contour plots of 𝑪𝑪𝑪𝐂𝐂𝐂𝐂𝐂𝐂𝐂 (left) and Carnot fraction of 𝑪𝑪𝑪𝐂𝐂𝐂𝐂𝐂𝐂𝐂 (right) versus ambient temperature and heat source temperature for different step isotherm locations. The evaporator is assumed to operate at 10 °C. (a,b) 𝑷𝐒𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂)/𝑷𝐒𝐒𝐒(𝑻 = 𝟐𝟐 °𝐂) = 𝟎. 𝟎𝟎 , (c,d) 𝑷𝐒𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂)/𝑷𝐒𝐒𝐒(𝑻 = 𝟐𝟐 °𝐂) = 𝟎. 𝟎𝟎 , (e,f) 𝑷𝐒𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂)/𝑷𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂) = 𝟎. 𝟏 , (g,h) 𝑷𝐒𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂)/𝑷𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂) = 𝟎. 𝟏𝟏 , i,j) 𝑷𝐒𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂)/𝑷𝐒𝐒𝐒 (𝑻 = 𝟐𝟐 °𝐂) = 𝟎. 𝟐.
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Figure 4 captures the effect of step location on 𝐶𝐶𝐶Cooling and fraction of Carnot 𝐶𝐶𝐶Cooling . Materials possessing lower 𝑃Step /𝑃Sat can operate at higher ambient temperatures, but also require hotter regeneration temperatures than lower 𝑃Step /𝑃Sat
materials. The stepwise nature of these isotherm leads to sharp minimum regeneration temperatures, beyond which the efficiency drops to zero, as the refrigerant cannot be desorbed. There is also a sharp maximum ambient operating temperature beyond which the bed will not adsorb vapor from the evaporator at 10 °C. This indicates that stepwise adsorbent would fail abruptly, in hotter than designed ambient conditions. If ambient temperature is higher than the stepwise design limit, then the intended evaporator temperature would be impossible to reach. Refrigeration could still occur, but warmer evaporator temperatures would occur. The coefficient of performance (efficiency) for any single-effect adsorption cycle asymptotes to ℎfg /ℎAds neglecting
specific heat losses, so smaller ratios of ℎAds /ℎfg are desirable from purely a 𝐶𝐶𝐶Cooling
perspective. Despite lower efficiency, one benefit of non-stepwise isotherms is a more graceful failure when deviating from optimal design conditions (e.g. hotter than expected ambient temperatures or less than expected regeneration temperatures). Meanwhile, larger adsorption capacity while maintaining ℎAds /ℎfg and 𝑃Step /𝑃Sat will slightly improve performance, as it will reduce the fraction of heating going to raise the temperature of the adsorbent bed per unit of cooling (Eq 9). The enhancement from doubling the net uptake swing for this stepwise material would only modestly increase the maximum COP by about 2.5%. However, increased uptake will also increase the volumetric and gravimetric power densities, as less adsorbent will be required for the same performance, which is very important.9–12,16 This model assumes an average heat of adsorption, and specific heat, for simplicity and because these properties are not well known for the adsorbed phase as a function of uptake, temperature, and pressure.31 With an adsorption cycle that has a (𝑇Hot − 𝑇Evap ) of 100 °C, using the average ℎfg value will leads to 5% error (assuming water as the
refrigerant). Similar variation occurs for ℎAds versus temperature. This uncertainty in thermodynamic properties over the operating temperature range leads to errors in 𝐶𝐶𝐶Cooling of approximately 5% and moves the constant 𝐶𝐶𝐶Cooling contours by less than 1 °C for a �𝑇Hot − 𝑇Evap �
