Outflow rate modeling

To illustrate the combined effects of chemical reaction and mass transport, a simple lake model treated as a continuous stirred tank reactor (CSTR) will now he examined. The inflow and outflow rates are constant and equal to one another ... 

Using this model, the outflow rates can be fitted quite well, as Figure 2.18 shows. 

Fig. 9.6. Model simulation for Hg. Curve 1 gives the values for Hg-concentration in lake water. The values do not reach a perfect steady-state level due to the fact that so much Hg has been accumulated in the catchment area during the last 50 years (initial amount in the catchment is 15 000 g in the entire catchment situated in central Sweden data for our "mean" lake), the outflow rate from the catchment is 0.0025 (1/year). Curve 5 illustrates a simulated liming during year 20 which would increase pH from 6 to 6.7. Curves 2, 3 and 4 show the effects of such a liming on Hg-concentrations in phytoplankton, prey (bottom fauna, zooplankton, small fish) and predatory fish (pike, large perch, etc.)...

Fig. 9.8. A. Model simulation for Cs. The driving function is an atmospheric fallout during month 24, with a peak value of 25 kBq/m. Curves 7, 2, 3 and 4 show the model-predicted concentrations in water, phytoplankton, prey and predatory fish. Curve 5 gives the assumed time-dependent outflow rate from the catchment. Default Kd=0.1 default phytoplankton uptake rate 68.3 10 (1/month)...

Figure 9.10 tries to answer this question by direct comparisons between "Hg" and "Cs" in water, in phytoplankton (Fig. 9.1 OB), and in prey and predator (Fig. 9.10A). One can note significant differences. This is due to two factors The longer outflow rates (twice as long for "Hg") and the faster uptake for "Cs" the pelagic uptake rate is 21 3.25 10 (1/month) for "Cs" and 3.25 10 (1/year) for "Hg". So, the model and the processes accounted for in the model can describe the empirical results. But it should be stressed that similar results could also be obtained by other combinations of the rates in the model.

The purpose of this chapter is to present the experimental results for the full-scale LAD outflow tests in liquid hydrogen. Test conditions were taken over a wide range of liquid temperatures (20.3-24.2 K), tank pressures (100-350 kPa), and outflow rates (0.010-0.055 kg/s) thermally and operationally representative of an in-space propellant transfer from a depot storage tank or to a smaller scale in-space engine. Horizontal LAD tests were conducted to measure independently the frictional and dynamic losses down the channel. Flow-through-screen tests were performed to measure independently the dominate pressure loss in LEO, the FTS resistance. Meanwhile, 1-g inverted vertical LAD outflow tests were conducted to obtain performance data for two full-scale 325 x 2300 LAD channels. One of the channels had a perforated plate and a custom-built internal thermodynamic vent system to enhance performance. Model predictions from Chapter 3 are compared to each set of experimental data. 

Data on weather conditions, especially temperature and rainfall (temporal distribution and intensity) in the study area are essential for the evaluation of the dissipation data. It is very important to understand the water balance in the paddy field as accurately as possible when calculating the rate of outflow. Records of changes in water temperature and sediment temperature are also helpful for modeling the behavior of a chemical in the rice paddy field. 

A simulation model needs to be developed for each reactor compartment within each time interval. An ideal-batch reactor has neither inflow nor outflow of reactants or products while the reaction is carried out. Assuming the reaction mixture is perfectly mixed within each reactor compartment, there is no variation in the rate of reaction throughout the reactor volume. The design equation for a batch reactor in differential form is from Chapter 5 ... 

Simple steady-state models may be used in order to relate quantitatively the mean concentration in the lake water column and the residence time of metal ions to the removal rate by sedimentation (for a detailed treatment of lake models see Imboden and Schwarzenbach, 1985). In a simple steady-state model, the inputs to the lake equal the removal by sedimentation and by outflow the water column is considered as fully mixed mean concentrations and residence times in the water column can be derived from the measured sedimentation fluxes. The binding of metals to the particles is fast in comparison to the settling. 

If the DMS inventory in Salt Pond is at steady state in summer (5), production should approximately balance removal. Tidal removal of DMS to Vineyard Sound is minimal. Outflow from Salt Pond is thought to be primarily surface water, and using a maximum tidal range of 0-0.2 m/d and a mean surface water concentration of 10 nmol/L, we calculate an export rate of less than 2 /imol/m2/d. The water-air flux of DMS may be calculated using the two film model of liss and Slater (22 flux = -ki C, ). With the same surface water DMS concentration (C ) and an estimated mass transfer coefficient (ki) for DMS of 1.5 cm/h, the projected flux of DMS from the pond into the atmosphere would be 4 /unol/m2/d. This compares with the range of estimated emissions from the ocean of 5-12 /imol/m2/d (1). 

The properties of wood(7,14) were used to analyze time scales of physical and chemical processes during wood pyrolysis as done in Russel, et al (15) for coal. Even at combustion level heat fluxes, intraparticle heat transfer is one to two orders of magnitude slower than mass transfer (volatiles outflow) or chemical reaction. A mathematical model reflecting these facts is briefly presented here and detailed elsewhere(16). It predicts volatiles release rate and composition as a function of particle physical properties, and simulates the experiments described herein in order to determine adequate kinetic models for individual product formation rates. 

In order to assess whether secondary reactions to form CO could be responsible for the experimental CO versus time curve shape, a series-parallel kinetic mechanism was added to the model. Tar and gas are produced in the initial weight loss reaction, but the tar also reacts to form gas. The rate coefficients used are similar to hydrocarbon cracking reactions. Fig. 5 presents the model predictions for a single pellet length. It is observed that the second volatiles maximum is enhanced. For other pellet lengths, the time of the second peak follows the same trends as in the experiments. While the physical model might be improved by the inclusion of finite rates of mass transfer, the porosity is quite large and Lee, et al have verified volatiles outflow is... 

This is a less accurate but much quicker way to estimate generation time than measuring the amount of outflow over a few hours (Models 1 and 3). Model 2 has incorporated a pipette in the tubing between the bottle of medium and the pump to measure the flow rate. The pipette is filled by gravity when the stopcock leading to the pipette is opened. When the pipette is full, the stopcock to the medium bottle is closed. The rate of removal of medium from the pipette is measured to obtain the flow rate. 

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