Fluid volume

AletabolicFunctions. The chlorides are essential in the homeostatic processes maintaining fluid volume, osmotic pressure, and acid—base equihbria (11). Most chloride is present in body fluids a Htde is in bone salts. Chloride is the principal anion accompanying Na" in the extracellular fluid. Less than 15 wt % of the CF is associated with K" in the intracellular fluid. Chloride passively and freely diffuses between intra- and extracellular fluids through the cell membrane. If chloride diffuses freely, but most CF remains in the extracellular fluid, it follows that there is some restriction on the diffusion of phosphate. As of this writing (ca 1994), the nature of this restriction has not been conclusively estabUshed. There may be a transport device (60), or cell membranes may not be very permeable to phosphate ions minimising the loss of HPO from intracellular fluid (61). 

Urea Pharmacokinetics. Pharmacokinetics summarizes the relationships between solute generation, solute removal, and concentration in a patient s blood stream. In the context of hemodialysis, this analysis is most readily appHed to urea, which has, as a consequence, become a surrogate for other uremic toxins in the quantitation of therapy and in attempts to describe its adequacy. In the simplest case, a patient is assumed to have no residual renal function. Urea is generated from the breakdown of dietary protein, accumulates in a single pool equivalent to the patient s fluid volume, and is removed uniformly from that pool during hemodialysis. A mass balance around the patient yields the following differential equation ... 

Two general cases are considered (1) adsorption under conditions of constant or nearly constant external solution concentration (equivalent to infinite fluid volume) and (2) adsorption in a batch with finite volume. In the latter case, the fluid concentration varies from cf to when equihbrium is eventually attained. = (cf — =... 

For a Langmuir isotherm with neghgible solute accumulation in the particle pores, the solution for an infinite fluid volume ... 

For a finite fluid volume (A > 0), the fractional approach to equihbrium is given by b l-R-... 

For a constant diffiisivity and an infinite fluid volume the solution is F=l-- y 4rexp (16-96)... 

For values of F > 0.8, the first term n = I) in Eq. (16-96) is generally sufficient. If the controUing resistance is diffusion in the subpai ticles of a bidispersed adsorbent, Eq. (16-96) apphes with /y replacing / p. For a finite fluid volume the solution is ... 

FIG. 16-14 Constant separation factor batch adsorption curves for external mass-transfer control with an infinite fluid volume and n j = 0. 

A numerical solution of this equation for a constant surface concentration (infinite fluid volume) is given by Garg and Ruthven [Chem. Eng. ScL, 27, 417 (1972)]. The solution depends on the value of A. = n i — n )/ n — n ). Because of the effect of adsorbate concentration on the effective diffusivity, for large concentration steps adsorption is faster than desorption, while for small concentration steps, when D, can be taken to he essentially constant, adsorption and desorption curves are mirror images of each other as predicted by Eq. (16-96) see Ruthven, gen. refs., p. 175. 

In binary ion-exchange, intraparticle mass transfer is described by Eq. (16-75) and is dependent on the ionic self diffusivities of the exchanging counterions. A numerical solution of the corresponding conseiwation equation for spherical particles with an infinite fluid volume is given by Helfferich and Plesset [J. Chem. Phy.s., 66, 28, 418... 

FIG. 16-16 Batch adsorption curves for solid diffusion control. The curve for A = 0 corresponds to an infinite fluid volume (adapted from Ruthven, gen. refs., with permission). 

For a linear isotherm tij = KjCj), this equation is identical to the con-seiwation equation for sohd diffusion, except that the solid diffusivity D,i is replaced by the equivalent diffusivity = pDj,i/ p + Ppi< ). Thus, Eqs. (16-96) and (16-99) can be used for pore diffusion control with infinite and finite fluid volumes simply by replacing D,j with D. When the adsorption isotherm is nonhnear, a numerical solution is... 

In the irreversible limit R < 0.1), the adsorption front within the particle approaches a shock transition separating an inner core into which the adsorbate has not yet penetrated from an outer layer in which the adsorbed phase concentration is uniform at the saturation value. The dynamics of this process is described approximately by the shrinldng-core model [Yagi and Kunii, Chem. Eng. (Japan), 19, 500 (1955)]. For an infinite fluid volume, the solution is ... 

External Mass Transfer and Intraparticle Diffusion Control With a linear isotherm, the solution for combined external mass transfer and pore diffusion control with an infinite fluid volume is (Crank, Mathematics of Diffusion, 2d ed., Clarendon Press, 1975) ... 

In the irreversible limit, the sohidon for combined external resistance and pore diffusion with infinite fluid volume is (Yagi and Knnii) ... 

Bidispersed Particles For particles of radius Cp comprising adsorptive subparticles of radius r, that define a macropore network, conservation equations are needed to describe transport both within the macropores and within the subparticles and are given in Table 16-11, item D. Detailed equations and solutions for a hnear isotherm are given in Ruthven (gen. refs., p. 183) and Ruckenstein et al. [Chem. Eng. Sci., 26, 1306 (1971)]. The solution for a linear isotherm with no external resistance and an infinite fluid volume is ... 

Lee [AJChE J., 24, 531 (1978)] mes the solution for batch adsorption with bidispersed particles for the case of a finite fluid volume. 

This form is partieularly appropriate when the gas is of low solubility in the liquid and "liquid film resistanee" eontrols the rate of transfer. More eomplex forms whieh use an overall mass transfer eoeffieient whieh ineludes the effeets of gas film resistanee must be used otherwise. Also, if ehemieal reaetions are involved, they are not rate limiting. The approaeh given here, however, illustrates the required ealeulation steps. The nature of the mixing or agitation primarily affeets the interfaeial area per unit volume, a. The liquid phase mass transfer eoeffieient, kL, is primarily a funetion of the physieal properties of the fluid. The interfaeial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dj, whieh is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraetion of the total fluid volume (gas plus liquid) whieh is oeeupied by gas bubbles. 

The integrity of mammalian kidneys is vital to body homeostasis, because the kidneys play the principal role in the excretion of metabolic wastes and the regulation of extracellular fluid volume, electrolyte balance, and acid-base... 

Heat or contaminant. sources can also be assigned to parts of the fluid volume to account for very small real sources or a distribution of a large number of small sources. Care must be taken, however, to make sure that this representation of distributed sources describes correctly the real situation (see the earlier section Geometric Modeling ). 

Explosion energy can be calculated by employing a slight variation on Eq. (6.3.26), by multiplying expansion work per unit volume by fluid volume, instead of multiplying expansion work per unit mass by fluid mass. Both propane and butane must be considered. This gives, for example, for vapor energy for the 50% fill-ratio case ... 

Abnormal Formation Pressure Detection from Kicks. The kicks, or flow of formation fluids into the borehole, are the ultimate indication that the well has encountered an overpressured zone. Kick detection during drilling usually is achieved by use of a pit-volume indicator and/or a flow indicator. The usual pit-volume alert is 10 barrels drilling fluid volume increase. A differential mud flow indicator can also be used to detect kicks more quickly. 

If the kick is gained while tripping, the only warning signal we have is an increase in fluid volume at the surface (pit gain). Once it is determined that the pressure overbalance is lost, the well must be closed as quickly as possible. The sequence of operations involved in closing the well is as follows ... 

---