Input/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... 

The input/output structure defines the material balance boundary of the flowsheet Often it is referred as the inside battery limit envelope. A golden rule requires that the total mass flow of all components entering the process must be equal with the total mass flow of all components leaving it. It should be kept in mind that the recycles affect only the internal process streams, but not the input/output material balance. 

Total Mass Balance (generation = 0. consumption = 0) accumulation = input — output Mass in reactor A/(g) = V (L)p(g/L)... 

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 ... 

Those based on strictly empirical descriptions Mathematical models based on physical and chemical laws (e.g., mass and energy balances, thermodynamics, chemical reaction kinefics) are frequently employed in optimization apphcations. These models are conceptually attractive because a gener model for any system size can be developed before the system is constructed. On the other hand, an empirical model can be devised that simply correlates input-output data without any physiochemical analysis of the process. For... 

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). 

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 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... 

Total mass balance, that is, the sum of inputs has to be equal to the sum of outputs. This will be particularly interesting for long term and generally for continuously operated investigations in order to detect a possible leakage... 

Generally, a continuous recording of electrically available data - for example, current, cell voltage, electrode potentials, temperatures - is beneficial to supervise the proper procedure of each experiment. Especially in case of a failure this will be a valuable help to find the reason. Today, the best way is to use a data acquisition system in a computer that offers the results directly for further calculations, for example, integration of the consumed current (converted charge). For continuously operated experiments the addition of scales, which acquire the weight of input and output reservoirs, will be advantageous in order to supervise the mass balances continuously. 

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