Variablerate And Pressure Filtration

The dynamics of variable-rate and -pressure filiations can be illustrated by pressure profiles that exist across the filter medium. Figure 7 shows the graphical representation of those profiles. According to this plot, the compressed force in the cake section is:

where p, = pressure exerted on the sludge over the entire cake thickness ps = static pressure over the same section of cake p corresponds to the local specific cake resistance (rw)x. At the sludge-cake interface ps( = pj and p = 0; and for the interface between the cake and filter plate pst = pst and p = p, -p's(. p'sl corresponds to the resistance of filter plate pf, and is expressed where W = rate of filtration (m3/m2-sec).

Figure 7. Distribution of static pressure pst in liquid and p along the cake thickness and filter plate: I, II -boundaries between the cake and sludge at x" and t'; III, IV-boundaries between cake layers or cake and filter plate at x" and t' ; V- boundary line between the cake and filter plate or free surface of filter plate; 1,3-curves p^f^) and p=f(hoc) at t'; 2, 4 -curves ps[=f(hoc) and

Figure 7. Distribution of static pressure pst in liquid and p along the cake thickness and filter plate: I, II -boundaries between the cake and sludge at x" and t'; III, IV-boundaries between cake layers or cake and filter plate at x" and t' ; V- boundary line between the cake and filter plate or free surface of filter plate; 1,3-curves p^f^) and p=f(hoc) at t'; 2, 4 -curves ps[=f(hoc) and

Note that Apr is constant during the operation. Pressure p is also the driving force of the process. Therefore, starting from the governing filtration equations, the general expression for an infinitesimal increment of solid particle weight in a cake of unit of area is xwdq (q = filtrate volume obtained from 1 m2 filtering area, m3/m2). The responding increment dp may be expressed as:

xw is not sensitive to changes in p. In practice, an average value for xw can be assumed. Note that W is constant for any cross section of the cake. Hence, Equation 33 may he integrated over the cake thickness between the limits of p = 0 and p=p, -p'sl, from q = 0 to q = q:

l*xwW

Parameters q and W are variables when filtration conditions change. Coefficient (rw)x is a function of pressure:

The exact relationship can be derived from experiments in a device called a compression-permeability cell. Once this relationship is defined, the integral of the right side of Equation 34 may be evaluated analytically (or if the relationship is in the form of a curve, the evaluation may be made graphically). The interrelation between W and Pi is established by the pump characteristics, which define q = f(W) in Equation 34. Filtration time may then be determined from the following definition:

dq dx

Hence,

Waste Management And Control

Waste Management And Control

Get All The Support And Guidance You Need To Be A Success At Understanding Waste Management. This Book Is One Of The Most Valuable Resources In The World When It Comes To The Truth about Environment, Waste and Landfills.

Get My Free Ebook


Post a comment