Linear flowrate

Calculation of TMB flowrates To calculate TMB flowrates, linear behavior of the adsorption isotherms for a feed concentration of 1 g is assessed. To check this point, we will use the criterion given in Equation (10). 

The relationship between the flowrate (Q) towards the well and the pressure drawdown is approximately linear, and is defined by the productivity index (PI). 

In the dynamic simulation run, the pressures and flowrates at the input and output of each module are known. It is, therefore, possible to perform non-linear correction of the control mode, such that the changes in regenerator pressure in the event of load shedding are minimized. In a test performed with a correspondingly corrected controller structure, the pressure drop after load shedding was reduced from 46 mbar to 19 mbar. The subsequent pressure rise of 27 mbar is just below the specified threshold. 

An estimate of the linear velocity of air through ductwork is a common exercise for process engineers. The calculation requires information on the static pressure drop and volumetric flowrate at any given temperature and pressure. 

Permeability is normally determined using linear flow in the incompressible or compressible form, depending on whether a liquid or gas is used as the flowing fluid. The volumetric flowrate Q (or Q ,) is determined at several pressure drops. Q (or Q ,) is plotted versus the average pressure p . The slope of this line will yield the fluid conductivity K or, if the fluid density and viscosity are known, it provides the intrinsic permeability k. For gases, the fluid conductivity depends on pressure, so that... 

A countercurrent moving-bed adsorption column is used to remove benzene from a gaseous emission. Activated carbon is employed as the adsorbent. The flowrate of the gas is 1.2 kg/s and it contains 0.027 wt/wt% of benzene. It is desired to recover 99% of this pollutant. The activated carbon entering the column has 2 X 10 wt/wt% of benzene. Over the operating range, the adsorption isotherm (Yaws et al., 1995) is linearized to... 

The cost for piping and pumping is a assumed to be linear with the mass flowrate of the stream. The cost of piping (Cpipe) is approximated by ... 

The above equations coupled with Eqs. (9.10)-<9.18) represent the constraints of the CHARMEN-synthesis formulation. The objective is to minimize the cost of MSAs and heating/cooling utilities. This is a linear-programming formulation whose solution determines the optimal flowrate and temperature of each substream and heating/cooling utilities. In order to demonstrate this formulation, let us consider the following example. 

The finalequationtellsusthattherateofpressureriseinthevesselwillbeaconstantequal to the product of the ratio of the feed gas pressure to the vessel volume and the volumetric flowrate ofthe feed gas. (Assumingthat the volume of the line leading from the valve tothevesselisnegligible.)Therefore,wecanseeimmediatelythatthepressurerisewillbe linear ... 

Fig. 3-2. Semipreparative RP-HPLC profile of eyelo(Arg-Lys-X-Pro-X-Ala). The erude sublibrary (160 mol) was dissolved in 0.1 % (v/v) TFA and applied to a Whatman Partisil 10 pm ODS-2 (1 x 50 em) eolumn. The peaks were eluted using a 40-min linear gradient of 0-25 % aeetonitrile in water at a flowrate of 7 mL min . Fractions were collected every 2 min and pooled in three fractions as indicated by arrows 130 pmol of peptides was reeovered (yield 81 %). (Reprinted with permission from ref. [75]. Copyright 1998, Ameriean Chemieal Soeiety.)...

Assuming a linear behavior, the conditions that have to be fulfilled by the different flowrates can be shown to be ... 

It may be noted that equations 4.29, 4.30 and 4.31 give a linear relation between Gmax and Pi. Comparison with equation 4.15 shows that the maximum flowrate Gmax is (0.685/0.607) = 1.13 times greater than for isothermal flow for a diatomic gas. 

Steam turbines are used to convert part of the energy of the steam into power and can be configured in different ways. Steam turbines can be divided into two basic classes back-pressure turbines and condensing turbines. The efficiency of the turbine and its power output depend on the flowrate of steam to the turbine. The performance characteristics can be modeled by a simple linear relationship over a reasonable range of operation. 

Show that the results may be interpreted on the assumptions that the solids are completely mixed, that the gas leaves in equilibrium with the solids and that the adsorption isotherm is linear over the range considered. If the flowrate of gas is 0.679 x 10-6 kmol/s and the mass of solids in the bed is 4.66 g, calculate the slope of the adsorption isotherm. What evidence do the results provide concerning the flow pattern of the gas ... 

COMPOSITION OF GRADIENT ELUTION FOR THE SEPARATION OF COLOUR PIGMENTS OF PAPRIKA CAPSICUM ANNUUM) POWDERS IN NORMAL (150 X 4 MM I.D.) AND MICROBORE (150 X 2 MM I.D.) OCTADECYLSILICA COLUMNS. A = ACN - METHANOL (1 4, V/V) B = BIDISTILLED WATER. EACH GRADIENT STEP WAS LINEAR. FLOWRATES FOR NORMAL AND MICROBORE COLUMNS WERE 2 ML/MIN AND 0.6 ML/MIN, RESPECTIVELY... 

Fig. 2.22. Chromatograms of methanohwater (50 per cent, v/v) saffron extracts from Mancha (a), Rio (b) and Sierra (c) types, simultaneously recorded at 250, 310 and 440 nm, including 4-nitroaniline as internal standard. The mobile and stationary phases were a linear gradient of methanol-water from 20 to 70 per cent in 50min, and an ODS column, respectively. The flowrate was lml/min, temperature 30°C and sample size 50/jl. The following compounds are present picrocrocin (1), HTCC (2), 3-entiobiosile-kaempferol (3), a-crocin (4), crocin 2 (5), crocin 3 (6), safranal (7), crocin 4 (8), crocin 5 (9), crocin 6(10) and internal standard (I>S.). Reprinted with permission from R Lozano et al. [47].

In a cube of side X, the volume of free space is eX3 so that the mean cross-sectional area for flow is the free volume divided by the height, or eX2. The volume flowrate through this cube is ucX2, so that the average linear velocity through the pores, u, is given by ... 

This equation relates the hold-up to the flowrates of the phases and column diameter through the characteristic velocity, u0. It therefore gives a method of calculating the holdup for a given set of flowrates if u0 is known. Conversely, equation 13.33 may be used to calculate uq from experimental hold-up measurements made at different flowrates. Thus, if hold-up data are plotted with L d + (J/( 1 — j))L c as the ordinate against j( 1 — j) as the abscissa, a linear plot is obtained which passes through the origin and which has a slope equal to fir, Wl. 

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