Mass fraction of water

An important property of high-T systems is the reservoir formation porosity and the mass fractions of water and steam occupying the pores. These mass fractions and the formation porosity determine how large a fraction of the heat of the system is stored in the fluid and how large a fraction in the rock. Usually the quantity of heat stored in the reservoir rock is considerably larger than that stored in the fluid. This is particularly the case for vapour-dominated systems. For a liquid-dominated system at 250 °C with 10% porosity and no steam, the quantity of heat stored in the fluid in 1 m3 of reservoir rock is about 87 MJ, but that stored in the rock is some 500 MJ. The corresponding number for the heat stored in steam in a vapour-dominated system is only 5.6 MJ. 

To make the energy balance, we have to know the enthalpy of the 15% solution as a function of temperature. What value should be used for Cp Usually, for not too concentrated solutions, we can assume the Cp of the solution is the Cp of water multiplied by the mass fraction of water in the solution. 

Calculate the mass fraction of water in the turbine exit stream, xg, assuming an isentropic expansion of the steam from P1 to P2 (Equations 5.11.3 and 5.11.11). 

The mass fraction of water in the exit stream for an isentropic process, Xs, is equal to 0.1760. 

A rotary-drum filter filters 20 m /h (706 ft /h) of a calcium carbonate slurry at 20 °C (68 °F). The pressure drop across the cake is 0.658 bar (9.541 psi). If the slimy contains 0.15 mass fraction of calcium carbonate, and the filter cake contains 0.40 mass fraction of water, estimate the surface area of the rotary-drum filter. 

We now know everything about the product, including the mass fraction of water (what is it ). A water balance serves only to check the solution. 

Two systems contain water, acetone, and methyl isobutyi ketone in equilibrium at 25 C. The first system contains equal masses of the three species, and the second one contains 9.0% acetone, 21.0% water, and 70.0% MIBK by mass. Let Xa.aq and Xa.org, respectively, denote the mass fractions of acetone in the aqueous phase (the phase that contains most of the water in the system) and the organic phase (the phase that contains most of the MIBK), and let. r. aq and Xw.org denote the mass fractions of water in the two phases. 

Since the psychrometric chart plots the mass ratio kg HaO/kg dry air rather than the mass fraction of water, it is usually convenient to assume a quantity of dry air in a feed or product stream as a basis of calculation if the chart is to be used in the solution. 

The magnitude of the last term is determined by its coefficient. This is yielded by setting for cp, a mean value (cpa + cpb)/2 = 1.42514kJ/kgK and putting a< — ao = 1, that means that we assume the mass fraction of water vapour to be low a< = 0 in the core flow, and large ao = 1 at the wall, because this is where the water vapour condenses. With a/D = 1 the magnitude of the coefficient is 0.593. As all the other expressions are of order 1 the mass transfer term cannot be neglected. This would only be possible if (ao — ao was very small and of the order 10 A... 

Assuming null all vinegar lost (Li), we have 17 unknown variables (i.e., six streams with two components, that is, water and solutes five streams with one component, i.e., water), 12 mass balance equations, and constraints DOF = 22-E-11-5. The mass transfer becomes a solvable problem if we have 11 independent equation (E). zvl and s,- are the mass fraction of water and dry solutes within the streams, respectively Ri+ l f refers to the vinegar volume withdrawn from the barrel z + 1 and used to refill the barrel z Wt are the water volume lost by evaporation m,- are the mass fluxes z is the number of the barrel (with 1 < i < 5 and 1" is the smaller barrel). 

FIGURE 5.16 Examples of hindered diffusion, (a) The effective diffusion coefficient (D ) of water in various materials as a function of their mass fraction of water (o>w). (Adapted from Bruin and Luyben see Bibliography.) (b) The effective diffusion coefficient (D ) of some molecules and a virus in polymer gels of various concentrations (%). (Very approximate results, obtained from Muhr and Blanshard see Bibliography.)... 

FIGURE 8.2 Approximate water activity ( w) of some foods versus mass fraction of water (w). 

Most authors plot relative reaction rates against water activity, as in Figure 8.10, but this is not always practical, and Figure 8.11, below, gives rates against mass fraction of water w. These figures show that the relations can vary widely. Important factors affecting reaction rates are... 

FIGURE 8.11 First-order reaction rate constants k for heat inactivation, plotted against mass fraction of water w. AP alkaline phosphatase, in skim milk, 80°C. Ec killing of Eschericia coli, in skim milk, 63°C. Ch chymosin, in whey, 80°C. Li lipoxygenase, in sucrose/calcium alginate, 72°C. 

FIGURE 16.5 Glass transition temperature Tg as a function of mass fraction of water i/rw, for some substances (indicated near the curves starch means native wheat starch). 

It was mentioned above that the crystallization of lactose can occur at a critical water content, just above the glass transition. It was further (implicitly) assumed that this would happen at the same mass fraction of water i/fw in skim milk powder. Experiments show that this is not precisely correct but that the critical conditions for crystallization are at the same water activity. Does this imply that the glass transition is determined by aw rather than i//w ... 

In this case, one could ask will the solid stream from the strainer contain any water It might, of course, but this amount is probably very small compared to both the amount of solids that are captured and how much is strained, provided that it is cleaned regularly and designed well. If we make this assumption, then this specifies that the mass fraction of water in the waste stream is zero (or equivalently, that the mass fraction of solids is one). Therefore, we know one additional piece of information and the degrees of freedom for the overall system become zero. 

If there is a higher concentration of a solute on one side of the membrane, there is consequently a lower concoitration of water (as long as total pressures mi both sides of the membrane are approximately equal). In other words, if the mass fraction of solute is higher, the mass fraction of water must be lower. 

In this system, we designate water as species A and air is referred to as species B. The mass fractions are denoted by xa and xb and they are defined as the mass of the individual species divided by the sum of the masses of the species. The molar fractions yx and jb equal the moles of species A or B with respect to the total number of moles. Remember that the total molar density equals for gases. Figure 7.12 demonstrates the evolution of the mass fraction of water as a function of time. The first vertical solid line represents the semi-permeable membrane. The fabric extends from the membrane to the dotted line. Initially, the mass fraction of water in the fabric equals zero. At the beginning of the experiment, the mass fraction of water at the membrane equals one and it is zero in the fabric. As time advances, the mass fraction in the fabric increases (third image from the top). With time, the concentration profile of species A eventually becomes a straight line, as shown in Figure 7.12. 

The droplet surface temperature (TJ and surface mass fraction of water and fuel (F vs and Fps) are obtained from the liquid phase and interface equations, to be discussed later. The fractional mass vaporization rate of fuel (ef) is obtained from (40.4). The mass vaporization rate is then calculated using (40.5) and (40.7). Using (40.1) and (40.2a and b), H may be calculated. The transient heating rate of droplet, 2l is obtained from (40.3). 

To view the data in a graphical manner, we shall borrow an idea from Section 2.1.2 and plot the mass fraction of NaCl and H2O, each on an axis in two-dimensional mass fraction space. For this particular example, we choose the x-axis to represent the mass fraction of NaCl in solution the mass fraction of water in solution is then placed on the y-axis. 

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