Humidity material balances

The main principles of instrument design are summarized in Table 10.23. In filtration, e.g. for gravimetric analysis, selection of filter material (Table 10.22) requires careful consideration in terms of application, strength, collection efficiency, compatibility with pump, water uptake, etc. Humidity-controlled balance rooms, iTiicrobalances and careful handling techniques may be required. 

You can analyze material balance problems involving water vapor in air in exactly the same feshion as you analyzed the material balance problems for the drying of leather (or paper, etc.), depending on the information provided and sought. (Humidity and saturation problems that include the use of energy balances and humidity charts are discussed in Chap. 4.)... 

As depicted in Fig. 7.28, the process is divided into four systems (Si, S2, S3, and S4). hi addition, as mentioned in systems Si, S2, and S3, we can formulate two material balances in each one and write one more material balance (total mass balance) in system S4. In addition, as shown in the flow diagram, there are seven unknowns, and we can formulate seven equations. Before formulating the equations of systems Si, S2, S3, and S4 it is necessary to have consistent units in aU variables. For example, the humidity of the recycled air stream is given in pounds of water per pound of dry air (lb H20/lb dry air). To be consistent, it is necessary to express this as pounds of water per pound... 

Derivation of equations. To derive the equations for this case, no heat losses will be assumed, so the system is adiabatic. The drying will be for unbound moisture in the wet granular solids. We shall consider a bed of uniform cross-sectional area A m, where a gas flow of G kg dry gas/h m cross section enters with a humidity of//i. By a material balance on the gas at a given time, the gas leaves the bed with a humidity H. The amount of water removed from the bed by the gas is equal to the rate of drying at this time. 

For drying in a compartment or tray dryer where the air passes in parallel flow over the surface of the tray, the air conditions do not remain constant. Heat and material balances similar to those for through circulation must be made to determine the exit-gas temperature and humidity. 

In zone II, unsaturated surface and bound moisture are evaporated and the solid is dried to its final value Xj. The humidity of the entering gas entering zone II isH and it rises to The material-balance equation (9.10-23) may be used to calculate f/c as... 

The problems experienced in drying process calculations can be divided into two categories the boundary layer factors outside the material and humidity conditions, and the heat transfer problem inside the material. The latter are more difficult to solve mathematically, due mostly to the moving liquid by capillary flow. Capillary flow tends to balance the moisture differences inside the material during the drying process. The mathematical discussion of capillary flow requires consideration of the linear momentum equation for water and requires knowledge of the water pressure, its dependency on moisture content and temperature, and the flow resistance force between water and the material. Due to the complex nature of this, it is not considered here. 

In Differential vapour sorption a sample of material is placed on an accurate balance in a temperature controlled environment where the humidity of the gas phase can be accurately controlled. The adsorption and desorption behaviour of the sample is quantified with respect to water and hysteresis phenomena are identified. 

Wood is a hygroscopic material, due to the fact that the cell wall polymers contain hydroxyl groups. In an environment containing moisture, dry wood will absorb moisture until it is in equilibrium with the surrounding atmosphere. Similarly, saturated wood, when placed in an atmosphere of lower relative humidity (RH), will lose moisture until equilibrium is attained. If the wood is placed in an environment where the RH is stable, it will attain a constant moisture content (MC), known as the equilibrium moisture content (EMC). At this point, the flux of water molecules into the cell wall is exactly balanced by the outward flux into the atmosphere. 

Drying with Changing Humidity of Air in a Tunnel Dryer A granular material deposited on trays or a belt is moved through a tunnel dryer countercurrently to air that is maintained at 170°F with steam-heated tubes. The stock enters at 14001bdry/hr with W = 1.16 lb/lb and leaves with O.llb/lb. The air enters at 5% relative humidity (Hg = 0.0125 lb/lb) and leaves at 60% relative humidity at 170°F Hg = 0.203 lb/lb). The air rate found by moisture balance is 7790 lb dry/hr ... 

A gas-liquid contact operation is illustrated in Figure 3.8. Gas is contacted with a liquid from a spray, resulting in both diffusion and heat transfer between the gas and liquid. The gas exits the system at conditions of humidity and temperature quite different from the entrance conditions. Assume the operation to be adiabatic. Perform a material and energy balance for the system. 

There are many examples of second-order analyzers that are used in analytical chemistry including many hyphenated spectroscopic tools such as FTIR-TGA, IR-microscopy, as well as GC-MS, or even two-dimensional spectroscopic techniques. Another hyphenated technique that is being developed for the study of solid-state transitions in crystalline materials is dynamic vapor sorption coupled with NIR spectroscopy (DVS-NIR).26 DVS is a water sorption balance by which the weight of a sample is carefully monitored during exposure to defined temperature and humidity. It can be used to study the stability of materials, and in this case has been used to induce solid-state transitions in anhydrous theophylline. By interfacing an NIR spectrometer with a fiber-optic probe to the DVS, the transitions of the theophylline can be monitored spectroscopically. The DVS-NIR has proven to be a useful tool in the study of the solid-state transitions of theophylline. It has been used to identify a transition that exists in the conversion of the anhydrous form to the hydrate during the course of water sorption. 

However, a SIM during formulation development involves more than the above four steps, since the formulation development is a dynamic process where the formulation is optimized as the clinical program moves further along the development process. To continue the list from above, the following three steps must be added to the Ust (5) compatibility studies with excipients, (6) stability trending (variables would be temperature, humidity, and packaging material), and (7) mass balance for assay. An analytical chemist must revisit the separation of all components in the related substances method after steps 3,5, and 6 to ensure that the test method is truly a SIM. 

Define the dry-bulb temperature, wet-bulb temperature, and humid volume of humid air. Given values of any two of the variables plotted on the psychrometric chart (dry-buib and wet-bulb temperatures, absolute and relative humidity, dew point, humid volume), determine the remaining variable values and the specific enthalpy of the humid air. Use the psychrometric chart to carry out material and energy balance calculations on a heating, cooling, humidification, or dehumidification process involving air and water at 1 atm. 

This result (which is far from obvious) allows us to perform adiabatic cooling calculations with relative ease using the psychrometric chart. First locate the initial state of the air on the chart then locate the final state on the constant wet-bulb temperature line that passes through the initial state (or on the 100% humidity curve if cooling below the adiabatic saturation temperature takes place) and finally perform whatever material and energy balance calculations are required. Example 8.4-7 illustrates such a calculation for an adiabatic humidification operation. 

The psychrometric chart (oT humidity chart) conlam values of a number of process variables for air-water vapor systems at 1 atm. The values listed on the chart include dry-bulb temperature (the temperature measured by common temperature-measurement instruments), moisture content or absolute humidity (mass ratio of water vapor to dry air), relative humidity, humid volume (volume per mass of dry air), wet-bulb temperature (the temperature reading on a thermometer with a water-saturated wick around the bulb immersed in a flowing stream of humid air), and enthalpy per mass of dry air. If you know the values of any two of these variables for humid air at or near 1 atm, you can use the chart to determine the values of the other four, which can greatly simplify material and energy balance calculations. 

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