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A modelling and simulation language for combined lumped and distributed systems

21.05.2012. Paper 5 2005. IntroductionThe gProms modelling languageVariable distributionsDistributed expressions and equationsPartial differential operatorIntegral operatorSolution methodsIllustrative examplesProcess with mixed lumped/distributed unit operationsFixed-bed catalytic reactor

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A modelling and simulation language for combined lumped and distributed systems

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    1. 22.05.2012 Paper 5 2005 A modelling and simulation language for combined lumped and distributed systems Paper by M. Oh and C. C. Pantelides

    2. 22.05.2012 Paper 5 2005 Introduction The gProms modelling language Variable distributions Distributed expressions and equations Partial differential operator Integral operator Solution methods Illustrative examples Process with mixed lumped/distributed unit operations Fixed-bed catalytic reactor with cooling jacket Pressure swing adsorption Concluding remarks

    3. 22.05.2012 Paper 5 2005 Packed bed tubular reactors Packed bed absorption Adsorption and distillation columns Pipelines A substantial proportion of key unit operations in chemical an biochemical processes takes place in distributed parameter systems in which properties vary with respect to one ore more space dimensions as well as time. Examples:

    4. 22.05.2012 Paper 5 2005 In other types of units, some of the properties of the material are characterized by probability density functions instead of single scalar values. Examples: Crystallisation units Polymerisation reactors

    5. 22.05.2012 Paper 5 2005 The paper presents a general modelling language that handles both lumped and distribution processes. Attention is restricted to systems that are distributed over rectangular domains. The starting point for the work described is the gPROMS package. gPROMS is a modeling system for complex lumped parameter processes with both discrete and continuous characteristics Extended to allow the definition of models of distributed parameter unit operations.

    6. 22.05.2012 Paper 5 2005 The gPROMS modelling language It distinguishes two fundamental types of modeling entity -MODELs describe the physical, chemical and biological laws that govern the intrinsic behaviour of a system -TASKs are descriptions of the external actions and disturbances imposed on such a system -PROCESS is a third type of entity that is formed by a TASK driving a MODEL, thereby defining a complete simulation of the process.

    7. 22.05.2012 Paper 5 2005 Lumped parameter model in gPROMS The lowest-level MODELs in gPROMS are primarily sets of variables and the ordinary differential and algebraic equations relating to them. The latter are expressed in a high-level declarative language as shown in figure The gPROMS modelling language II

    8. 22.05.2012 Paper 5 2005 Main challenges involved extending gPROMS: The provision of general language constructs for the description of distributed systems at the lowest level of MODEL entities Numerical methods to deal with the resulting Integral, Partial Differential, and Algebraic Equations (IPDAEs)

    9. 22.05.2012 Paper 5 2005 -Tubular reactor vessel used to carry out an exothermic chemical reaction -The properties of the fluid vary with both radial and axial positions, as well as time -Temperature of cooling water is just a function of time

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    11. 22.05.2012 Paper 5 2005 Partial differential operator Partial differentiation of a distributed variable or expression is achieved trough the use of the operator PARTIAL In the simplest form: PARTIAL {Expression, DistributionDomain} -where Expression is an expression involving one or more distributed variables, and DistributionDomain is one of the distribution domains in the system. Lines 23 and 36- 40 in the figure.

    12. 22.05.2012 Paper 5 2005 Integral operator The syntax of integrals in the language is: INTEGRAL {IntegralRange ; Expression} -where expression is an expression distributed over a number of continuous or discrete domains, and IntegralRange represents the range of integration of the integrand

    13. 22.05.2012 Paper 5 2005 For instance, in the case with the tubular reactor model, an energy balance on the cooling water bath yields the equation: In the proposed language, the above equation is written like these:

    14. 22.05.2012 Paper 5 2005 Solution methods The systems of IPDAEs defined in the gPROMS MODELs are normally solved using the method-of-lines(MOL) family of numerical methods The resulting DAE system of this method can be solved reliably using any of the currently available DAE solvers such as DASSL or DASOLV The proposed modeling language allows the user to specify the type of spatial approximation method, as well as the granularity, and the order of approximation.

    15. 22.05.2012 Paper 5 2005 It is possible to specify numerical solution information within the MODEL itself But it is often better to associate it with specific instances of the model. These are created in the PROCESS entities of gPROMS A typical declaration of such information is showed here: Solution methods II

    16. 22.05.2012 Paper 5 2005 The process comprises a well-stirred mixer tank, a tubular reactor and a gas absorption column The reactor carries out the gas phase reaction A + B = 2C Illustrative example I

    17. 22.05.2012 Paper 5 2005 Illustrative example II

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