Kari I. Keskinen

Simulation of the population balances for liquid–liquid systems in a nonideal stirred tank. Part 2—parameter fitting and the use of the multiblock model for dense dispersions

Abstract In the previous part of this work (Chem. Eng. Sci. 54 (1999) 5887), a multiblock simulation model was developed in order to allow the close examination of different regions of a stirred tank for drop size distribution calculations. In this paper, that model is tested in a parameter fitting procedure. The drop breakage and coalescence parameters are fitted against drop size measurements from dense liquid–liquid dispersions, which were assumed fully turbulent. Since the local turbulence and flow values of a stirred tank are used in the present model, the fundamental breakage and coalescence phenomena can be examined more closely. Furthermore, the present model is capable of predicting inhomogeneities occurring in a stirred tank. It is also to be considered as an improved tool for process scale-up, compared to the simple vessel-averaged population balance approach, or use of correlations of dimensionless numbers only. The present model can use two sources of data for fitting parameters in the drop rate functions. One is to use transient data of the measured drop size distribution as the impeller speed is changed. The other is to use time-averaged data measured at different locations of the stirred tank. It is shown in this paper that the different flow regions can be chosen from the CFD simulations in a straightforward manner. CFD flow simulation results can be used to select the flow regions when no experimentally obtained flow conditions are available. This is especially useful for non-standard vessels, such as reactors containing cooling coils. After fitting the parameters with a multiblock model, the population balance model can be rather easily incorporated into a commercial CFD program to investigate different flow conditions.

Simulation of the population balances for liquid-liquid systems in a nonideal stirred tank.Part 1 Description and qualitative validation of the model

Abstract A simulation model has been developed to model drop populations in a stirred tank. A multiblock stirred tank model has been used with the drop population balance equations developed in the literature. The stirred tank is modeled separately so that local turbulent energy dissipation values and fluid flows are used in the drop breakage and coalescence functions. This model has several attractive features, e.g. it can predict the inhomogenity of dispersions and some scale-up phenomena. Because local conditions can be used in the drop rate functions needed in the population balances, it is possible to take these fundamental processes into closer examination. It seems that the parameter values in the drop breakage and coalescence models depend on flow and turbulence averaging for the vessel. This proposes that for “intrinsic” drop breakage and coalescence rates, a multiblock model for the stirred tank is needed in parameter estimation as well. The stirred tank flow model may be obtained from measurements or from computational fluid dynamics simulations in a straightforward manner.

Modelling of a side reactor configuration combining reaction and distillation

A new software tool to simulate and optimise processes that combine distillation column with a reactor sequence has been developed. This kind of combination is particularly interesting when new intensified and integrated processes are developed. The unit block contains both the distillation column model and the models for the coupled reactors. The model equations are solved simultaneously in one block and not sequentially as it is done when the reactor/distillation systems are solved by present flowsheet programs. This software module has been implemented into a flowsheet simulator environment that contains all required physical and chemical data banks and enables large-scale process optimisation. The applicability of the new module is demonstrated by solving two presently interesting processes: production of MTBE and isooctene. The model has shown good convergence properties.

An improved correlation for compressed liquid densities of hydrocarbons. Part 1. Pure compounds

A new model for calculating compressed liquid densities is proposed. In the new model, the Hankinson-Thomson correlation (Hankinson and Thomson, 1979) is used to calculate saturated liquid densities, and a slightly modified Chang-Zhao equation (Chang and Zhao, 1990) is used in the compressed liquid region. Parameters of the new model are fitted from a data base consisting of 4426 density points for 29 pure alkanes and alkenes. The new model is compared with HBT (Thomson et al., 1982) and Chang-Zhao (Chang and Zhao, 1990) models, and it is found to be the most accurate of the three models. With the new model, densities of compressed liquids can also be calculated in the near critical region with good accuracy. The average absolute deviation was 0.38% for the region Tr < 0.95 and 0.44% for the whole region Tr < 1.0. The new model is also tested against compressed liquid density data for several other organic substances and inorganic light compounds, that were not included in the data set used to fit the parameters. The average absolute deviation was 0.72% for the region Tr < 0.95 and 0.86% for the whole region Tr < 1.0 indicating that though fitted from alkane and alkene data, the new model can be applied to many other compounds.

An improved correlation for compressed liquid densities of hydrocarbons. Part 2. Mixtures

Abstract A recently presented model for compressed liquid densities of pure hydrocarbons (Aalto et al., 1995) is extended to mixtures. Mixing rules for the parameters V ∗ , Tc. HBT, ωSRK and Pc are given. A collection of mixing rules was compiled. 75 combinations of the mixing rules were evaluated using a compressed liquid density data base. The data base was collected during this work and it contained 4223 density data points for 49 binary and ternary hydrocarbon systems. The set of mixing rules recommended in this work gave an average absolute deviation (AAD) of 0.45%. The new model was compared to the original HBT correlation (Thomson et al., 1982), which gave an AAD of 0.57%. Based on the comparison done, it was found that the new model is more accurate than HBT and it can be used at higher temperatures near the vapor-liquid critical point. No binary interaction parameters are needed.

Utilization of Population Balances in Simulation of Liquid-Liquid Systems in Mixed Tanks

A simulation model has been developed to model drop populations in a mixed tank. A multiblock mixed tank model has been used with the drop population balance equations developed in the literature. The drop breakage and coalescence functions used in the population balance model take into account the local turbulent energy dissipation values. The drop breakage and coalescence function parameters are fitted against drop size measurements from dense liquid-liquid dispersions, which were assumed fully turbulent. Since the local turbulence and flow values of a mixed tank are used in the present model, the fundamental breakage and coalescence phenomena can be taken into closer examination. Furthermore, the present model is capable of predicting inhomogeneities occurring in a mixed tank. It is also considered as an improved tool for process scale-up, compared to the simple vessel-averaged population balance approach, or use of correlations of dimensionless numbers only. The present model can use two sources of data for fitting parameters in the drop rate functions. One is the transient data of the measured drop size distribution as the impeller speed is changed. The other is the time-averaged data measured at different locations of the mixed tank. Different flow regions can be chosen from direct measurements or from the CFD simulations in a straightforward manner. CFD flow simulation results can be used when no experimentally obtained flow conditions are available. This is especially useful for nonstandard vessels, such as reactors containing cooling coils.

Remarks on computing the density of dense fluids by Aalto-Keskinen model

Aalto and Keskinen (Fluid Phase Equilibria 166 (1999) 183) propose a model for compressed liquid densities. In this model, the critical temperature and pressure are estimated from pseudocritical mixing rules and bubble point pressure from a correlation. In this work, an equation of state (EOS) is used to get more accurate critical properties and bubble point pressures. This extends the application range of the model, and one would expect to see improvement in accuracy, as well. Four alternatives are studied and it is found that the original model of Aalto and Keskinen (Fluid Phase Equilibria 166 (1999) 183) is the most accurate in density. On the other hand, the modification where the rigorous critical point and bubble point pressure is computed extends the application range, although it is not as accurate in density as the original model.

Modelling Emergency Relief for Processes at Near Critical Conditions

Abstract A simulation tool for the preliminary design of a pressure relieving device for processes at near critical conditions is described. The selection of a pressure relieving device can be divided into two stages. The first stage is to determine the required emergency outflow as a function of time, which provides information to select a pressure relief valve or a rupture disk. The second stage is to simulate the process with the pressure relieving device selected at the first stage to find out the behaviour of the process as a function of time. A comparison between the proposed and the API 520 method is shown with the aid of an example.

Data reconciliation of streams with low concentrations of sulphur compounds in distillation operation

Abstract Traditionally data reconciliation of continuous processes operating in steady states is performed by constrained nonlinear optimization where the difference between measured and reconciled variables is minimized. In the present procedures weighting factors and statistical methods are applied to restrict the optimization problem. As the analyzed compositions and streams also have errors this approach might lead to misleading results. For example after reconciliation components may split into distillate and bottom streams against their true physical nature. Here a procedure is proposed to reconciliate information from distillation columns. In the procedure a column model is used to retain the real behavior of components more soundly than in traditional approaches. The procedure is discussed with the help of three industrial scale test cases.

Gas-liquid and liquid-liquid system modeling using population balances for local mass transfer

Abstract Gas-liquid and liquid-liquid stirred tank reactors are frequently used in chemical process industries. The design and operation of such reactors are very often based on empirical design equations and heuristic rules based on measurements over the whole vessel. This makes it difficult to use a more profound understanding of the process details, especially local phenomena. The scale-up task often fails when the local phenomena are not taken into account. By using CFD, the fluid flows can be taken into closer examination. Rigorous submodels can be implemented into commercial CFD codes to calculate local two-phase properties. These models are: Population balance equations for bubble/droplet size distribution, mass transfer calculation, chemical kinetics and thermodynamics. Simulation of a two-phase stirred tank reactor proved to be a reasonable task. The results revealed details of the reactor operation that cannot be observed directly. It is clear that this methodology is applicable also for other multiphase process equipment than reactors.