(531f) Minimal Irreversibilities for Heat Exchanger Networks with Compression and Expansion of the Process Streams

Summary This paper combines three of the most widely used tools in process design; Mathematical Programming (MP), Pinch Analysis (PA) and Exergy Analysis (EA), in a new optimization tool. The optimization model extends standard PA by allowing for compression and expansion of the process streams to reduce the need for utilities and to establish the minimal irreversibilities for the process. The optimization model is applied to improve the field site process in an alternative energy chain for utilization of natural gas for power production with carbon capture and sequestration (CCS). In the process, natural gas is liquefied by liquid nitrogen and captured liquid CO2, which are used as cold carriers. Nitrogen is emitted to the atmosphere and the CO2 is injected into the reservoir for enhanced oil recovery (EOR). Introduction and problem definition Although there have been extensive efforts on the optimization of heat exchanger networks, there have been few papers describing how the pressure of the streams can be manipulated in order to achieve more energy- and cost-effective processes. This is especially important in energy intensive cryogenic processes, such as liquefaction of natural gas or hydrogen, where temperature is closely related to both pressure through boiling/condensation and power through expansion/compression. As an example, a pressurized stream can be expanded to produce thermal (cold) exergy from pressure exergy. Thus, it would be very advantageous to have PA tools that include the effect of pressure. Some initial efforts have been made to develop an Extended Pinch Analysis and Design procedure (ExPAnD) [1]. However, this procedure is based on heuristics, and it would be convenient to formulate the problem as a mathematical program. This calls for an updated problem definition: ?Given a set of process streams with a supply state (temperature, pressure and the resulting phase) and a target state, as well as utilities for heating and cooling; design a system of heat exchangers, expanders and compressors in such a way that the irreversibilities (alternatively the utilities or total annualized cost) are minimized?. It should be emphasized that this problem definition is significantly more complex than in standard PA. First, the issue of soft target temperatures is now expanded to also include soft target pressures. Second, the thermodynamic process from the initial to the final condition is not specified, and the change in temperature and pressure may follow a large set of different routes. Third, the distinction between process streams and utilities as well as between hot and cold streams is no longer obvious; in fact streams may change identity. Some process streams act like utilities and a cold process stream or utility may temporarily change to a hot stream and vice versa. Finally, stream properties such as phase can be changed by manipulating the pressure. Description of the optimization model Compression and expansion of the process streams can easily be calculated using the ideal gas model and isentropic efficiencies. The exergy efficiency is defined as the useful outlet exergy divided by the inlet exergy. The inlet exergy is defined as the sum of the thermo-mechanical exergy of inlet process streams and utilities and the net work required, whereas the outlet exergy is the sum of the thermo-mechanical exergy in the outlet streams and the net work produced. The heart of the optimization model is the pinch operator, which calculates the minimum required hot and cold utilities. Since the pressure is allowed to change through compressors and expanders, the inlet temperatures will vary, thus creating difficulties for the standard transshipment model proposed by Papoulias and Grossmann (1983) [2], since a restructuring of the temperature intervals implies making discrete changes that will lead to nondifferentiabilities. Also, since the model allows for pressure manipulation, each process stream will result in several streams in the pinch model, enlarging the problem significantly. Since changing the pressure will change the inlet temperature, and possibly the pinch point, further complexity is added to the model due to nonlinearity and nonconvexity. The pinch point location method is an optimization formulation to find the minimum utility requirement that was developed in 1986 by Duran and Grossmann [3]. The methodology is developed for simultaneous optimization and heat integration of chemical processes and therefore allows for variable inlet temperatures to the pinch operator. The model is based on a graphical understanding and representation of the problem, where the heating and cooling duty can be formulated using the sources and sinks above pinch. The pinch location method finds the hot utility requirement (QH) when all supply temperatures are regarded as potential pinch candidates. The one that results in the largest QH is selected and provides the pinch point. The cold utility requirement (QC) is found by total heat balance. Although this method is well suited for the current problem, as the computational requirements are small, it involves two expressions of the form max {a, b}. One expression is needed to exclude streams that do not appear above pinch, the other to find the largest QH. The nonsmoothness of this expression creates difficulties for both local and global optimization codes. A reformulation of this model based on disjunctive programming that can be used in global solvers was presented by Grossmann et al. (1998) [4]. This reformulation assigns three binary variables to each stream, which will determine whether it is always below the pinch point, above the pinch point or crossing the pinch point. The pinch point can be any supply temperature; hence each hot or cold stream is regarded as a possible pinch candidate. The model works well for smaller problems and Grossmann et al. [4] report solving problems with up to 12 streams. We have implemented this in GAMS/BARON and our experiments show that it fails to converge for a total of 20 streams or more. Two alternative formulations are developed and implemented in GAMS/BARON. One formulation is a reformulation of the pinch location method, where QH and QC can be found using the sources and sinks above pinch. To reduce the number of binary variables, the continuous variables THCutA and TCCutA are introduced for each hot and cold stream and assume the value of the pinch point if the stream crosses the pinch temperature, and the outlet temperature of the hot stream or inlet temperature of the cold stream if not. Furthermore, if a stream is always below the pinch point, a binary variable is assigned so that it does not contribute to the hot or cold streams above the pinch. This introduces a bilinear term, which is reformulated by using the big M method. In the second formulation the hot streams delivers heat to the cold streams in predetermined number of stages with variable inlet and outlet temperatures. Excess heat from one stage is delivered to the next stage using residuals. Binary parameters are required to ensure that heat is not transferred from a cold sink to a hot source. Results The model is used to minimize the irreversibilities in a new field-site process for liquefaction of natural gas [5]. The process utilizes liquid nitrogen and liquid CO2 as cooling agents. It is shown that the exergy efficiency can be improved from 50%, in the case of heat exchange only, to 87% if the process streams are pumped, compressed and expanded throughout the process. The optimal process, see Figure 1, consists of two plate fin heat exchangers, three pumps, three compressors and two expanders and is self supported with power and does not need hot or cold utilities, thereby providing a safer, more compact and more cost-effective natural gas liquefaction process. Figure 1 PFD of the LNG process. There are several other applications for the proposed model, for example the extremely energy intensive liquefaction of hydrogen, where hydrogen is compressed and expanded to produce cold duty at low temperature. Also, processes for utilization of the cryogenic exergy in LNG at receiving terminals can be designed and optimized. A special case of this is the market site for the new LNG process, where nitrogen and CO2 are liquefied by vaporization of LNG. This regasification process needs additional shaft work and requires pressure manipulation for the process to work, however, the overall energy requirement for transport of natural gas and CO2 is reduced to one third compared to a conventional transport chain. References [1] Aspelund, A., Berstad, D. O., Gundersen, T., 2007, An Extended Pinch Analysis and Design Procedure utilizing Pressure Based Exergy for Subambient Cooling, Applied Thermal Eng, Vol. 27/16 pp 2633-2649. [2] Papoulias, S. A., Grossmann, I., E., 1983, A Structural Optimization Approach in Process Synthesis. II: Heat Recovery Networks, Computers and Chem. Eng. Vol 7, 707-722. [3] Duran, M. A., Grossmann I. E., 1986, Simultaneous Optimization and Heat Integration of Chemical Processes, AIChE Journal, Vol. 31, No. 1., 123-138. [4] Grossmann I. E., Yeomans, H., Kravanja, Z., 1998, A Rigorous Disjunctive Optimization Model for Simultaneous Flowsheet Optimization and Heat Integration, Computers Chem. Eng. Vol. 22, 157-164. [5] Aspelund, A, 2006, A novel concept for offshore production of LNG, proceedings CryoPrague, CR06-238, Prague.