Water Absorption Refrigeration

1944

Ind. Eng. Chem. Res. 2009, 48, 1944–1956

Design and Analysis of an Ammonia/Water Absorption Refrigeration Cycle by Means of an Equation-Oriented Method Luz Marıá Cha´vez-Islas and Christopher L. Heard* Posgrado, Instituto Mexicano del Petro´leo, Eje Central Lazaro Cardenas Norte No. 152, Col. San Bartolo Atepehuacan, Delegacioń GustaVo A. Madero, 07730 Me´xico D.F., Mexico

An equation-oriented model for the design of a simple ammonia/water absorption refrigeration cycle is presented, which due to the nature of the working mixture, includes high-quality thermodynamic and thermophysical property models. There are four versions of the model, depending on heat rejection media and distillation column feed conditions. Solution of the model requires the given variables and designer competence-based variables. The column equilibrium stages, diameter, and height use binary decision variables. The solution of the equation set was developed with a General Algebraic Modeling System (GAMS) general purpose nonlinear solver. An equation solution strategy is described. Once solved, exergy balances are made and irreversibilities and exergy efficiency are calculated globally and for each unit operation. Two examples are compared. The great number of factors that can be varied in the absorption refrigeration system makes manual optimization of an industrial design a formidable task. However, good design makes a decisive difference in regard to the use of waste heat absorption refrigeration. The model forms the basis for the simultaneous optimization of design variables with an appropriate objective function. Introduction The ammonia-water absorption refrigeration system (AWRS) is one of the oldest technologies for the industrial production of ice. More recently, its development has been associated with periods of high energy costs. In addition, it has not only been associated with lower operating costs and/or industrial process optimization, but also with environmental impact considerations, with respect to the use of lower-grade thermal energy sources. In contrast with mechanical vapor compression refrigeration, which requires electric power or direct mechanical drives, absorption refrigeration systems can be operated with low-grade heat (80-150 °C), even near-atmospheric-pressure geothermal steam, depending on the refrigeration temperature that is required.1 Waste heat from many industrial processes can be harnessed to provide useful cooling. In the case of ammoniawater absorption refrigeration, the working substances occur naturally in the environment to such a degree that manmade emissions from these systems have a negligible impact on a global scale. Thus, they are classified as being environmentally friendly.2 The development and application of this technology requires reliable and effective system simulations. The energy savings that can be achieved using ammonia-water absorption refrigeration instead of mechanical vapor compression were estimated in three cases by Bogart:3 (i) natural gas liquefaction for storage and transport, (ii) ethylene production by hydrocarbon pyrolysis, and (iii) air separation plants for oxygen production. The savings were obtained from the use of low-grade waste heat instead of high-grade mechanical energy. The foregoing is dependent on the availability, nature, and optimization of the use of waste heat, which varies widely from case to case. Also note that AWRSs are considered to be favored for capacities of >3.5 MWth (1000 TR). In petroleum processing industries such as oil refining, parts of the process require considerable refrigeration capacities, which are frequently met with mechanical vapor compression * To whom correspondence should be addressed. Tel.: +52 55 91758446. Fax: +52 55 91758258. E-mail: [email protected].

systems driven with either electric power or high-grade steam. It is not uncommon to observe that such refineries have a surplus of low-pressure steam, which goes to waste. It is often feasible to meet such refrigeration loads with an AWRS. However, as Bogart4 has noted, the design of such systems within the constraints of the available heat temperature and available heat rejection media and temperatures, while meeting the refrigeration temperature within the particular economic criteria of the project in hand, is far from trivial. For example, in an application to refinery gas condensate recovery, a double temperature generation system was necessary.5 The design choices are not only related to the thermodynamics and process scheme options, but also to the cost impact of such decisions as whether to use air or water cooling, what type of heat-exchanger technology to use in each exchanger, or what type of rectification system should be used. Thus, there is a mixture of continuously variable factors, such as temperatures and flow ratios and either/or decisions involved in the design process. To improve the design and/or operation of an AWRS, research into the design of the components of the system and the application of a variety of configurations have been presented in the literature.6 Various authors have treated the optimization of various parts of the AWRS cycle, cycle configurations, etc. For example, Fernańdez-Seara and Sieres7 reported on the optimization of a flooded evaporator blow-down or purge, which allows the use of lower-grade heat under given conditions of evaporator and heat rejection temperature. The Fernańdez-Seara and Sieres paper should be consulted for a detailed description of the effect of an evaporator purge. Fernańdez-Seara et al.8 examined the effect of various distillation column configurations on the performance of the refrigerant generation system. All other things being equal, it is concluded that a partial condenser cooled with the refrigerant-rich solution provides the highest coefficient of performance. However, the required refrigerant purity cannot always be obtained via this configuration. Water-cooled partial condensers lead to low coefficients of performance, because useful heat is taken out of the cycle. In both cases, the column

10.1021/ie800827z CCC: $40.75  2009 American Chemical Society Published on Web 01/09/2009

Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 1945

Figure 1. Process flow diagram.

design is mechanically much more complex and thus more expensive than for a complete condensation process layout. When using waste heat of little or no value, it is most likely that process simplification will be the best solution, i.e. complete condensation external to the column. S¸encan taught a simulated neural network, using the design results from the tabulated performance data of Sun.9 Sun’s results included solution concentrations, a coefficient of performance, and the thermal duties of the evaporator, generator, condenser, and absorber. However, the data do not include the economizer duty and only considers a fixed refrigerant water content: 1% by mass, which is rather high for most applications. The limited nature of the training data for the simulated neural network will constrain the network’s ability to extrapolate to conditions outside of its experience. Thus, it is apparent that optimizations, based on parametric studies of the many different cycle parameters that can be adjusted, would be a herculean task. This paper shows that it is feasible to develop a simulation model by means of an equation oriented method for the purposes of process optimization. Problem Statement Given a simple ammonia-water refrigeration cycle, the goal is simulate it in such a way as to allow evaluation of the cooling water or cooling air demands, as well as their impact on system design, preliminary dimensioning of the main system components, and exergy analysis, and lay the basis for optimizations of the design. Model Basis The ammonia-water refrigeration cycle modeled is simple, as shown in Figure 1, where the refrigerant is ammonia and the absorbent is water. At low pressure, the refrigerant is vaporized in the evaporator and subsequently is absorbed into the

ammonia-poor solution (which comes from the generator) in the absorber. The resulting solution that leaves the absorber is rich in ammonia. The heat of solution released in the absorber is removed using an appropriate cooling medium (e.g., cooling water or air). The pump receives the ammonia-rich solution at low pressure and increases its pressure to supply it to the economizer. where it is preheated before entering the refrigerant generation column. In this column, the solution is distilled to produce the refrigerant and the ammonia-poor solution from the bottom of the column. This separation is driven by heat supplied to the column reboiler. The refrigerant vapor with traces of water, which is produced from the top of the column, goes to complete condensation in the condenser. A fraction of the liquid obtained is returned to the top of the column as reflux, while the remainder goes to the refrigerant subcooler. Here, the liquid refrigerant is cooled against the vapor, which comes from the evaporator and then passes through the expansion valve. The liquid/vapor mixture from the expansion valve goes to the evaporator at low pressure and its vaporization produces the cooling effect for the process stream to be cooled. The economizer allows heat to be exchanged between the refrigerantpoor and refrigerant-rich solutions. In the evaporator, because of the impure nature of the refrigerant, the liquid phase will concentrate the traces of water in the ammonia, raising the evaporation temperature for a given operating pressure. As previously mentioned, a liquid phase purge can be used to alleviate this situation. This liquid is returned to the absorber and mixed with the superheated vapor from the subcooler and the refrigerant-poor solution. The Fernańdez-Seara and Sieres paper describes a similar process layout;7 however, the evaporator liquid purge in that case is mixed with the absorber exit stream. In practice, this might cause problems of cavitation in the solution pump; therefore, in this case, the purge is considered to go to the absorber entrance mixer.

1946 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009

Figure 2. Temperature approaches for (a) water-cooled and (b) air-cooled condensers.

The system simulation considers two types of cooling: cooling water or air in the condenser and in the absorber. The condenser, in both the water-cooled case and the air-cooled case, is considered to have four tube passes and one shell pass. In the case of cooling water, this is on the tube side, and in the case of air cooling, the ammonia-water mixture is inside the tubes. The minimum approach temperatures in each case are established in various ways. With the cooling water case, they are defined as the difference between the cooling water return temperature and the exit temperature of the ammonia-water mixture (see Figure 2a). In the case of air cooling, it is the difference between the initial dry bulb temperature and the ammonia-water mixture exit temperature (Figure 2b). When employing cooling water, four tube passes were chosen, to avoid a large heat-transfer area at the expense of a pressure drop on the tube side. In addition, the condenser performs total condensation unlike many refinery condensers. However, in the case of the absorber, the approach temperatures are the same, regardless of the cooling medium. When cooling water is used, the absorber is considered to be a vertical shell and tube exchanger, with the absorption occurring in a downward flow on the tube side in a single pass (see Figure 3a). For the aircooled case, the ammonia-water mixture on the tube side has four passes and one pass on the air side (see Figure 3b). For the water-cooled absorber, an approach temperature of 5.6 K (10 °R) is used, and for the air-cooled case, an approach temperature of 22.2 K (40 °R) is used. Properties of the Working Fluids. Many studies of the thermodynamic properties and the vapor/liquid equilibrium of the ammonia-water mixture have been published. In this study, the correlations of Xu and Goswami10 were used to estimate the enthalpy, entropy, and specific volume, and to determine the dew-point and bubble-point temperatures. These researchers used the method of Gibbs free energy to calculate the thermodynamic properties of the pure componentes (ammonia and water) and those of the mixture. The phase equilibria were determined using the dew-point and bubble-point temperatures, following El-Sayed and Tribus.11 This avoided the conventional method of using fugacities and, thus, reduced the computational load. The properties produced with these correlations were compared with experimental and theoretical data from the literature,12 and a good approximation was obtained. The range of application of these correlations is 0.2-110 bar and 230-600 K. Note that the ammonia-water mixture is a particularly demanding one to model. Even at very low concentrations of one or other components in the mixture, the properties have significant differences from those of the principal component. This is important when one simulates an ammonia-

water refrigeration cycle, because this situation occurs in important parts of the process, especially condensation and evaporation of the refrigerant. Estimation of Transport Properties. The method described by Conde13 was used to estimate the surface tension and viscosity. Method of Calculation for Equilibrium Stages in the Distillation Column. The Ponchon-Savarit method for the design of the distillation column was chosen because of the highly nonideal nature of the binary ammonia-water mixture. MESH methods can be difficult to solve for highly nonideal mixtures

Figure 3. Temperature approaches for (a) water-cooled and (b) air-cooled absorbers.


and, given good-quality enthalpy/composition data, the PonchonSavarit method is sufficiently rigorous for binary mixtures and the purposes of this study. The low tray count of the column makes the constant pressure supposition of the method of minor consequence.4,14 To obtain the optimum reflux ratio, a rule of thumb was applied that it should be in the range of 1.05-1.25 times the minimum reflux ratio,15 to avoid an excessive number of equilibrium stages:

( RL )

1.05

min

e

( RL )

opt

( RL )

e 1.25

min

(1)

The ammonia-water absorption refrigeration cycle simulation considers the column feed separately, under two conditions: either as a vapor-liquid mixture with a small vapor fraction or as a slightly subcooled liquid. Predesign of the Main Equipment. For the heat exchangers, global heat-transfer coefficients were used from the literature, which are dependent on the type of fluids that are exchanging heat.16,17 The decision was made to model the distillation column as a sieve plate column, because of the size of the cooling loads of interest to the authors, which implies the use of column diameters of >0.6 m.18 Fernandez-Seara et al.19 researched the design of packed distillation columns for ammonia-water absorption refrigeration. However, for large-capacity systems, packed columns can have serious flow channelling problems, which greatly reduces the efficacy of the column. Most of the factors that affect the column size are a strong function of the vapor flows inside the column. The column diameter is estimated using the Fair correlation to determine the vapor velocity at flooding (FLG), the plate spacing, the cross-sectional area, and the downcomers.20-22 Plate efficiencies are estimated using the O’Connell correlation. The height of the column is the number of plates or stages divided by the plate efficiency, multiplied by the plate-to-plate distance of 0.3 m (1 ft) plus 1.22 m (4 ft) for the top-plate-to-dome height and 3 m (10 ft) from the bottom of the column to the lowest plate. Parameters for the Simulation. The parameters for the simulation are as follows: (1) Approach temperatures in the evaporator, condenser, refrigerant subcooler, column reboiler, and absorber; (2) Pressure drops in the evaporator, condenser, refrigerant subcooler, absorber, and economizer, and that from the evaporator to the absorber accumulator; (3) Global heat-transfer coefficients: evaporator, refrigerant subcooler, absorber, economizer, condenser, and the column reboiler; (4) The rate of purge of the evaporator liquid phase and the ratio of reflux to minimum reflux; (5) Supply and return conditions of the heat source and cooling medium, as well as their respective properties; (6) The refrigeration duty and the inlet and outlet conditions of the process stream to be cooled; and (7) The design parameters needed in the calculation of the height and weight of the column. Parameters for the Exergy Balance. The parameters for the exergy balance are as follows: (1) The ambient pressure and temperature (dry bulb) where the refrigeration system would be installed; and (2) The entropy of process streams, as well as heating and cooling media, together with their physical exergy. Formulation of the Problem or Model. The model for simulating a simple absorption refrigeration cycle considers the following aspects.

Figure 4. Calculation of vapor-liquid equilibrium conditions.

(1) Recursion in the calculation of thermodynamic properties of the mixture in various points in the system (See Figure 4). (2a) Application of disjunctive programming techniques, involving the number of equilibrium stages,23 can be described as follows. To establish the number of equilibrium stages needed for the required refrigerant purity in both the stripping and rectification stages, the model considers five fixed stages both for the rectification and stripping sections. However, not all are required to achieve the desired level of top product purity. Rectification Section: The criterion used was that in the rectification section, while the ammonia concentration in the stage under consideration is higher than that of the feed. Then, this is an equilibrium stage; otherwise, it is not. Y1[)]Z7-mz,NH3 e xpzr,NH3 f (“pzr” is an equilibrium stage) (Zone 1) Z7-mz,NH3 - xpzr,NH3 e 0 ∀ pzr ) 1, 2, 3,..., 5 ¬ Y1[)]Z7-mz,NH3 g xpzr,NH3 f (“pzr” is ¬ equilibrium stage) (Zone 2) Z7-mz,NH3 - xpzr,NH3 g 0 ∀ pzr ) 1, 2, 3,..., 5 Y1 - logical variable (2) Definition: dRpzr ) Z7-mz,NH3 - xpzr,NH3

Disjunction:

[

Zone 1

Y1 -1 e dRpzr e 0 yRpzr ) 1

][

∀ pzr ) 1, 2, 3,..., 5 (3) Zone 2

]

¬Y1 ∨ 0 e dRpzr e 1 yRpzr ) 0 ∀ pzr ) 1, 2, 3,..., 5 (4)

Application of the convex hull technique yields dRpzr ) dR1pzr + dR2pzr ∀ pzr ) 1, 2, 3,..., 5 yRpzr ) yR1pzr + yR2pzr ∀ pzr ) 1, 2, 3,..., 5 dR1pzr g -1yRz1pzr ∀ pzr ) 1, 2, 3,..., 5 dR1pzr e 0yRz1pzr ∀ pzr ) 1, 2, 3,..., 5 dR2pzr g 0yRz2pzr ∀ pzr ) 1, 2, 3..., 5 dR2pzr e 1yRz2pzr ∀ pzr ) 1, 2, 3,..., 5 yR1pzr ) yRz1pzr ∀ pzr ) 1, 2, 3,..., 5 ∀ pzr ) 1, 2, 3,..., 5 yR2pzr ) 0yRz2pzr yRz1pzr ) + yRz2pzr ) 1 ∀ pzr ) 1, 2, 3,..., 5 dRpzr, dR1pzr, dR2pzr, yRpzr, yR1pzr, yR2pzr ∈ R yRz1pzr ) 0, 1; yRz2pzr ) 0, 1; ∀ pzr ) 1, 2, 3,..., 5 (5)


Stripping Section: To decide whether a stage is an equilibrium stage or not, the criterion applied was to compare the slope of the operating line for the entire column with that of the operating line between stages. If the slope of the line between stages is greater than that of the global operating line, then this is an equilibrium stage; otherwise, it is not. The formulation of the equations is similar to those of the rectification section. (2b) To determine the plate efficiencies, the O’Connell correlation has a lower limit to the mathematical product of relative volatility and liquid viscosity (0.1), which corresponds to a maximum efficiency of 0.8648. If, during the simulation, this product is 0.1 f

Disjunction:

[( ) ] [( ) [( ) ] Zone 1

∀ n ) 1, 2, 3 ,..., 11 (13)

n,jCn,j,NH3) ) 0

where Cn,i,NH3[)]xn,i,NH3,yn,i,NH3 or zn,i,NH3 Cn,j,NH3[)]xn,i,NH3,yn,j,NH3 or zn,j,NH3 out

in

Energy balance :

∑

(Fn,ihn,i) -

∑ j)1

i)1

out

∑ (Q

∑ (Q

n,k) -

l)1

in

n,l) +

l)1

in

(Fn,jhn,j) +

∑ (W

n,m) ) 0

m)1

∀ n ) 1, 3, 4, 5, 6, 7, 9, 10, 11 (14)


Energy balance in expansion valves: in

∑h

n,i -

i)1

out

∑h

n,j ) 0

∀ n ) 2, 8 (15)

j)1

Energy balance in the ammonia-rich solution pump: VSR(Pn,j - Pn,i) Wn,m ) ∀ n ) 6 (16) ηpump Energy balance for air-cooled heat exchangers: EEairn ) 20An ∀ n ) 5, 10 (17) Economizer effectiveness: εEco )

t9(s-1) - t8(e) t9(s-1) - t6(s)

Equilibrium balances: hw ) f(tw, xw, Pw) Hw+1 ) f(tw+1, yw+1, Pw+1) xw ) f(tw, yw)

(18)

Swing point at minimum reflux ratio: Acmin ) mmin(x10(s),NH3 - x7(s-lscol),NH3) + h7(s-lscol) (27) The rest of the equations are not dependent on the thermal state of the column feed: Minimum reflux ratio: Normal reflux ratio:

Lr R

) min

nor

Acmin - H10(e) H10(e) - h10(s)

) FRR

Acmin - H10(e) H10(e) - h10(s)

(28) (29)

1.05 e FRR e 1.25 (19)

Swing point for normal reflux ratio: Acnor ) Hpzr)1 +

w ) pzr or pza ∀ pzr ) 1, 2, 3,..., 5; ∀ pza ) 1, 2, 3, ..., 6 Evaporator purge : Fn,s-l ) βFn,s-V ∀n)3 (20) where β is the purge mass fraction of the refrigerate flow rate.

() Lr R

(Hpzr)1 - h10(s)) (30)

nor

Operating lines for normal reflux: Acnor - hpzr Hpzr+1 - hpzr mpzr ) ) x10(s),NH3 - xpzr,NH3 ypzr+1,NH3 - xpzr,NH3 ∀ pzr ) 1, 2, 3, 4 (31) The mass balances (operating line) and equilibrium relationships (dew and bubble points) are simultaneously resolved. Stripping Section: The column reboiler is an additional equilibrium stage (pza ) 1), where the following condition applies:

(21)

Here, the coefficeint of performance is defined as the ratio of the refrigeration provided by the system to the energy required to operate it. Ponchon/Savarit method equations are used to describe the ratio of minimum reflux and operating lines, equilibrium lines, and operating lines. These last two concepts are applied both to the rectification section and to the stripping section, to determine the equilibrium stages. Rectification Section: Based on the study, complete condensation is considered and, thus, the first equilibrium stage of the rectification section must comply with the following: ypzr)1,NH3 ) y10(e),NH3 ) x10(s),NH3 Hpzr)1 ) H10(e)

Lr R

where

where

Q3 Coefficient of Performance : COPAE ) Q9 + W6 or Q3 COPair ) Q9 + W6 + EE _ air5 + EE _ air10

() ()

(22)

The slope of the operating line at the minimum reflux ratio is dependent on the feed conditions, which, in the present study, are considered to be either a vapor/liquid mixture or a subcooled liquid. Each case is described below. The following conditions exist for a two-phase column feed: Slope of the operating line at the minimum reflux ratio: H7-vmz - h7-lmz mmin ) (23) y7-vmz,NH3 - x7-vmz,NH3 Swing point: Acmin ) mmin(x10(s),NH3 - y7-vmz,NH3) + H7-vmz (24)

x7(e-SP),NH3 ) xpza)1,NH3

(32)

Swing point : Awnor ) [h7-mz(s)(x10(s),NH3 - x7(e-SP),NH3) - Acnor(z7-mz,NH3 - x7(e-SP),NH3)] (x10(s),NH3 - z7-mz,NH3) (33) The aforementioned equation applies when the thermal condition of the feed is two-phase. If the feed is subcooled liquid, then the enthalpy and the feed composition are given as h7(out-lscol) (instead of h7-mz(out)) and x7(out-lscol),NH3 (instead of z7-mz,NH3). Operating line for normal reflux: Hpza - Awnor Hpza - hpza+1 mpza ) ) ypza,NH3 - x7(e-SP),NH3 ypza,NH3 - xpza+1,NH3 ∀ pza ) 1, 2, 3,..., 5 (34) Overall column operating line :

mtot )

Acnor - Awnor x10(s),NH3 - x7(e-SP),NH3 (35)

Determination of the consumption of heating and cooling services and their respective mass flow rates can be expressed as follows: Qn hSCn,i - hSCn,j

The following conditions exist for a subcooled liquid column feed:

Heat duty: FSCn )

Slope of the operating line at the minimum reflux ratio : hIso-l - hs-lscol HIso-V - hIso-l mmin ) ) (25) xIso-l,NH3 - xs-lscol,NH3 yIso-V,NH3 - xIso-l,NH3

Cooling duty (cooling water): FAEn )

Qn hAEnj - hAEni Qn + EEairn

∀n)9

(36)

∀ n ) 5, 10 (37)

In this case, the slope of the operating line corresponds to the isotherm that, when extrapolated, passes through the feed point. The equilibrium conditions are as follows:

Cooling duty (air) :

tiso-bubl(xIso-l,NH3, P7(s-lscol)) ) tiso-dew(yIso-V,NH3, P7(s-lscol))

Design equations for equipment dimensioning involve expressions for the approximate logarithmic mean temperature

(26)

Fair )

hairn,j - hairn,i

∀ n ) 5, 10 (38)


difference,24,25 the heat-transfer area for the heat exchangers, and column height and diameter.

Column Height: The tray efficiency, using the O’Connell correlation, is given as

Approximation of the logarithmic mean

E0 ) 0.492(RNH3-H2OµNH3-H2O,l)-0.245

[ (

)]

tn,1 + tn,2 1 ⁄ 3 temperature difference : LMTDn,approx ) tn,1tn,2 2 ∀ n ) 1, 3, 5, 7, 9, 10 (39)

The relative volatility is given as

where tn,1 ) Tn,i - tn,j Heat-transfer area :

An )

tn,2 ) Tn,j - tn,i

RNH3-H2O )

Qn UnLMTDn,approx ∀ n ) 1, 3, 5, 7, 9, 10 (40)

where Qn ) Qn,k or Qn,1 Column Diameter: In estimating the column diameter for sieve trays, flooding due to liquid carryover in the vapor stream is considered. The estimation is performed for both the rectification section and the stripping section. The flow parameter FLG describes the liquid flux over the plate:22 FLG )

( VL )( F ) FG

1⁄2

(41)

{

(for FLG e 0.1)

0.1

Ad (F - 0.1) (for 0.1 e FLG e 1.0) ) 0.1 + LG AT 9 (for FLG g 1.0) 0.2

(42)

where Ad is the cross-sectional area of the downcomer and AT is the cross-sectional area of the tray. The Kessler and Wankat26 correlation was applied for the capacity factor, based on data from Fair and Matthews27 for a 12-in. (0.3-m) vertical tray spacing. log CSB ) -1.0674 - 0.55789 log FLG - 0.17919(log FLG)2 (43) Vapor flooding velocity :

uf ) CSB

σ 20

0.2

( )

FFFHA

(

FL - FG FG

)

1⁄2

(44) where σ is the surface tension of the liquid-phase NH3/H2O mixture, FF ) 1 (if the fluid system is considered to be nonfoaming), and FHA ) 1. The liquid surface tension in the first equilibrium stage in the rectification zone (from top to bottom) is defined as σNH3-H2O,1,zr ) f(xpzr)2,NH3, tpzr)1)

(45)

The liquid surface tension in the second stage in the stripping section (from bottom to top) is defined as σNH3-H2O,1,za ) f(xpza)2,NH3, tpza)2) Column diameter :

DT )

{

4F fufπ[1 - (Ad ⁄ AT)]FG

(46)

}

1⁄2

(47)

where DT is the column diameter, F the mass flow, f the fraction of flooding velocity, uf the flooding velocity, Ad the crosssectional area of the downcomer, AT the cross-sectional area of the tray, and FG the vapor density.

( (

y7-vmz,NH3

(10%) (48)

) )

1 - y7-vmz,NH3 y7-lmz,NH3 1 - y7-lmz,NH3

(49)

The aforementioned expression is applied to the case where a two-phase feed to the column exists. When the feed is a subcooled liquid, a simplification is applied, using the compositions of the isotherm, which, when extrapolated, passes through the feed point (xIso-l,NH3, yIso-l,NH3). The liquid feed fraction viscosities for the two-phase feed and the subcooled feed are given as Two-phase feed :

µNH3-H2O,l ) f(x7-lmz,NH3, t7(s-mz))

(50)

Subcooled feed :

µNH3-H2O,l ) f(xIso-l,NH3, tIso)

(51)

The column height (HColumn) then is given as

L

The area ratio downcomer/sectional area is dependent on the liquid flux:21

(error )

Column height :

HColumn )

( )

NES TS + LD + LS E0

(52)

where TS is the intertray height, LD the dome height to allow phase disengagement (LD ) 1.22 m (4 ft)), and LS the bottom height to allow phase disengagement (LS ) 3.05 m (10 ft)). With regard to establishment of upper and lower bounds for continuous variables such as enthalpy, specific volume, compositions (mass fraction) for both liquid and vapor phases, vapor fractions for those parts of the system where two phases occur (l-v), pressure, temperature and flow rates, etc., these values are dependent on each specific case simulated. In equationoriented simulators, considerable effort can be required to initialize these problems. In addition, because a general purpose equation solver is used, it is more difficult to incorporate the unit structure of the equations into the solution procedure. Because of the previous discussion, a strategy to improve the initialization of the variables in the equation set has been proposed. This consists of resolving a relaxed problem, by first simplifying the model in the binary variables (removing the column diameter and height equations). The complete problem then is solved in a relaxed manner initially, using the values from the previous stage. With the values from the relaxed solution, a stable feasible solution with mixed-integer equations is obtained. For the relaxed problem, the CONOPT solver was used and, for the mixed integer, one SBB was used, with the NLP subproblems being solved with CONOPT. Because GAMS is an optimization tool, a fixed-value objective function was used to obtain a feasible solution. After the model has been resolved, an exergy balance is produced from the simulation results (enthalpies, mass flow rates, and electric power requirements) and by calculating the entropies from the correlation of Xu and Goswami10 both for the stream conditions and under ambient conditions. The irreversibility and the exergy efficiency for each major equipment item, and the overall values, are calculated.

Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 1951 in

∑

Exergy balance :

Table 3. Heating Medium Characteristicsa

out

(Fn,iExn,i) -

i)1

∑

(Fn,jExn,j) +

out

∑ (W

n,m) ) Irrevn g 0

∀ n ) 1, 2,..., 11 (53)

m)1

The second law of thermodynamics shows how energy is always degraded in any process and, thus, loses quality. The quality of the energy in a process can be expressed by the thermodynamic function called exergy. The total energy in a system can be considered as consisting of two types: useful energy, i.e., that which can be used to perform an action (exergy), and not useful energy (anergy). ) (H - H0) - T0(S - S0)

Ex V Useful Energy

V

V

Total Energy

Nonuseful Energy

a

value

pressure initial temperature entropy enthalpy exergy exit temperature entropy enthalpy exergy latent heat

2.9 bar (42.2 psia) 132 °C (270 °F) 7.002 kJ/(kg K) (1.67 btu/(lb °F)) 2723 kJ/kg (1170.5 btu/lb) 663.7 kJ/kg (285.3 btu/lb) 132 °C (270 °F) 1660 kJ/(kg K) (0.3964 btu/lb °F) 556.6 kJ/kg (239.3 btu/lb °F) 69.03 kJ/kg (29.68 btu/lb) 2166 kJ/kg (931.3 btu/lb)

ηn )

(54)

Exn-ts Irrevn )1Exn-te Exn-te ∀ n ) 1, 2, 3, ..., 11 (55) Exn-te )

a

concept

value

mass flow rate initial temperature entropy enthalpy exergy exit temperature entropy enthalpy exergy

7.603 kg/s (60 340 lb/h) 32.2 °C (89.96 °F) 3.293 kJ/(kg K) (0.7866 btu/(lb °F)) -505 kJ/kg (-217 btu/lb) 96.6 kW (330 mbtu/h) 29.3 °C (84.74 °F) 2.068 kJ/(kg K) (0.4941 btu/(lb °F)) -877.4 kJ/kg (-377.2 btu/lb) 2.08 kW (7.11 mbtu/h)

The process stream is 2-methyl-1-butene.

Table 5. Characteristics of the Heat Sink Media

in

Total exergy entering the process :

Low-pressure steam.

Table 4. Process Stream Characteristicsa

The useful energy can be obtained by taking the system to equilibrium with the environment. Or, in other words, exergy is the degree of distance from the environment, in terms of properties such as temperature, pressure, and composition. Exergy efficiency :

parameter

j)1

∑F

n,iExn,i +

concept

value

j)1

Cooling Water

in

∑W

n,m

∀ n ) 1, 2, 3,..., 11 (56)

m)1

out

Total exergy leaving the process :

Exn-ts )

∑F

n,jExn,j

j)1

∀ n ) 1, 2, 3,..., 11 (57)

initial temperature entropy enthalpy exergy return temperature entropy enthalpy exergy

23 °C (73.4 °F) 0.3315 kJ/(kg K) (0.0792 btu/(lb °F)) 96.3 kJ/kg (41.4 btu/lb) 0.6220 kJ/kg (0.2674 btu/lb) 40.5 °C (104.9 °F) 0.577 kJ/(kg K) (0.1379) 169.6 kJ/kg (72.9 btu/lb) 1.512 kJ/kg (0.6499 btu/lb)

value

Application Examples, Results, and Analysis Case studies are reported, as well as the corresponding results from the simulations, both for water cooling and air cooling. These results are analyzed. The environmental conditions used for both case studies are those reported for the city of Salamanca Gto. in central Mexico (see Table 1). These are necessary for the exergy analysis. Description of the Case Studies. A. Case 1. Case 1 involves a refrigeration duty of 2.7 MWth (9.7 mmbtu/h) at a refrigerant boiling point of 5.6 °C (42 °F) (see Table 2), using cooling water and air as heat sinks for the ammonia-water refrigeration cycle simulation. The driving heat supply was considered to be low-pressure saturated steam (2.9 bar). In Table 3, the thermodynamic properties of the heating medium and the exergy data, both entering and leaving, are shown. Table 1. Environmental Conditions for the Exergy Analysis parameter

value

temperature, T0 pressure, P0

21 °C (69.8 °F) 0.84 bar (12.2 psia)

Table 2. Refrigeration Requirementsa

a

parameter

value

approach temperature refrigerant temperature refrigeration duty

26.6 K (47.96 °R) 5.56 °C (42 °F) 2.84 MWth (9.7 mmbtu/h)

Refrigerant levels are shown.

Condenser

Absorber

Cooling Air initial temperature entropy enthalpy exergy return temperature entropy

37 °C (98.6 °F) 6.783 kJ/(kg K) (1.62 btu/(lb °F))

enthalpy

-160.5 kJ/kg (-68.986 btu/lb)

exergy

0.0949 kJ/kg (0.0408 btu/lb)

21 °C (69.8 °F) 6.741 kJ/(kg K) (1.61 btu/(lb °F)) -176.5 kJ/kg (-75.9 btu/lb) 0 kJ/kg (0 btu/lb) 40.9 °C (105.6 °F) 6.795 kJ/(kg K) (1.623 btu/(lb °F)) -156.5 kJ/kg (-67.3 btu/lb) 0.227 kJ/kg (0.0976 btu/lb)

Tables 4 and 5 show the pressure, temperature, and thermodynamic properties of the process stream (to be cooled) and of the two cooling media, respectively. In addition, the exergy values for the exergy analysis are shown. Table 6 shows values of some of the parameters considered in the simulation. B. Case 2. The objective of the dewaxing is to remove straight-chained paraffins from oils, which will be used as a basis of lubricants. The oils are mixed with a solvent that reduces their viscosity and allows precipitated waxes to be removed via filtration at low temperature. A refrigeration system is used to precipitate the waxes from the solution. Usually, the refrigeration system used is a mechanical vapor compression system that uses propane as a refrigerant and a medium-pressure-steam-driven turbine. Much of the cooling duty could be met with a low-

1952 Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 Table 6. Simulation Parameters

Table 9. Simulation Parameters Value

Value

parameter

cooling water

air

parameter

Cooling water

Air

purge subcooler ∆t economizer effectiveness reflux ratio, (Lr/R)minb reboiler ∆t absorber ∆t condenser-column ∆t

0.0239 8.3 K (15 °R) 86.6% 1.0514 5.6 K (10 °R) 5.6 K (10 °R) 5.6 K (10 °R)

0.0519 2.8 K (5 °R) 86.5% 1.05 5.6 K (10 °R) 22.2 K (40 °R) 22.2 K (40 °R)

purgea subcooler ∆t economizer effectiveness reflux ratio, (Lr/R)minb reboiler ∆t absorber ∆t condenser-column ∆t

0.0238 8.3 K (15 °R) 86.5% 1.0514 4.4 K (8 °R) 5.6 K (10 °R) 5.6 K (10 °R)

0.0334 2.8 K (5 °R) 86.5% 1.075 2.8 K (5 °R) 22.2 K (40 °R) 22.2 K (40 °R)

a

a Expressed as a mass fraction. ratio.

b

Multiplier for the minimum reflux

Table 7. Refrigeration Requirementsa

a

parameter

value

approach temperature refrigerant temperature cooling duty

4.4 K (8 °R) -13.9 °C (7 °F) 1.16 MW (3.96 mmbtu/h)

Cooling level/refrigerant conditions are given.

Table 8. Process Stream Characteristicsa concept

Value

mass flow rate initial temperature entropy enthalpy exergy exit temperature entropy enthalpy exergy

46.6 kg/s (370 000 lb/h) 4.4 °C (40 °F) -0.0418 kJ/(kg K)(-0.01 btu/(lb °F)) -1691 kJ/kg (-726.8 btu/lb) 303.8 kW (1038 mbtu/h) -9.4 °C (15 °F) -0.1339 kJ/(kg K) (-0.03197 btu/(lb °F)) -1715 kJ/kg (-737.5 btu/lb) 3215 kJ/kg (1382.1 btu/lb)

a

Black oil was used as the process stream.

pressure-steam-driven ammonia-water absorption refrigeration system. Because of the nature of heat demands in a refinery, medium-pressure steam is at a premium and low-pressure steam may even be in surplus. The costs of medium- and low-pressure steam will most likely reflect these circumstances, making absorption refrigeration highly cost-effective. Given that (i) propane mechanical vapor compression refrigeration systems have large rotating systems that require highly skilled maintenance and (ii) absorption refrigeration systems have little rotating equipment, the latter has much higher reliability and low maintenance costs. However, the optimization of the design of ammonia-water absorption refrigeration equipment is nontrivial, given the large number of degress of freedom in the design and the high capital cost of the installations. Simplistic designs will frequently favor mechanical vapor compression, notwithstanding that good absorption system designs can be much more cost-effective. In the oil dewaxing process, cooling duties exist at a series of temperatures. For this case study, a cooling duty at a temperature that is feasible with ammonia-water absorption cooling was chosen. Table 7 shows the refrigerant conditions that were required. The heating and heat-sink media conditions are the same as those for the previous case. Table 8 shows the thermodynamic properties of the process stream to be cooled, and the simulation parameters considered are shown in Table 9. Discussion Note that the refrigeration level has an impact on the feed condition at the generation column. In the first case, the feed is a two-phase feed, whereas in the second case, it is a slightly subcooled liquid. This means that the simulation model must

a Expressed as a mass fraction. ratio.

b

Multiplier for the minimum reflux

be able to model both situations correctly and, thus, requires two calculation methods for the minimum reflux ratio. The results for both cases are shown in Tables 10 and 11 for both types of heat-sink media. Table 10 reports the coefficient of performance of the ammonia-water absorption refrigeration cycle, and the heat and heat rejection used, as well as the refrigerant-rich solution flow rate per unit cooling duty refrigeration duty. In addition, the approximate heat exchange areas needed for the various heat exchangers per unit refrigeration duty are given, as well as the ratio of areas for each case, with the two types of heat-sink media. The estimated dimensions of the distillation column (diameter, height, number of equilibrium stages, plate efficiency, distribution of the equilibrium stages between the rectification and stripping sections, number of real stages, operating pressure, and compositions of the feed and top product) also are given. In Table 11, the results of the exergy analysis are reported; the overall efficiency, the overall irreversibility per unit refrigeration duty, and the contribution of each component of the cycle are given in this table. In both cases, the coefficients of performance are higher when cooling water is used, rather than air. However, the air-cooling option becomes relevant in places where there is a scarcity of water or the price of cooling water is very high and, thus, not economical. A lower temperature level in the evaporator, as is to be expected, increases the electrical energy consumption for the solution pump, as well as the driving heat and the heat rejected per unit cooling. Most of the heat-exchange areas also increase. The economizer heat-exchange area is particularly sensitive, because of the increasing flow ratio and, thus, the flows of refrigerant-rich and refrigerant-poor solutions. The approach temperature in this exchanger will have a large impact on the thermodynamic cycle efficiency and, hence, the heat consumption. The cooling medium has an impact on the refrigerant-rich solution concentration and, thus, the size of the generation column. However, other factors are involved, such as the liquid purge in the evaporator, which reduces the water content of the refrigerant and thus increases its vapor pressure for a given temperature. This, in turn, affects not only the necessary refrigerant flow rate but also its purity. This interaction results in effects such as those observed with water cooling: the column in the first case has a greater diameter than that in the second case, despite the evaporation temperature being much lower in the second case. In the air-cooled versions of these cases, the second case column has a slightly larger diameter. The exergy balances show that the absorber is one of the major contributors to irreversibility, accounting for between 20% (water-cooled) and 31% (air-cooled) of the total irreversibility. The impact of the approach temperature is clearly demonstrated in the case of the evaporator and generator where small approaches can be used. The worse approach temperatures with

Ind. Eng. Chem. Res., Vol. 48, No. 4, 2009 1953 Table 10. Results for Cases 1 and 2 with Both Cooling Media Cooling Water

Air-Cooled

Concept

Case 1

Case 2

coefficient of performance, COP electrical power consumption (kJ/MJcooling) air-cooling fans refrigerant pump cooling-water consumption low-pressure-steam consumption refrigerant-rich solution column feed equipment size estimates, heat-transfer areas (m2/MWcooling) subcooler evaporator absorber economizer condenser reboiler

0.6473

0.4943

4.7 34.8 0.7 2.4

13.3 41.4 0.9 6.3

2.8 1.2 1.3 2.6

22 58 243 48 37 127

43 124 651 250 32 267

18.4 1.01 6.3

18.2 0.84 6.3

2 3 5 0.7519 7 0.5692 0.9989

3 3 6 0.8942 7 0.3975 0.9972

distillation column properties pressure (bar) diameter, stripping section (m) height (m) number of equilibrium stages rectification section stripping section total plate efficiency number of real stages feed compositiona top product compositiona a

ratio between cases

Case 1

Case 2

0.5781

0.3705

25.9 5.9

42.1 29.2

1.6 5.0

0.8 3.6

1.2 16.1

1.5 4.4

2.0 2.1 2.7 5.2 0.9 2.1

40 58 81 95 81 165

42 124 182 867 80 614

1.1 2.1 2.3 9.1 1.0 3.7

0.8

16.9 1.1 6.1

16.8 1.1 6.0

1.0

2 3 5 0.8281 6 0.4694 0.9977

3 2 5 0.8942 6 0.3158 0.9961

30.2% 0.2%

ratio between cases

32.7% 0.2%

Expressed as a mass fraction.

Table 11. Exergy Analysis Results

Table 12. Summary of Solutions Generated in GAMS

Cooling Water concept a

overall efficiency overall irreversibilityb (kJ) efficiencyc (%) evaporator refrigerant expansion valve refrigerant subcooler mixer before absorber absorber ammonia-rich solution pump economizer solution expansion valve condenser reboiler distillation column

Air-Cooled

Cooling Water

Air

Case 1

Case 2

Case 1

Case 2

concept

Case 1

Case 2

Case 1

Case 2

0.1924 430

0.5187 441

0.1352 507

0.4103 671

21.3 1.6 1.3 3.8 20.4 0.1 9.8 0.4 17.4 17.3 6.6

13.5 3.1 2.6 1.8 18.2 0.4 22.4 1.8 19.2 9.8 7.2

18.2 1.1 0.9 4.3 30.8 0.1 8.5 0.6 18.4 11.7 5.4

8.8 1.9 1.6 2.1 30.5 0.6 23.5 2.9 16 3.4 8.7

binary variables continuous variables restrictions number of iterations CPU time (s)

30 737 800 71 0.81

30 751 814 87 1.8

30 741 804 96 1.6

30 755 818 62 0.87

a

Expressed as a fraction. b Per MJ refrigeration duty. with respect to total irreversibilities.

c

Percentage

air cooling produce 18% more irreversibility, with respect to water cooling in the first case and 52% in the second case.

General Algebraic Modeling System (GAMS) In the GAMS28 environment, the objective function is a constant that is equal to unity, which allows the simulation of the system as previously described. The branch-and-bound (B&B)29,30 solver algorithm was used. The CONOPT31 solver was used for the nonlinear subproblems. Table 12 shows a summary of the solutions for both cases generated in GAMS. The upper and lower bounds, as well as initial values of some variables in the model, must be assigned with care, because the convergence of the solution method is dependent on these values. These values are specific to each problem. That is to say, they are dependent on parameters such as the refrigeration temperature that is required (the boiling point of the refrigerant),

the characteristics of the heat supply/heat rejection medium, and the approach temperature, among others. Conclusions A new formulation has been presented, based on an equationoriented method for the analysis of ammonia-water absorption refrigeration systems. The analysis of the way these systems work involves complex relationships, because of the functions used to calculate the ammonia-water mixture properties and the mass, energy, and equilibrium (Ponchon) balance equations, which are nonlinear. The mathematical model has been implemented in a General Algebraic Modeling System (GAMS) environment, to analyze the functional characteristics of an ammonia-water absorption refrigeration system, and the results from two case studies have been presented. The model for the simulation of a simple ammonia-water absorption cooling cycle, formulated herein, considers engineering aspects that have not been reported in other studies. These aspects include the number of tube passes in the absorber and condenser when cooling water is used or the use of air cooling and the approach temperature in both cooling media, the approximate dimensioning of the main equipment items, a heuristic rule for real reflux in the column, and use of the Ponchon method to estimate the number of theoretical equilibrium stages in the column. In addition, the model includes correlations for the calculation of thermophysical properties and physical equilibrium (recursivity) with equations for mass and energy balances.


The model has two ways of calculating the minimum reflux ratio, the selection of which is dependent on the column feed thermal condition, whether it is a two-phase or subcooled liquid. This gives flexibility to the application, allowing a greater number of cases to be studied. When the model is applied to two case studies, it can be seen that the variation in the characteristics of the absorption system is dependent on the refrigeration levels and the heat rejection medium used. The large number of factors that can be varied in an ammonia-water absorption refrigeration system makes the manual optimization of an industrial design a formidable task. However, a good design can make the difference between whether the use of absorption refrigeration based on waste heat is economically attractive or not. This is exemplified by the results from the two case studies. The refrigeration level that is required has an impact of the thermal state of the feed to the distillation column. In both cases, the coefficients of performance are higher when water, instead of air, is used as a heat rejection medium. A lower refrigerant evaporation temperature causes increases in the power used in the solution pump and heat rejection media, as well as increases in the driving heat requirement. In the refrigerant generation column, the rectification section has a large number of stages in case 2, compared to that observed for case 1, independent of the heat rejection medium used in the condenser. In both cases, when water is used for heat rejection, the column diameter is smaller in case 2. However, when air is used for heat rejection, the behavior is reversed. For both heat rejection media, case 1 has the lower exergy efficiency. The absorber contributes the most to the total irreversibility of the system. The implementation of the model in GAMS generates fast results with machine times of

Water Absorption Refrigeration

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