Gas-phase Polyethylene Reactor Research Articles

Reliable and straightforward PID tuning rules for highly underdamped systems

Proportional-Integral-Derivative (PID) controllers reign absolute when automatic control is applied. There is an expressive number of tuning rules for these controllers in literature. However, for highly oscillatory (or highly underdamped) systems, such as the ones found in oil production and polymerization reactors, the available methods provide poor closed-loop performance and robustness. Besides, most of these tuning rules are developed for systems based on a first-order with pure time delay (FOPTD) transfer function and for parallel form PID controllers. Therefore, the focus of this paper is the development of appropriate tuning rules for highly underdamped systems through non-cancellation of dominant poles and easily adjustable robust performance, making them applicable for both series and parallel PID controllers, since the proposed tuning only places the controller zeros at the real axis. The new tuning rules were developed for these systems and were tested on 15,000 different transfer functions described by a second-order with pure time delay (SOPTD) expression. Additionally, a recommendation interval is also provided in which the controller gain can be varied online or by simulations to achieve the desired trade-off between performance and robustness. The proposed rules are also validated using two case studies: the suppression of slugging in oil production and the temperature control of an industrial gas phase polyethylene reactor.

CFD-DEM Study of Temperature and Concentration Distribution in a Polyethylene Fluidized Bed Reactor

Comprehensive modeling of the gas-phase polyethylene reactor was developed by combining discrete element method (for predicting motion of particulates), Navier-Stokes equation (for predicting velocity fields of gas phase), mass conservation equation (for predicting concentration of reactants), and energy conservation equation (for predicting temperature). A comprehensive kinetic mechanism was used to evaluate the rate of ethylene and 1-butene copolymerization reactions. Simultaneous solution of these equations provided information about concentration, temperature, and velocity fields and their effect on the final performance of the reactor, as well as detection of possible hot spot zones. The effect of critical reactor operating parameters (such as inlet gas velocity and operating pressure) on the temperature distributions of gas and particles in the bed was also studied to investigate the possibility of hot spot formation in the reactor. The results showed that bed temperature decreases with increasing inlet gas velocity. Also, the bed temperature profile decreases at higher pressures due to more efficient contact between gas and particles.

A Method of Online Safety Assessment for Industrial Process Operations Based on Hopf Bifurcation Analysis

This paper proposes an approach of online safety assessment for industrial process operations. The core idea is to apply the Hopf bifurcation analysis of nonlinear systems in safety assessment. Herein, the Hopf bifurcation equations are used to characterize the critical stability boundary or manifold of the system, which is taken as the safety limit. Then, a safety index (SI) is constructed to denote the integrated exponential distances between each parameter and their bifurcation points. In the online implementation, the parameters are estimated by the extended Kalman filter (EKF), and the Hopf bifurcation points are generated by solving the nonlinear bifurcation equations. Afterward, the value of the SI can be online calculated. The introduced approach was then applied to a simulated gas phase polyethylene reactor process, in which the efficiency of the proposed method was verified in indicating the distance to the potential unsafe oscillation and in the early identification of potential threats.

Control of Polymer Quality in Gas Phase Polyethylene Reactors Using Feed Flow Rates

Control of Polymer Quality in Gas Phase Polyethylene Reactors Using Feed Flow Rates

Broadening the polyethylene molecular weight distribution by controlling the hydrogen concentration and catalyst feed rates

This paper discusses the control of an industrial gas-phase polyethylene reactor to produce a desired molecular weight distribution (MWD) of the polymer. The controller objective is to regulate online the entire molecular weight distribution by either manipulating the hydrogen content inside the reactor or coordinating the feed rates of two different types of catalysts. In this work, the molecular weight distribution is modeled as a function of the reaction kinetics and hydrogen to monomer ratio. Nonlinear model predictive controller (NLMPC) algorithm is used to maintain the desired molecular weight distribution online. The closed-loop simulations indicated the effectiveness of NLMPC to achieve its goal even in the presence of modeling errors. Moreover, the results showed that, altering the hydrogen concentration solely can produce the required polymer quality provided that an efficient mechanism is available to readily alter the hydrogen composition. Alternatively, the desired MWD can also be guaranteed with proper manipulation of the catalyst feed rates while the other process inputs are kept constant.

Multivariable control strategy based on bifurcation analysis of an industrial gas-phase polymerization reactor

In an industrial gas-phase polyethylene reactor, the safe operating range of temperature is rather narrow. Even within this temperature range, temperature excursions must be avoided because they can result in low catalyst productivity and significant changes in product properties. If the manipulated variable for temperature control saturates (i.e., the cooling water valve position is completely open), then the reactor operates without a feedback temperature controller, leading to oscillatory behavior and limit cycles. In this work, it has been demonstrated that the saturation in the manipulated variable and the complex non-linear dynamic behavior are removed when auxiliary manipulated variables, obtained by bifurcation analysis, are used in a multivariable control strategy for the reactor temperature control. Two control structures are proposed and compared considering their impact in the reactor production and polymer melt index. In the first control structure, the designed PID controller for the reactor temperature is considered and a switching strategy with a PI controller for the auxiliary manipulated variables is included. In the second control structure, the designed PID controller for the reactor temperature is also used, however, a MPC controller for the auxiliary manipulated variables is considered. The results suggest that the use of gain-scheduling strategy in the PID temperature controller with a MPC controller for the auxiliary manipulated variables avoids the saturation of the manipulated variable and, hence, the undesired non-linear dynamic behavior, reducing the production loss and improving the product quality.

Particle Size Distribution in Gas-phase Polyethylene Reactors

A population balance model is developed to investigate the particle size distribution (PSD) developments in a gas-phase fluidized bed ethylene polymerization reactor. The model considers the combined effects of particle growth and elutriation for size-distributed prepolymer feed. In the proposed model, the bed is divided into several perfectly mixed serial sections. The population balance differential equations written for each section were simultaneously solved to determine the density function of the size distribution of the polymer particles in each section. The model is able to predict the profiles of the PSD along the reactor height. It was shown that the mean size of the particles is larger at the bottom of the bed and becomes smaller when moving toward the top of the reactor. The size distribution of the polymer particles in the product becomes sharper and their mean size decreases by increasing the superficial gas velocity. Also, the mean size of the particles in the product increases by increasing the temperature of the reactor.

Fault-tolerant control of a polyethylene reactor

This work focuses on fault-tolerant control of a gas phase polyethylene reactor. Initially, a family of candidate control configurations, characterized by different manipulated inputs, is identified. For each control configuration, a bounded nonlinear feedback controller, that enforces asymptotic closed-loop stability in the presence of constraints, is designed, and the constrained stability region associated with it is explicitly characterized using Lyapunov-based tools. Next, a fault-detection filter is designed to detect the occurrence of a fault in the control actuator by observing the deviation of the process states from the expected closed-loop behavior. A switching policy is then derived, on the basis of the stability regions, to orchestrate the activation/deactivation of the constituent control configurations in a way that guarantees closed-loop stability in the event of control system faults. Closed-loop system simulations demonstrate the effectiveness of the fault-tolerant control strategy.

Two-phase modeling of a gas phase polyethylene fluidized bed reactor

A two-phase model is proposed for describing the behavior of a fluidized bed reactor used for polyethylene production. In the proposed model, the bed is divided into several sequential sections where flow of the gas is considered to be plug flow through the bubbles and perfectly mixed through the emulsion phase. Polymerization reactions occur not only in the emulsion phase but also in the bubble phase. Voidages of the emulsion and bubble phases are estimated from the dynamic two phase structure hydrodynamic model. The kinetic model employed in this study is based on the moment equations. The hydrodynamic and kinetic models are combined in order to develop a comprehensive model for gas-phase polyethylene reactor. The results of the model are compared with the experimental data in terms of molecular weight distribution and polydispersity of the produced polymer. A good agreement is observed between the model predictions and actual plant data. It has been shown that about 20% of the polymer is produced inside the bubble phase and as such cannot be neglected in modeling such reactors.

MULTIVARIABLE CONTROL STRATEGY BASED ON BIFURCATION ANALYSIS OF AN INDUSTRIAL GAS-PHASE POLYMERIZATION REACTOR

In an industrial gas-phase polyethylene reactor, the safe operating range of temperature is rather narrow. Even within this temperature range, temperature excursions must be avoided because they can result in low catalyst productivity and significant changes in product properties. In previous work, using a first-principles model, including the recycle stream and the heat exchange system, a PID temperature controller with robust performance was designed via optimization in the frequency domain for different operating points. For the reactor total pressure, ethylene partial pressure, H2/C2 and C4/C2 molar ratios, PI controllers were designed. In the PID temperature controller, if the manipulated variable (cooling water valve opening) saturates then the reactor operates without a feedback temperature controller, leading to oscillatory behaviour and limit cycles. It has been demonstrated that the manipulated variable saturation and the nonlinear dynamic behaviour are removed when auxiliary manipulated variables, obtained by bifurcation analysis, are used in a multivariable control strategy for the reactor temperature control. In this work, two control structures are compared to define the most suitable proposal for implementation in an industrial reactor and the impact of these control structures in the reactor production and in the polymer melt index are analyzed. The first control structure considers the control problem using the designed PID controller for the reactor temperature and includes a switching strategy with a PI controller for the auxiliary manipulated variables. The second control structure considers the control problem also using the designed PID controller for the reactor temperature, however including a MPC controller for the auxiliary manipulated variables.

Bifurcation Analysis of the Fluidized Bed Polyethylene Reactor with Internal Cooler

AbstractA mathematical model has been developed to simulate a gas‐phase ethylene polymerization reactor with internal cooler. The model was analyzed to determine the effects of reactor operating conditions on dynamics and stability. The reactor model employed assumed that both the gas and polymer phase in the reactor are well mixed. Comparing the present model to one with external heat exchanger confirms that, in either form, gas‐phase polyethylene reactors are prone to show unstable steady states, limit cycles and excursions toward unacceptably high temperature steady states. It was also observed that, with internal cooler, minor design changes in the cooler area available for heat transfer and in the inlet temperature of the coolant have a significant effect on the low stable steady state range of catalyst feed rates. With internal cooler, the suitable operating range increased with the increase in the area available for heat transfer. This effect is insignificant in the case of a reactor with external heat exchanger. Manipulating the reactor coolant inlet temperature and/or gas velocity can increase the stability range in the reactor with internal cooler as against one with external heat exchanger.

Simulation, Optimization and Parametric Studies of a Solid Catalyzed Gas Phase Ethylene Polymerization Fluidized Bed Reactor

A steady-state model incorporating interactions between separate bubbles and emulsion phases in a fluidized-bed polyethylene reactor is employed to study the effect of operating conditions on the stability of gas-phase polyethylene reactors. A simple optimization program is developed to find the optimum combination of operating parameters at which the maximum polyethylene production rate is achieved with the constraints only on the reactor temperature, which should not exceed the melting point of polymer. Using the optimum values found, the parametric investigation for the effect of the catalyst deactivation rate constant and process operating parameters, such as the catalyst feed rate and the gas superficial to minimum fluidization velocity on system behavior are investigated. The investigations reveal that, the fluidized bed polyethylene reactor is prone to show unstable behavior and temperature oscillations, and the optimum polyethylene production rate could be achieved when it operates close to its melting point under a suitable controller to avoid polymer melting.

Multivariable Control of a Simulated Industrial Gas-Phase Polyethylene Reactor

A multivariable control problem of an industrial gas-phase polyethylene reactor is investigated in this paper. This multivariable control problem affects directly the polymer properties and consequently the plant economics. The control task is particularly challenging because of the two-time-scale behavior of the process and because of the multirate sampling of the process controlled variables. Two control schemes and two control algorithms are tested and compared. One control scheme considers the overall control problem using one multivariable control algorithm such as model predictive controller (MPC). Another control scheme separates the overall control problem into two levels. One level takes care of the controlled variables with fast dynamics via a multi-loop PI algorithm and the other level takes care of the slow controlled variables via a multivariable control algorithm such as MPC. The simulated comparison revealed the superiority of the second scheme only in providing faster response. Other than the speed of response, the performance of the two schemes is almost comparable. Further, the first scheme may outperform the second one in the presence of input limitation. On the other hand, linear MPC and nonlinear MPC algorithms were compared for the two control schemes. Simulation results indicated that the nonlinear MPC outweighs the linear MPC in terms of performance, tuning requirements and robustness.

Selection of Parameters for Updating in On-line Models

Predictions from dynamic mechanistic models used for process monitoring and control often exhibit sustained offset from process measurements. This offset is caused by imperfect measurements and by model deficiencies that result from simplifying assumptions, unmodeled disturbances, and uncertain parameter estimates. Extended Kalman filter (EKF) state estimation can eliminate offset by on-line updating of a subset of the model parameters. Offset elimination is accomplished by incorporating nonstationary stochastic states in the model equations. A difficult problem faced by practitioners when implementing state estimators is deciding which model parameters to update using on-line measurements. In this article, simple screening tools are developed to aid in updateable parameter selection. These tools are extensions of the relative gain array (RGA), the relative disturbance gain (RDG), and the disturbance condition number (DCN), which have been used in multivariable control applications to determine appropriate manipulated variable/control variable pairings and to examine disturbance effects. The application of these techniques for updateable parameter selection is demonstrated using simulations of a gas-phase polyethylene reactor system. A benefit of these screening tools over past trial-and-error parameter screening practices is that neither tuning of the state estimator nor running of simulations is required. We show that the RGA is an effective tool for determining when problems will arise due to correlated effects of different parameters on model outputs. The RDG is shown to be an effective tool for reducing the number of adjustable parameters when only particular types of disturbances are anticipated. We demonstrate that the DCN can be used to screen out parameter sets that will lead to excessive and physically unrealistic adjustment of model parameters.

Gas Phase Polyethylene Reactors A Global Study of Stability Behaviour

A global study of the occurrence of steady state multiplicity and limit cycles in gas phase polyethylene reactors is carried out using elementary concepts of singularity theory and continuation techniques, for both open loop and closed loop operations. The well-mixed model of the unit consisting of the reactor, the heat exchanger and the ethylene partial-pressure controller, is reduced analytically to one single algebraic equation. The singularity theory is efficiently used for the classification, in multidimensional parameter space, of the different static and dynamic behaviour exhibited by the unit. This includes regions of unique and stable behaviour, regions of hysteresis, regions of limit cycles as well as regions of bistability resulting from interactions between hysteresis and limit cycles. A useful and practical picture of the effect of the different kinetic and operating parameters of the unit is constructed. The tools developed for a single site type are also extended to study the dynamics induced by multiple catalytic site types. The dynamics of the process under a conventional temperature PI controller are also studied. It is shown that while the integral action eliminates the steady state multiplicity, it introduces instability for some ranges of catalyst feed rates. The stability analysis allows the construction of practical diagrams showing the effect of model parameters on the closed loop stability behaviour of the process.

Improved Regulatory Control of Industrial Gas-Phase Ethylene Polymerization Reactors

This paper investigates the application of two techniques to improve the proportional−integral (PI) control performance when implemented to stabilize the operation of gas-phase polyethylene reactors around an optimal operating point which is open-loop unstable. The first technique deals with improving the performance of a single input−single output control loop through employing an on-line adaptive tuning strategy. The purpose of the tuning strategy is to force the closed-loop response to fit inside a desired time-domain specification envelope by automatically adapting the PI setting values. The second technique deals with improving the multiple input−multiple output control performance by simple selection of the proper control structure design. The objective of the proposed control design is to avoid the procedure of screening various control structure candidates. Moreover, because there are more inputs than outputs, a split-range configuration is used to utilize all available manipulated variables. This configuration allows for tight control. Simulation results demonstrated the success of the proposed methods to provide a better regulatory control performance when compared to those that have been reported in earlier work.

Heat Removal from Gas-Phase Polyethylene Reactors in the Supercondensed Mode

For gas-phase fluidized bed polyethylene reactors, heat removal is one of the controlling factors that limits the production rate. Since the invention of condensed mode operation, several process i...

Temperature control of industrial gas phase polyethylene reactors

Abstract The performance of linear and nonlinear temperature control schemes is assessed for an open-loop unstable gas-phase polyethylene reactor (GPPER), based on speed, damping, robustness and the ability to maintain closed-loop stability in different operating regimes. An existing industrial GPPER model is improved by modelling the temperature states in the external heat exchanger using linear and nonlinear driving force models with varying numbers of heat transfer stages. Differences in heat exchanger models do not produce gain mismatch but do result in phase mismatch. It is shown that the nonlinear error trajectory controller (ETC) exhibits significantly superior responses in terms of speed, damping and robustness compared with an optimally-tuned PID controller. Therefore, substantial benefits could be realized using nonlinear controllers because they can provide good disturbance rejection capabilities and ensure closed-loop stability over a wide range of operating conditions. An approach is presented for tuning ETCs for minimum-phase processes of arbitrary relative degree.

Interactions Between Production Rate Optimization and Temperature Control in Gas Phase Polyethylene Reactors

A nonlinear (feedback) error trajectory temperature controller is used to stabilize a gas phase polyethylene reactor (GPPER) which is open-loop unstable. The controller can saturate when a production rate optimization scheme increases the polymer production rate, and pushes the plant to operate at or near the maximum cooling capacity. The tendency of the reactor system to approach extraneous equilibria is examined using recently developed methods for nonlinear processes. Sufficient conditions for the existence of extraneous equilibria are given. Simulation results are compared with predictions obtained using saturated equilibria equations implied by the temperature output.

159 Nonlinear multivariable control of product properties in an industrial gas phase polyethylene reactor

159 Nonlinear multivariable control of product properties in an industrial gas phase polyethylene reactor