Dynamics of the cooling jacket

In simple cases the Jacket or cooling temperature, Tj, may be assumed to be constant. In more complex dynamic problems, however, it may be necessary to allow for the dynamics of the cooling jacket, in which case Tj becomes a system variable. The model representation of this is shown in Fig. 3.3. 

Intensive heat transfer may be obtained with a channel-like jacket, where the cooling water circulates at a high constant flow rate. This can be described by the following model that neglects the dynamics of the cooling jacket ... 

Figure 3.3. Dynamic model representation of the cooling jacket.

In the following, the model-based controller-observer adaptive scheme in [15] is presented. Namely, an observer is designed to estimate the effect of the heat released by the reaction on the reactor temperature dynamics then, this estimate is used by a cascade temperature control scheme, based on the closure of two temperature feedback loops, where the output of the reactor temperature controller becomes the setpoint of the cooling jacket temperature controller. Model-free variants of this control scheme are developed as well. The convergence of the overall controller-observer scheme, in terms of observer estimation errors and controller tracking errors, is proven via a Lyapunov-like argument. Noticeably, the scheme is developed for the general class of irreversible nonchain reactions presented in Sect. 2.5. 

In some situations the dynamics of the cooling system may be such that effective temperature control cannot be accomplished by manipulation of the coolant side. This could be the situation for fluidized beds using air coolers to cool the recirculating gases or for jacketed CSTRs with thick reactor walls. The solution to this problem is to balance the rate of heat generation with the net rate of removal by adjusting a reactant concentration or the catalyst flow. Such a scheme is shown in Fig. 4.24. 

A dynamic differential equation energy balance was written taking into account enthalpy accumulation, inflow, outflow, heats of reaction, and removal through the cooling jacket. This balance can be used to calculate the reactor temperature in a nonisothermal operation. 

The two steady-state heat-transfer coefficients, hr and hj, could be further described in terms of the physical properties of the system. The solution-to-wall coefficient for heat transfer, hT in Equation 8.8, is strongly dependent on the physical properties of the reaction mixture (heat capacity, density, viscosity and thermal conductivity) as well as on the fluid dynamics inside the reactor. Similarly, the wall-to-jacket coefficient for heat transfer, hj, depends on the properties and on the fluid dynamics of the chosen cooling liquid. Thus, U generally varies during measurements on a chemical reaction mainly for the following two reasons. 

Dynamic. The coolant is assumed to be perfectly mixed as would be the situation in a circulating cooling water system. The holdup of the coolant is specified, so the dynamics of the jacket, coil, or external heat exchanger are taken into consideration. 

Jayakumar, N. S. Farouq, S. M. 2008. The Dynamics of Liquid Cooling in Half-coil Jackets. Chemical Product and Process Modeling 3(1) 1-16. 

The overall heat transfer coefficient, Ug, in the presence of steam on the jacket side is higher than that when cooling water is present. Notice that during heating, there will be no need to worry about the dynamics of the jacket and the jacket will assume a constant temperature equal to the steam saturation... 

The example simulation THERMFF illustrates this method of using a dynamic process model to develop a feedforward control strategy. At the desired setpoint the process will be at steady-state. Therefore the steady-state form of the model is used to make the feedforward calculations. This example involves a continuous tank reactor with exothermic reaction and jacket cooling. It is assumed here that variations of inlet concentration and inlet temperature will disturb the reactor operation. As shown in the example description, the steady state material balance is used to calculate the required response of flowrate and the steady state energy balance is used to calculate the required variation in jacket temperature. This feedforward strategy results in perfect control of the simulated process, but limitations required on the jacket temperature lead to imperfections in the control. 

For example, it is important to have large enough holdups in surge vessels, reflux drums, column bases, etc., to provide effective damping of disturbances (a much-used rule of thumb is 5 to 10 minutes). A sufficient excess of heat transfer area must be available in reboilers, condensers, cooling Jackets, etc., to be able to handle the dynamic changes and upsets during operation. The same is true of flow rates of manipulated variables. Measurements and sensors should be located so that they can be used for eflcctive control. 

However, there is an important dynamic effect as the size of the heat exchanger is increased. The larger holdup in the heat exchanger introduces more dynamic lag in the heat transfer process, which could degrade dynamic performance. We observed this in the jacket-cooled system discussed in Section 3.1.5. The smaller the thickness of the jacket, the better the temperature control. 

The ethylbenzene CSTR considered in Chapter 2 (Section 2.8) is used in this section as an example to illustrate how dynamic controllability can be studied using Aspen Dynamics. In the numerical example the 100-m3 reactor operates at 430 K with two feedstreams 0.2 kmol/s of ethylene and 0.4 kmol/s of benzene. The vessel is jacket-cooled with a jacket heat transfer area of 100.5 m2 and a heat transfer rate of 13.46 x 106 W. As we will see in the discussion below, the steady-state simulator Aspen Plus does not consider heat transfer area or heat transfer coefficients, but simply calculates a required UA given the type of heat removal specified. 

The nonlinear dynamic model of this fed-batch reactor consists of a total mass balance, component balances for three components, an energy balance for the liquid in the reactor, and an energy balance for the cooling water in the jacket ... 

The flow of heat across the heat-transfer surface is linear with both temperatures, leaving the primary loop with a constant gain. Using the coolant exit temperature as the secondary controlled variable as shown in Fig. 8-55 places the jacket ( mamics in the secondary loop, thereby reducing the period of the primary loop. This is dynamically advanti reous for a stirred-tank reactor because of the slow response of its large heat capacity. However, a plug flow reactor cooled by an external heat exchanger lacks this heat capacity and requires the faster response of the coolant inlet temperature loop. 

Figure Test chamber for the dynamic mechanical moisture sorp-tlon/desorptlon experiments The design of this chamber enables exposure of the sample to a variety of liquid and/or vapor environments. Temperature of the chamber can be controlled by adjusting flow or temperature In the liquid or gas supply lines. Alternatively, the chamber can be jacketed with cooling water or heat tape.

For energy exchange equipment Supply sufficient excess of heat transfer area in reboilers, condensers, cooling jackets, and heat removal systems for reactors to be able to handle the anticipated upsets and dynamic changes. Sometimes extra area is needed in overhead condensers to subcool the condensate to prevent flashing in the downstream control valves. Too frequently, overzealous engineers size the optimum heat exchangers based on an economic minimum based on steady-state conditions and produce uncontrollable systems. 

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