Heat integration dynamic simulation

We emphasize that traditional procedures tackle plantwide control and heat integration toward the end of the design. The newly introduced reactor/separation/recycle level (Chapters 2 and 4) allows an early solution to these problems, with the result of avoiding unnecessary loops in the design process. Rigorous design and closed-loop dynamic simulation prove the effectiveness of the approach (Section 9.6). 

Molecular dynamics simulations entail integrating Newton s second law of motion for an ensemble of atoms in order to derive the thermodynamic and transport properties of the ensemble. The two most common approaches to predict thermal conductivities by means of molecular dynamics include the direct and the Green-Kubo methods. The direct method is a non-equilibrium molecular dynamics approach that simulates the experimental setup by imposing a temperature gradient across the simulation cell. The Green-Kubo method is an equilibrium molecular dynamics approach, in which the thermal conductivity is obtained from the heat current fluctuations by means of the fluctuation-dissipation theorem. Comparisons of both methods show that results obtained by either method are consistent with each other [55]. Studies have shown that molecular dynamics can predict the thermal conductivity of crystalline materials [24, 55-60], superlattices [10-12], silicon nanowires [7] and amorphous materials [61, 62]. Recently, non-equilibrium molecular dynamics was used to study the thermal conductivity of argon thin films, using a pair-wise Lennard-Jones interatomic potential [56]. 

Before performing a controllability analysis, ensure the stability of the plant. The first step is to close all inventory control loops, by means of level and pressure controllers. Then, check the stability, by dynamic simulation. If the plant is unstable, it will drift away from the nominal operating point. Eventually, the dynamic simulator will report variables exceeding bounds, or will fail due to numerical errors. Try to Identify the reasons and add stabilizing control loops. Often a simple explanation can be found in uncontrolled inventories. In other situations the origin is subtler. Some units are inherently unstable, as with CSTR s or the heat-integrated reactors. The special case when the instability has a plantwide origin will be discussed in Chapter 13. 

Controllability indices, as Closed Loop Disturbance Gain (CLDG) and Performance Relative Gain Array (PRGA) predict in all situations better dynamic properties for the forward heat-integration scheme, compared with the reverse one. This behaviour is verified by closed loop simulation with the full non-linear model. 

The heat-integrated process provides an excellent example of the power and usefidness of dynamic simulation of distillation column systems. Alternative control structures can be easily and quickly evaluated. 

Molecular dynamics attempts to solve the dynamically evolving ensemble of molecules given the interactions between molecules. The form of the forces between molecules or atoms, the number of interactions (i.e., two- or three-body interactions), and the number of molecules that can be tackled by the program determine the success of the model. Molecular dynamics simulations can predict the internal energy, heat capacity, viscosity, and infrared spectrum of the studied compound and form an integral part in the determination and refinement of structures from X-ray crystallography or nuclear magnetic resonance (NMR) experiments. 

Certainly the bio-process with heat integration considered here would be a challenging test for many of these approaches in terms of the size and scope of what must be considered, the number of potential design alternatives, and the type of control objectives and disturbances that must be considered. A typical industrial approach would be to work through systematically all of the control objectives using a nonlinear dynamic simulation of the process to assess alternatives and to analyze performance (Fig. 11). 

The goal of plantwide control structure synthesis is to develop feasible control structures that address the objectives of the entire chemical plant and account for the interactions associated with complex recycle and heat integration schemes, and the expected multivariate nature of the plant. Many strategies have been proposed for accomplishing this task, and the majority of them have been demonstrated using dynamic process simulations. However, none have been accepted as the universal approach, in a manner similar to the steady-state process design synthesis hierarchy of Douglas [1]. 

Achieving dynamic simulations that rigorously capmre the neat heat integration require the use of Flowsheet Equations in Aspen Dynamics. Two conditions must exist at each point in time during the dynamic simulation. First, the heat transfer in the condenser/reboiler must be equal to the product of the area, the overall heat-transfer coefficient, and the current temperature difference between the reflux drum of the high-pressure column and the base of the low-pressure column. These two temperatures both change dynamically as compositions and pressures vary. The pressure in the high-pressure column is not controlled but floats. 

Implementing heat integration in Aspen Dynamics requires the used of Flowsheet Equations, as discussed in detail in Ghapter 6. There are two conditions that must be satisfied at each point in time during the dynamic simulation. 

In making these comparisons, we developed the core model, a level/flow/composition model that neglects the effect of thermal (temperature) and pressure dynamics. For this plant, with only one recycle stream and no heat integration, the assumption is that the temperature and pressure control loops are largely isolated and noninteracting. This assumption has to be tested for accuracy via simulation. 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

Various levels of models can be used to describe the behavior of pilot-scale jacketed batch reactors. For online reaction calorimetry and for rapid scale-up, a simple model characterizing the heat transfer from the reactor to the jacket can be used. Another level of modeling detail includes both the jacket and reactor dynamics. Finally, the complete set of equations simultaneously describing the integrated reactor/jacket and recirculating system dynamics can be used for feedback control system design and simulation. The complete model can more accurately assess the operability and safety of the pilot-scale system and can be used for more accurate process scale-up. 

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