Numerical simulations software

The MathWorks Inc. (1993) SIMULINK Numerical Simulation Software - Reference Guide, The MathWorks Inc., Natick, Mass. 

Process validation is the procedure that allows one to establish the critical operating parameters of a manufacturing process. Hence, the constraints imposed by the FDA as part of process control and validation of an SMB process. The total industrial SMB system, as described, is a continuous closed-loop chromatographic process, from the chromatographic to recycling unit and, with the use of numerical simulation software allows the pharmaceutical manufacturer rapidly to design and develop worst-case studies. 

Before each separation, process parameters have to be determined through a numerical simulation software. Knowing the size of the system and the adsorption isotherm of the components, the software is able to compute the optimal set of flowrates allowing to perform the separation. 

The pilot plant is carried out about 24 h with the following parameter setting determined with the numerical simulation software ... 

In complex extractions, when both diffusion and thermodynamic are linked, or when the extract is a complex mixture of several components recovered at different rates, a numerical simulation software of the extraction can be very useful to estimate quickly any configuration and to optimize more precisely the industrial plant. A lot of different models have been proposed in the literature, and we built a versatile simulation software allowing to represent a lot of different systems [6],... 

In front of the diversity and the complexity of supercritical fluid extraction, we dispose of all experimental and theoretical tools to compute and extrapolate pilot plant experimental data to an industrial unit. A lot of theoretical thermodynamic and kinetic data are now available, and experimental extractions carried out on pilot plants allow to build extrapolation models, from the very simple ones (like it is described in this case study) to the very sophisticated ones based on a numerical simulation software and taking into account hydrodynamic, thermodynamic and kinetic phenomena. 

The numerical model adopts FLAC3D numerical simulation software developed by American Itasca Company. The model has a embedded depth of 1100 m, and its length x width x height is equal to 200 m X 120 m x 150 m. The coal seam dip angle has four circumstances covering 15°, 35°, 55° and 75°. Figure 1 is the numerical calculation model with the coal seam dip angle of 35°, and the model... 

In order to analyze the mechanical process of surrounding rock force and deformation in the shallow-buried coal seam comprehensively and systematically, the paper uses FLAC ° numerical simulation software to study the changing rule of... 

In this paper, a series of numerical simulations have been done, which is based on dynamic failure for hard coal containing gas with RFPA2D-Flow numerical simulation software developed (Xu T. 2004). On the one hand, evolution of stress field, fracture field and seepage field can be known clearly in the process of dynamic failure for hard coal containing gas. On the other hand, vacancy of data in the physical experiment can be made up. 

In the present, work for hydrate formation prediction a well known numerical simulation software (Pipeline Studio-TGNET) is employed [2]. In addition, to calibrate the model, the results of an experiment carried out in a part of Tehran gas network are used. Some research works related to hydrate formation and numerical simulation of natural gas flow in a network can be found in [3-6]. 

Use the numeric simulation software to forecast the production target after well pattern adjustment. When the water cut of simulation area reaches 98%, the experimental area stUl does not reach the ultimate water cut. But the degree of reserve recovery is greatly improved. Compare and analyze the production target of each plan (zhang jicheng, 2007). The result is showed in Table 2. 

Numerical simulation softwares are widely used by engineers, researchers, and university students and are very powerful to solve various problems. At the same time, it often happens that a user of a software is not well versed in its use. Also, physically nonexistent input data may give erroneous result, which caimot be realized if a user does not understand the practical problems that may arise. This partially comes from the fact that software technology is highly advanced and does not require a physical understanding of the phenomenon... 

There have been considerable efforts toward modeling ADME/Tox properties and the biophysical properties of molecules (see chapters 18-20, 22, 28), including numerous commercial software solutions. Simulations Plus (http //www.simulations-plus.com/) have developed GastroPlus, a product... 

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 functionOptimisation 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 a numerical optimisation algorithms. The first method is easily applied with ISIM, 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 however becomes extremely cumbersome. 

The spatial temperature distribution established under steady-state conditions is the result both of thermal conduction in the fluid and in the matrix material and of convective flow. Figure 2. 9.10, top row, shows temperature maps representing this combined effect in a random-site percolation cluster. The convection rolls distorted by the flow obstacles in the model object are represented by the velocity maps in Figure 2.9.10. All experimental data (left column) were recorded with the NMR methods described above, and compare well with the simulated data obtained with the aid of the FLUENT 5.5.1 [40] software package (right-hand column). Details both of the experimental set-up and the numerical simulations can be found in Ref. [8], The spatial resolution is limited by the same restrictions associated with spin... 

Many different digital simulation software simulation software packages are available on the market Modern tools are numerically powerful, highly interactive and allow sophisticated types of graphical and numerical output Many packages also allow optimisation and parameter estimation. 

Full conversion of the feed was achieved at a 170 °C reaction temperature. Numerical simulations of the reaction system were performed applying C HEM KIN software and a network of eight species in the gas phase, eight surface species and 28 reactions not provided here. The simulation described the experimental performance of the reactor very well. It revealed that oxidation of carbon monoxide occurs by the reaction between adsorbed CO and OH species and not by the reaction between adsorbed CO and O species, as the rate of the latter reaction was 10 orders of magnitude lower. Thus a simplified mechanism of the reaction according to Besser [86] could be formulated as follows ((S) standing for adsorbed species) ... 

Monte Carlo simulation can involve several methods for using a pseudo-random number generator to simulate random values from the probability distribution of each model input. The conceptually simplest method is the inverse cumulative distribution function (CDF) method, in which each pseudo-random number represents a percentile of the CDF of the model input. The corresponding numerical value of the model input, or fractile, is then sampled and entered into the model for one iteration of the model. For a given model iteration, one random number is sampled in a similar way for all probabilistic inputs to the model. For example, if there are 10 inputs with probability distributions, there will be one random sample drawn from each of the 10 and entered into the model, to produce one estimate of the model output of interest. This process is repeated perhaps hundreds or thousands of times to arrive at many estimates of the model output. These estimates are used to describe an empirical CDF of the model output. From the empirical CDF, any statistic of interest can be inferred, such as a particular fractile, the mean, the variance and so on. However, in practice, the inverse CDF method is just one of several methods used by Monte Carlo simulation software in order to generate samples from model inputs. Others include the composition and the function of random variable methods (e.g. Ang Tang, 1984). However, the details of the random number generation process are typically contained within the chosen Monte Carlo simulation software and thus are not usually chosen by the user. 

Warner [176] has given a comprehensive discussion of the principal approaches to the solution of stiff differential equations, including a hundred references among the most pertinent books, papers and application packages directed at simulating kinetic models. Emphasis has been put not only on numerical and software problems such as robustness, improving the linear equation solvers, using sparse matrix techniques, etc., but also on the availability of a chemical compiler, i.e. a powerful interface between kineticist and computer. 

The CAT model was further modified to include pH-dependent solubility, dis-solution/precipitation, absorption in the stomach or colon, first-pass metabolism in gut or liver, and degradation in the lumen. Physiological and biochemical factors such as changes in absorption surface area, transporter, and efflux protein densities have also been incorporated. This advanced version of CAT, called ACAT [176], has been formulated in a commercially available simulation software product under the trademark name GastroPlus . A set of differential equations, which is solved by numerical integration, is used to describe the various drug processes of ACAT as depicted in Figure 6.4. 

After explaining the process concept, this paper presents the two steps of the process development. First a simulation software allows to set the different process parameters and gives an idea of the SF-SMB performances. Then, the pilot plant is described and experimental results confirm the numerical simulation expectations and prove the great interest of this process. 

For large-scale problems, the most widely useful mathematical tool available is computational/numerical simulation. A great number of computer tools are available for simulation of ordinary differential equation (ODE) based models, such as Equations (3.27). Here we demonstrate how this system may be simulated using the ubiquitous Matlab software package. 

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