Choice of system boundary

The conservation law holds for the complete process and any sub-division of the process. The system boundary defines the part of the process being considered. The flows into and out of the system are those crossing the boundary and must balance with material generated or consumed within the boundary. 

Any process can be divided up in an arbitrary way to facilitate the material balance calculations. The judicious choice of the system boundaries can often greatly simplify what would otherwise be difficult and tortuous calculations. 

No hard and fast rules can be given on the selection of suitable boundaries for all types of material balance problems. Selection of the best sub-division for any particular process is a matter of judgement, and depends on insight into the structure of the problem, which can only be gained by practice. The following general rules will serve as a guide  

With complex processes, first take the boundary round the complete process and if possible calculate the flows in and out. Raw materials in, products and by-products out. 

Select the boundaries to sub-divide the process into simple stages and make a balance over each stage separately. 

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Only those flows necessary to illustrate the choice of system boundaries and method of calculation are given in the Solution. 

The correct choice of the basis for a calculation will often determine whether the calculation proves to be simple or complex. As with the choice of system boundaries, no all-embracing rules or procedures can be given for the selection of the right basis for any problem. The selection depends on judgement gained by experience. Some guide rules that will help in the choice are ... 

Each product system consists of a variable number of processes involved in the product life cycle. However, the product under consideration is often related to other processes that may no longer be important for the LCA study. The system boundary serves to the separation of essential and non-essential processes of the product life cycle. Since the choice of system boundaries significantly affects LCA study outcomes and in addition, its intensity and complexity, system boundaries should always be well considered and clearly defined. The choice of system boundaries is carried out with regard to the studied processes, studied environmental impacts and selected complexity of the study. Not-including any life cycle stages, processes or data must be logically reasoned and clearly explained [32]. 

Choice of lattice linear dimensions Lx, Ly (usually Lx = Ly = L, apart from physically anisotropic situations, such as the ANWII model ). Only finite lattices can be simulated. Usually boundary effects are diminished by the choice of periodic boundary conditions, but occasionally studies with free boundaries are made. Note that Lx, Ly must be chosen such that there is no distortion of the expected orderings in the system e.g. for the model of where due to a third nearest neighbor interaction superstructures with unit cells as large as 4 x 4 did occur, L must be a multiple of 4. 

In Chapter 21 we will show that the construction of any environmental model first consists of the appropriate choice of a boundary between the system and the outside world (see Fig. 21.1). Here we choose the simplest possible system [i.e., a homogeneous (completely mixed) box that is connected to the outside world by an input I and an output O, Fig. 12.5]. We consider one single chemical compound that shall be described either by the total amount in the system, M, or by its mean concentration, C=IM/V, where V is the volume of the system. Note that for simplicity we omit the subscript i in the following derivation. Several reaction processes, Rj, act on the compound in the inteior of the system we characterize them by the total rate Rlal ... 

However, several exothermic reactions are characterized by moderate or low values of the B number here, the transition stages from safe to runaway conditions may cover a quite wide range of the parameter values, and the choice of the boundaries for the safe region is very discretional. Hence, not surprisingly, the main discrepancies among the different criteria are found at low B numbers [14, 15]. Moreover, in this case, runaway is a less dramatic phenomenon posing the problem to decide whether a bland explosion still represents a safety issue. In this case, an effective runaway criterion should be more properly determined on the basis of the actual ability of the system to comply with certain levels of temperature and pressure. 

Complex eigenenergies, which appear because of the special choice of the boundary condition, are convenient for describing dissociating systems. In experiment, however, one deals exclusively with real energies. The physical meaning of the imaginary part of the eigenenergy in a spectroscopic... 

Quirke and Sheng have studied the 13-particle Ar-like cluster in detail. Performing MC simulations of much greater length than those of Kaelberer and Etters, they attempted to determine whether the abrupt melting behavior reported by Etters and Kaelberer accurately reflected the physics of the 13-particle system or was merely an artifact of the metastability associated with their choice of free boundary conditions. 

In implementing the above approach, there are no limitations on the geometry of the compartmentalized system or on the nature of the boundary conditions imposed. The price paid for this generality is that the problem must be resolved for every choice of system geometry, and for each temporal boundary condition. One is then left with the task of extracting from the numerical data, in the spirit of an experimentalist, trends and correlations, rather than having at one s disposal an analytic solution from which the... 

Lifecycle assessment begins with the question to be answered, for example, the choice between package A and package B-the goal. The next step is to define the system to be studied, including the choice of appropriate boundaries-the scope. There is, of course, a strong connection between the type of question to be answered... 

Unfortunately at times this approach may result in that the initial choice of performance boundary/requirements is too restrictive. In order to analyze a given engineering system fully it may be necessary to expand the performance boundaries to include other sub-performance systems that strongly affect the operation of the model under study. As an example, a manufacturer finishes products that are mounted on an assembly line and decorate. In an initial study of the secondary decorating operation one may consider it separate from the rest of the assembly line. However, one may find that the optimal batch size and method of attachment sequence are strongly influenced by the operation of the RP fabrication department that produces the fabricated products (as an example problems of contaminated surface and other detriments in the product could interfere with applying the decoration). 

These ideas may seem obvious, but the choice of system and surroundings is not always clear. For example, if the system to be studied is the atmosphere of the earth, the definition of the boundary is somewhat challenging. The atmosphere simply gets gradually less dense, and we must make some arbitrary decision as to where it ends. In most cases, the main requirement is that we be consistent. The same choice of system and surroundings must be used throughout a particular problem, even if the choice is somewhat arbitrary. 

Unfortunately at times this approach may result in that the initial choice of performance boundary/requirements is too restrictive. In order to analyze a given engineering system fully it may be necessary to expand the performance boundaries to include other sub-performance systems that strongly affect the operation of the model under study. As an example, a manufacturer finishes products that are mounted on an assembly line and... 

For example, say we wish to study the piston-cylinder assembly in Figure 1.1. The usual choice of system, surroundings, and boundary are labeled. The boundary is depicted by the dashed line just inside the walls of the cylinder and below the piston. The system contains the gas within the piston-cylinder assembly but not the physical housing. The surroundings are on the other side of the boundary and comprise the rest of the universe. Likewise the system, surroundings, and boundary of an open system are labeled in Figure 1.2. In this case, the inlet and outlet flow streams, labeled in and out, respectively, allow mass to flow into and out of the system, across the system boundary. 

The choice of where to locate the boundary between regions of the system is important. A number of studies have shown that very poor end results will be obtained if this is chosen improperly. There is no rigorous way to choose the best partitioning, but some general rules of thumb can be stated ... 

The study of the peak temperature sensitivity to the reactor operating parameters and the construction of sensitivity boundary curves for stable reactor operation were previously reported ( l). This paper presents a computer study on conceptual relationships between the conversion-product properties and the reactor operating parameters in a plug flow tubular reactor of free radical polymerization. In particular, a contour map of conversion-molecular weight relationships in a reactor of fixed size is presented and the sensitivity of its relationship to the choice of initiator system, solvent system and heat transfer system are discussed. 

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