Optimisation

Optimisation may be used, for example, to minimise the cost of reactor operation or to maximise conversion. Having set up a mathematical model of a reactor system, it is only necessary to define a cost or profit function and then to minimise or maximise this by variation of the operational parameters, such as temperature, feed flow rate or coolant flow rate. The extremum can then be found either manually by trial and error or by the use of numerical optimisation algorithms. The first method is easily applied with MADONNA, or with any other simulation software, if only one operational parameter is allowed to vary at any one time. If two or more parameters are to be optimised this method becomes extremely cumbersome. To handle such problems, MADONNA has a built-in optimisation algorithm for the minimisation of a user-defined objective function. This can be activated by the OPTIMIZE command from the Parameter menu. In MADONNA the use of parametric plots for a single variable optimisation is easy and straight-forward. It often suffices to identify optimal conditions, as shown in Case A below. 

Basically two search procedures for non-linear parameter estimation applications apply (Nash and Walker-Smith, 1987). The first of these is derived from Newton s gradient method and numerous improvements on this method have been developed. The second method uses direct search techniques, one of which, the Nelder-Mead search algorithm, is derived from a simplex-like approach. Many of these methods are part of important mathematical packages, e.g., ASCL and MATLAB. 

Optimal Cooling for a Reactor with an Exothermic Reversible Reaction 

CONTINUOUS STIRRED TANK REACTOR EQUILIBRIUM REACTION AND JACKET COOLING A = B  

The optimization in SIMUSOLV requires three self-explanatory statements 

In non-linear systems one can usually not predict a priori whether the optimum found is global or whether the optimum obtained represents only a local condition. A good judgement on the behaviour of the model can be seen in contour and three-dimensional plots, which are easily obtained using other alternative software packages, such as ACSL-Optimize or Matlab. 

Design is optimisation the designer seeks the best, the optimum, solution to a problem. 

Much of the selection and choice in the design process will depend on the intuitive judgement of the designer who must decide when more formal optimisation techniques can be used to advantage. 

In this book the discussion of optimisation methods will, of necessity, be limited to a brief review of the main techniques used in process and equipment design. The extensive literature on the subject should be consulted for full details of the methods available, and their application and limitations see Beightler and Wilde (1967), Beveridge and Schechter (1970), Stoecker (1989), Rudd and Watson (1968), Edgar and Himmelblau (2001). The books by Rudd and Watson (1968) and Edgar and Himmelblau (2001) are particularly recommended to students. 

If a separation is to be performed at large scale, it is usually necessary to carry out at least some level of optimisation. This may be simply to limit the time and cost of isolating a compound for further study, or may be to minimise the costs of production. It is important to remember that the reason for optimisation often influences the conditions chosen. This is because selection of conditions to give, for example, the maximum production rate (in kg h ) may not result in product which is isolat- 

Ignoring the last item for the moment, one can derive for a particular separation the individual contribution of these costs to the total for a given annual production requirement. Such a breakdown is shown in Fig. 2-12 the assumptions made in deriving it are given in Table 2-2. Equipment costs were taken from Prochrom price lists. 

It is clear that at low production rates the cost of equipment and labour make up the vast proportion of the cost per kg of material purified. In these cases, the purification should be carried out under conditions which minimise these fixed costs, generally by operating the unit at the highest possible production rate. At very high pro- 

2 The Practical Application of Theory in Preparative Liquid Chromatography 

Once a mode of HPLC has been selected, and also usually after a column and conditions have been determined under which there is reasonable peak shape and retention for the main peak, the process of optimisation begins. This generally involves manipulation of experimental variables relating to the mobile phase until the desired separation has been achieved. 

In the preceeding discussion of complex reactions, attention has been given to the relationships between reaction kinetics, reactor conditions and relative yields of particular products. Although it might be possible to 

Few companies are as dependent upon research as those in the pharmaceutical industry. The development of a new drug is enormously costly, so companies invest heavily in computational approaches to drug design, with the aim of reducing the number of chemicals that need to be screened for therapeutic activity, and thereby shortening the time to market for new drugs. Typically, pharmaceutical companies use structure-based design to address computational questions such as 

The number of compounds whose molecular weight is less than 250 Da is, of course, vast, and many of these compounds will be capable of fitting into the active site of a given protein and binding to it. However, these potentially valuable molecules will be hugely outnumbered by those which cannot fit into the active site, or which bind to it only weakly. To identify compounds of potential therapeutic interest, the relatively tiny proportion of molecules which meet the specified criteria need to be pinpointed among the huge number of unsuitable molecules. 

We can picture the algorithm whose task is to pick out the potentially valuable molecules as wandering across an extensive search space, on which are located 

The search space in a problem of this sort is much too large to permit an exhaustive search, in which every solution is inspected individually. Problems which have similarly large search spaces abound in chemistry, and if the search across any very large space is to succeed, the algorithm must be able to locate optima even though it is able to sample just a small fraction of that space. It can only do this if it is able somehow to identify the best places to look, that is, promising regions of the search space in which it is likely that the best solutions are located. 

This volume discusses some iterative optimisation methods drawn from within AI. Iterative methods of the sort discussed here are often computationally intensive, and as long as computers were of modest power these algorithms struggled to compete with other methods. Indeed, their computational demands had the effect of severely limiting the interests of scientists in them until the last decade of the twentieth century. However, evolutionary methods have, as we shall see, special advantages and they have become increasingly attractive as computer power has grown. 

Polymer compounding in most cases not only influences the properties of the end product but also has a considerable effect on the processing conditions. Compounding is used not only to produce changes in thermodynamic properties, but also in rheological properties [12-15]. 

The addition of fillers leads to an increase in the viscosity of a compound. Filler, when used in the compounding process, significantly raises the thermal conductivity of the system as a whole. When used, the thermal conductivities of the compound are higher than those of the individual polymers. While using inorganic filler, the thermal conductivity of the compound declines [16]. 

In compounding, the development of melt temperature is heavily linked to the melting of solid material in the screw channel. The temperature around the granules is important for the melting process. In particle/fluid systems, the shear rate increases as the flow cross-section of the liquid is reduced by the presence of the solid material. 

Before compounding, the following important parameters related to 

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Usually a company will have a portfolio of assets which are at different stages of the described life cycle. Proper management of the asset base will allow optimisation of financial, technical and human resources. 

It is fair to say that advances in seismic surveys over the last decade have changed the way fields are developed and managed. From being a predominantly exploration focused tool, seismic has progressed to become one of the most cost effective methods for optimising field production. In many cases, seismic has allowed operators to extend the life of mature fields by several years. 

To optimise the design of a well it is desirable to have an accurate a picture as possible of the subsurface. Therefore, a number of disciplines will have to provide information... 

The timely acquisition of static and dynamic reservoir data is critical for the optimisation of development options and production operations. Reservoir data enables the description and quantification of fluid and rock properties. The amount and accuracy of the data available will determine the range of uncertainty associated with estimates made by the subsurface engineer. 

By adding or subtracting parameter maps (see Figure 6.3 in Section 6.1.2) additional information can be obtained. They show trends in the parameters and are used to optimise reserves development and management. 

The number and shape of the grid blocks in the model depend upon the objectives of the simulation. A 100 grid block model may be sufficient to confirm rate dependent processes described in the previous section, but a full field simulation to be used to optimise well locations and perforation intervals for a large field may contain up to 100,000 grid blocks. The larger the model, the more time consuming to build, and slower to run on the computer. 

An example of an application of CAO is its use in optimising the distribution of gas in a gas lift system (Fig. 11.3). Each well will have a particular optimum gas-liquid ratio (GLR), which would maximise the oil production from that well. A CAO system may be used to determine the optimum distribution of a fixed amount of compressed gas between the gas lifted wells, with the objective of maximising the overall oil production from the field. Measurement of the production rate of each well and its producing GOR (using the test separator) provides a CAO system with the information to calculate the optimum gas lift gas required by each well, and then distributes the available gas lift gas (a limited resource) between the producing wells. 

With unlimited resources, the investor would take on all projects which meet the screening criteria. Project ranking is necessary to optimise the business when the investor s resources are limited and there are two or more projects to choose between. 

Artificial lift techniques are discussed in Section 9.6. During production, the operating conditions of any artificial lift technique will be optimised with the objective of maximising production. For example, the optimum gas-liquid ratio will be applied for gas lifting, possibly using computer assisted operations (CAO) as discussed in Section 11.2. Artificial lift may not be installed from the beginning of a development, but at the point where the natural drive energy of the reservoir has reduced. The implementation of artificial lift will be justified, like any other incremental project, on the basis of a positive net present value (see Section 13.4). 

It enables first to explain the phenomena that happen in the thin-skin regime concerning the electromagnetic skin depth and the interaetion between induced eddy eurrent and the slots. Modelling can explain impedance signals from probes in order to verify experimental measurements. Parametric studies can be performed on probes and the defect in order to optimise NDT system or qualify it for several configurations. 

Figure 3.3 shows the increasing attenuation for cracks in a depth between 5 and 30 mm, using the optimised excitation frequency for each depth. The coils (circular, double-D) have a current density of lOWm. In case of circular and double-D coil, this corresponds to an... 

An advantage of Real Time X-Ray is that since only one section of the part is inspected at the time the X-Ray parameter settings can be optimised per section. At the same time each section is irradiated almost perpendicular which gives less distortion in the image of the top and the bottom section of blades. 

Shear Horizontal (SH) waves generated by Electromagnetic Acoustic Transducer (EMAT) have been used for sizing fatigue cracks and machined notches in steels by Time-of-Flight Diffraction (TOED) method. The used EMATs have been Phased Array-Probes and have been operated by State-of-the-art PC based phased array systems. Test and system parameters have been optimised to maximise defect detection and signal processing methods have been applied to improve accuracy in the transit time measurements. 

Prompted by the success, TOFD measurements were conducted on a fatigue crack in a stainless steel compact tension specimen. Test and system parameters were optimised following the same procedure used for carbon steel specimens. A clear diffracted signal was observed with relatively good SNR and its depth as measured from the time-of-flight measurements matched exactly with the actual depth. 

The transducer parameters (position, frequency, diameter) are optimised in order to obtain a sound beam which enables a good echo from the crack. 

In order to optimise the general on-site system performance, time and resource consuming motion calculations are done immediately after execution of the previous path in the current scaiming program - simultaneously with the storing of digital A-scan data by the PS-4 system. 

Optimised robot motion calculations in order to reduce inspection time further. 

These are just a few examples, but there are many more. At the moment. Joint Industry Projects are underway to identify and validate NDT methods for certain applications, and to optimise them where necessary. 

OPTIMISE, a joint industry project, supported by EC-ESPRIT funding is such a project, where techniques are identified, optimised and validated for the inspection of bulk carriers, with the aim to increase the inspection scope and thus the safety level, at the same time reducing the time needed for the inspections. 

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