On the optimization of oil shale pyrolysis

Luss, Rein

doi:10.1016/0009-2509(78)85127-6

Cited by 13 publications

(7 citation statements)

References 1 publication

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“…The objective of this problem is to determine the optimal temperature profile T ( t ), by which the final product of x 2 ( t f ) is maximized at t f = 9.3 min. This problem has been reported to be difficult to optimize using the minimum principle. , Using IDP with 80 equal time divisions, the production is maximized to be 0.35382 . This value is further refined to 0.35381 for P = 5 and 0.35382 for P = 10 by IDP with variable time divisions .…”

Section: Case Studiesmentioning

confidence: 99%

Integrating Controlled Random Search into the Line-Up Competition Algorithm To Solve Unsteady Operation Problems

Sun

Lin

2008

Ind. Eng. Chem. Res.

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In this work, a line-up competition algorithm (LCA) is applied to solve the dynamic optimization problems derived from unsteady chemical systems. The problems are first converted ito nonlinear programming problems using the concept of control vector parametrization. The parameters embedded in the converted problems then are selected by LCA. To improve numerical accuracy, the normal (Gaussian) sampling policy is introduced to replace the uniform sampling policy used in basic LCA. Variable step input (VSI) and variable ramp input (VRI) are respectively considered to rebuild the control policy in solutions. Some typical examples are provided to demonstrate the robustness and efficiency of this modification.

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Section: Case Studiesmentioning

confidence: 99%

Integrating Controlled Random Search into the Line-Up Competition Algorithm To Solve Unsteady Operation Problems

Sun

Lin

2008

Ind. Eng. Chem. Res.

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“…Then by comparing these profiles, we found that the optimal one starts with an initial temperature of 703 K. This profile, shown in Figure 2, is similar to the one obtained using Pontryagin's Maximum Principle, differing only by the approximation made in having T constant during a stage. The final value of x2 is 0.35372, which is within 0.009% of the value reported by Luus (1978). The computation time needed to obtain the optimal solution to this problem is somewhat larger (0.683 min) than needed when using Pontryagin's Maximum Principle (0.295 min).…”

Section: Optimal Policy Using the Proposed Algorithmmentioning

confidence: 50%

“…The problem of finding the optimum temperature profile for oil-shale pyrolysis in a tubular reactor to yield the maximum concentration of pyrolitic bitumen was solved previously by Luus (1978) using Pontryagin's Maximum Principle. This example is thus particularly attractive to test the computational aspect of the proposed algorithm.…”

Section: Optimum Temperature Profile In a Tubular Reactormentioning

confidence: 99%

“…It was observed by Luus (1978), that the optimal residence time should be slightly less than 9.5 minutes and that the initial temperature should be 698.15"K instead of 705 K. The problem was therefore run with several final times tf to determine the one yielding the highest value of x2 (9). The problem was set the same way as previously with 25 stages and u and x discretized into 11 values.…”

Section: Optimal Residence Timementioning

confidence: 99%

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Optimization of non‐steady‐state operation of reactors

Tremblay

Luus

1989

Can J Chem Eng

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Non‐steady‐state operation of reactors is approached from the optimal control point of view. To find the best type of input, dynamic programming is used. The results show that for some systems, the optimal input is oscillatory in nature as has been found experimentally by others. A modification to conventional dynamic programming is used to avoid the need for interpolation and thus allow high‐dimensional systems to be handled more readily. Three chemical engineering systems of different complexity were considered to test the computational aspect of the approach. In all cases, dynamic programming gives the optimum policy with respect to the period, cycle‐split and amplitude.

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“…The optimal control problem is to find the control policy u ( f ) in the time interval 0 5 t < tf such that the performance index given in Equation (3) is maximized. The final time f f is usually specified, but there are problems like the oil shale pyrolysis (Luus, 1978) where the final time is a free parameter.…”

Section: (3)mentioning

confidence: 99%

Effect of the choice of final time in optimal control of nonlinear systems

Luus

1991

Can J Chem Eng

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The choice of the final time, tj, in the optimal control of nonlinear systems is shown to be very important. By choosing tf to be small, and repeatedly optimizing the system operation over the short time intervals gives a highly oscillatory type of control for a particular nonlinear chemical reactor. The cumulative profit as compared to that obtained by choosing tf to be large, is substantially lower. In the operation of a batch reactor it is shown that if tf is small, bang‐bang control with singular sub‐arcs results. When tf is large, the optimal control policy tends to be relatively smooth and the profitability is substantially improved.

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On the optimization of oil shale pyrolysis

Cited by 13 publications

References 1 publication

Integrating Controlled Random Search into the Line-Up Competition Algorithm To Solve Unsteady Operation Problems

Integrating Controlled Random Search into the Line-Up Competition Algorithm To Solve Unsteady Operation Problems

Optimization of non‐steady‐state operation of reactors

Effect of the choice of final time in optimal control of nonlinear systems

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