Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

Simultaneous synthesis of heat exchanger networks with pressure recovery: optimal integration between heat and work

The optimal integration between heat and work may significantly reduce the energy demand and consequently the process cost. This paper introduces a new mathematical model for the simultaneous synthesis of heat exchanger networks (HENs) in which the pressure levels of the process streams can be adjusted to enhance the heat integration. A superstructure is proposed for the HEN design with pressure recovery, developed via generalized disjunctive programming (GDP) and mixed-integer nonlinear programming (MINLP) formulation. The process conditions (stream temperature and pressure) must be optimized. Furthermore, the approach allows for coupling of the turbines and compressors and selection of the turbines and valves to minimize the total annualized cost, which consists of the operational and capital expenses. The model is tested for its applicability in three case studies, including a cryogenic application. The results indicate that the energy integration reduces the quantity of utilities required, thus decreasing the overall cost.

MINLP Model for the Synthesis of Heat Exchanger Networks with Handling Pressure of Process Streams

This paper introduces a new mathematical model for the simultaneous synthesis of heat exchanger networks (HENs), wherein the handling pressure of process streams is used to enhance the heat integration. The proposed approach combines generalized disjunctive programming (GDP) and mixed-integer nonlinear programming (MINLP) formulation, in order to minimize the total annualized cost composed by operational and capital expenses. A multi-stage superstructure is developed for the HEN synthesis, assuming constant heat capacity flow rates and isothermal mixing, and allowing for streams splits. In this model, the pressure and temperature of streams must be treated as optimization variables, increasing further the complexity and difficulty to solve the problem. In addition, the model allows for coupling of compressors and turbines to save energy. A case study is performed to verify the accuracy of the proposed model. In this example, the optimal integration between the heat and work decreases the need for thermal utilities in the HEN design. As a result, the total annualized cost is also reduced due to the decrease in the operational expenses related to the heating and cooling of the streams.

Retrofit of heat exchanger networks with pressure recovery of process streams at sub-ambient conditions

This paper presents a new mathematical programming model for the retrofit of heat exchanger networks (HENs), wherein the pressure recovery of process streams is conducted to enhance heat integration. Particularly applied to cryogenic processes, HENs retrofit with combined heat and work integration is mainly aimed at reducing the use of expensive cold services. The proposed multi-stage superstructure allows the increment of the existing heat transfer area, as well as the use of new equipment for both heat exchange and pressure manipulation. The pressure recovery of streams is carried out simultaneously with the HEN design, such that the process conditions (streams pressure and temperature) are variables of optimization. The mathematical model is formulated using generalized disjunctive programming (GDP) and is optimized via mixed-integer nonlinear programming (MINLP), through the minimization of the retrofit total annualized cost, considering the turbine and compressor coupling with a helper motor. Three case studies are performed to assess the accuracy of the developed approach, including a real industrial example related to liquefied natural gas (LNG) production. The results show that the pressure recovery of streams is efficient for energy savings and, consequently, for decreasing the HEN retrofit total cost especially in sub-ambient processes.

MINLP Optimization Algorithm for the Synthesis of Heat and Work Exchange Networks

This paper introduces a new optimization model for the simultaneous synthesis of heat and work exchange networks. The work integration is performed in the work exchange network (WEN), while the heat integration is carried out in the heat exchanger network (HEN). In the WEN synthesis, streams at high-pressure (HP) and low-pressure (LP) are subjected to pressure manipulation stages, via turbines and compressors running on common shafts and stand-alone equipment. The model allows the use of several units of single-shaft-turbine-compressor (SSTC), as well as helper motors and generators to respond to any shortage and/or excess of energy, respectively, in the SSTC axes. The heat integration of the streams occurs in the HEN between each WEN stage. Thus, as the inlet and outlet streams temperatures in the HEN are dependent of the WEN design, they must be considered as optimization variables. The proposed multi-stage superstructure is formulated in mixed-integer nonlinear programming (MINLP), in order to minimize the total annualized cost composed by capital and operational expenses. A case study is conducted to verify the accuracy of the proposed approach. The results indicate that the heat integration between the WEN stages is essential to enhance the work integration, and to reduce the total cost of process due the need of a smaller amount of hot and cold utilities.

A hybrid simulation-optimization approach for the design of internally heat-integrated distillation columns

Paper submitted to AIChE 2012 Annual Meeting: Energy Efficiency by Process Intensification, Pittsburgh, PA, October 28-November 2, 2012.

Evidence of different thermoregulatory mechanisms between two sympatric Scarabaeus species using infrared thermography and micro-computer tomography

In endotherms insects, the thermoregulatory mechanisms modulate heat transfer from the thorax to the abdomen to avoid overheating or cooling in order to obtain a prolonged flight performance. Scarabaeus sacer and S. cicatricosus, two sympatric species with the same habitat and food preferences, showed daily temporal segregation with S. cicatricosus being more active during warmer hours of the day in opposition to S. sacer who avoid it. In the case of S. sacer, their endothermy pattern suggested an adaptive capacity for thorax heat retention. In S. cicatricosus, an active ‘heat exchanger’ mechanism was suggested. However, no empirical evidence had been documented until now. Thermographic sequences recorded during flight performance showed evidence of the existence of both thermoregulatory mechanisms. In S. sacer, infrared sequences showed a possible heat insulator (passive thermal window), which prevents heat transfer from meso- and metathorax to the abdomen during flight. In S. cicatricosus, infrared sequences revealed clear and effective heat flow between the thorax and abdomen (abdominal heat transfer) that should be considered the main mechanism of thermoregulation. This was related to a subsequent increase in abdominal pumping (as a cooling mechanism) during flight. Computer microtomography scanning, anatomical dissections and internal air volume measurements showed two possible heat retention mechanisms for S. sacer; the abdominal air sacs and the development of the internal abdominal sternites that could explain the thermoregulation between thorax and abdomen. Our results suggest that interspecific interactions between sympatric species are regulated by very different mechanisms. These mechanisms create unique thermal niches for the different species, thereby preventing competition and modulating spatio-temporal distribution and the composition of dung beetle assemblages.

Simultaneous synthesis of work exchange networks with heat integration

The optimal integration of work and its interaction with heat can represent large energy savings in industrial plants. This paper introduces a new optimization model for the simultaneous synthesis of work exchange networks (WENs), with heat integration for the optimal pressure recovery of process gaseous streams. The proposed approach for the WEN synthesis is analogous to the well-known problem of synthesis of heat exchanger networks (HENs). Thus, there is work exchange between high-pressure (HP) and low-pressure (LP) streams, achieved by pressure manipulation equipment running on common axes. The model allows the use of several units of single-shaft-turbine-compressor (SSTC), as well as stand-alone compressors, turbines and valves. Helper motors and generators are used to respond to any demand and excess of energy. Moreover, between the WEN stages the streams are sent to the HEN to promote thermal recovery, aiming to enhance the work integration. A multi-stage superstructure is proposed to represent the process. The WEN superstructure is optimized in a mixed-integer nonlinear programming (MINLP) formulation and solved with the GAMS software, with the goal of minimizing the total annualized cost. Three examples are conducted to verify the accuracy of the proposed method. In all case studies, the heat integration between WEN stages is essential to improve the pressure recovery, and to reduce the total costs involved in the process.

DSC study of transitions involved in thermal treatment of foamable mixtures of PE and EVA copolymer with azodicarbonamide

The transitions and reactions involved in the thermal processing of binary mixtures of polyethylene and poly(ethylene-co-vinyl acetate) copolymers with different concentrations of a foaming agent (azodicarbonamide) were studied using differential scanning calorimetry (DSC). The effect of ZnO as a kicker also was discussed. The temperature at the maximum rate and the heat evolved were measured for all the processes—melting, transitions, and reactions—all the mixtures prepared were measured and compared. Azodicarbonamide decomposed differently depending on the polymeric matrix. These data can be very useful for the plastic processing industry.

Difference schemes for numerical solutions of lagging models of heat conduction

Non-Fourier models of heat conduction are increasingly being considered in the modeling of microscale heat transfer in engineering and biomedical heat transfer problems. The dual-phase-lagging model, incorporating time lags in the heat flux and the temperature gradient, and some of its particular cases and approximations, result in heat conduction modeling equations in the form of delayed or hyperbolic partial differential equations. In this work, the application of difference schemes for the numerical solution of lagging models of heat conduction is considered. Numerical schemes for some DPL approximations are developed, characterizing their properties of convergence and stability. Examples of numerical computations are included.

A compact difference scheme for numerical solutions of second order dual-phase-lagging models of microscale heat transfer

Dual-phase-lagging (DPL) models constitute a family of non-Fourier models of heat conduction that allow for the presence of time lags in the heat flux and the temperature gradient. These lags may need to be considered when modeling microscale heat transfer, and thus DPL models have found application in the last years in a wide range of theoretical and technical heat transfer problems. Consequently, analytical solutions and methods for computing numerical approximations have been proposed for particular DPL models in different settings. In this work, a compact difference scheme for second order DPL models is developed, providing higher order precision than a previously proposed method. The scheme is shown to be unconditionally stable and convergent, and its accuracy is illustrated with numerical examples.

Large scale optimization of a sour water stripping plant using surrogate models

In this work, we propose a new methodology for the large scale optimization and process integration of complex chemical processes that have been simulated using modular chemical process simulators. Units with significant numerical noise or large CPU times are substituted by surrogate models based on Kriging interpolation. Using a degree of freedom analysis, some of those units can be aggregated into a single unit to reduce the complexity of the resulting model. As a result, we solve a hybrid simulation-optimization model formed by units in the original flowsheet, Kriging models, and explicit equations. We present a case study of the optimization of a sour water stripping plant in which we simultaneously consider economics, heat integration and environmental impact using the ReCiPe indicator, which incorporates the recent advances made in Life Cycle Assessment (LCA). The optimization strategy guarantees the convergence to a local optimum inside the tolerance of the numerical noise.

Pore size distributions derived from adsorption isotherms, immersion calorimetry, and isosteric heats: A comparative study

We compare the pore size distribution of a well-characterized activated carbon derived from model-dependent, adsorption integral equation (AIE) methods with those from model-independent, immersion calorimetry and isosteric heat analyses. The AIE approach applied to nitrogen gave a mean pore width of 0.57 nm; the CO2 distribution exhibited wider dispersion. Spherical model application to CO2 and diffusion limitations for nitrogen and argon were proposed as primary reasons for inconsistency. Immersion enthalpy revealed a sharp decrease in available area equivalent to a cut-off due to molecular exclusion when the accessible surface was assessed against probe kinetic diameter. Mean pore width was identified as 0.58 ± 0.02 nm, endorsing the underlying assumptions for the nitrogen-based AIE approach. A comparison of the zero-coverage isosteric heat of adsorption for various non-polar adsorptives by the porous test sample was compared with the same adsorptives in contact with a non-porous reference adsorbent, leading to an energy ratio or adsorption enhancement factor. A linear relationship between the energy ratio and probe kinetic diameter indicated a primary pore size at 0.59 nm. The advantage of this enthalpy, model-independent methods over AIE were due to no assumptions regarding probe molecular shape, and no assumptions for pore shape and/or connectivity.