Dynamic model heat exchanger

Eluor Daniel has the ability to perform a heat exchanger tube rupture transient analysis consistent with the method referred to in RP-521 ("Model to Predict Transient Consequences of a Heat Exchanger Tube Rupture," by Sumaria et ah). This methodology accounts for effects such as the inertia of the low-pressure liquid, the compressibility of the liquid, the expansion of the exchanger shell or tube chaimels, and the relief valve dynamics. Dynamic simulation can be used to meet the following objectives ... 

The modelling procedure is again based on that of Franks (1967). A simple, single-pass, countercurrent flow, heat exchanger is considered. Heat losses and heat conduction along the metal wall are assumed to be negligible, but the dynamics of the wall (thick-walled metal tube) are significant. 

Figure 5.236. Finite differencing the heat exchanger for dynamic modelling.

Example SHELL AND TUBE HEAT EXCHANGER DYNAMIC MODEL WITH 8 FINITE DIFFERENCE ELEMENTS CONSTANT HTM=20,HMS=20 HEAT EXCHANGE CONSTANTS... 

Finally, we will neglect the dynamics of the condenser and the reboiler. In commercial-scale colunms, the dynamic response of these heat exchangers is usually much faster than the response of the column itself In some systems, however, the dynamics of this peripheral equipment are important and must be included in the model... 

From the energy balance, and by considering the total volume of the heat exchanger, the following dynamical model can be obtained for the liquid-liquid heat exchanger... 

Show that the steady- state and dynamic models for a double-pipe, counter-current heat exchanger can have the same form as the model of a packed bed absorber. Discuss the assumptions inherent in both the heat exchanger and the absorber models which might lead to significant differences in the kinds of model equations used to describe each system. 

The reaction considered is the gas-phase, irreversible, exothermic reaction A + B — C occurring in a packed tubular reactor. The reactor and the heat exchanger are both distributed systems, which are rigorously modeled by partial differential equations. Lumped-model approximations are used in this study, which capture the important dynamics with a minimum of programming complexity. There are no sharp temperature or composition gradients in the reactor because of the low per-pass conversion and high recycle flowrate. 

FEHE Model There are no phase changes or small pinch temperatures in the heat exchanger. Therefore a 10-lump model is used for this unit. The steady-state exit temperatures predicted by the lumped model are close to those calculated by the rigorous countercurrent model used in the steady-state design. Table 7.2 compares the steady-state conditions for the process obtained from the dynamic model with those obtained in the steady-state design. 

JAEA conducted an improvement of the RELAP5 MOD3 code (US NRC, 1995), the system analysis code originally developed for LWR systems, to extend its applicability to VHTR systems (Takamatsu, 2004). Also, a chemistry model for the IS process was incorporated into the code to evaluate the dynamic characteristics of process heat exchangers in the IS process (Sato, 2007). The code covers reactor power behaviour, thermal-hydraulics of helium gases, thermal-hydraulics of the two-phase steam-water mixture, chemical reactions in the process heat exchangers and control system characteristics. Field equations consist of mass continuity, momentum conservation and energy conservation with a two-fluid model and reactor power is calculated by point reactor kinetics equations. The code was validated by the experimental data obtained by the HTTR operations and mock-up test facility (Takamatsu, 2004 Ohashi, 2006). 

The dynamic behavior of processes (pipe-vessel combinations, heat exchangers, transport pipelines, furnaces, boilers, pumps, compressors, turbines, and distillation columns) can be described using simplified models composed of process gains, dead times, and process dynamics. 

Problem. In this example, we consider the flow around a body. Air, at atmospheric pressure, flows at 20 m s 1 across a bank of heat exchanger tubes. A l/10th-scale model is built. At what velocity must air flow over the model bank of tubes to achieve dynamic similarity ... 

Solving dynamic models that employ the LMTD can, however, be problematic because the LMTD is not well defined when the temperature gradient along the heat exchanger is constant i.e., Tr = Tc and Tr = Tm (note that heat transfer in a physical exchanger would still take place under these circumstances). Moreover, the LMTD is not well defined in the case of a temperature cross-over (e.g., Tr > Tc and Tr < Tn), a situation that can arise temporarily during transient operation. These issues were recognized relatively early (Paterson 1984), and several approximate formulations with improved numerical properties have been... 

Listing C.l. Symbolic derivation of reduced-order model of the slow dynamics, and of the input-output linearizing temperature controller for the reactor-feed effluent heat exchanger system in Section 6.6... 

These questions touch on the theoretical fundamentals of models, these being based on dimensional analysis. Although they have been used in the field of fluid dynamics and heat transfer for more than a century - cars, aircraft, vessels and heat exchangers were scaled up according to these principles - these methods have gained only a modest acceptance in chemical engineering. The reasons for this have already been explained in the preface. 

If we consider plug flow models for both fluids, the heat exchanger dynamics can be described using the following model ... 

Chapter 4 is devoted to the description of stochastic mathematical modelling and the methods used to solve these models such as analytical, asymptotic or numerical methods. The evolution of processes is then analyzed by using different concepts, theories and methods. The concept of Markov chains or of complete connected chains, probability balance, the similarity between the Fokker-Plank-Kolmogorov equation and the property transport equation, and the stochastic differential equation systems are presented as the basic elements of stochastic process modelling. Mathematical models of the application of continuous and discrete polystochastic processes to chemical engineering processes are discussed. They include liquid and gas flow in a column with a mobile packed bed, mechanical stirring of a liquid in a tank, solid motion in a liquid fluidized bed, species movement and transfer in a porous media. Deep bed filtration and heat exchanger dynamics are also analyzed. 

In the present work, the transient and steady-state characteristics of a fluidized bed combustor are studied by solving numerically a dynamic model in which lateral solids and gas dispersion, lateral temperature distribution and wide size distribution of coal feed are taken into account. The influences of bubble size, excess air rate, specific area of heat exchangers and coal feed rate on the performance of the fluidized combustor are examined by means of simulation with the model. 

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