Dynamics cooling jacket

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. 

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. 

Figure 3.3. Dynamic model representation of the cooling jacket.

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. 

Our examples above demonstrated this quantitatively. For this reason, it is vital to design a reactor control system with very fast measurement dynamics and very fast heat-removal dynamics. If the thermal lags in the temperature sensor and in the cooling jacket are not small, it may not be possible to stabilize the reactor with feedback control. 

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. 

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 ... 

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. 

This can be seen in the simulation of the PID control of polymerization reactor temperature by Houston and Schork [34]. Reactor temperature is often controlled by manipulating the temperature or flow rate of coolant in the reactor cooling jacket. This scheme is hindered by the slow dynamics of heat removal and the nonlinear nature of the heat evolution process (especially in... 

A typical example of dynamic optimization in ch ical engineering is the change between steady states in a continuous-stured tank reactor (CSTR) in which the irreversible reaction A B takes place ([21,22]) (Figure 14.4). The reaction is first order and exothermic and follows Arrhenius rate law. The reactor is equipped with a cooling jacket with refrigerant fluid at constant temperature T . To develop model equations, we formulate mass and energy balances. 

Reactor Control with Cooling Jacket Dynamics... 

Reactor temperature is often controlled by manipulating the temperature or flowrate of coolant in the reactor cooling jacket. This scheme is hindered by the slow dynamics of heat... 

The source term in the species conservation Eq. (3.1) can represent the mass created or depleted by a chemical reaction besides the mass transferred from one phase to the other. Thus, CMT model can be used for simulating the chemical reactor. A catalytic reactor with water-cooled jacket is chosen as typical example for illustration. The CMT model equations are regularly comprises mass transfer equation set and the accompanied fluid-dynamic equation set and heat transfer equation set. Note that the source term is calculated in terms of reaction rate. The simulated results of a wall-cooled catalytic reactor for the synthesis of vinyl acetate from acetic acid and acetylene by both — Sc model and Reynolds mass flux model for simulating the axial concentration and temperature distributions are in agreement with the experimental measurement. As the distribution of /r, shows dissimilarity with D, and t, the 5c, or Pr, are varying throughout the reactor. The wavy shape of axial dififusivity D, along the radial direction indicates the important influence of porosity distribution on the performance of a reactor. 

CSTR WITH EXOTHERMIC REACTION AND JACKET COOLING Dynamic solution for phase-plane plots Located steady-states with THERMPLO and use same parameters. 

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. 

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. 

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. 

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. 

---