Towards the dynamic initialization of C4 splitter models

Dones, Ivan; Preisig, Heinz A.; Graaf, Stefan de

doi:10.1016/b978-0-444-53292-3.50014-6

Cited by 2 publications

(8 citation statements)

References 5 publications

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“…Since no plant data were available, they were substituted with data obtained by simulating the full model. The same model was previously described in other contributions, , and only the fundamental explanations are reported hereinafter.…”

Section: Validation Case: Distillation Columnmentioning

confidence: 99%

Nonlinear Model Predictive Control: A Self-Adaptive Approach

Dones

Manenti

Preisig

et al. 2010

Ind. Eng. Chem. Res.

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Model predictive control (MPC) is an online application based on dynamic models. Its application faces two major obstacles: (i) computational constraints and (ii) the need to accurately simulate the process by a model that properly predicts how the plant will behave in the future. Implementation of MPC is not always possible in large-scale or industrial applications due to the computational complexity of MPC and to the dimensionality of the models. To facilitate MPC implementations, this paper proposes a self-adaptive approach based on simplified (or reduced-order) nonlinear models. The proposed methodology yields an MPC that adjusts the dimension of the model according to both the current process conditions and the control objectives. The self-adaptive approach is described and validated on an industrial case study, a C4-splitter.

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Section: Validation Case: Distillation Columnmentioning

confidence: 99%

Nonlinear Model Predictive Control: A Self-Adaptive Approach

Dones

Manenti

Preisig

et al. 2010

Ind. Eng. Chem. Res.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The resulting four-blocks system is which can be solved readily Even though in eq 4 an inverse matrix appears, it is necessary to solve the problem without explicitly inverting the same matrix. 27 To exploit the sparsity of unstructured submatrices, depending on the sparsity degree of the two matrices A 1,2 and A 2,1 , two alternative solving strategies are defined, which are similar in the evaluation of the product z ) A 1,1…”

Section: Dae Solver For Partially Structured Systemsmentioning

confidence: 99%

“…First principles distillation models yield a tridiagonal block structure, each block representing the properties of a single distillation stage. 27,29 A fully dynamic model of an isobutane and normal-butane splitter with control structure is shown in Figure 3.…”

Section: Case Study For Solver Validation Nonequilibrium Distillation...mentioning

confidence: 99%

“…While the details of the model can be taken from the literature, 27 here a brief summary: each stage of the column is considered as a nonequilibrium dynamic flash containment, where the liquid phase and gas phase are two uniform lumps exchanging extensive quantities. The main differences with the traditional models are as follows: dynamic mass and energy balance for both phases; gas capacity included; no chemical equilibrium assumption; no thermal equilibrium assumption; no assumption about the liquid density.…”

Section: Case Study For Solver Validation Nonequilibrium Distillation...mentioning

confidence: 99%

“…The discussion of the importance of correct volume calculations can be found elsewhere. 27 The dimension of the state is 2NC + 6 states per column stage, where NC stands for the number of components: NC dynamic liquid mass balances; NC dynamic gas mass balances; one dynamic energy balance for the liquid phase; one dynamic energy balance for the gas phase; one algebraic equation for liquid temperature calculation; one algebraic equation for gas temperature calculation; one algebraic equation for liquid volume calculation; one algebraic equation for gas volume calculation.…”

Section: Case Study For Solver Validation Nonequilibrium Distillation...mentioning

confidence: 99%

See 2 more Smart Citations

Efficient Numerical Solver for Partially Structured Differential and Algebraic Equation Systems

Manenti¹,

Dones²,

Buzzi‐Ferraris³

et al. 2009

Ind. Eng. Chem. Res.

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Given a sparse set of differential and algebraic equations (DAEs), it is always recommended to exploit the structure of the system’s sparsity (e.g., tridiagonal blocks matrix, band matrix, and staircase matrix, etc.), thus to use tailored numerical solvers in order to reduce the computation time. Very frequently, though, while highly structured, a couple of elements enter the description which make it difficult for the solvers to reach a solution. They are common in process control applications, where the states added to the plant description by the integral parts of the controllers introduce unstructured elements in the otherwise very structured Jacobian of the mathematical model. Such systems are characterized by a partially structured Jacobian, which inhibits the use of the solvers tailored to fit problems with fully structured matrices. In such cases, one can either use a solver with lower performance, resulting in larger computation times, or alternatively one seeks an approximation for the unstructured points. A solution to the handling of “dirty” Jacobians is presented, which is implemented in a DAE solver package available freely on the Internet. This novel DAE solver fully exploits the overall structure of the system’s sparsity, without compromising CPU computation time and precision of the results. A numerical comparison with different approaches is given by solving a DAE model representing an existing nonequilibrium distillation column.

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Towards the dynamic initialization of C4 splitter models

Cited by 2 publications

References 5 publications

Nonlinear Model Predictive Control: A Self-Adaptive Approach

Nonlinear Model Predictive Control: A Self-Adaptive Approach

Efficient Numerical Solver for Partially Structured Differential and Algebraic Equation Systems

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