Mass Balance Inputs

Sensible heat Chemical heat Gas composition and mass Dust 

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ENERGY BALANCES. An energy balance may be made for a process, or part of a process, hat is separated from the surroundings by an imaginary boundary. As in a mass balance, input across the boundary must equal output plus any accumulation if conditions are steady and unvarying with time, input equals output. 

Thus, we can easily write the steady-state mass balance, input = output, in these units. The mass balance around the top of the column using the mass balance envelope shown in Figure 12-1 is... 

This section describes a proposed methodology to evaluate the environmental impact of a chemical industrial process chain in the most accurate way possible. It includes a procedure to compute the LCI based on the concept of eco-vectors [Sonneman et al., 2000], Each process stream (feed, product, intermediate or waste) has an associated eco-vector whose elements are expressed as Environmental Loads (EL, e.g. SO2, NOJ per functional unit (ton of main product). All input eco-vectors, corresponding to material or energy streams, have to be distributed among the output streams of the process (or subsystem). In this sense, a balance of each EL of the eco-vector can be stated similarly to the mass-balance (input = output + generation ). This is the reason why all output streams are labelled as products or emissions. The eco-vector has negative elements for the pollutants contained in streams that are emissions and/or waste. Figure 1 illustrates these ideas for an example of a chain of three processes that produces a unique product. The proposed procedure associates inventory data with specific environmental impacts and helps to understand the effect of those impacts in human health, natural resources and the ecosystem. 

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). 

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."... 

Secondly, these quotations emphasize the fact that the same river input that fuels longitudinal heterogeneity in reservoirs also forms a strong link between the reservoir and its watershed (e.g., [6]). This link has been conceptualized mostly in the form of load-response empirical models [7, 8], or mass-balance approaches [9]. Curiously, empirical modelers usually consider reservoirs as stirred reactors, ignoring the longitudinal spatial heterogeneity present in most situations and processes. 

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. 

Closure normally begins by satisfying the overall mass balance i.e., by equating the input and outlet mass flow rates for a steady-state system. For the present case, the outlet flow was measured. The inlet flow was unmeasured so it must be assumed to be equal to the outlet flow. We suppose that A and B are the only reactive components. Then, for a constant-density system, it must be that... 

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.

However, the significance of results from such analyses depends on the quality of the input data. For example, laboratory recipes often do not meticulously document solvent and auxiliary input masses. In many cases, water inputs and waste management are not determined before the pilot stage is reached. Estimates similar to those applied in LCA may be used in order to complete a preliminary mass balance. While such estimations cause considerable uncertainty, it seems more appropriate to evaluate alternatives based on preliminary information, that is, experience-based assumptions concerning the production of substrate or catalyst, than to simply ignore potentially important contributions to the mass balance. 

In the previous discussion of the one- and two-compartment models we have loaded the system with a single-dose D at time zero, and subsequently we observed its transient response until a steady state was reached. It has been shown that an analysis of the response in the central plasma compartment allows to estimate the transfer constants of the system. Once the transfer constants have been established, it is possible to study the behaviour of the model with different types of input functions. The case when the input is delivered at a constant rate during a certain time interval is of special importance. It applies when a drug is delivered by continuous intravenous infusion. We assume that an amount Z) of a drug is delivered during the time of infusion x at a constant rate (Fig. 39.10). The first part of the mass balance differential equation for this one-compartment open system, for times t between 0 and x, is given by ... 

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). 

A total mass balance is necessary, owing to the feed input to the reactor, where... 

Input functions [i.e., I(t)], describing the rate at which the administered dose enters a compartment, may have various forms depending on the administration schedule. The input function /(f) is added to the appropriate mass balance equation and can describe any drug administration pattern. First-order absorption... 

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. 

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