Heat exchanger dynamics

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. 

Heat balance equations on the element of heat exchanger length AZ, according to enthalpy balance relationship. 

Alternatively, the difference-equation model form can be derived directly by dividing the length of the heat exchanger into N finite-difference elements or segments, each of length AZ, as shown in Fig. 4.27. 

The heat balance equation can now be applied to segment n, of the heat exchanger. The heat transfer rate equations are given by the following terms 

Rate of heat transfer from tube contents to the metal wall 

In this problem W is the mass flow rate (kg/s), T is temperature (K), Cp is the specific heat capacity (kJ/kg K), D is the diameter (m), U is the heat transfer coefficient (kJ/m s K), Q is the rate of heat transfer (kJ/s), V is the volume (m ), pis the density (kg/m ) and A is the heat transfer area, (m ). The subscripts are as follows t refers to tube conditions, s to shellside conditions, and m to the metal wall. 

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

This chapter has two alternative structures for feed preheating. Both use a feed effluent heat exchanger, but one also uses a furnace. Steady-state economics favor use of only a heat exchanger. Dynamic controllability favors the use of both a heat exchanger and a furnace. 

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. 

The temperature of the cooling medium in the condenser or the temperature of the heating medium in the reboiler are set, and then Aspen calculates the required UA product (overall heat-transfer coefficient U and heat-transfer area A) from the known heat-transfer rate and temperature differential driving force. This temperature is manipulated in the dynamic simulations. No heat-exchanger dynamics are considered. 

There is one heat-exchanger model in the standard model that considers heat-exchanger dynamics, but is only available for the reboUer. The Dynamic model uses the holdup of the... 

MODEL WITH EXPLICIT HEAT-EXCHANGER DYNAMICS... 

The standard basic RadFrac model in Aspen simulations does not accurately predict the rapid pressure changes during emergency situations because the default heat-exchanger models do not account for heat-exchanger dynamics (condenser and reboiler). Simulations can be developed that include external heat exchangers whose dynamics can be incorporated with the model of the column vessel. 

Figure 8.11 MATLAB file ex83.m which uses the sparse matrix formulation to solve for heat exchanger dynamics.

A numerical study of the effect of area ratio on the flow distribution in parallel flow manifolds used in a Hquid cooling module for electronic packaging demonstrate the useflilness of such a computational fluid dynamic code. The manifolds have rectangular headers and channels divided with thin baffles, as shown in Figure 12. Because the flow is laminar in small heat exchangers designed for electronic packaging or biochemical process, the inlet Reynolds numbers of 5, 50, and 250 were used for three different area ratio cases, ie, AR = 4, 8, and 16. 

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 ... 

H is the height of the plates in the heat exchanger (assuming the plates are in a vertical position, which is normal), and is the number of gaps between the plates, p. in Eq. (9.37) is the dynamic viscosity of the gas. 

Convective heat transmission occurs within a fluid, and between a fluid and a surface, by virtue of relative movement of the fluid particles (that is, by mass transfer). Heat exchange between fluid particles in mixing and between fluid particles and a surface is by conduction. The overall rate of heat transfer in convection is, however, also dependent on the capacity of the fluid for energy storage and on its resistance to flow in mixing. The fluid properties which characterize convective heat transfer are thus thermal conductivity, specific heat capacity and dynamic viscosity. 

N., Cabassud, M., Douglas, C., and Demissy, M. (2008) Dynamic behaviour of a continuous heat exchanger/reactor after flow failure. Int.J. Chem. React. Eng., 6 (A23), Available at http //nnnv.bepress.com/ijcre/vol6/A23. 

Off-the-shelf catalogue sales of micro reactors have just started [15]. With an increasing number of commercial products, quality control will become more important. Brandner et al. describe quality control for micro heat exchangers/reactors at the Forschungszentrum Karlsruhe [23]. All manufacturing steps are accompanied by quality control and documentation. Leak rates (down to 10 mbar 1 s for He) and overpressure resistance (up to 1000 bar at ambient temperature) are measured. Under standardized conditions, the mean hydraulic diameter is determined. Dynamic tests supplement this quality control. 

HEATEX - Dynamics of a Shell-and-Tube Heat Exchanger... 

A shell-and-tube heat exchanger is to be investigated for its dynamic and steady-state behaviour. 

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

Derive a dimensionless form of the equations and thus obtain the important dimensionless groups governing the dynamic behaviour of the heat exchanger. 

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