Output mass balance

Neglecting the light byproducts, and assimilating all the heavy byproducts with dodecane, the input-output mass balance can be written using the reaction extents (kmol/h) ... 

The steady-state input-output mass balance equations are simple and transparent, namely... 

Phase II Mass Balance. (/) Determine raw material iaputs. 2) Record water usage. 3) Assess present practice and procedures. (4) Quantify process outputs. (5) Account for emissions to atmosphere, to wastewater, and to off-site disposal. (6) Assemble iaput and output information. (7) Derive a preliminary mass balance. (8) Evaluate and refine the mass balance. 

Nonlinear versus Linear Models If F, and k are constant, then Eq. (8-1) is an example of a linear differential equation model. In a linear equation, the output and input variables and their derivatives only appear to the first power. If the rate of reac tion were second order, then the resiilting dynamic mass balance woiild be ... 

Develop via mathematical expressions a valid process or equipment model that relates the input-output variables of the process and associated coefficients. Include both equality and inequality constraints. Use well-known physical principles (mass balances, energy balances), empirical relations, implicit concepts, and external restrictions. Identify the independent and dependent variables (number of degrees of freedom). 

It was shown in Chapter 7 that the performance of continuous crystallizers is determined by the characteristics of a feedback loop relating the output performance expressed as crystal size distribution and to the feed concentration and residence time. Thus, an increase in crystallizer residence time, or decrease in feed concentration, reduces the working level of supersaturation. This decrease in supersaturation results in a decrease in both nucleation and crystal growth. This in turn leads to a decrease in crystal surface area. By mass balance, this then causes an increase in the working solute concentration and hence an increase in the working level of supersaturation and so on. There is thus a complex feedback loop within a continuous crystallizer, as considered in Chapter 7 and illustrated in Figure 8.11. 

Identification of the input and output streams used in the overall mass balance equation. 

Input and Output Streams in the Overall Mass Balance... 

The failure to identify the necessary authigenic silicate phases in sufficient quantities in marine sediments has led oceanographers to consider different approaches. The current models for seawater composition emphasize the dominant role played by the balance between the various inputs and outputs from the ocean. Mass balance calculations have become more important than solubility relationships in explaining oceanic chemistry. The difference between the equilibrium and mass balance points of view is not just a matter of mathematical and chemical formalism. In the equilibrium case, one would expect a very constant composition of the ocean and its sediments over geological time. In the other case, historical variations in the rates of input and removal should be reflected by changes in ocean composition and may be preserved in the sedimentary record. Models that emphasize the role of kinetic and material balance considerations are called kinetic models of seawater. This reasoning was pulled together by Broecker (1971) in a paper called "A kinetic model for the chemical composition of sea water."... 

Equations (1.1) to (1.3) are diflerent ways of expressing the overall mass balance for a flow system with variable inventory. In steady-state flow, the derivatives vanish, the total mass in the system is constant, and the overall mass balance simply states that input equals output. In batch systems, the flow terms are zero, the time derivative is zero, and the total mass in the system remains constant. We will return to the general form of Equation (1.3) when unsteady reactors are treated in Chapter 14. Until then, the overall mass balance merely serves as a consistency check on more detailed component balances that apply to individual substances. 

Inputs and outputs assessed in mass balancing are shown in Figure 5.3. The software EATOS was used to calculate all mass balances of processes. Outputs of EATOS are the mass index (equation (5.1), mass of raw material per mass of product output), and the environmental factor (equation (5.2), mass of waste output per mass of product output). EATOS also allows the calculation of cost indices (e.g., reference [15]) (equation (5.3), cost of raw material per mass of product output). 

Figure 5.3 Diagram showing boundaries for Mass Balance (encompassed by black dashed lines) and LCA with processes and flows included. Black arrows and flow names show inputs and outputs of the methods, grey arrows and boxes represent processes analysed to set up mass and energy balances. The process networks for the supply of energy, resources and so on are greatly simplified.

In this section the application of the total mass balance principles is presented. Consider some arbitrary balance region, as shown in Fig. 1.14 by the shaded area. Mass accumulates within the system at a rate dM/dt, owing to the competing effects of a convective flow input (mass flow rate in) and an output stream (mass flow rate out). 

The amount of product sold may vary seasonally or randomly. The usual way to adjust for this is to increase or decrease the feed rate to the system, according to expected demand for the product or the size of the product inventory. The altering of the feed rate, in turn, increases or decreases the feed to each of the succeeding units, and eventually the output is changed. This is diagrammed in Figure 7-3 and is called mass balance control in the feed direction. 

The environmental compartments are represented by boxes and the concentration of a chemical in these boxes is affected by processes that cause mass flows of the chemical to and from the boxes. The chemical can be input into a box from outside the system, output from a box to outside the system, or transported by means of advective or diffusive processes to and from other boxes. A mass balance equation can be written for each of the boxes representing the mass flow of the chemical. Generally, the magnitude of these mass flows depends on the concentration of the chemical in the boxes. If mathematical expressions which relate the mass flows to the concentrations are available, the set of mass balance equations (one for... 

I mass balance model at the farm level Calculation of inputs and outputs. 

Material Balances. The material (mass) balances for the ingredients of an emulsion recipe are of the general form (Accumulation) = (Input) - (Output) + (Production) -(Loss), and their development is quite straightforward. Appendix I contains these equations together with the oligomeric radical concentration balance, which is required in deriving an expression for the net polymer particle generation (nucleation) rate, f(t). 

If one considers the overall CTL process, considering the input to and outputs from the process, the overall mass balance for the system can be written as follows ... 

Thus, by considering the overall mass balance, i.e., looking at the inputs and outputs of the process, one can gain many insights into a process and also identify opportunities for C02 emissions reduction and enhancing feedstock utilization. 

This mass balance presents the possible links in the biogeochemical food web for various heavy metals. Some items may be neglected, like degassing of Pb, Cd, Cu and Zn metals. However, this process is of crucial importance for mercury (see Section 3.2). The output of the heavy metals with soil erosion may also be neglected. After elimination of these processes, the simplified following equation is workable. The sum of inputs by deposition, fertilizing, and waste and rubbish as fertilizer stands as the term Critical Load . 

The input of airborne lead to the Forest ecosystems has been studied at the Hubbard Brook Experimental Forest in New Hampshire. The small catchment approach has been used to study the lead biogeochemical cycle since 1963 (Likens et al., 1977 Driscoll et al., 1994). By monitoring precipitation inputs and stream output from small watersheds that are essentially free of deep seepage, it is possible to constmct accurate lead mass balance. The detailed study of soil and soil solution chemistry and forest floor and vegetation dynamics supplemented the deposition monitoring. 

This problem, taken from Floudas (1995), involves the manufacture of a chemical C in process 1 that uses raw material B (see Figure E9.3a). B can either be purchased or manufactured via two processes, 2 or 3, both of which use chemical A as a raw material. Data and specifications for this example problem, involving several nonlinear input-output relations (mass balances), are shown in Table E9.3A. We want to determine which processes to use and their production levels in order to maximize profit. The processes represent design alternatives that have not yet been built. Their fixed costs include amortized design and construction costs over their anticipated lifetime, which are incurred only if the process is used. 

Chapter 1) that its concentration in the reservoir can be modified only by processes taking place at the boundaries. Species i can be added to or subtracted from the system by solid, liquid or gaseous input and output, not by chemical reaction or radioactive decay inside the reservoir. For the sake of illustration, we will consider a water reservoir, whose properties will be labeled liq . Mass balance requires... 

Geochemical mass balance studies (also known as input-output budgets) invoke a simple conservation-of-mass principle. If the flux of any element leaving a watershed (e.g., via streams), and the flux of that element into the watershed (e.g., via atmospheric precipitation) are known, the difference between the two can be calculated, and this difference must be due to the sum of all reactions and transformations involving that element which took place within the watershed. Pioneering mass balance studies on weathering profiles and/or small watersheds include those of Garrels and Mackenzie (,51, 52) and Cleaves and Bricker and their... 

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