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Ind. Eng. Chem. Res. 2009, 48, 2972–2990
Synthesis and Optimization of an Ammonia-Water Absorption Refrigeration Cycle Considering Different Types of Heat Exchangers by Application of Mixed-Integer Nonlinear Programming Luz Marı´a Cha´vez-Islas, Christopher L. Heard,* and Ignacio E. Grossmann Instituto Mexicano del Petro´leo, Eje Central Lazaro Cardenas Norte No. 152, Col. San Bartolo Atepehuacan, Delegacio´n GustaVo A. Madero, 07730 Me´xico D.F., Mexico
Optimization of the operating conditions and process scheme of an ammonia-water absorption refrigeration system, minimizing operating and annualized capital costs, is described. Various heat-exchanger technologies, the effect of the evaporator purge, and the thermodynamic restrictions of the system are taken into account. The objective is to make optimum use of various heat-exchange technologies to reduce the capital cost and meet the process refrigeration service requirements. A procedure to take account of the film coefficients and pressure drops of the different types of heat exchangers considered is proposed, which gives a solid basis for making decisions regarding the use of industrial ammonia-water absorption refrigeration. Introduction A problem arises when there are no firm values for the heattransfer coefficients that are assumed during the process synthesis stage of absorption refrigeration cycle optimization and the assumed coefficients are significantly different from those determined at the detailed equipment design stage. The majority of heat-exchanger network synthesis techniques are based on the assumption of constant film coefficients, and the detailed design of heat exchangers is dependent on satisfying three main objectives:1 the required duty, the tube-side maximum permissible pressure drop, and the shell-side maximum permissible pressure drop. Various heat-exchanger technologies were added to the modified mixed-integer nonlinear programming (MINLP) model of Cha´vez and Heard,2 such that they are considered for each heat exchanger in the absorption refrigeration process scheme, except those which are determined by the industrial process that is served. The overall heat-transfer coefficients and pressure drops are calculated using semirigorous and rigorous methods. The values obtained are introduced into the new MINLP model herein developed as parameters, and the refrigeration process scheme and the design variables are optimized, with respect to total costs (operation plus annualized capital costs). The modified model was developed for two scenarios, which are distinguished by the heat-rejection medium used in the absorber and the condenser. The first scenario corresponds to the use of cooling water and the second to the use of air. The objective is to evaluate the impact of the cooling medium on the operating conditions and the economics of the ammonia-water refrigeration cycle. The selection of the heat-exchanger types is modeled by disjunctions based on the overall heat-transfer coefficient and the pressure drop. The consideration of different types of heat exchanger drastically increases the combinations, the size, and the computation needed to resolve the problem. The interaction between the MINLP model implemented in GAMS and the heat* To whom correspondence should be addressed. Tel.: +52 55 91758446. Fax: +52 55 91758258. E-mail:
[email protected].
exchanger film coefficient calculation models in Excel reduces the complexity of the model and avoids more nonlinear expressions. Previous Studies Sorsak and Kravanja3 described the simultaneous synthesis MINLP of integrated heat-exchange networks, considering different types of heat exchangers. This was extended to the heat-exchanger network superstructures that were proposed by Yee and Grossmann4 with alternative types of heat exchangers. The selection of heat-exchanger types was modeled on disjunctions based on operational limits and required heat-transfer area. Because the different types of heat exchangers involve different geometries, which, in turn, influence the entering and leaving temperatures, additional restrictions were applied to guarantee a feasible temperature distribution. The consideration of different heat-exchanger types drastically increases the combinations, size, and computation required to resolve the problem. The MINLP specification of integer-infeasible path was applied. This performs an efficient initialization and halves the machine time for modified OA/ER algorithm resolution of the master MINLP. A multilevel MINLP procedure for a reduced integer space was proposed to resolve heat-exchanger network problems of g103 binary variables. The main objective of this work was, first, to develop a robust representation of a model that covered different types of heat exchanger and, second, to propose improvements in the OA/ER solution algorithm to enable the solution of highly combinatory MINLP problems. Within the assumptions, with the exception of U-tube shell-and-tube exchangers, all the other types of heat exchangers in the superstructure have countercurrent flow. These types were double-tube and plate-frame exchangers. In addition, the latter had a limitation of not being used when one of the streams was toxic. The heat-exchange coefficients of the film were considered constant. A further simplification was the linearization of Guthrie’s cost functions.5 The cost of the plate frame heat exchanger was specified to be 70% of the cost of a U-tube shell-and-tube exchanger.6 The correction factor to the temperature driving force (Ft) is incorporated into the model (LMTDapprox)7 and, thus, the values of R and S. The value of Ft was estimated using an approximation of Underwood’s equation. The solution produced heatexchanger network designs that were not only feasible, but also
10.1021/ie801309h CCC: $40.75 2009 American Chemical Society Published on Web 02/13/2009
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Figure 1. Superstructure when water cooling is applied.
Figure 2. Superstructure when air cooling is applied. Table 1. Coefficients for Shell-and-Tube Heat Exchangers with Low Fin Tubing
Table 2. Coefficients for Shell-and-Tube Heat Exchangers with Corrugated Tubing
region
RITBAC
βITBAC
application range (m2)
region
RITCC
βITCC
application range (m2)
1 2 3 4 5
19.459 16.633 6.065 0.280 0.418
0.145 0.198 0.414 0.910 0.838
9.3 < AITBAC < 37.2 37.2 e AITBAC < 92.9 92.9 e AITBAC < 557.4 557.4 e AITBAC < 836.1 836.1 e AITBAC < 3716.1
1 2 3 4 5
16.216 13.861 5.054 0.233 0.504
0.145 0.198 0.414 0.910 0.838
9.3 < AITCC < 37.2 37.2 e AITCC < 92.9 92.9 e AITCC < 557.4 557.4 e AITCC < 836.1 836.1 e AITCC < 3716.1
less expensive, in terms of heat supply, heat rejection, heattransfer area required, and the type of heat exchanger selected. Frausto et al.8 reported modifications to the Yee and Grossmann model that eliminated the assumption of constant film coefficients, and, in their place, they proposed a determination in terms of stream pressure drops and exchanger heat-transfer areas. In addition, given that the pressure drops were model variables, it was possible to determine an optimum value for them within permissible limits for each stream. The new proposal allowed integration of the synthesis stage with the detailed equipment design. It was shown that, although finding
the global optimum could not be guaranteed, because of the nonconvex parts of the model, the results were sufficiently promising to motivate further exploration of this research area. All the network heat exchangers were assumed to have the same geometry: plain tubes and a shell, with one pass on each side. It was specified that all the hot streams were on the shell side and, therefore, the cold streams were on the tube side. The modified model had nonlinearities in the objective function and in the permissible pressure drop for each stream with the respective film heat-transfer coefficient on both the shell and tube sides. These correlations were based on the Bell-Delaware
2974 Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009 Table 3. Heat-Exchanger Stream Localizations Cooling-Water Scenario region condenser
tubes
Air-Cooled Scenario shell
tubes
shell or ambient
cooling water
vapor-phase refrigerant with phase vapor-phase refrigerant with phase ambient air change to liquid change to liquid absorber ammonia-water vapor/liquid mixture cooling water ammonia-water vapor/liquid mixture ambient air with phase change to liquid with phase change to liquid liquid refrigerant liquid refrigerant vapor refrigerant liquid refrigerant vapor refrigerant subcooler economizer refrigerant-rich solution refrigerant-poor solution refrigerant-rich solution refrigerant-poor solution reboiler liquid solution with phase low-pressure steam liquid solution with phase low-pressure steam change to liquid/vapor mixture change to liquid/vapor mixture evaporator process stream refrigerant liquid/vapor mixture process stream refrigerant liquid/vapor mixture with phase change to vapor with phase change to vapor
Table 4. Film Coefficient Methods Cooling Water Scenario exchanger type
Air-Cooled Scenario
tubes
shell
tubes
ambient
refs 15 and 16
refs 16, 18, 19, and 20
refs 15 and 16
refs 16, 18, 19, and 20
Condenser shell and plain tube shell and corrugated tube plate frame air-cooled
ref 14 ref 16 ref 15
ref 15 ref 15 ref 17 Liquid Refrigerant Subcooler
shell and plain tubes
ref 14
refs 14, 15, 21, and 22 Economizer
shell and plain tubes shell and low fin tubes shell and corrugated tubes plate frame
ref 14 ref 14 ref 16 ref 15
shell and plain tubes shell and low fin tubes plate frame air-cooled
ref 15 refs 15 and 22 ref 17
refs 14, 15, 16, 21, and 22 refs 14, 15, 16, 21, and 22 refs 14, 15, 16, 21, and 22 ref 15 Absorber refs 14, 15, 16, 21, and 22 refs 14, 15, 16, 21, and 22 ref 15 Reboiler
Thermosyphona
refs 16 and 23
ref 15 Evaporator
scraped-tube exchanger a
A typical value is considered from the available information.
ref 15
From Bayramoglu and Bulgan.11
Table 5. Heat-Exchanger Types
a
unit
shell-and-tube heat exchangersa
plate frame exchangers
condenser absorber liquid refrigerant subcooler economizer reboiler evaporator
horizontal, four tube passes, one shell pass: condensation shell side vertical, one shell pass, one tube pass, absorption tube side one shell pass, one tube pass one shell pass, one tube pass vertical, Thermosyphon, only plain tubes due to pressure drop scraped concentric tube
2-2 1-1 1-1
Includes shell-and-tube exchangers with plain tubes, low fin tubes, and corrugated tubes.
method for turbulent flow for streams without phase change. The film coefficients for cooling water and steam, the heat sink, and the source services were considered to be constant. The simplified approximation of Shenoy9 was used for the pressure drop calculation in each of the superstructure stages of the network. This approximation reduced the complexity of the model by avoiding nonlinearities for each stage of the superstructure and, thus, different heat-transfer coefficients. The transport properties of all the streams were considered to be constant. The objective function of this work has two additional terms, with respect to that of Yee and Grossmann: the cost of pumping power for the hot and cold streams. De los Santos and Rico10 integrated the concepts and advantages of the strategies described by Sorsak and Kravanja3 and Frausto et al.8 and proposed modifications that
reduced the model’s nonlinearities, favoring the numerical solution of the problem. The result was a MINLP heatexchanger network model that simultaneously considered heat-exchanger and service costs, power costs, pump costs, and the possibility of including different types of heat exchangers and flow patterns in the network. The proposed modifications avoided the need to disaggregate the variables that corresponded to the stream pressure drops (total and stagewise) or the heat-transfer areas. Thus, the number of equations in the model was reduced. Correction factors that were dependent on the type of heat exchanger were used for the pressure drop in each stage. The correlations that related the permissible pressure drop for each stream to their respective film heat-transfer coefficient corresponded to
Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009 2975 Table 6. Standard Configuration for Plain Tube Heat Exchangers Economizer characteristic
absorber
condenser
liquid refrigerant subcooler
tube length tube outside diameter tube wall thickness, BWG tube layout tube pitch baffle cut ratio baffle spacing ratio shell baffle spacing tube baffle spacing spacing shell I.D. - bundle O.D. spacing
6.096 m 0.01905 m 16 ∆ (30°) 0.02381 m 0.2 0.45 5.72 mm 0.65 mm 17.216 mm
6.096 m 0.01905 m 16 ∆ (30°) 0.02381 m 0.2 0.45 5.72 mm 0.65 mm 13.970 mm
3.6576 m 0.016 m 16 ∆ (30°) 0.02000 m 0.25 0.45 5.72 mm 0.65 mm 11.667 mm
air-cooled cases
cooling-water cases
6.096 m 0.01905 m 16 ∆ (30°) 0.02381 m 0.2 0.45 5.72 mm 0.65 mm 11.856 mm
4.8768 m 0.01905 m 16 ∆ (30°) 0.02381 m 0.2 0.45 5.72 mm 0.65 mm 12.606 mm
0.319 2.142 0.015748 m
0.319 2.142 0.015748 m
Parameters for Estimating Bundle O.D. k1 n1 tube inside diameter spacing
0.319 2.142 0.015748 m
0.175 2.285 0.015748 m
Table 7. Standard Configuration for Low Fin Tube Heat Exchangers
0.319 2.142 0.015748 m
Table 9. Standard Configuration for Corrugated Tube Heat Exchangers
Economizer characteristic
absorber
air-cooled cases
tube length tube outside diameter tube wall thickness, BWG tube layout tube pitch baffle cut ratio baffle spacing ratio shell baffle spacing tube baffle spacing shell I.D. - bundle O.D.
6.096 m 0.01676 m 16 ∆ (30°) 0.02095 m 0.2 0.45 5.72 mm 0.65 mm 15.705 mm
6.096 m 0.01676 m 16 ∆ (30°) 0.02095 m 0.2 0.45 5.72 mm 0.65 mm 11.378 mm
cooling-water cases 4.877 m 0.01676 m 16 ∆ (30°) 0.02095 m 0.2 0.45 5.72 mm 0.65 mm 12.033 mm
Economizer characteristic
absorber
air-cooled cases
tube length tube outside diameter tube wall thickness, BWG tube layout tube pitch baffle cut ratio baffle spacing ratio shell baffle spacing tube baffle spacing shell I.D. - bundle O.D.
6.096 m 0.01905 m 16 ∆ (30°) 0.02381 m 0.2 0.45 5.72 mm 0.65 mm 13.923 mm
6.096 m 0.01905 m 16 ∆ (30°) 0.02381 m 0.2 0.45 5.72 mm 0.65 mm 11.290 mm
Parameters for Estimating Bundle O.D. k1 n1 tube inside diameter number of tube-side passes
0.319 2.142 0.01335 m 1
0.319 2.142 0.015748 m 1
fin density outside diameter of the fin diameter at the root of the fin inside diameter in the finned section fin height equivalent diameter fin thickness external area per unit length ratio of finned external area to total area ratio of plain external area to total area thermal conductivity of the fin
4.8768 m 0.01905 m 16 ∆ (30°) 0.02381 m 0.2 0.45 5.72 mm 0.65 mm 11.698 mm
Parameters for Estimating Bundle O.D. 0.319 2.142 0.015748 m 1
Table 8. Low Fin Tube Geometries characteristic
cooling-water cases
k1 n1 tube inside diameter number of tube-side passes
0.249 2.207 0.015748 m 2
0.319 2.142 0.015748 m 1
0.319 2.142 0.015748 m 1
Table 10. Standard Configuration for Plate Frame Heat Exchangers value for the absorber and economizer 748 fins/m 18.75 mm 15.85 mm 13.35 mm 1.45 mm 16.76 mm 0.4195 mm 0.151 m2/m 0.8 0.2 mm 53.9 W/(m K)
turbulent flow and were based on the Bell-Delaware method, which were only applicable to streams without phase change. The MINLP proposed by Yee and Grossmann searched for a balance between the consumption of services (heating and cooling), the number of heat-transfer units, and the heat-transfer area. The model was based on a superstructure divided into stages where the temperatures were considered as optimizable variables. The superstructure considered the possibility of matching all the hot streams with all the cold streams involved in the process at each stage. This included the possibility of matching in series as well as in parallel and also rematching in different stages. The topology of the network was determined by the binary variable vector, whose values were obtained during the optimization. The resultant formulation consisted of the
Value characteristic
absorber
condenser
economizer
flow arrangement number of passes effective plate area effective plate length plate width length/width ratio plate spacing nozzle diameter (mm)
parallel 1 0.75 m2 1.5 m 0.5 m 2.5 3 mm variable, Schedule 40 seamless piping 3.048 m/s 0.75 mm
parallel 2 0.75 m2 1.5 m 0.5 m 2.5 3 mm variable, Schedule 40 seamless piping 3.048 m/s 0.75 mm
parallel 1 0.75 m2 1.5 m 0.5 m 2.5 3 mm variable, Schedule 40 seamless piping 3.048 m/s 0.75 mm
nozzle velocity plate thickness
following restrictions: energy balances for each stream, energy balances for each stage of the superstructure, assignment of stream inlet and outlet temperatures to the corresponding model variables, restrictions to ensure the feasibility of the temperatures obtained in the optimization scheme, heating and cooling duties, logical restrictions in terms of the model binary variables, calculation of temperature differences between hot and cold streams, and a cost function that included the heat-exchanger areas. All the restrictions, except the objective function, were linear. The objective function was the annualized cost of the heat-exchanger network, which was composed of the cost of services (hot and cold), fixed charges, and the heat-transfer area of each exchanger. The nonlinearity of the objective function is derived from the calculation of the heat-transfer area. Constant
2976 Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009
Figure 3. Interaction between the MINLP model and the heat-exchanger models given in the spreadsheet.
values for the film coefficients of each process stream were used for this derivation. Problem Statement Given an ammonia-water absorption refrigeration cycle, a set of design variables, and the available heat-exchange technologies, there is a need to find a process scheme and operating conditions that minimize the system’s annualized capital and operating costs. Within the cycle, there are the following heat-exchange units: evaporator, refrigerant subcooler, absorber, economizer, reboiler, and condenser. The heat-exchange technologies herein considered are plate frame exchangers and shell-and-tube exchangers with plain tubes, low fin tubes, or corrugated tubes. The selection of the type of heat exchanger in each unit implies a balance between the overall heat-exchange coefficient, the pressure drop, and the capital and operating costs. The overall heat-transfer coefficients are estimated by rigorous and semirigorous methods, according to the conditions inside the exchanger. Note that there is no phase change in either of the streams in the refrigerant subcooler, whereas in the evaporator, absorber, reboiler, and condenser, there is a phase change (either condensation or evaporation). Another aspect to be taken into account is the location of the streams, i.e., whether they pass through the tubes or the shell and whether the tubes are vertical or horizontal.
Figure 4. Flow diagram for calculation strategy.
These aspects have an impact on the determination of the overall coefficient and the pressure drop in a given exchanger. Two scenarios are considered, depending on the medium of heat rejection used in the absorber and the condenser: air or cooling water. Based on these scenarios, two superstructures are considered, one for each medium. The objective is to minimize the capital and operating costs of a simple ammonia-water refrigeration cycle via the synthesis and optimization of the selection of the type of heat exchanger (plate frame exchangers or shell-and-tube exchangers with plain, low fin, or corrugated tubes) and of the design conditions (evaporator purge, approach temperatures in the heat exchangers (refrigerant subcooler, absorber, reboiler, and condenser)), the economizer efficiency, and the ratio between the rectification column reflux ratio and its minimum reflux ratio. To this end, the two heat-rejection media are considered separately. Basis for the Expanded MINLP Model. Development of Superstructures. In the present work, we attempt to determine not only the design conditions that minimize the total cost (annualized capital and operating), but also the selection of the appropriate heat-exchange technology for the absorber, condenser, economizer, and refrigerant subcooler. When air is used as a heat-rejection medium for the absorber and the condenser, the search only considers the economizer and the refrigerant subcooler. The heat-exchanger technologies considered are listed in the previously given problem description. However, as noted, the type of heat exchanger to be considered for each individual unit is dependent on the heat-rejection medium scenario under examination. Thus, two superstructures were developed, which contain the types of heat exchanger to be considered for each unit. Figures 1 and 2 show the ammonia-water refrigeration process for each scenario. The consideration of different types of heat-exchange technology is to show its impact on the capital and operating costs of the ammonia-water absorption refrigeration cycle. This allows the exploitation of heat-exchanger technologies to reduce system costs. Various film coefficients are taken into consideration, to obtain the overall heat-transfer coefficients and the pressure drop for each type of heat exchanger considered in the superstructure,
Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009 2977
as well as the effect of these values on determination of the configuration of the cycle and its respective operating conditions. The evaporator is a concentric-tube scraped-surface heat exchanger where paraffin waxes, in a process stream, are precipitated by cooling. Because of the fact that this is a specialized heat exchanger, other options are not considered for the optimization. The refrigerant distillation column reboiler is considered to be a vertical tube Thermosyphon heat exchanger. Bayramoglu and Bulgan11 and Koc et al.12 both reported the use of this type of heat exchanger as a column reboiler for ammonia-water absorption refrigeration systems. In the liquid refrigerant subcooler, there is a stringent restriction on the pressure drop for the vapor-phase refrigerant, which, in the case of a shell-and-tube exchanger, is on the tube side. This is because of the lower pressure limit in the absorbate tank (zero gauge pressure). This is to comply with a practical design recommendation: subatmospheric pressures in an ammonia-water absorption refrigeration system can result in air ingress, which leads to the formation of carbamates and, hence, corrosive toxic sludges. Economic Basis. The annualized capital cost for shell-andtube heat exchangers is given as follows: CAITIC ) RTICATICβTIC
(for TIC ) ITBAC, ITCC) (1)
Correlations of the form of eq 1 are used to estimate the cost of shell-and-tube heat exchangers with low fin tubes or corrugated tubes. Tables 1 and 2 show the coefficients and ranges of application for the correlations for shell-and-tube heat exchangers with low fin and corrugated tubes, respectively. The annualized capital cost correlation for stainless-steel plate frame heat exchangers is given as follows: CAIIP ) 11.565665AIP0.42
(2)
where
exchanger for the various services resulting from the spreadsheet are incorporated as parameters in the MINLP model in GAMS, which includes the various heat-exchanger technologies in its superstructure. The resulting flow rates, temperatures, etc. are then supplied anew to the spreadsheet and the resulting overall heat-transfer coefficients are reintroduced to the MINLP model. When the differences between the previous and present iteration is
