R. de P. Soares

EMSO: A new environment for modelling, simulation and optimisation

Abstract A new tool, named EMSO (Environment for modelling, Simulation and Optimisation), for modelling, simulation and optimisation of general process dynamic systems is presented. In this tool the consistency of measurement units, system solvability and initial conditions consistency are automatically checked. The solvability test is carried out by an index reduction method which reduces the index of the resulting system of differential-algebraic equations (DAE) to zero by adding new variables and equations when necessary. The index reduction requires time derivatives of the original equations that are provided by a built-in symbolic differentiation system. The partial derivatives required during the initialisation and integration are generated by a built-in automatic differentiation system. For the description of processes a new object-oriented modelling language was developed. The extensive usage of the object-oriented paradigm in the proposed tool leads to a system naturally CAPE-OPEN which combined with the automatic and symbolic differentiation and index reduction forms a software with several enhancements, when compared with the popular ones.

Finding all real solutions of nonlinear systems of equations with discontinuities by a modified affine arithmetic

Abstract Chemical engineering is a rich area when comes to nonlinear systems of equations, possibly with multiple solutions, (unbounded) discontinuities, or functions which become undefined in terms of real values. In this work, a new approach is proposed for finding all real solutions of such systems within prescribed bounds. A modified affine arithmetic is used in an interval Newton method plus generalized bisection. A special constraint propagation is used to automatically remove regions where the functions are undefined for real numbers. Results for test problems have shown that the proposed implementation requires less computation effort than similar methods available in the literature for small continuous systems. Further, the method is able to find all real solutions of nonlinear systems of equations even when there are unbounded discontinuities or when functions become undefined within the given variable bounds.

Structural analysis for static and dynamic models

Abstract Modeling and simulation is an expanding area in several domains. In this work, the currently available methods for detecting inconsistencies in systems of equations coming from both static and dynamic models are briefly reviewed. For the dynamic case, a new algorithm is proposed. The proposed algorithm allows a detailed diagnosis of the dynamic degrees of freedom and valid initial conditions of differential-algebraic equation (DAE) systems. The algorithm is scalable for large problems and is a promising diagnosis tool to spread the usage of equation-oriented dynamic simulators.

Phase stability analysis using a modified affine arithmetic

Abstract Phase stability analysis is a crucial step in the determination of multiphase equilibrium. This analysis by the tangent plane distance (TPD) minimization is a well-known technique, as well as the difficulties in providing guarantees that the global minimum has been found. On this regard, interval methods are powerful tools since they provide such guarantees. In this work, an interval Newton method plus generalized bisection, based on a modified affine arithmetic, is used to reliably find all possible stationary points of the TPD function. Additionally, an improved convergence test is suggested as well as a special treatment for mole fraction weighted averages. Several mixtures with up to 5 components, including LLE island type ternary systems, were studied. Both activity coefficient models and cubic equations of state were considered. For all the cases tested, the proposed modified affine arithmetic method was superior to other interval-based methods.