COMPUTER SIMULATION OF HYDRODEMETALLATION IN FIXED-BED REACTORS

An isothermal model for hydrodemetallation (HDM) of crude oils in catalytic fixed-bed reactors is proposed. This model involves a consecutive reaction mechanism, which is capable of accounting for particle deposit profiles with interior maxima. Consistent with the fact that HDM catalysts are conglomerates formed by precipitation, the porous catalyst itself is modeled as randomly overlapping spheres of equal size. The metal is deposited as growing metal sulfide crystallites on the inner surface of the catalyst. These crystallites originate from a certain number of randomly scattered nuclei and increase in size as the deposition proceeds. The random sphere model for the catalyst and the deposit provides the changes in the catalyst pore structure—local porosity and surface area.

The mass transport within the domain of the particle is due to restricted liquid diffusion, since the diameter of the metal bearing compound (porphyrin) and the intermediate are comparable to the pore size. The diffusion restrictions taken into account are the enhanced drag imposed on a molecule by adjacent pore walls and steric partitioning.

Since the deposition process is much slower than diffusion and reaction, the pseudo-steady-state assumption can be justified. The equations of conservation for mass are solved by orthogonal collocation on finite elements. Based on this solution technique a computer simulation program of HDM is designed that allows two modes of operation: constant temperature and constant conversion. The simulation program “SIMULA” is highly flexible with regard to reaction kinetics, catalyst structure, reactor design, and operating conditions. In comparison to a base case with uniform activity, the effect of intraparticle (radial) and bed (axial) activity profiles on the conversion rate is discussed. For the case investigated, a radial distribution of activity higher at the center of the particle than at the edge can increase catalyst life by 25%, but axial distribution was less successful.     

A Dantzig–Wolfe decomposition algorithm for linear economic model predictive control of dynamically decoupled subsystems

This paper presents a warm-started Dantzig–Wolfe decomposition algorithm tailored to economic model predictive control of dynamically decoupled subsystems. We formulate the constrained optimal control problem solved at each sampling instant as a linear program with state space constraints, input limits, input rate limits, and soft output limits. The objective function of the linear program is related directly to the cost of operating the subsystems, and the cost of violating the soft output constraints. Simulations for large-scale economic power dispatch problems show that the proposed algorithm is significantly faster than both state-of-the-art linear programming solvers, and a structure exploiting implementation of the alternating direction method of multipliers. It is also demonstrated that the control strategy presented in this paper can be tuned using a weighted ℓ₁-regularization term. In the presence of process and measurement noise, such a regularization term is critical for achieving a well-behaved closed-loop performance.     

Propylene epoxidation in a microreactor with electric heating

Gas phase propylene epoxidation on gold catalysts has attracted wide attention from industry and academia due to its high selectivity. However, it suffers from low propylene conversion and rapid catalyst deactivation. Experiments showed that propylene conversion could be increased by raising H₂, O₂, or C₃H₆ concentration in the feed, but the feed compositions were within the explosion limit. It was also shown that the activity of the used catalyst could be fully recovered, but the regeneration temperature was 280 °C, much higher than that for reaction. Therefore a microchannel reactor was devised to suppress explosion and was constructed with Fecralloy, to raise the temperature rapidly for catalyst regeneration by electric heating. In two minutes the temperature of the reactor could be raised from 50 to 300 °C. Catalysts were coated on the alloy belt by dip coating, and the performance of the reactor was evaluated under different operating conditions. Results showed that in the microreactor the overall reaction rate was controlled mainly by the intrinsic reaction rate, and also influenced by film diffusion to a certain extent. The deactivated catalyst was regenerated in the microchannel reactor and the activity was fully recovered.     

美国能源部的浆态床F－T合成技术

浆态床Ｆ－Ｔ合成技术是美国能源部Ｆ－Ｔ合成技术的主要开发项目。本文就浆态相Ｆ－Ｔ合成催化剂的开发、中试示范实验和浆态反应器的化工基础研究作一扼要的介绍。     

FORMATION AND FLOW OF GAS BUBBLES IN A PRESSURIZED BUBBLE COLUMN WITH A SINGLE ORIFICE OR NOZZLE GAS DISTRIBUTOR

The characteristics of gas bubbles in a 5 cm diameter bubble column equipped with a single orifice of 1,3 or 5 mm diameter were investigated under system pressure of 0.1-15 MPa. The formation of gas bubbles was strongly affected by the system pressure. Under high pressures a dispersed gas jet was formed at gas velocities where spherical gas bubbles would have been formed at atmospheric pressure. The critical gas velocity between the bubbling regime and the jetting regime was correlated with the liquid phase Weber number and the gas phase Reynolds number based on the gas velocity at the orifice. Bubble size and gas holdup in the main part of the bubble column were also affected by the bubble formation pattern at the distributor     

A SIMPLE METHOD FOR STUDYING THE KINETICS OF GAS-SOLID REACTIONS IN A FLUIDIZED BED REACTOR

A methodology for studying the kinetics of gas-solid reactions in a fluidized bed reactor is presented. This procedure is based on the analysis of the response of the system (flue gases) when batches of solids of different weight are added to the reactor. The method has been applied to the study of limestone particle calcination. The calcination rate constants obtained are in good agreement with those found in the literature. The method offers the advantage of simplicity and avoids the use of model assumptions or empirical correlations.     

ESTIMATION OF EFFECTIVE SHEAR RATE FOR AERATED NON-NEWTONIAN LIQUIDS IN AIRLIFT BIOREACTOR”“

Effective shear rate is one of the indispensable parameters for the design of aerobic fermentors using a viscous non-Newtonian system. The estimation of effective shear rate in airlift loop bioreactors has been investigated with liquid circulation velocity. An empirical correlation of effective shear rate in airlift loop reactors is proposed.

γ_eπ= 3.26-3.51 ; 10²U_G + 1.48 10⁴U²_G

It is found that the effective shear rate is lower in airlift reactors than in bubble columns. This equation can be used for the cultivation of cells sensitive to shear stress.     

Gas hold-up in highly viscous pseudoplastic non-newtonian solutions in three phase sparged reactors

Gas hold-up structure was studied in a three phase sparged reactor of 200 mm diameter. Air and aqueous solutions of carboxymethyl cellulose were used as gas and liquid phases. Spherical glass beads formed the solid phase. The superficial gas velocity, rheological properties, particle size and solid loading were varied over a wide range and their effects on gas hold-up structure were studied. A correlation for the estimation of the gas hold-up as a function of superficial gas velocity, apparent liquid viscosity, particle settling velocity and solid loading was established.     

Optimal control of the production–inventory system with deteriorating items and tradable emission permits

Using the well-known Arrow and Karlin (1958) Arrow, K.J., and Karlin, S. (1958), ‘Production over Time with Increasing Marginal Costs’, in Studies in the Mathematical Theory of Inventory and Production, eds. K.J. Arrow and S. Karlin, Stanford: Stanford University Press, pp. 61–69. [Google Scholar] dynamic production–inventory model and the model with tradable emission permits which was presented by Dobos (2005 Dobos, I. (2005), ‘The Effects of Emission Trading on Production and Inventories in the Arrow–Karlin Model’, International Journal of Production Economics, 93–94, 301–308.[Crossref], [Web of Science ®] , [Google Scholar], 2007) Dobos I. (2007), ‘Tradable Emission Permits and Production-inventory Strategies of the Firm’, International Journal of Production Economics, 108, 329–333.[Crossref], [Web of Science ®] , [Google Scholar], we develop a model of the production–inventory system with deteriorating items and tradable emission permits. The objective of this paper is to apply the optimal control theory to solve the production–inventory problem with deteriorating items and tradable emission permits, and derive the optimal inventory level and the optimal production rate that minimise the total cost. The results are discussed with a numerical example and a sensitivity analysis of the optimal solution with respect to the parameters of the production–inventory system is carried out.