Contaminant mass

The zoning of the space is based on the assumption of constant temperature, concentration, and humidity in each separate zone." - The boundaries between the zones can be vertical or horizontal. The balances for air mass flow, contaminant mass flow, water vapor mass flow, and beat flow arc determined between zones and between zone and outer boundaries. 

The calculation of the two-zone model is based on the balance equations for air mass flow, contaminant mass flow, water vapor mass flow, and heat flow of both zones. 

Contaminant mass flow balance for the lower zone ... 

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. 

Contaminant mass transport in an air stripper is schematically shown in Figure 18.12. The removal process can be described mathematically by a mass balance for the contaminant assuming that there is no change in the accumulated contaminant in the stripper under steady-state conditions ... 

This air/water ratio is the theoretical or minimum air/water ratio for a given removal. However, in practice, the contaminant mass transfer is a long way from being at ideal equilibrium. A higher air/water ratio, denoted as (G/L)actual, the actual air/water ratio, is required for that removal. 

May be difficult to implement in low-permeability aquifers Reinjection wells or infiltration galleries may require permits or may be prohibited Biodegradation pathways may be site-specific, potentially requiring pilot testing or treatability studies A relatively large amount of oxidant may be needed for treatment of large contaminant mass... 

Operation number Contaminant mass (g-tr1) r - in (ppm) Cout (ppm) Limiting water flowrate (t-h 1)... 

Analysis of the data in Table 26.4 can be started by calculating the flowrate that would be required for each of these operations, if each operation was fed by freshwater with zero concentration. The relationship between mass pickup of contaminant, mass flowrate of water and concentration change is given by ... 

Operation Contaminant mass (kg-lr1) Cin,max (ppm) Cout,max (ppffl) Limiting flowrate (t-h )... 

Finally, the relative contaminant mass load on the two treatment processes can usually be varied within reasonable limits. As load is shifted from TPI to TPII, and vice versa, their relative capital and operating costs will change. This is a degree of freedom that can be optimized. 

Since the formulation of the constraints has been presented in detail in Section 4.3 using, only the new constraints will be presented in this section. The new constraints were necessitated by the existence of operations C and E for which the contaminant mass load is zero as aforementioned. Without any modifications in the presented mathematical formulations for scenarios 1 and 3, i.e. fixed outlet concentration, this condition would suggest that there is no need for the utilization of water in operations C and E (see constraints (4.3)). However, water is required in these operations for polishing purposes, although this is not associated with any contaminant removal. The minimum amount of water required in these operations is 300 kg. Therefore, the following new constraints is added to the mathematical formulations for scenarios 1 and 3. 

Scenario 1 Formulation for fixed outlet concentration and fixed contaminant mass load... 

Constraints (5.1) states that the inlet stream into any operation j is made up of recycle/reuse stream, fresh water stream and a stream from reusable water storage. On the other hand, the outlet stream from operation j can be removed as effluent, reused in other processes, recycled to the same operation and/or sent to reusable water storage as shown in constraints (5.2). Constraints (5.3) is the mass balance around unit j. It states that the contaminant mass-load difference between outlet and inlet streams for the same unit j is the contaminant mass-load picked up in unit j. The inlet concentration into operation j is the ratio of the contaminant amount in the inlet stream and the quantity of the inlet stream as stated in constraints (5.4). The amount of contaminant in the inlet stream to operation j consists of the contaminant in the recycle/reuse stream and the contaminant in the reusable water storage stream. Constraints (5.5) states that the outlet concentration from any unit j is fixed at a maximum predefined concentration corresponding to the same unit. It should be noted that streams are expressed in quantities instead of flowrates, which is indicative of any batch operation. The total quantity of water used at any point in time must be within bounds of the equipment unit involved as stated in constraints (5.6). Following are the storage-specific constraints. 

One would notice that there are a number of nonlinearities in the above constraints, more specifically in the contaminant mass balances around a unit and the central storage vessel. The nonlinearities arise due to the fact that the outlet concentration of each contaminant may not necessarily be at its respective maximum. Unlike the single contaminant case where one could replace the outlet concentration with the maximum outlet concentration, in the multiple contaminant case the outlet concentration of each contaminant remains a variable. Furthermore, the concentration within the central storage vessel is always variable, since the contaminant mass and mass of water within the vessel changes each time a stream enters or exits the vessel. To deal with this situation the following procedure is considered. 

In a typical multiple contaminant problem the maximum amount of water that can be used, while still obeying any concentration constraints, is determined by a limiting component and there is generally contaminant mass added for each contaminant present. In this problem, contaminant mass is only added to the water for one contaminant, namely the residue left from the specific product in a mixer. This then makes the limiting component in each mixer the component that leaves residue in the mixer. For example mixer 1 has shampoo as the limiting contaminant, since this is the only component which leaves a residue in the mixer. The maximum amount of water for each mixer is given for each mixer in Table 6.10. 

Due to the presence of contaminants in the system, contaminant balances also have to be derived around a unit. The first of these is an inlet contaminant balance, given in constraint (7.3). This constraint states that the contaminant mass entering a unit comprises of the contaminant mass present in the directly recycled/reused water and the contaminant mass present in water from various storage vessels. Important to note is that constraint (7.3) holds for every contaminant in the system. 

Apart from the mass balances associated with water, one also has to consider a product mass balance. Constraint (7.11) states that the amount of product leaving a unit is the amount of raw material that entered the unit less the total contaminant mass load transferred to the water stream. 

The inlet concentration of a contaminant c into a storage vessel is defined in constraint (7.14). This constraint states that the inlet concentration of contaminant c is the ratio of the contaminant mass in water sent to a vessel to the total amount... 

Unit Mass Balances with Negligible Contaminant Mass in the Wastewater... 

Constraint (8.1) is a raw material mass balance into a unit. The amount of raw material into a unit is the sum of the directly reused water, freshwater, water from storage and any other raw materials required for the specific final product. Constraint (8.1) is the form of the raw material balance where the contaminant mass in the reused water is negligible. Constraint (8.1) for the case where the contaminant mass is not negligible will be given at a later stage. It is important to note that only compatible water can be reused in product. The reuse streams each contain information on the contaminant present in the water through the state indices in the variables describing the reuse flows. 

Due to the fact that the contaminant mass in the wastewater is assumed to be negligible at this stage, one does not have to consider contaminant balances. 

As with the mass balances over a unit, contaminant balances around a storage vessel are not required due to the contaminant mass being negligible at this stage. 

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