# Course in Modern Icelandic by Jon Fridjonsson

By Jon Fridjonsson

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Extra info for Course in Modern Icelandic

Example text

The local equilibrium assumption, used in the majority of the cases dealt with in this text and in the remainder of this chapter, is discussed more below. Table 2-2 summarizes the overall balance equations needed for a complete description of isothermal, multicomponent, multiphase flow in permeable media. Column 1 in Table 2-2 gives the differential form of the equation named in column 2. Column 3 gives the number of scalar equations represented by the equation in column 1. Columns 4 and 5 give the identity and number of independent variables added to the formulation by the equation in column 1.

Here we consider only the rate of work done against a pressure field WPV , although other types of work could be included (see exercise 2P). In this derivation, there is no compression or expansion work done on volume V since it is assumed to be fixed. 28 Returning to Fig. 2-4(b), consider an element in the multiphase, multicomponent flow field crossing ΔA. Since work is the product of force times a distance, the rate of work is force times a velocity. The element crossing ΔA is, therefore, doing work ΔWPV , where NP ΔWPV = −∑ Pj ΔAn iu j .

A careful examination of the possible configurations shows further that a state with one or two molecules on each side is more likely to exist than the initial state, which has a probability of only 2-4 or 1/16, the initial state being just one of 16 possible states. A true equilibrium state with two molecules on either side of the original partition (no gradients) is also more likely to exist (probability of 6/16 or 3/8) than the initial state. 35 Figure 2-6: Illustration of configurations for four molecules in a closed composite system (after Smith et al.