First-principle model

First-principles models of solid surfaces and adsorption and reaction of atoms and molecules on those surfaces range from ab initio quantum chemistry (HF configuration interaction (Cl), perturbation theory (PT), etc for details see chapter B3.1 ) on small, finite clusters of atoms to HF or DFT on two-dimensionally infinite slabs. In between these... 

Transfer function models are linear in nature, but chemical processes are known to exhibit nonhnear behavior. One could use the same type of optimization objective as given in Eq. (8-26) to determine parameters in nonlinear first-principle models, such as Eq. (8-3) presented earlier. Also, nonhnear empirical models, such as neural network models, have recently been proposed for process applications. The key to the use of these nonlinear empirical models is naving high-quality process data, which allows the important nonhnearities to be identified. 

In the past three decades, industrial polymerization research and development aimed at controlling average polymer properties such as molecular weight averages, melt flow index and copolymer composition. These properties were modeled using either first principle models or empirical models represented by differential equations or statistical model equations. However, recent advances in polymerization chemistry, polymerization catalysis, polymer characterization techniques, and computational tools are making the molecular level design and control of polymer microstructure a reality. 

In this chapter we revisited an old problem, namely, exploring the information provided by a set of (x, y) operation data records and learn from it how to improve the behavior of the performance variable, y. Although some of the ideas and methodologies presented can be applied to other types of situations, we defined as our primary target an analysis at the supervisory control level of (x, y) data, generated by systems that cannot be described effectively through first-principles models, and whose performance depends to a large extent on quality-related issues and measurements. 

Taylor C, Kelly RG, Neurock M. 2009b. First principles modeling of the structure and reactivity of water at the metal/water interface. Submitted. 

Off-line analysis, controller design, and optimization are now performed in the area of dynamics. The largest dynamic simulation has been about 100,000 differential algebraic equations (DAEs) for analysis of control systems. Simulations formulated with process models having over 10,000 DAEs are considered frequently. Also, detailed training simulators have models with over 10,000 DAEs. On-line model predictive control (MPC) and nonlinear MPC using first-principle models are seeing a number of industrial applications, particularly in polymeric reactions and processes. At this point, systems with over 100 DAEs have been implemented for on-line dynamic optimization and control. 

Simplified mathematical models These models typically begin with the basic conservation equations of the first principle models but make simplifying assumptions (typically related to similarity theory) to reduce the problem to the solution of (simultaneous) ordinary differential equations. In the verification process, such models must also address the relevant physical phenomenon as well as be validated for the application being considered. Such models are typically easily solved on a computer with typically less user interaction than required for the solution of PDEs. Simplified mathematical models may also be used as screening tools to identify the most important release scenarios however, other modeling approaches should be considered only if they address and have been validated for the important aspects of the scenario under consideration. 

The purpose of the present review is to summarize the current status of fundamental models for fuel cell engineering and indicate where this burgeoning field is heading. By choice, this review is limited to hydrogen/air polymer electrolyte fuel cells (PEFCs), direct methanol fuel cells (DMFCs), and solid oxide fuel cells (SOFCs). Also, the review does not include microscopic, first-principle modeling of fuel cell materials, such as proton conducting membranes and catalyst surfaces. For good overviews of the latter fields, the reader can turn to Kreuer, Paddison, and Koper, for example. 

The second contribution comes from a major catalyst manufacturer and illustrates how insight in the reaction paths involved in three-way conversion leads to a fundamental, i.e. based on first principles, model. The emphasis in this contribution is on the chemistry rather than on the reactor model, i.e. on the description of the physical phenomena occurring in the monolith reactor. In this sense, this contribution is the bridge from the first to the third contribution. 

Physical Models versus Empirical Models In developing a dynamic process model, there are two distinct approaches that can be taken. The first involves models based on first principles, called physical or first principles models, and the second involves empirical models. The conservation laws of mass, energy, and momentum form the basis for developing physical models. The resulting models typically involve sets of differential and algebraic equations that must be solved simultaneously. Empirical models, by contrast, involve postulating the form of a dynamic model, usually as a transfer function, which is discussed below. This transfer function contains a number of parameters that need to be estimated from data. For the development of both physical and empirical models, the most expensive step normally involves verification of their accuracy in predicting plant behavior. 

White-box or first-principle modeling. A dynamic model for well-understood processes derived from mass, energy, and momentum balances. 

Dynamic Optimisation Framework Using First Principle Model... 

On the surface it might appear that partial control does not require a first-principles model for its implementation. After all, M is a regression model and controller tuning is based on relay-feedback information. For simple systems this may be correct. However, for most industrially relevant systems it is not intuitively obvious what constitutes the dominant variables in the system and how to identify appropriate manipulators to control the dominant variables. This requires nonlinear, first-principles models. The models are run off-line and need only contain enough information to predict the correct trends and relations in the system. The purpose is not to predict outputs from inputs precisely and accurately, but to identify dominant variables and their relations to possible manipulators. 

To overcome these drawbacks of the controller based on first principles model, various identification techniques were applied. Neural network based model predictive control was used for the dynamic control of SMB unit [1 ], however, its implementation to actual process can be very difficult because of the complexity of identified neural net model. 

The first principles model of the SMB unit is constructed with reference to the previous works[4,6] and considered to be the actual plant. 

In order to solve the first principles model, finite difference method or finite element method can be used but the number of states increases exponentially when these methods are used to solve the problem. Lee et u/.[8] used the model reduction technique to reslove the size problem. However, the information on the concentration distribution is scarce and the physical meaning of the reduced state is hard to be interpreted. Therefore, we intend to construct the input/output data mapping. Because the conventional linear identification method cannot be applied to a hybrid SMB process, we construct the artificial continuous input/output mapping by keeping the discrete inputs such as the switching time constant. The averaged concentrations of rich component in raffinate and extract are selected as the output variables while the flow rate ratios in sections 2 and 3 are selected as the input variables. Since these output variables are directly correlated with the product purities, the control of product purities is also accomplished. 

We adopt the input/output data-based prediction model using the subspace identification technique. To find the correlation between the inputs and outputs, we need to obtain the input and output data. On the basis of the triangle Aeoiy[6], the optimal feed flow rate ratios at steady state are calculated. Then, the pseudo random binary input signal is generated on the basis of this optimal value. Figure 1 compares the output from the identified model (dot) with that from the first principles model (solid curve). Clearly, we observe that the identified model based on the subspace identification method shows an excellent prediction performance. The variance accounted for (VAF) indices for both outputs are higher than 99%. The detailed identification procedure can be founded in the literature [3,5,9,10]. 

AIMD simulations appear as a promising tool for a first-principles modeling of enzymes. Indeed, they enable in situ simulations of chemical reactions furthermore, they are capable of tEiking crucial thermal effects [53] into account finally, they automatically include many of the physical effects so difficult to model in force-field based simulations, such as polarization effects, many-body forces, resonance stabilization of aromatic rings and hydration phenomena. 

Fig. 13 Optimal temperature profile calculated from a first-principle model for maximizing the mean crystal size for unseeded crystallization of paracetamol in water and the simulated change in mean crystal size during crystallization.

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