Mole balance

The calculation for a point on the flash curve that is intermediate between the bubble point and the dew point is referred to as an isothermal-flash calculation because To is specified. Except for an ideal binary mixture, procedures for calculating an isothermal flash are iterative. A popular method is the following due to Rachford and Rice [I. Pet. Technol, 4(10), sec. 1, p. 19, and sec. 2, p. 3 (October 1952)]. The component mole balance (FZi = Vy, + LXi), phase-distribution relation (K = yJXi), and total mole balance (F = V + L) can be combined to give... 

Equation (13-14) is solved iteratively for V/F, followed by the calculation of values ofx, andy from Eqs. (13-12) and (13-13) andL from the total mole balance. Any one of a number of numerical root-finding... 

In Fig. 13-25, ifPg and the feed-stream conditions (i.e., F, Zi, T, Pi) are known, then the calculation of T9, V, L, yi, and Xi is referred to as an adiabatic flash. In addition to Eqs. (13-12) to (13-14) and the total mole balance, the following energy balance around both the valve and the flash drum combined must be included ... 

Taking a basis of F = 1.0 mol and eliminating L with the total mole balance, Eq. (13-17) becomes... 

Component mole balances for total-coudeuser-reflux drum, trays, and reboiler, respectively ... 

Since the volume depends on conversion or time in a constant pressure batch reactor, consider the mole balance in relation to the fractional conversion X. From the stoichiometry. 

Since two moles of B are formed for every mole of A that disappears, then the mole balance table becomes... 

Note that from Eqs. (7.17) and (7.18), R EmCw(0/EpCp(O) for t > Tlag- The substitution of the apparent partition coefficient with the retention ratio allows us to state the mole balance at time t (provided t > Tlag) in a much simplified form ... 

Figure AC-2 shows the quantities represented by the mole balance of Equation AC-7. The mole balance is honored only if point M lies on the straight line between points R and S. This can be shown in Figure AC-2 using similar triangles.2...

For isothermal, first-order chemical reactions, the mole balances form a system of linear equations. A non-ideal reactor can then be modeled as a collection of Lagrangian fluid elements moving independe n tly through the system. When parameterized by the amount of time it has spent in the system (i.e., its residence time), each fluid element behaves as abatch reactor. The species concentrations for such a system can be completely characterized by the inlet concentrations, the chemical rate constants, and the residence time distribution (RTD) of the reactor. The latter can be found from simple tracer experiments carried out under identical flow conditions. A brief overview of RTD theory is given below. 

The CSTR model, on the other hand, is based on a stirred vessel with continuous inflow and outflow (see Fig. 1.2). The principal assumption made when deriving the model is that the vessel is stirred vigorously enough to eliminate all concentration gradients inside the reactor (i.e., the assumption of well stirred). The outlet concentrations will then be identical to the reactor concentrations, and a simple mole balance yields the CSTR model equation ... 

Denoting the transport rate of fluid from zone i to zone j by a zone model can be expressed mathematically in terms of mole balances for each of the N zones ... 

The batch electrolyzer discussed in detail by Scott31 for the reversible process of type Az+ + ze <-> B is employed for illustration. With no discharged product at zero time, the governing mole balances may be written as (Eqs. 2.20 and 2.21 in Ref.31) ... 

In studying residence time distribution in a tank-flow electrolyzer, a tracer injected into it is recovered in a mixing tank placed downstream. If both tanks are perfectly stirred, then with a tracer pulse, the mole balance for the tracer can be written as... 

In this context, the mole balance for a reacting element (e.g., active ion) ... 

Stoichacmetry and reaction equilibria. Homogeneous reactions kinetics. Mole balances batch, continuous-shn-ed tank and plug flow reactors. Collection and analysis of rate data. Catalytic reaction kinetics and isothermal catalytic radar desttpi. Diffusion effects. 

Figure 5. Titration of a suspension of Ti02 in KNOj at three different concentrations. CTq is the protonic surface charge, calculated from the acid-base mole balance equations, specific surface area of 20 nr g" and the solids...

The remaining equations are phase equilibria for ammonia (eq. K4) and water (eq. K5), mass balances for ammonia (eq. XV) and hydrogen sulfide (eq. XVII), the condition of bulk electroneutrality (eq. XIX), the mole balance in the vapor phase (eq. XX), and the assumption that, for the ammonia-rich systems considered exclusively, in the mass balance for the liquid hydrogen sulfide may be neglected. The system of eight equations can easily be solved ... 

Mole balance expressions were developed for a general series reaction by Agarwalla and Lund [16], and the same procedures were used here to develop the species balance equations shown in Table I. Boundary conditions and parameter definitions are presented in Tables II and III. Note that the boundary conditions are given only for co-current flow of reactants and inert, which is the only configuration studied. Previous work [16], has shown that counter-current operation is less effective than co-current operation. 

The total moles of added M (= C1 VM) must equal the moles of MJ in solution (= [MxJ(Vm + V ) plus the moles of precipitated MX(i). (This equality is called a mass balance, even though it is really a mole balance). In a similar manner, we can write a mass balance for X. 

For the model involving a desorption limitation (model c) a component mole balance is written over the gas phase and crystallite phase for product D (A + B - D). These are, respectively ... 

It is useful to examine the consequences of a closed ion source on kinetics measurements. We approach this with a simple mathematical model from which it is possible to make quantitative estimates of the distortion of concentration-time curves due to the ion source residence time. The ion source pressure is normally low enough that flow through it is in the Knudsen regime where all collisions are with the walls, backmixing is complete, and the source can be treated as a continuous stirred tank reactor (CSTR). The isothermal mole balance with a first-order reaction occurring in the source can be written as... 

A) The hydrogen-ion dynamic mole balances in the two compartments are given by... 

Note that the entries of f feed have already been incorporated into the equations (A) to (E) on p. 226 to 227. The eight component functions Fjy for k = 1,. ..,4 and j = 1,2 are the dynamic mole balance equations in normalized form. They are given in equations (4.103) to (4.106) as follows. 

---