Flow rates space time

The time-space resolution that may be achieved with filter sampling techniques is dependent on the collection rate, limit of detection, and ambient concentrations. In aircraft applications, filters are typically operated at high flows (100-500 L/min) to maximize the mass accumulation rate. At these flow rates, sampling times on the order of 20 to 30 min are generally sufficient for measurement of substances in the urban troposphere. For sampling in the upper troposphere or in areas remote from pollutant sources, collection times of several hours may be necessary to obtain measurable quantities of material. 

The concentrations of reactant and products at the outlet of a packed bed reactor can be easily calculated with the mass balances for each compound supposing ideal plug flow behavior. For irreversible first-order consecutive reactions (Eq. (11.5)), the concentrations at the reactor outlet depend on the inlet concentration, Cj g, the rate constant, and the residence time, r. For reaction systems with constant fluid density, the residence time corresponds to the space-time defined as, r = V/Vg, with V the reactor volume and Vq the volumetric inlet flow. The space time... 

These design fundamentals result in the requirement that space velocity, effective space—time, fraction of bubble gas exchanged with the emulsion gas, bubble residence time, bed expansion relative to settled bed height, and length-to-diameter ratio be held constant. Effective space—time, the product of bubble residence time and fraction of bubble gas exchanged, accounts for the reduction in gas residence time because of the rapid ascent of bubbles, and thereby for the lower conversions compared with a fixed bed with equal gas flow rates and catalyst weights. 

For convenience, the loading on a flow reactor is expressed as a size of reactor per unit of flow rate, say V /V, and is labeled the. space velocity. Some of the units in practical use are stated in the Introduction. How the actual residence time is calculated when the density of flowvaries is illustrated in Table 7-8. 

Other advantages of gravity beds include flexibility in gas and sohds flow rates and capacities, variable retention times from minutes to several hours, space economy, ease of startup and shutdown, the potentially large number of contacting stages, and ease of control by using the inlet- and exit-gas temperatures. 

A numerical value is obtainable by integrating the trend curve for the flow received from the Flow Recorder (FR), from the start of the reaction to a time selected. Doing this from zero to each of 20 equally spaced times gives the conversion of the solid soda. Correlating the rates with the calculated X s, a mathematical model for the dependence of rate on X can be developed. 

Skaret presents a general air and contaminant mass flow model for a space where the air volume, ventilation, filtration, and contaminant emission have been divided for both the zones and the turbulent mixing (diffusion) between the zones is included. A time-dependent behavior of the concentration in the zones with constant pollutant flow rate is presented. 

Materials handling applications can be made wherever materials are transported, positioned, or.stored, the most extensive use being in mahufg. Manufg involves elements of motion, time, quantity, and space motion to transport materials between work stations, time to process and handle materials, quantity to establish work schedules and.material flow rates, and space to house materials, machines, and employees. The... 

PFPE, AI2O3, and X-IP were 500 mg, 200 mg, and 100 mg, respectively. The materials in Samples 2 to 4 were sufficiently mixed to ensure that the liquid PFPE and X-IP completely wet the alumina powders. These specimens were put in a closed space hlled with inert nitrogen. The flow rate of the nitrogen gas was kept at 20 milliliters per minute. The environmental temperature of the system was set at 220 ° C and the duration time was 250 minutes per sample for each individual operation procedure. PFPE used in the experiment was Z-dol and the alumina was in ultra-fine powders with chemical analytic grade purity. 

Run the reactor continuously. Observe the space-time yield, SPTYC. Set TIMEON = 0, and set FCON to the desired cooling flow rate. 

Compliance with U.S. EPA s design performance standards can be demonstrated through one-dimensional, steady-state flow calculations, instead of field tests. For detection sensitivity, the calculation of flow rates should assume uniform top liner leakage. For detection time, factors such as drain spacing, drainage media, bottom slope, and top and bottom liners should all be considered, and the worst-case leakage scenario calculated. 

Example 4.5 Derive the state space representation of two continuous flow stirred-tank reactors in series (CSTR-in-series). Chemical reaction is first order in both reactors. The reactor volumes are fixed, but the volumetric flow rate and inlet concentration are functions of time. 

The dilution rate D is dependent on the volumetric flow rate Q and the volume V, and really is the reciprocal of the space time of the fermentor. In this problem, the fermentor volume, V, is fixed, and we vary the flow rate, Q. Hence, it is more logical to use D (and easier to think) as it is proportional to Q. 

Although the concept of mean residence time is easily visualized in terms of the average time necessary to cover the distance between reactor inlet and outlet, it is not the most fundamental characteristic time parameter for purposes of reactor design. A more useful concept is that of the reactor space time. For continuous flow reactors the space time (t) is defined as the ratio of the reactor volume (VR) to a characteristic volumetric flow rate of fluid (Y). 

The reactor volume is taken as the volume of the reactor physically occupied by the reacting fluids. It does not include the volume occupied by agitation devices, heat exchange equipment, or head-room above liquids. One may arbitrarily select the temperature, pressure, and even the state of aggregation (gas or liquid) at which the volumetric flow rate to the reactor will be measured. For design calculations it is usually convenient to choose the reference conditions as those that prevail at the the inlet to the reactor. However, it is easy to convert to any other basis if the pressure-volume-temperature behavior of the system is known. Since the reference volumetric flow rate is arbitrary, care must be taken to specify precisely the reference conditions in order to allow for proper interpretation of the resultant space time. Unless an explicit statement is made to the contrary, we will choose our reference state as that prevailing at the reactor inlet and emphasize this choice by the use of the subscript zero. Henceforth,... 

The space time is not necessarily equal to the average residence time of an element of fluid in the reactor. Variations in the number of moles on reaction as well as variations in temperature and pressure can cause the volumetric flow rate at arbitrary points in the reactor to differ appreciably from that corresponding to inlet conditions. Consequently, even though the reference conditions may be taken as those prevailing at the reactor inlet, the space time need not be equal to the mean residence time of the fluid. The two quantities are equal only if all of the following conditions are met. 

Like the definition of the space time, the definition of the space velocity involves the volumetric flow rate of the reactant stream measured at some reference condition. A space velocity of 10 hr-1 implies that every hour, 10 reactor volumes of feed can be processed. 

From the definition of the space time and the inlet volumetric flow rate,... 

It is particularly convenient to choose the reference conditions at which the volumetric flow rate is measured as the temperature and pressure prevailing at the reactor inlet, because this choice leads to a convenient physical interpretation of the parameters and CA0 and, in many cases, one finds that the latter quantity cancels a similar term appearing in the reaction rate expression. Unless otherwise specified, this choice of reference conditions is used throughout the remainder of this text. For constant density systems and this choice of reference conditions, the space time t then becomes numerically equal to the average residence time of the fluid in the reactor. 

Each of these problems will be considered in turn. Consider the three ideal CSTR s shown in Figure 8.11. The characteristic space times of these reactors may differ widely. Note that the direction of flow is from right to left. The first step in the analysis requires the preparation of a plot o>f reaction rate versus reactant concentration based on experimental data (i.e., the generation of a graphical representation of equation 8.3.30). It is presented as curve I in Figure 8.11. 

One may define a space time for an entire cascade (tc) in terms of the ratio of the sum of the component reactor volumes to the inlet volumetric flow rate. Hence... 

If a monomer solution at a concentration of 1 mole/liter is fed to a CSTR at 0 °C, determine the space time necessary to achieve a conversion corresponding to 90% of the equilibrium value. If the reactor volume is 100 liters, what is the corresponding volumetric flow rate ... 

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