J.A. Bandoni

Large-scale dynamic optimization for grade transitions in a low density polyethylene plant

This paper presents the optimal control policy of an industrial low-density polyethylene (LDPE) plant. Based on a dynamic model of the whole plant, optimal feed profiles are determined to minimize the transient states generated during the switching between different steady states. The industrial process under study produces LDPE by high-pressure polymerization of ethylene in a tubular reactor using oxygen and organic peroxides as initiators. The plant produces polyethylene of different grades that require continuous changes from one steady state to another, in order to switch among the different final products. These changes generate disturbances that keep the product out of specifications during the transient states, with a consequent economic loss. The plant model consists of two parts; the first one corresponds to the tubular reactor. Here, the partial differential equations corresponding to the mass and energy dynamic balances are discretized along the distance coordinate by using finite differences. The resulting ordinary differential equations include the energy balance and individual mass balances for oxygen, peroxides, ethylene, butane, free radicals and polymer. Although, methane is also present in the plant, in the reactor model it is considered as a nonreacting impurity along with the other impurities coming from the rest of the process. The second part of the model corresponds to the rest of the plant. Here we considered four components: ethylene, butane, methane and impurities. An interesting aspect of this process is the presence of many time delays that are incorporated in the optimization model. The resulting differential algebraic equation (DAE) plant model includes over five hundred equations. The dynamic optimization problem is solved using a simultaneous nonlinear programming (NLP) approach. The continuous state and control variables are discretized, by applying orthogonal collocation on finite elements. The resulting NLP is solved with a reduced space Interior Point Algorithm, which is applied directly to the NLP. In addition, a new mesh refinement strategy is applied to this model to confirm that no further improvement can be found in the optimal control profiles. The paper studies two cases of switching among different polymer grades, determining the optimal profiles of butane fed to the plant, in order to minimize the time to reach the steady state operation corresponding to the desired new product quality. The results are also compared with simpler model where reactor was considered as a black-box with the conversion level taken as constant data for each polymer grade. As a result, the dynamic model we developed and the solution methodology used is a flexible and practical tool to help process engineers for taking decisions during the plant operation.

Robust characteristic polynomial assignment

In this paper a computational method for designing controllers which attempt to place the characteristic polynomial of an uncertain system inside some prescribed region is presented. An objective function consisting on two terms is proposed, penalizing both the distance to a given controller and the size of the uncertainty region developed to solve the robust assignment problem. The algorithm is based on semi-infinite programming theory, and the special structure of the problem is exploited to get both simpler methods and convergence proof. The way in which the uncertain parameters affect the plant coefficients is realistic, since it includes multinomial dependence. An example of application is given to illustrate the approach.

A mixed integer optimization strategy for a large scale chemical plant in operation

Abstract Over the last 10 years much effort has been devoted to the study of optimization strategies for models involving both continuous and integer variables (Mixed-Integer Nonlinear Programming (MINLP) formulations). Several algorithms have been proposed and a large number of research applications have been presented. However, only a few applications have been reported for real large scale plants. This paper presents the structural and operational optimization of a real ethylene plant in operation. A procedure is used involving the Outer-Approximation (OA) method for the MINLP problem and an existing ad-hoc simulator. The optimization algorithm interfaces the simulation code at the nonlinear programming step. The model handles four continuous independent variables, 33 integer variables, more than 200 dependent variables and 48 process constraints. As compared with the best continuous solution, the results show that an increase of 296,337 US

Dynamic simulation and optimisation of tubular polymerisation reactors in gPROMS

/yr in gross profit can be obtained by simultaneous parameter and structural optimization using a MINLP model. This study also shows that the OA method works very well on real problems reaching convergence in few iterations. This characteristic makes the method a practical tool for large applications, and confirms its potential to be introduced as a standard option in commercial process simulators.

Synthesis and optimization of ethane recovery process

Abstract In this paper a dynamic model of the high-pressure polymerisation of ethylene in tubular reactors is introduced and a dynamic optimisation problem is formulated for studying start-up strategies. The optimisation objectives proposed are to maximise outlet conversion and optimise the time necessary for its stabilisation while keeping product molecular properties between commercial ranges. Results are shown giving the time responses for temperature, number-average molecular weight and conversion along the reactor axial distance, which were obtained using different control variable profiles. Improving in reactor productivity is achieved. The interface gOPT of the gPROMS simulator was used to resolve the optimisation problem and to perform the simulations.

Optimization of ethane extraction plants from natural gas containing carbon dioxide

Abstract The selection of process alternatives for extracting ethane and NGL from natural gas is based on an energy analysis over the cold section of a gas processing plant. This analysis gives, as a function of the C2+ fraction in the feed, clear guidelines for selection between Joule-Thompson, turbo-expansion, external refrigeration or combined processes.

A New Strategy for the Optimization Level in Model Predictive Control

Abstract The extraction of ethane and NGL from natural gas is generally based on some of the following alternatives: turboexpansion (TE), Joule-Thompson expansion (JT); external refrigeration; and absorption. In many processing schemes a combination of these effects is used to improve the energy efficiency or to obtain greater recoveries. The selection of the basic process technology is based on an energy analysis. The determination of the final structure and optimum process conditions are found by successive quadratic programming. The optimization process is based on a rigorous simulation of the plant. An initial feasible point for the optimization procedure is derived from the feed phase-envelope properties. The effect of carbon dioxide on process design is taken into account by introducing as a constraint, in the optimization process, the conditions of carbon dioxide precipitation in the demethanizer unit. The sensitivity of the optimum design to different configurations, residual gas pressures, C2+ fraction and carbon dioxide concentration are presented.

Control of Uncertain Process with Hard Constraints

Abstract The desired operating point in Model Predictive Control is determined by a local steady-state optimization, which may be based on an economic objective and a linear model. In this paper, we incorporate the solution of a back-off problem to obtain a hierarchical scheme that ensures feasible operation in despite of possible disturbances. In particular, we use a relaxed version of the classical back-off algorithm, assuming linear models for the process and the constraints and a quadratic objective function.

Uncertain Optimization in MPC: A Case Study

Abstract A significant number of model predictive control algorithms solve on-line appropriate optimization problem and do so at every sample time. The major attraction of such algorithms, like the Quadratic Dynamic Matrix Control, lies in the fact that they can handle hard constraints on the inputs and outputs of the system. The presence of such constraints results in an on-line optimization problem that produces a nonlinear controller, even when the plant and model dynamics are assumed linear. The problem became more complex if we want to control uncertain processes. In this paper, an algorithm is presented to solve the problem of control of a uncertain linear process with hard constraints.

Modelling and optimisation of polymerisation reactors in gPROMS

Abstract A significant number of model predictive control algorithms solve on-line appropriate optimization problem and do so at every sample time. The major attraction of such algorithms lies in the fact that they can handle hard constraints on variables of the system. The presence of such constraints results in an on-line optimization problem that produces a nonlinear controller. The problem became more complex if we want to control uncertain processes. In this paper, an algorithm to solve the problem of control of a uncertain linear process with hard constraints is applied to a Steam Generating Unit.