Abstract
Fixed-bed tubular reactors have important commercial applications in the chemical and allied process industries. A typical reactor consists of a cylindrical tube filled with solid catalyst particles and is mounted in a vertical upright position. After the reacting fluid has entered the reactor, it moves along the packed bed and reacts on the catalyst particles to produce the desired products. While fixed-bed reactors, relatively to other types of catalytic reactors, are flexible, efficient, low-cost, and require low maintenance, their most serious disadvantage is poor heat transfer with attendant poor temperature control (e.g., see Bartholemew and Farrauto, 2006). When a highly exothermic reaction is carried out in a packed bed reactor some problems associated with the operation of the reactor may arise. In this case, if the reaction generates heat faster than it can escape the reactor, viz., through reactor walls, the temperature of the fixed bed increases. The reaction and heat generation rates then increase, which causes a further rise in the reactor temperature. This can result in thermal runaway, with the temperature increasing ever more rapidly until the reactants have been finally exhausted. Runaway, or parametric sensitivity, describes a situation in which a small change in an operating variable such as feed temperature, concentration, or flow rate induces a large change in the temperature profile of the reactor. Further, a number of runaways occur due to scale-up, inadequate procedures and training, raw material quality control, maintenance, etc (Etchells, 1997; Barton and Rogers, 1997). Runaway can promote undesired side reactions, catalyst deactivation, productivity loss, and deterioration of product selectivity. Because of the risk associated with thermal runaway, many industrial reactors are operated under overly suboptimal conditions. It should be noted that near-runaway operation is potentially advantageous to catalytic processes as it may result in optimum reactor operation, especially if energy savings can be attained. For these reasons, understanding thermal runaway is of significant industrial importance. The concept of thermal runaway was first introduced to chemical reactor analysis in late 1950s (Bilous and Amundson, 1956). There have been many studies in the literature on the derivation of runaway criteria, e.g., in tubular and fixed-bed reactors with a single reaction (van Welsenaere and Froment 1970; McGreavy and Adderley, 1973; Morbidelli and Varma 1982, 1988; Bashir et al. 1992), in reactors with multiple reactions (Hosten and Froment, 1986; Henning and Perez, 1986; Morbidelli and Varma, 1989; van Woezik and Westerterp, 2000,
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