Low-density Polyethylene Reactors Research Articles

Multi-objective Bonobo optimisers of industrial low-density polyethylene reactor

Abstract A multi-objective optimization (MOO) technique to produce a low-density polyethylene (LDPE) is applied to address these two problems: increasing conversion and reducing operating cost (as the first optimization problem, P1) and increasing productivity and reducing operating cost (as the second optimization problem, P2). ASPEN Plus software was utilized for the model-based optimization by executing the MOO algorithm using the tubular reactor model. The multi-objective optimization of multi-objective Bonobo optimisers (MOBO-I, MOBO-II and MOBO-III) are utilised to solve the optimization problem. The performance matrices, including hypervolume, pure diversity, and distance, are used to decide on the best MOO method. An inequality constraint was introduced on the temperature of the reactor to prevent run-away. According to the findings of the study, the MOBO-II for Problems 1 and 2 was the most effective MOO strategy. The reason is that the solution set found represents the most accurate, diversified, and acceptable distribution points alongside the Pareto Front (PF) in terms of homogeneity. The minimum operating cost, the maximum conversion and productivity obtained by MOBO-II are Mil. RM/year 114.3, 31.45 %, Mil. RM/year 545.3, respectively.

Mixing in High‐Pressure Polymerization Reactors: A Combined Experimental and Modeling Approach

AbstractMixing in low‐density polyethylene (LDPE) reactors is crucial regarding process safety as well as process efficiency. The extreme process conditions of pressures up to 3000 bar make it difficult to get an insight into LDPE reactors. This problem is tackled by a combined experimental and modeling approach. A poly(methylmethacrylate) duplicate of a laboratory high‐pressure reactor is set up to measure residence times and visualize flow lines. Experimental results are then compared to a computational fluid dynamics model.

Leveraging fuzzy Logic PID controllers for accelerating chemical reactor CFD

A control technique comprising three Fuzzy Logic Proportional Integral Derivative (FLPID) controllers was evaluated to determine their ability to shorten convergence times for the computationally expensive globally unsteady model of a low-density polyethylene reactor. The numerical reactor contained millions of computational elements, a rotating stirrer shaft, intricate near-wall geometry, and highly exothermic polymerization kinetics. Catalyst feed rates were instantaneously increased by 50% to evaluate the FLPID’s performance during a hypothetical process excursion. FLPID achieved quasi-steady state (QSS) 54% faster than conventionally tuned PID controllers. Reducing the percent overshoot of the error and rise time of the controller output, the FLPID demonstrated its ability to lower computational cost. FLPID in CFD offers the potential to improve control methods on actual plant scale processes. In particular, the reduction in error overshoot could reduce the likelihood of reactor overheat events as the temperatures are kept within a tighter operational window.

Melt flow index of low-density polyethylene determination based on molecular weight and branching properties

Industrially, a low-density polyethylene (LDPE) is characterized based on their Melt Flow Index (MFI). In numerous publication, LDPE’s MFI is correlated to its average molecular weight (Mw). An overview of modeling studies on LDPE reactors available in the open literature indicates significant discrepancies among researchers for the correlation of MFI-Mw, therefore a research to produce reliable correlation need to be carried out. This research gathers various experimental and industrial data of different LDPE product grades. Empirical correlations between MFI and Mw are developed and the analysis on the MFI and Mw relation is addressed. The percentage of error between the model prediction and industrial data varies from 0.1% to 2.4% which can be considered minimum. The nonlinear model obtained indicates the competency of the developed equation to describe the variation of industrial data, thus allowing greater confidence in LDPE’s MFI prediction.

Model-Based Optimization of the Cooling System of an Industrial Tubular LDPE Reactor

The model-based optimization of the cooling system of an industrial tubular reactor for the production of low-density polyethylene (LDPE) is studied in this paper. First a detailed reactor simulator is presented. Second, a series of well-posed optimization problems are formulated and solved. To this end, the optimization problems are presented with an increasing number of degrees of freedom. Moreover, economic cost functions consisting of conversion and energy terms are derived and constraints due to operational and safety reasons are added. The degrees of freedom involve parameters such as the initiator feed rates, the cooling water temperatures, and the switching position between hot and cold cooling water. The optimization results indicate that a dual water circuit operating at a low and a high temperature allows significant improvements in conversion with respect to the reference case of a single temperature circuit, while maintaining similar molecular characteristics.

Unscented Kalman filter based nonlinear model predictive control of a LDPE autoclave reactor

This paper presents a multivariable nonlinear model predictive control (NMPC) scheme for the regulation of a low-density polyethylene (LDPE) autoclave reactor. A detailed mechanistic process model developed previously was used to describe the dynamics of the LDPE reactor and the properties of the polymer product. Closed-loop simulations are used to demonstrate the disturbance rejection and tracking performance of the NMPC algorithm for control of reactor temperature and weight-averaged molecular weight (WAMW). In addition, the effect of parametric uncertainty in the kinetic rate constants of the LDPE reactor model on closed-loop performance is discussed. The unscented Kalman filtering (UKF) algorithm is employed to estimate plant states and disturbances. All control simulations were performed under conditions of noisy process measurements and structural plant–model mismatch. Where appropriate, the performance of the NMPC algorithm is contrasted with that of linear model predictive control (LMPC). It is shown that for this application the closed-loop performance of the UKF based NMPC scheme is very good and is superior to that of the linear predictive controller.

Innovative design of an LDPE reactor bay against gas explosion using a risk-based approach coupled with high fidelity computer tools

High pressure tubular reactors for the production of Low Density Polyethylene (LDPE) are, for safety reasons, enclosed in a protective bay open towards the sky. They are becoming longer and larger due to production capacity increases. TECHNIP has historically designed these reactor bays based on Licensor information, which include more or less empirical correlations. Further capacity developments require the design of these concrete enclosures to be challenged. With this in mind, the present study shows the interest of implementing an innovative methodology based upon a risk-based approach to define new design criteria for the enclosure walls. The method, which combines both risk analysis with computational fluid dynamics modelling (3D CFD) and non-linear finite element analysis (NLFEA) tools, allows a clear determination of the design overpressure loads applied on walls and offers an optimisation of the concrete wall thickness. The CFD study also leads to a better understanding of the ventilation and efficiency of safety systems (gas detection, depressurisation) with possibility for improvement of the hazardous area classification rating.

A PCA Based Fault Detection Scheme for an Industrial High Pressure Polyethylene Reactor

AbstractA data‐based monitoring scheme is proposed to detect decomposition in low density polyethylene reactors by combining principal component analysis with a priori information on the heat balance equations around the reactor. During normal operating conditions, the heat balance equation should close at all times within reasonable limits. If excess heat is generated in the reactor, the heat balance closure error will exceed a user specified threshold limit to indicate the possible onset of decomposition. However, since precise information required to formulate the exact energy balance equations was not available, principal component analysis (PCA) was used as a model identification tool. Results from a number of decompositions case studies from an industrial low density polyethylene/ethylene vinyl acetate autoclave reactor indicate that the method was able to detect the onset of decomposition with reasonable lead time.magnified image

A comprehensive dynamic model for high-pressure tubular LDPE reactors

A comprehensive dynamic model for high-pressure tubular LDPE (low-density polyethylene) reactors (HPTLR) is presented. The model is capable of predicting molecular weight distribution (MWD) characteristics of the polymer and the influence of process conditions on the same. The physico-chemical phenomena considered in the model include polymerization kinetics, monomer (ethylene) decomposition kinetics, turbulent micromixing and heat transfer. A two-environment (2E) model is used to describe micromixing following the approach proposed originally by Fox (1998). Since the model considers the effect of ethylene decomposition on the dynamic behavior of the reactor, dynamic changes in the process conditions leading to ethylene decomposition (decomp) and reactor runaway are studied. Furthermore, a consistent dynamic model for pressure-pulsing due to kick-valve operation (Zabisky, 1992) has been included, making the model more relevant to plant operations. Model parameters have been fit to plant data in order to satisfactorily emulate plant behavior. The model can thus be reliably used in off-line studies and should prove to be an effective tool to the plant engineer in making critical operational decisions.

Prediction of Polymer Properties in LDPE Reactors

AbstractSummary: A new analysis tool is presented that uses the governing kinetic scheme to predict properties of low‐density polyethylene (LDPE) such as the detailed shape of the molecular weight distribution (MWD). A model that captures mixing details of autoclave reactor operation is used to provide a new criterion for the onset of MWD shouldering. Kinetic effects are shown to govern the existence of MWD shoulders in LDPE reactors, even when operation is far from perfectly‐mixed. MWD shoulders occur when the mean reaction environment has a relatively high radical concentration and has a high polymer content, and is at a low temperature. Such conditions maximize long chain formation by polymer transfer and combination‐termination, while limiting chain scission. For imperfectly‐mixed reactors, the blending of polymer‐distributions produced in different spatial locations has a small effect on the composite MWD. However, for adiabatic LDPE autoclaves, imperfect mixing broadens the stable range of mean reactor conditions, and thereby increases the possibility for MWD shouldering.Polymer MWD produced in an LDPE autoclave reactor by various kinetic mechanisms.magnified imagePolymer MWD produced in an LDPE autoclave reactor by various kinetic mechanisms.

Methodology for modeling detailed imperfect mixing effects in complex reactors

AbstractA powerful new modeling technique is presented for exploring mixing effects in reactive flow systems. The technique combines the detailed mixing representation of computational fluid dynamics (CFD) simulations with the simplicity and computational efficiency of stirred‐tank compartment models. The method can be generally applied to many reactive systems, and requires only that appropriate criteria be specified to select compartment models from a single converged CFD simulation. A 1000‐fold increase in computational speed is achieved by the new compartment model/CFD technique when modeling steady‐state operation of low‐density polyethylene (LDPE) autoclave reactors, making broad studies of operating conditions and stability possible. Results from compartment models are shown to capture the accuracy and detail of CFD simulations over a wide range of LDPE reactor operation, and the new technique provides a combination of modeling detail and computational ease not previously available for this type of reactor. © 2005 American Institute of Chemical Engineers AIChE J, 2005

PDF simulations of ethylene decomposition in tubular LDPE reactors

AbstractThe present study deals with turbulent reacting flow simulation inside low‐density polyethylene (LDPE) tubular reactors, based on a detailed computational fluid dynamics (CFD) technique—transported probability density function (PDF) methods. The ability of the PDF methods to provide an exact representation of chemical source terms is ideally suited for coupling complex LDPE chemistry with small‐scale fluid dynamic fluctuations in turbulent flow. LDPE chemistry with a total of 16 scalars provides an ideal test case for illustrating the applicability of an efficient chemistry algorithm based on in‐situ adaptive tabulation. A particle‐based Monte Carlo algorithm is used to solve the joint‐composition PDF equation, whereas a finite‐volume code is used to obtain hydrodynamic fields from the standard k–ε turbulence model. The influence of feed temperature, initiator concentration, and degree of premixing is investigated to gain detailed knowledge of micromixing effects on steady‐state reactor performance. The computational approach provides a low‐cost alternative to experimental and pilot‐plant tests for exploring a variety of design options when making important design and operational decisions, or for investigating unstable reactor operating conditions. The ability of a simplified, but otherwise equivalent multi‐environment‐presumed PDF model to predict turbulence–chemistry interactions close to physical reality is validated using the detailed transported PDF simulations. The transported PDF method is shown to be an excellent tool for obtaining fundamental information on turbulent reacting flows, as well as for deriving simplified models for faster and easier interpretation of these flows when developing safe and efficient chemical processes. © 2005 American Institute of Chemical Engineers AIChE J, 51: 585–606, 2005

Modeling, Simulation and Optimal Control of Ethylene Polymerization in Non-Isothermal, High-Pressure Tubular Reactors

Low-density polyethylene (LDPE) is a very important polymer, which is usually produced through a free radical polymerization process in high-pressure tubular reactors. In this study, the mathematical model of this process is developed on the basis of a comprehensive reaction mechanism to accurately determine polymerization rate, and polymer properties under extreme temperature conditions. The model comprises of (i) the mass balances of monomer, initiator, solvent, live radicals and dead polymer chains, and (ii) the energy balances of a tubular LDPE reactor, and its jacket under steady state condition. The model considers the variations in the density and viscosity of reactants along reactor length. Computer simulation of the model is successfully carried out to accurately describe the performance of a non-isothermal, high-pressure, industrial LDPE reactor with multiple initiator injections. Based on the developed non-linear model, the optimal control of the industrial reactor is carried out using genetic algorithms to maximize monomer conversion using jacket temperature as a control function of reactor length. The application of optimal control leads to significant improvements in the final monomer conversion, and capacity utilization of the reactor.

CFD analysis of micromixing effects on polymerization in tubular low-density polyethylene reactors

A novel multi-environment CFD micromixing model is used to describe the small-scale mixing of chemical species inside a tubular low-density polyethylene (LDPE) reactor under different operating conditions. The model is coupled with a comprehensive kinetic scheme describing ethylene polymerization that includes kinetic mechanisms describing polymer properties and ethylene decomposition. The simulation results show that imperfect mixing between initiator and monomer reduces monomer conversion and increases the polydispersity index. Insufficient micromixing also causes local hot spots, which may lead the reactor to thermal runaway. Thus, the small-scale mixing has a significant impact on the reactor stability. The study not only illustrates the importance of mixing effects on LDPE polymerization but also provides important insights into the physical phenomena occurring inside the reactor, which are extremely helpful in evolving a criteria for stable operation of the reactor while controlling the product quality in the plant-scale tubular LDPE reactor. Compared to full probability density function (PDF) methods used in the literature for similar studies, the multi-environment CFD micromixing model offers a computationally highly efficient description of the turbulent reacting flow inside the LDPE reactor.

Supervisory Control of High Pressure LDPE Reactors

A comprehensive mathematical model was employed to simulate the dynamic behaviour of ethylene polymerization in high-pressure autoclave reactors. The model was capable of describing the complex mixing patterns occurring in multizone, multifeed low density polyethylene (LDPE) autoclaves. To represent the kinetics of ethylene polymerization a general reaction mechanism was considered and the method of moments was used to calculate the molecular properties. A two-zone autoclave reactor model was considered for our control studies. The reactor opiated at an unstable steady-state, thus, the temperature in each zone was controlled by manipulating the corresponding initiator flow rate. A Quadratic Dynamic Matrix Controller (QDMC) was designed for controlling the polymerization temperature in a twozone autoclave and its performance was compared to that of two SISO PI controllers, usually employed to control the polymerization temperature. Finally, a supervisory QDMC controller was implemented to a simulated reactor model for the optimal control of polymer quality (e.g., melt index) during reactor start-up and grade transitions.

Simultaneous optimization of mixing patterns and feed distribution in LDPE autoclave reactors

In this work, a model for simultaneous optimization of mixing patterns and feed distribution in LDPE (Low Density PolyEthylene) reactors is presented. The formulation is based on a a novel technique for optimizing mixing patterns in chemical reactors, resulting in an optimal control formulation which is solved as an NLP. The kinetic model is based on representing the molecular weight distribution by statistical moments.

Simulations of a LDPE reactor using computational fluid dynamics

AbstractComputational fluid dynamics methods are used to provide three‐dimensional simulations of a low‐density polyethylene (LDPE) autoclave reactor under normal operating conditions. For the conditions used, the reactor is not very well mixed; thus, the common model approximation of a perfectly stirred reactor is not warranted. The simulations verify the sensitive nature of the polymerization reactors and indicate a need for optimizing operating parameters.

Non-Linear Projection to Latent Structures

Traditional statistical approaches for the development of process models has focused on multiple linear regression (MLR). In practice, data collected on a process is corrupted by noise and variables exhibit collinearity, hence MLR is inappropriate. The statistical projection technique of projection to latent structures (PLS) has thus become increasingly important for the identification of process models. This paper briefly reviews linear PLS prior to extending the method to handle non-linear systems through the integration of a neural network into the PLS algorithm. A modification to Qin and McAvoy's (1992) non-linear PLS is introduced and compared through a bench-mark problem. A further study is carried out on a continuous low density polyethylene reactor.

Dynamic simulation and quadratic dynamic matrix control of an industrial low density polyethylene reactor

In this study, a reliable rigorous dynamic model of an industrial low density polyethylene (LDPE) reactor, one of the two 250 litre reactors at an LDPE plant in a petrochemical complex, is developed. The model predicts temperature profile, conversion and some of the polymer properties such as weight average molecular weight, and initiator composition. The predictions are in quite satisfactory agreement with actual plant data. Considering the multi-input, multi-output characteristics of the plant and interaction between control loops, dynamic matrix control algorithm with a quadratic programming routine is applied to the system through simulation. Simulation results showing the performance of the quadratic dynamic matrix control are presented, and are compared to the PI control employed in the plant. The results obtained from this algorithm show promise for a better control of the system, particularly for set point tarcking, compared to the conventional control currently employed.

On-line optimization of a high-pressure low-density polyethylene tubular reactor

Low-density polyethylene (LDPE) is a high-volume commodity polymer that is produced in high-capacity tubular and autoclave reactors. The extreme operating conditions employed in the high-pressure free-radical polymerization of ethylene, and the tight profit margins of the LDPE market provide a strong economic incentive to seek the optimal operation of a high-pressure LDPE reactor. In the present work, an on-line multi-level optimization procedure is developed for a high-pressure tubular LDPE reactor based on a comprehensive steady-state mathematical model of the process. Following the well-established separation hypothesis, the problem is hierarchically decomposed in two phases: (i) the parameter estimation phase where certain key model parameters are adjusted, based on selected process measurements, in order to eliminate any process/model mismatch; (ii) the optimization phase where the adapted model is optimized by minimizing a specified objective function defined in terms of the ethylene conversion and the “quality” of the final polymer product. The proposed optimization algorithm is successfully tested against the operation of a large-scale industrial reactor. The most prominent features of the procedure are highlighted. These include the development of a comprehensive mathematical model of the process, the disturbance oriented selection of the adjustable model parameters, the appropriate spatial decomposition of the parameter estimation problem into a number of subproblems and the conditional structuring of the optimization problem.