MAXIMIZING SELECTIVITY OF LIQUID-LIQUID REACTION SYSTEMS. CONTROL OF THE DISPERSION PROCESS

Currently available information on droplet coalescence and break-up rates in turbulent flows in mixing vessels can be used to control drop sizes in dispersed phase equipment. The effect of drop size distributions on the selectivity and productivity in multi-reaction systems is examined in this paper.

The reaction system features the primary desired product (C) as resulting from reaction (in the bulk phase) between a reactant (A) in the drop phase and a second reactant (B) in the bulk phase. An adverse reaction is also envisaged which consumes (C) by further reaction with (B) to form a waste product. While small drops promote conversion because of large interfacial area, larger drops promote selectivity because of the facility of the product to re-enter the drop phase avoiding further reaction (to form waste) in the bulk phase. The effect of the bivariate distribution of drop size and reactant (A) concentration in the feed to a continuous stirred tank reactor on the selectivity and productivity of (C) is investigated within the framework of film theory while neglecting drop dynamics such as coalescence and break-up.

The results show the selectivity can be substantially improved by controlling drop size and distribution of the reactants among the differently sized droplets. Contrary to conventional wisdom which emphasizes creation of interfacial area by promoting very small droplets, it emerges that optimal distributions of drop size and reactant concentration which maximize productivity of the desired product exist. The practical implications are discussed.     

A New Bad Data Detection & Identification Algorithm

A fast and reliable algorithm for detecting and indentifying bad data in active-power measurements is proposed. The states are chosen to be the bus-voltage magnitudes and bus-voltage angle-differences. The bus-voltage angle-differences satisfy a set of loop equations derived from the topology of the network and a set of power-flow equations at nodes with no generations and loads. The algorithm is based on inspecting a similar set of equations. The proposed algorithm is tested on a realistic example and the results are compared with those of the conventional bad data elimination scheme.     

Analysis of axially dispersed systems with general boundary conditions—III: Solution for unmixed and well-mixed appended sections

The axial dispersion problem formulated in Part I[1] of this series is solved for cases 2–4 and 7 identified therein. The cases analyzed here conside appendages to the finite axially dispersed reactor which are either semi-infinite sections of finite dispersion or well-mixed sections of finite capaci The findings possess features akin to those found in Part II[7] for case. 1 but obviously displaying variations in detail.     

Conjugated Graetz problems—II: Fluid-fluid problems

Conjugated Graetz problems [1], involving two co- or counter-currently flowing phases are discussed following the general formalism of [1]. Although the difficulty, which arises from the changing sign of the velocity profile over the total cross-section of the two-fluid conduit of the counter-current problems, may be readily handled by the general formalism, the inclusion of axial heat conduction in the analysis presents special difficulties in obtaining analytical and/or computationally efficient solutions. The present analysis shows that analytical and computationally efficient solutions may be obtained only for these problems where the temperature profile at the entrance of the heating section is known for at least one of the fluids. The solution of a class of problems with long heating sections is obtained untilizing the general formalism together with the Gram-Schmidt orthonormalization process in the spirit of [5]. Problems with low Peclet numbers for both fluids and with an adiabatic section preceding the heating section or problems with very short heating sections are also briefly discussed.     

Acoustic emission in dynamic compression and its relevance to tribology

In the present work an acoustic emission (AE) technique is used to detect the initiation and propagation of short cracks in compressive cyclic loading. A mild steel surface was subjected to cyclic compressive stress of 100 cycles s⁻¹ by an electromagnetic exciter system. The compressive load applied was in the range of 2.5 to 25 N in each cycle. The stressing was done with an En31 steel ball in the presence of turbine oil. Acoustic emission was detected by placing an AE sensor 1.5 cm away from the point of contact of ball and plate. The surface damage was observed to be negligible until 10⁴ cycles. Microcrack nucleation and/or growth were inferred until 0.6 × 10⁵ cycles. Thereafter the acoustic emission activity decreased, suggesting possible arrest mechanisms were operating. The emission activity again became very significant beyond 6.0 × 10⁵ cycles, which may be due to possible subsurface crack growth. This information is related to previous one-pass sliding experiments.     

Inverse problems in population balances: Growth and nucleation from dynamic data

Particulate process modeling is critical for system design and control used widely in the chemical industly. Previous methods have focused on the assumption of appropriate models that can capture system behavior. A new technique presented is based on viewing the population balance from an inverse problem perspective that allows to determine appropriate models directly from experimental data. Under suitable assumptions (deterministic growth rate, no aggregation), the population balance equation may be solved by the method of characteristics, which associates the number density for any size at any time with a single point from the initial or boundary condition. The key to using this is the recognition that these characteristics correspond to the size history of individual particles and can be associated with constant cumulative number densities (quantiles) of the population. These quantiles are easily identifiable from experimental data. The variation of size and number density along these characteristics provides decoupled equations used to determine the growth rate. Validity of the determined growth law is checked by the collapse of the experimental data onto initial and boundary conditions.     

Whither chemical engineering?

The 1988 Amundson Report on research needs in chemical engineering encouraged the pursuit of frontier areas in chemical engineering with the warning, however, that attention to core areas must be preserved. Indeed, the strong core base in chemical engineering during the latter half of the 20th century enabled chemical engineers to contribute extensively to many areas outside of the traditional. The depth of such involvement has led researchers to confront questions much more engaging to the field of application. This effort has led to adopting and cultivating expertise more native to the field of application than to secure chemical engineering as a discipline. It therefore seems appropriate to ask if the warning voiced in the Amundson Report needs to be reiterated. If chemical engineering research must leave a strong trail of fundamental understanding through developed methodologies to ensure continuing progress, then this article yields considerable scope for discussion.     

Robust fault-tolerant control using an accurate emulator-based identification technique

A robust fault-tolerant control scheme using an accurate and robustly identified model of a system operating in a closed loop is proposed. A robust identification of the system and the associated Kalman filter is proposed by the novel use of an emulator, which is a transfer function connected to the input, output or both, to mimic the likely operating scenarios, both normal and abnormal. From the emulator-generated data, a set of perturbed models are generated, which plays a crucial role in ensuring robustness of the identified model and subsequently that of the controller. The prediction error method is employed to identify the perturbed models and a robust optimal model is obtained as a best fit to the perturbed models. A robust Kalman filter-based state feedback controller is obtained from the parameterisation of all stabilising controllers generated using the emulator-perturbed models. It is shown theoretically that the proposed robust controller designed using the emulator-perturbed robustly identified model is superior to the conventional robust controller designed from the identified nominal model, and a significant improvement in robustness is confirmed using illustrative examples. A fault-tolerant control system is developed by exploiting the key properties of the freely available Kalman filter.     

Boundary value problems in transport with mixed or oblique derivative boundary conditions—I: Formulation of equivalent integral equations

When an internally heated body is cooled along its boundary by a peripherally flowing fluid that is continually replenished from an external source, a differential energy balance on the boundary leads to unfamiliar boundary conditions. Such boundary conditions involve mixed second derivatives with respect to spatial variables, which under additional assumptions (such as an infinite heat transfer coefficient) lead to oblique derivative boundary conditions; i.e. at the boundary an oblique derivative of the temperature is specified. Classical attempts at solution of elliptic partial differential equations with oblique derivative boundary conditions have been through the establishment of equivalent singular integral equations, using complex analytic continuation. The theory of singular integral equations is complicated, however.Using appropriate Green's functions, the boundary value problems of interest have been reduced to equivalent integral equations in this work. While oblique derivative boundary value problems are shown to lead to singular integral equations, the mixed derivative boundary value problem is shown to yield Fredholm integral equations directly. This surprising finding is mathematically significant, because Fredholm integral equations are solved more easily, and physically significant because the mixed derivative boundary condition is the more realistic condition in the present context. A method of solution of Fredholm integral equations is discussed.More complicated boundary conditions in which axial conduction in the coolant fluid is important have also been shown to lead to Fredholm integral equations. Finally a transient problem has been formulated.