Mass Balance and Units

Numerous other options exist for specifying a concentration common ones are parts per thousand (ppt or %o), parts per million (ppm), or parts per billion (ppb). For the soil and air cases just mentioned, ppm on a mass basis is numerically equal to milligrams (mg) of chemical per kilogram (kg) of soil or air. Parts per million is also sometimes used on a volume basis. This may be inferred from context or made clear by the term ppm(v) 1 ppm(v) of helium in air would correspond to 1 ml of helium in 1000 liters (1 m3) of air. For water, the density of which is approximately 1 g/cm3, parts per million corresponds to milligrams of chemical per liter of water (mg/liter) in dilute solutions. 

No matter which units are used, however, concentration is the measure of interest for predictions of a chemical s effects on an organism or the environment. Concentration is also critical in one of the most important concepts of environmental fate and transport the bookkeeping of chemical mass in the environment. 

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The balance over a dedicated intermediate storage unit has to be modified because of the possibility of latent storage. Constraint (3.34), provides the link for the inlet and outlet mass balance between units, as shown in constraints (3.17) and (3.18). Constraints (3.35), (3.36) and (3.37), are similar to constraints (3.4), (3.5) and (3.6), however they apply to the case where the PIS operational philosophy is taken into account. 

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. 

In catalytic reactors we assume that there is no reaction in the fluid phase, and all reaction occurs on the surface of the catalyst. The surface reaction rate has the units of moles per unit area of catalyst per unit time, which we will call r". We need a homogeneous rate r to insert in the mass balances, and we can write this as... 

For gas reactions when the density may vary throughout the bed, the mass fraction is sometimes to be preferred above the molar concentration in representing the composition. Then, if G is the mass flow rate per unit cross-sectional area of reactor and g/z) the mass fraction of A, at z, a mass balance for unit time and unit area gives... 

First, the chapter lists the possible unit operations in the Aspen Plus Model Library, because the process is a connected set of the units. Then an example process is illustrated that makes ammonia from nitrogen and hydrogen. You will be able to get both the mass balances and the energy balances for the process. With this information you can determine the size of most of the equipment needed, and hence its cost. You can also determine the operating cost for heating, cooling, compression, and other tasks. The process involves a... 

The overall total and component mass balances per unit time are, in terms of total mass flow rates and mass fractions... 

Coupled mass and thermal energy balances are required to analyze the nonisother-mal response of a well-mixed continuous-stirred tank reactor. These balances can be obtained by employing a macroscopic control volume that includes the entire contents of the CSTR, or by integrating plug-flow balances for a differential reactor under the assumption that temperature and concentrations are not a function of spatial coordinates in the macroscopic CSTR. The macroscopic approach is used for the mass balance, and the differential approach is employed for the thermal energy balance. At high-mass-transfer Peclet numbers, the steady-state macroscopic mass balance on reactant A with axial convection and one chemical reaction, and units of moles per time, is... 

The overall mass balance is helpful to develop an expression for the total outlet gas-phase flow rate. It is important to realize that there are no restrictions which require that the total outlet gas-phase flow rate be the same as the inlet flow rate of gaseous chlorine. If one adds all four of the hquid-phase mass balances and all four of the gas-phase mass balances, then the result is the overall mass balance, which does not represent another independent equation. It is interesting to note that the sum of the stoichiometric coefficients is zero, which implies that the total number of moles is conserved during the chemical reaction. Furthermore, all interphase transport terms cancel because they represent a redistribution of all four components between the two phases, but there are no input or output contributions from these terms when the control volume corresponds to the total contents of the CSTR. Hence, the overall mass balance is analyzed on a molar basis because the total number of moles is conserved. Each term in the equation has units of moles per time and represents convective mass transfer in either the feed streams or the exit streams. The input terms correspond to the flow rates of liquid benzene and chlorine gas in the two feed streams, (A b) + (A ci). The output terms in the liquid exit stream are J2j and Afgas represents convective mass transfer in the outlet gas stream. At steady state. 

The metal mass balance for unit area of lake bed depends on the competing input and output fluxes. The input flux, J, is balanced by burial, outflow in dissolved form, and outflow as suspended solids. Each of these outputs can be expressed in terms of the metal concentration on particles, C. The mass balance can thus be expressed ... 

Mass balance [6]. Why is it imperative to always do mass balance and not be tempted to do a volumetric balance when the streams are expressed in volumetric units ... 

Therefore, we can write one total mass balance and, in addition, one mass balance for each component (1,2,..., p). Since we have p components, we are able to write, in total, p + 1 equations, but ONLY p of them are independent Why For example, if we sum up all the material balance equations formulated for each component, then we discover that the result is equal to the total mass balance. Remember, the number of independent equations is equal to the number of components in the process unit (system). 

This process has two units and a recycle stream. As was stated earlier, the addition of a recycle stream means that we need to consider a division (add one total mass balance) and add a mixer (in this case adding three material balances because the stream has three components). 

A comparison of the residual NAPL saturations after surfactant flooding based on both partitioning tracers and mass balance measurements is presented in Table 6. The apparent final residual DNAPL saturation estimates range from —0.0038 to 0.0046 from the mass balance and from 0.0001 to 0.005 from the partitioning tracers. The negative values from the mass balance are obviously experimental error and indicate that the mass balance error is on the order of 0.004 saturation units. This corresponds to only about 0.2 mL of DNAPL. 

Now, we move one important step forward toward the mass balance of units with chemical reactions (chemical reactors). In order to reach this stage in a systematic way, we start by analyzing the different types of reaction and introduce the necessary additional information needed for the mass balance of units with chemical reactions. 

A reaction model is a typical component of simulation systems, along with unit operations, thermodynamic servers, physical properties databanks, etc. The reaction model may provide information on how it is built, or can choose not to provide such information but Just to provide computation mainly of reaction rates so that these terms may be readily used in mass balances within unit operation models. The same applies for energy terms. By implementing a common interface standard, a reaction model component may be deployed on its own, independently of the process simulator it is used in. That develops the reusability of reaction models throughout unit operations and process simulators. A reaction model is contained by a Reactions Package software component exhibiting the specific CAPE-OPEN interfaces discussed here. 

In contrast to the processes we encountered previously, which were largely or entirely isothermal in nature, distillation has substantial heat effects associated with it. Consequently, we expect heat balances to be involved in modeling the process, as well as the usual mass balances and equilibrium relations. These balances are formulated entirely in molar xmits because the underlying equilibrium relations, such as Raoult s law and its extension, or the separation factor a, are all described in terms of mole fractions. Thus, the flow rates L and G, which appear in Figure 7.16, are both in rmits of mol/s, enthalpies H in units of J/mol, and the liquid and vapor compositions are expressed as mole fractions x and y of a binary system. 

A common altemative used where possible is the diafUtration mode with a crossflow UF membrane unit and concentrate recycle (Figure 7.2.5(e)). Here the solution concentration and viscosity are not allowed to increase due to the continuous addition of buffer replacing the permeate volume lost Equations developed in Section 6.4.2.1 for well-stirred UF cells having continuous diafUtration may be used here with appropriate care since we can treat the crossflow UF device as a blackbox far the purpose of an overall process mass balance and solute selectivity analysis. Similarly, the equations developed in Section 6.4.2.1 for a batch concentration process may be utilized here to determine various quantities, such as the yield of macrosolute, retentate concentration, etc. 

Since the osygen is poorly soluble gas, tbe process is liquid-side controlled. In this case fimn the mass balance and from the basic equation of mass transfer per unit of apparatus cross section it follows ... 

Referring to Figure 2, by considering solute mass balances over n, (n — 1),. .. 2, 1 units in turn and eliminating intermediate solute mass fractions and flow rates, the amount of solute associated with the leached sohd may be calculated in terms of the composition of the sohd and solvent streams fed to the system. The resulting equation is (2)... 

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