Model-independent aspects of tracer chromatography theory

1973 ◽  
Vol 333 (1592) ◽  
pp. 89-98 ◽  
Keyword(s):  
Steady State ◽  
Thermodynamic Properties ◽  
Residence Time ◽  
Mean Residence Time ◽  
Chromatographic Determination ◽  
System Response ◽  
Chromatographic Process ◽  
The Mean ◽  
Population Balances ◽  
Mean Time

A theory of tracer chromatography is developed on the basis of population balances in the steady state. As well as to tracer systems the theory applies to chromatography with a carrier gas if the system response is linear. It is shown that the time of passage of a tracer peak can properly be taken to be the mean residence time of the tracer and that the mean time is directly related to thermodynamic properties. Many results of chromatography theory may be established easily without the need for the assumptions usually employed. Thus the methods already developed for the chromatographic determination of thermodynamic properties are more powerful, and there is more freedom in the design of experiments, than had been realized. The mean residence time of species i in the steady state is equal to the ratio of the holdup of i in the system to the rate of transmission of i through the system. By invoking the hypothesis that in the steady state the system is in equilibrium with its feed, the mean time can be related to thermodynamic properties contained in an expression for the holdup. This provides a powerful strategy for developing theoretical results without the need for a mathematical model of the chromatographic process.

scholarly journals APLIKASI MODEL RANTAI MARKOV UNTUK MENGANALISIS TINGKAT KENYAMANAN DI KOTA MAJENE BERDASARKAN TEMPERATURE HUMIDITY INDEX (THI)

2021 ◽  
Vol 15 (1) ◽  
pp. 009-014
Author(s):  
Muhammad Abdy ◽  
Wahidah Sanusi ◽  
Rahmawati Rahmawati
Keyword(s):  
Steady State ◽  
Residence Time ◽  
Mean Residence Time ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Temperature Humidity Index ◽  
Humidity Index ◽  
The Mean

This study applied the Markov chain model on the daily temperature and relative humidity data that was collected from the Meteorology and Geophysics Agency station in Majene district for the period 1983 to 2011. This study aims to analyze the comfortable level category in the Majene city based on the Temperature Humidity Index by calculating the probability of steady-state, the mean residence time and the mean first passage time. Categorizing the level of comfortable which is based on the Temperature Humidity Index consists of three categories, namely the comfortable, quite comfortable and uncomfortable. The trend of comfortable levels in the Majene city from 1983 to 2011 was fluctuated in the categories of quite comfortable and uncomfortable. Uncomfortable category occurs in October and November each year. The steady-state probability values indicates that the quite comfortable category has the highest chance of appearance, which is around 70%, and the comfortable category has the smallest chance of appearance, which is only about 5%. Meanwhile, the mean residence time and the mean first passage time indicate that the quite comfortable category have the longest duration of occurrence, which is around 5 days, and has the shortest duration to recur after occurring in the previous event, which is around 1.43 days.

Precipitation and filtration of zinc, magnesium, copper and aluminium hydroxides

1982 ◽  
Vol 47 (12) ◽  
pp. 3362-3370
Author(s):  
Otakar Söhnel ◽  
Eva Matějčková
Keyword(s):  
Residence Time ◽  
Mean Residence Time ◽  
Filtration Resistance ◽  
Filtration Pressure ◽  
Bed Porosity ◽  
The Mean ◽  
Filtration Properties

Filtration properties of batchwise precipitated suspensions of Zn(OH)2, Mg(OH)2 and Cu(OH)2 and continuously precipitated Al(OH)3 were studied. For batchwise precipitated suspensions was verified the theoretically predicted dependence of specific filtration resistance on initial supersaturation and for the continuously precipitated Al(OH)3 the relation between the specific filtration resistance and the mean residence time of suspension in the reactor. Dependences were also recorded between the bed porosity and concentration of precipitated solutions, specific filtration resistance and used filtration pressure and the effect of aging of the batchwise precipitated suspension of Mg(OH)2on its filtration properties. The used CST method for determination of filtration characteristics of Zn(OH)2 suspension was also studied.

Nitrogen use efficiency: does a trade-off exist between the N productivity and the mean residence time within species?

2008 ◽  
Vol 56 (3) ◽  
pp. 272 ◽  
Author(s):  
Zhi Y. Yuan ◽  
Han Y. H. Chen ◽  
Ling H. Li
Keyword(s):  
Residence Time ◽  
Nitrogen Use Efficiency ◽  
Mean Residence Time ◽  
Negative Relationship ◽  
Controlled Experiments ◽  
Nitrogen Use ◽  
Trade Off ◽  
N Supply ◽  
Use Efficiency ◽  
The Mean

Nitrogen use efficiency (NUE) can be divided into two components, i.e. N productivity (A) and the mean residence time (MRT). Controlled experiments indicate that there is not a trade-off between A and MRT within species, but this theory has not been well tested in field conditions. Here, we studied the A, MRT and NUE of Stipa krylovii Roshev. in a grassland over 4 years of N fertilisation experimentation. The three parameters (A, MRT and NUE) were significantly related to soil N supply and there was a negative relationship between A and MRT within this species (r = –0.775, P < 0.05), i.e. plants with higher A had lower MRT. Our results showed a trade-off between A and MRT within this Stipa species and this observed trade-off was attributed to different responses of A and MRT to soil fertility.

scholarly journals Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1299
Author(s):  
Shengli Lv
Keyword(s):  
Steady State ◽  
Transient State ◽  
Repairable System ◽  
Repair Rate ◽  
Numerical Illustration ◽  
Transform Method ◽  
Unreliable Server ◽  
Busy Time ◽  
The Mean ◽  
Mean Time

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

scholarly journals Submarine Groundwater Discharge From Sediments and Sand Boils Quantified by the Mean Residence Time of a Tracer Injection

2021 ◽  
Vol 9 ◽  
Author(s):  
Michael Schlüter ◽  
Philipp Maier
Keyword(s):  
Residence Time ◽  
Mean Residence Time ◽  
Submarine Groundwater Discharge ◽  
Groundwater Discharge ◽  
Tracer Injection ◽  
Discharge Rates ◽  
Seepage Meter ◽  
Submarine Groundwater ◽  
Sand Boils ◽  
The Mean

To quantify submarine groundwater discharge, we developed an inexpensive automated seepage meter that applies a tracer injection and the computation of the mean residence time. The SGD-MRT is designed to measure a wide range of discharge rates from about 30 to 800 cm³/min and allows minimizing backpressures caused by pipe friction or flow sensors. By modifying the inner volume of the flow-through unit, the range of measurement is adjustable to lower or higher discharge rates. For process control and data acquisition, an Arduino controller board is used. In addition, components like temperature, conductivity, and pressure sensors or pumps extend the scope of the seepage meter. During field tests in the Wadden Sea, covering tidal cycles, discharge rates of more than 700 cm³/min were released from sand boils. Based on the measured discharge rates and numerical integration of the time series data, a water volume of about 400 dm3 with a seawater content of less than 12% was released from the sand boil within 7 h.

An improved energy envelope stochastic averaging method and its application to a nonlinear oscillator

2016 ◽  
Vol 23 (1) ◽  
pp. 119-130 ◽  
Author(s):  
Yaping Zhao
Keyword(s):  
Steady State ◽  
Probability Density Function ◽  
Probability Density ◽  
Averaging Method ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
System Response ◽  
Mean Square ◽  
Fpk Equation ◽  
The Mean

An improved stochastic averaging method of the energy envelope is proposed, whose application sphere is extensive and whose implementation is convenient. An oscillating system with both nonlinear damping and stiffness is taken into account. Its averaged Fokker-Planck-Kolmogorov (FPK) equation in respect of the transition probability density function of the energy envelope is deduced by virtue of the method mentioned above. Under the initial and boundary conditions, the joint probability density function as to the displacement and velocity of the system is worked out in closed form after solving the averaged FPK equation by right of a technique based on the integral transformation. With the aid of the special functions, the transient solutions of the probabilistic characteristics of the system response are further derived analytically, including the probability density functions and the mean square values. A simple approach to generate the ideal white noise is drastically ameliorated in order to produce the stationary wide-band stochastic external excitation for the Monte Carlo simulating investigation of the nonlinear system. Both the theoretical solution and the numerical solution of the probabilistic properties of the system response are obtained, which are extremely coincident with each other. The numerical simulation and the theoretical computation all show that the time factor has a certain influence on the probability characteristics of the response. For example, the probabilistic distribution of the displacement tends to be scattered and the mean square displacement trends toward its steady-state value as time goes by. Of course the transient process to reach the steady-state value will obviously be shorter if the damping of the system is greater.

Modeling the Mean Residence Time of Liquid Phase in the Gas–Liquid Cyclone

2015 ◽  
Vol 54 (43) ◽  
pp. 10885-10892 ◽  
Author(s):  
Junwei Yang ◽  
Xupeng Zhang ◽  
Guoping Shen ◽  
Jiazhi Xiao ◽  
Youhai Jin
Keyword(s):  
Liquid Phase ◽  
Residence Time ◽  
Mean Residence Time ◽  
The Mean
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