Lennart Edsberg

Numerical tools for parameter estimation in ode-systems

The numerical problem of estimating unknown parameters in systems of ordinary differential equations from complete or incomplete data is treated. A new numerical method for the optimization part, based on the Gauss-Newton method with a trust region approach to subspace minimization for the weighted nonlinear least squares problem, is presented. The method is implemented in the framework of a toolbox (called diffpar) in Matlab and several test problems from applications, giving non-stiff and stiff ODE-systems, are treated

Simplified method for effectiveness factor calculations in irregular geometries of washcoats

A simplified method to calculate the effectiveness factors in irregular geometries of washcoats is presented. The method is based on sectioning the washcoat into particles and treating each particl ...

Simplified method of effectiveness factor calculations for irregular geometries of washcoats: A general case in a 3D concentration field

A simplified 3D-model for isothermal conditions has been developed to reduce the calculations of the combined rate of pore diffusion and chemical reaction in washcoats of irregular geometries. The method is based on sectioning the washcoat into particles thus treating the solid-phase according to a corresponding boundary value problem. The simplified 3D-model was compared with a rigorous model for five different geometrical configurations of a square monolith with uneven washcoat coating. For the first and power law (0.7th order) kinetics the solutions of the reduced model were in very good agreement in comparison with the more expensive 3D-model. The computational burden could be even further reduced by using a lumped model in spite of peripherally varying concentration profiles. The agreement using the lumped model was satisfactory whenever proper correlations for the mass-transfer coefficient and the effectiveness factor were used.

Natriuresis and the extracellular volume expansion by hypertonic saline

BACKGROUND The mechanisms governing the duration of the extracellular fluid volume (ECF) expansion as a result of intravenous infusion of hypertonic saline solution are poorly understood. We hypothesized that the duration is closely related to the sodium excretion. MATERIALS AND METHODS Six conscious splenectomized ewes with a mean body weight of 30 kg were given an intravenous infusion of 4 ml x kg(-1) of 7.5% saline solution on two occasions, one over a period of 5 min and another over a period of 20 min. Mass balance and volume kinetic calculations of the distribution and elimination of fluid were performed after repeated sampling of the plasma sodium concentration and the urinary excretion of water and sodium during 3 h. RESULTS On considering the addition of sodium to and its excretion from the body, the plasma sodium concentration indicated a 10% dilution of the extracellular space. The volume expansion decayed at an average rate of 20% of the volume expansion per hour, which, however, varied greatly in the animals, depending on their capacity to excrete sodium. After 1 h, increasing natriuresis promoted translocation of water into the cells, which amounted to 25-35% of the total elimination. Computer simulations indicated that tripled natriuresis (up to approximately 750 mmol l(-1)) would increase the rate of elimination to 45% of the volume expansion per hour. CONCLUSION The sodium excretion was inversely proportional to the duration of the extracellular volume expansion by 7.5% saline.

Numerical studies of wall effects with laminar methane flames

Wall effects in the combustion of lean methane mixtures have been studied numerically using the CHEMKIN software. To gain a deeper understanding of the flame-wall interaction in lean burn combustio ...

Integration Package for Chemical Kinetics

One important application area of digital simulation of dynamical systems is the field of chemical kinetics. The problem to be treated here concerns the simulation of chemical reaction kinetics in homogeneous solutions according to the mass action law. The subject is to study the concentrations versus time of the components involved in the system by solving the ordinary differential equations (ODE’s) describing the kinetics with some numerical method. Numerical problems in these kinds of systems especially concern stiffness and size, i.e. the number of ODE’s involved. The aim is to utilize the special structure in order to gain efficiency. The efficiency aspect is important also for systems of moderate size when you want the solution for several different sets of parameters involved in the system, e.g. rate constants or initial concentrations. This situation occurs e.g. in the estimation of parameters from empirical curves and in the problem of verification of a hypothetic mechanism for a system of reactions, i.e. the identification problem.

Volume kinetic analysis of fluid shifts accompanying intravenous infusions of glucose solution

Volume kinetics is a mathematical tool for macroscopic (whole-body) evaluation of the distribution and elimination of lfuid given by intravenous infusion. Although the kinetic system has mostly been applied to crystalloid fluids, such as Ringers solution, it has more recently been extended to glucose solution, which is characterized by interdependence between glucose and fluid kinetics. The elimination of glucose, as estimated by a one-compartment open model, serves as the driving force for cellular uptake of glucose and, by virtue of osmosis, of water. Key findings include the observation that the infused fluid, besides being accumulated in the cells, occupies a central body fluid space (V1), which is no larger than 3–4 L, and that the cellular hydration has a much longer time-course than the hydration of V1. This explains the risk of hypovolemia associated with rapid infusion of 5% glucose; the dilution of V1, which is quite substantial owing to the small size of this space at baseline, stimulates a brisk diuresis while the excess water is being “trapped” in the cells along with the glucose. Model linearity has been demonstrated for 2.5% glucose solution and this allows the construction of nomograms for administration of such fluid during surgery and critical illness.

Design and characterisation of a close-concentric annular reactor for kinetic studies at high temperatures

A novel annular reactor for kinetic studies at high temperature and flow conditions has been designed to keep eccentricity tolerances below 10%. In a previous work, we have shown that it is very important to keep such low eccentricity values in order to collect reliable kinetic data from this type of reactors. As proposed in this study, a modified reactor with the use of a spacer could guarantee an annular duct with low levels of eccentricity. Manufacturing tolerances or deformation effects giving rise to eccentricity can be significantly minimised when using this apparatus. The reactor has been both experimentally and theoretically characterised. Carbon monoxide oxidation was used as a model reaction under mass-transfer limited conditions revealing an eccentricity of ∼5%. With such small eccentricity levels, a concentric annular form can be assumed in the reactor analysis. Simple 1D or 2D models can therefore be inexpensively used in the evaluation of the kinetic data. Also, prior to the design of the annular reactor, a numerical investigation was carried out to clarify the effects of eccentricity, physical properties of the carrier gas and the annular aspect ratio on mass-transfer limitations. Contrary to expectations, a considerable increase in the fuel mass-diffusivity by carrier gas substitution did not change the mass-transfer rates for cases when eccentricity and aspect ratios were high.

Modeling of high-temperature catalytic combustors : Comparison between theory and experimental data

Abstract The objective of this work was to model experimental results using the simplest possible mathematical model. Here we report on preliminary results obtained with a one-dimensional model used for parameter-fitting of experimental combustion data with an inlet temperature ramp. It was possible to fit our one-dimensional model with simple power law kinetics to an experimental curve. It was also possible to use a quasi-steady state model with a computing time about a hundred times shorter than for a corresponding transient model.

A numerical study of side wall quenching with propane/air flames

The head-on (i.e., stagnation) configuration has generally been used to numerically and experimentally characterize the flame-wall interaction with complex chemistry and multicomponent transport. Other studies have treated the transient case of a flame propagating toward a wall, and combustion in a boundary layer has also been dealt with. In this paper, a two-dimensional stationary model has been used to study the sidewall quenching of laminar propane/air flames in a boundary-layer flow. This geometry may be described as a flame parallel to the wall that is swept away with a laminar boundary-layer flow while propagating toward and interacting with the wall. The main purpose has been to examine the extent to which the flame can propagate toward the cooled wall for lean flames compared to stoichiometric flames. A detailed kinetic model is used to examine the oxidation of both the fuel and the intermediate hydrocarbons (IHCs). For stoichiometric and near stoichiometric mixtures the thermal coupling between the flame and the wall is small but significant. However, for very lean flames, the thermal coupling between the flame and the wall is found to be very significant. The intermediate hydrocarbons are the dominant emissions for stoichiometric and near-stoichiometric flames in contrast to the leaner flames in which the fuel becomes more significant. This implies that the IHCs are very important for the overall hydrocarbon emissions from flame quenching: as a result detailed kinetics of complex fuels should be used when determining the unburned hydrocarbon emissions.