Modeling of SMB Processes

A linear model predictive control law is retained in both cases because of its attracting characteristics such as its multivariable aspects and the possibility of taking into account hard constraints on inputs and inputs variations as well as soft constraints on outputs (constraint violation is authorized during a short period of time). To practise model predictive control, first a linear model of the process must be obtained off-line before applying the optimization strategy to calculate on-line the manipulated inputs. The model of the SMB is described in [8] with its parameters. It is based on the partial differential equation for the mass balance and a mass transfer equation between the liquid and the solid phase, plus an equilibrium law. The PDE equation is discretized as an equivalent system of mixers in series. A typical SMB is divided in four zones, each zone includes two columns and each column is composed of twenty mixers. A nonlinear Langmuir isotherm describes the binary equilibrium for each component between the adsorbent and the liquid phase. 

Other control studies, such as robustness and other control strategies, will be carried out in next works. Although the SMB control was carried out in simulation based on a realistic model of the process, the application of these control strategies to a real SMB for validation purposes should be done. 

The benefits of model-based control strategies for the operation of SMB processes are demonstrated in Chapter 9. This is a rather new concept as, in today s industrial practice, SMB processes are still controlled" manually, based on the experience of the operators. A nonlinear model predictive (NMP) controller is described that can deal with the complex hybrid (continuous/discrete) dynamics of the SMB plant and takes hard process constraints (e.g. the maximal allowable pressure drop) and the purity requirements into account. The NMP controller employs a rigorous process model, the parameters of which are re-estimated online during plant operation, thus changes or drifting of the process parameters can be detected and compensated. The efficiency of this novel control concept is proven by an experimental study. 

Ever since the development and application of mathematical models for the design of SMB processes, beginning in the 1980s, efforts have been made to validate these models by comparing measured and simulated data. SMB and TMB models of different complexity have been used for this task, for example the ideal and equilibrium... 

Due to the simplifying assumptions made for the TMB approaches, accurate design and optimization of SMB processes is not possible. Several approaches based on SMB models have been suggested to improve the prediction and optimization of the SMB operation. Zhong and Guiochon (1996) have presented an analytical solution for an ideal SMB model and linear isotherms. The results of this ideal model are... 

Schramm et al. (2001) have presented a model-based control approach for direct control of the product purities of SMB processes. Based on wave theory, relationships between the front movements and the flow rates of the equivalent TMB process were derived. Using these relationships, a simple control concept with two PI controllers was proposed. This concept is very easy to implement however, it does not address the issue of optimizing the operating regime in the presence of disturbances or model mismatch. 

Starting with the simplest model, the true moving bed (TMB) model, first it will be demonstrated how to determine parameters for the operation of SMB processes. Based on these TMB shortcut methods, a more detailed optimization of operating... 

Few published papers deal with the detailed optimization of design parameters. Charton and Nicoud (1995) and Nicoud (1998) have presented a strategy based on a TMB stage model to optimize the operation as well as the design of SMB processes. 

Automatic control of purities is difficult due to the long time delays and the complex dynamics that are described by nonlinear distributed parameter models and switching of the inputs, leading to mixed discrete and continuous dynamics, small operating windows, and a pronouncedly nonlinear response of the purities to input variations. Because of the complex nonlinear dynamics of SMB processes, their automatic control has attracted the interest of many academic research groups and many different control schemes have been proposed however, few of them have been tested in experimental work for real plants with limited sensor information. 

Due to the complexity of the process, the modeling of SMB chromatography is the only acceptable possibility for optimizing the separation towards productivity and purity of fractions. 

In the literature various proposals for the mathematical description of SMB processes have been made. A summary of the models is given by Ruthven and Ching [7]. Criteria for a classification are ... 

The steps when designing a SMB which would allow one to process a given amount of feed per unit time have been described in detail [46, 57]. The procedure described was based on modeling of nonlinear chromatography. The procedure is rigorous, versatile and mainly requires the determination of competitive adsorption isotherms. If the adequate tools and methods are used, the procedure is not tedious and requires less work than is sometimes claimed. The procedure is briefly described below. 

A first model is used to compute the flowrates allowing to perform the separation with the greatest productivity. Then, the "mixed cell in series" model takes into account thermodynamic, hydrodynamic and kinetic properties of the system and compute the concentration profile inside the columns [14], In this model, we make the assumptions that the pressure drop inside the column is negligible compared to the pressure drop realized and controlled with the analogical valves, and we model the true moving bed assuming that the performance of SMB and TMB are equivalent. A mass balance equation is written for each stage and a classical Newton Raphson numerical method is used to solve the permanent state of the process [14],... 

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