Ind. Eng. Chem. Res. 2002, 41, 553-571
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Design of Integrated Refrigeration Systems G. Wu and X. X. Zhu* Department of Process Integration, UMIST, P.O. Box 88, Manchester M60 1QD, U.K.
Refrigeration systems are very important parts of processes below ambient temperature, because the high operating cost and very expensive compressors are involved. This paper introduces a new method for synthesizing integrated refrigeration systems, which combines mathematical optimization techniques and engineering knowledge to produce a systematic procedure capable of solving industrial problems. The major contribution of this method is in addressing the design of refrigeration cycle and heat integration simultaneously. In this approach, most of promising options, such as interevaporating, intercondensing, subcooling, aftercooling, economizing, and presaturating, are considered simultaneously and the capital implications (e.g., compressor, driver, flash drum, and heat exchangers) are addressed together with the operating cost. The method can be used to make major decisions in the conceptual design stage, such as the number of levels, temperature levels, heat transfer duties, approach temperatures of individual heat exchangers, etc. Several real industrial problems are solved using this method in reasonable CPU time in a PC computer. Introduction Refrigeration cycles are required for processes that operate below ambient temperature and the most commonly used refrigeration systems are vapor-recompression type. In Figure 1, an open vapor-recompression cycle is illustrated, which consists of the following steps: compression (1f 2), condensation (2f 3), expansion (3f 4), and evaporation processes (4f 1). In this open system, the vapor refrigerant enters the cycle at drum D1 and some liquid refrigerant leaves the cycle at a high pressure from drum D2 and some at a lower pressure from drum D1. For a given refrigerant, the highest possible condensing temperature is limited by its critical temperature, while the lowest evaporating temperature is limited by the compressor intake pressure, which is often slightly above the atmospheric pressure. These limitations determine a feasible temperature range, in which a refrigerant can operate. A single stage refrigeration cycle can be improved by introducing the following options Barnes and King (1974): interevaporators, intercondensers, intercoolers, after-coolers, economizers, presaturators, sub-coolers, suction vapor-superheated vapor heat exchangers (S-V option), and suction vapor-liquid heat exchangers (S-L option), as shown in Figure 2. Besides these options inside the refrigeration cycle, there are complex interactions between the cycles and the external heat sources/sinks, such as the number of refrigeration levels, the temperature levels, the approach temperature in each integrated heat exchanger, and the number of these of heat exchangers. These features call for development of a systematic method, which can address these interactions and handle design of both refrigeration cycle and heat integration in a more simultaneous manner. However, the conventional design methods for refrigeration systems are heavily dependent on heuristics and experience, without considering the complex integration (Barnes and King, 1974; Cheng and Mah, 1974). In these methods, the HEN and refrigeration cycle are designed separately: first, the number of refrigeration * Corresponding author. E-mail:
[email protected].
levels and the temperature levels are determined by the heuristic and experience. Then the relevant HEN is designed to determine the refrigeration duties at different levels. Finally, the refrigeration cycle is designed to meet the refrigeration requirement. So far, only very few researchers have considered the integration between these two parts (Shelton and Grossmman, 1986a, 1986b; Colmenares and Seider, 1989; and Vaidyaraman and Maranas, 1999). However, Shelton and Grossmman and Vaidyaraman and Maranas’s methods use too simple calculation for shaftwork, which may cause large errors in results. Colmenares and Seider’s method did not consider the capital cost at all. A common limitation for these methods is that many practical options were not addressed. In this paper, a systematic and practical method is proposed for synthesis of integrated refrigeration systems by using mathematical programming. First, a general refrigeration cycle is formulated and modeled. To consider the heat integration between the external heat sources/sinks and the general refrigeration cycle, the extended heat flow cascade models are proposed for the external heat sources/sinks. The heat integration between all heat sources and sinks is represented using a modified transportation model (Cerda et al. 1983). On the bases of general refrigeration, the extended heat flow cascades, and the heat integration, the overall model for design of integrated refrigeration system is formulated. General Refrigeration Cycle In industrial applications, there are three different arrangements of evaporators (Figure 3 A-C), which depend on the type of evaporator and the pattern of installation. Sometimes these evaporator arrangements are jointly used in a single refrigeration system. The common feature of these evaporator arrangements is the same heat transfer duty and area for an evaporator. At the conceptual design stage, the details of selecting the evaporator type and the installation pattern are not essential, since the most important parameters are the temperature level and evaporator duty, etc. Therefore, for the modeling purpose, all evaporator arrangements (Figure 3A-C) are general-
10.1021/ie000492o CCC: $22.00 © 2002 American Chemical Society Published on Web 01/15/2002
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Figure 1. An open refrigeration cycle and its corresponding P-H diagram.
Figure 2. Possible options in vapor-recompression cycles.
ized as Figure 3D. In this arrangement, the refrigerant in vapor-liquid (V-L) phases from the throttle valve enters the evaporator, where part of liquid refrigerant is vaporized to supply the required refrigeration duty and the remaining liquid leaves the evaporator for the drum. Once the temperature level and evaporator duty is determined, the detailed arrangement can be investigated. Subcooling the refrigerant liquid with cold process streams is widely used, provided that the cold process stream has small heat capacity flowrate and large temperature span. For a given integrated refrigeration system with subcooling match between a process stream and the refrigerant liquid, it is easy to identify the supply temperature, the target temperature and the
heat capacity of the refrigerant liquid. However, for a design problem, these parameters are unknown and subject to optimization. In the approach presented in this paper, the subcooling process is approximated with a series of flash-condensing pairs, where all the vapor from the flash drum is condensed with cold streams. This can be illustrated in Figure 4. Here is a given subcooling match with heat transfer duty Q. The supply/target temperatures of the liquid refrigerant are TS and TT, respectively. For the sake of explanation, two flash-condensing pairs are used to approximate this subcooling process. In flash-condensing processes, the vapors from the flash process are condensed and the condensing duties are QS1 and QS2 ,
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Figure 3. The evaporator arrangements at a level of refrigeration cycle.
Figure 4. A subcooling process is approximated with two of flash-condensing pairs.
respectively. The total condensing duty (QS1 + QS2 ) is equal to the subcooling duty Q. To obtain a better result, more pairs of the flashing-condensing processes can be used to approximate one subcooling process. After optimization, these flash-condensing pairs can be extracted from the results and replaced with one subcooling process. This approximation simplifies the representation of the refrigeration cycles significantly, because it makes possible the heat integration between refrigeration cycle and the external heat sinks only through condensers. To distinguish the condenser in the flashcondensing pairs from the inter-condenser, the former is referred to S-condenser and the latter N-condenser in this paper. Using the above evaporator arrangement and the subcooling approximation, we can combine the options described above to form a general refrigeration cycle (Figure 5). In this general refrigeration cycle, all refrigeration options are included except S-L and S-V options, which are considered in the fine-tuning stage (Wu and Zhu, 2001). The general refrigeration cycle can represent any complex refrigeration cycle with the considered
options by changing the number of sections included in the dotted line. After completing the synthesis procedure, the optimal cycle can be simplified by merging the adjacent stages to form a single stage if the considered options do not exist between them. If the focus is put on evaporators and condensers only, the layout of the general cycle forms two cascades: evaporating cascade and condensing cascade. The two cascades are partitioned with the actual refrigeration temperature levels. The evaporating cascade consists of evaporators and the condensing cascade includes both N-condensers and S-condensers. For a refrigeration cycle with K levels, the two cascades are drawn in Figure 6. Notice that neither evaporator nor S-condenser is present at the hottest level and neither Ncondenser nor S-condenser is present at the coldest level. In integrated refrigeration systems, the evaporating cascade is linked with external heat sources and the condensing cascade with external heat sinks. There is no heat transfer between these two cascades. The details about the connections between these two cascades and external heat sinks/sources will be given later.
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Figure 5. General refrigeration cycle.
ture level can be calculated based on the enthalpy of saturated liquid (hlk) and the latent heat of evaporation of refrigerant (∆Hk). Similarly, the latent heat is regarded as constant within a given temperature range, but it can be different from other temperature levels.
hgk ) hlk + ∆Hk
(2)
Within the operating pressure range of a refrigeration system, the saturated pressure of the refrigerant can be regressed as Pk ) PATRPk B with satisfactory accuracy, where PA and PB are constants. Then the compression ratio can be easily presented as a function of the corresponding temperature levels. Therefore, it is not necessary to calculate the saturated pressures in the models.
( )
Pk+1 TRk+1 ) Pk TRk
Figure 6. Evaporating cascade and condensing cascade.
Models for General Refrigeration Cycle. Here are given the models for the general refrigeration cycle. The relevant definitions of indices, parameters, and variables are provided at the end of this paper. (a) Properties of Saturated Refrigerant. The lowest temperature level (k ) 1) is defined as the reference temperature for enthalpy. The enthalpy hlk of the refrigerant liquid at other temperature levels can be calculated against this reference temperature and enthalpy. The specific heat capacity Cplk is regarded as constant within a given temperature range, but it can be different from other temperature levels.
hlk )
{
0, k)1 (1) l + Cplk(TRk - TRk-1), k ) 2, 3, ..., K hk-1
The enthalpy of saturation vapor (hgk) at a tempera-
PB
, k
