E. J. REEVES
M agnolia P etroleu m C om pany, B eau m on t, Texas
A
useful relation is derived fo r calcu latin g op tim u m dilution in viscous liqu id filtration. T his relation is based on an em pirical equ ation w h ich was developed fo r expressing viscosity o f filtrate as a fu n ctio n o f solvent diluLion.
By using pertinen t m a th em a tica l equations, the m eth od cun be adapted to d ilu tion filtration o f any viscous liquid.
Observed and calculated data are shown to he in good agreement.
V
ISCOSITY of the liquid subjected to filtering operation is one of the major factors governing filtering rates. Assuming all other variables constant, the rate of filtration is inversely proportional to the absolute viscosity of the filtrate; this sug
gests dilution of viscous liquids with nonviscous solvents in order to increase the filter output.
Diluent, Volume Per Cent but an increase in the amount of the solvent-free material in the filtrate. This shows that for raising the efficiency of filtering operations dilutions should not exceed a certain optimum, which varies with the nature of the material to be filtered. The opti
mum dilution is determined normally on the basis of plant experi
ence; however, it can be calculated mathematically from the known properties of the involved materials. The method de
scribed in this paper applies to filtration of petroleum oils in de- waxing operations but may be easily adapted to other engineering problems of a similar nature by employing pertinent mathemati
cal relations.
The general Poiseuille equation (2) for homogeneous sludges may be presented in the following form:
dV
Add y.[a{W/A) + r] (1)
Integration of Equation 1 for constant pressure filtration gives the relation between time and filtrate.
Assuming that F represents the fraction of solvent in the total filtrate, the rate of oil flow through the filter may be obtained by dividing Equation 2 by (1 — F); this leads to the expression
0 The solvent fraction and viscosity of the total filtrate in Equa
tion 3 are interdependent variables and should be expressed in the same terms in order to permit further analysis of the problem.
This requires determination of the function connecting the two variables.
Up to the present time no satisfactory relation has been found which could be employed for this purpose. This work was undertaken, therefore, to derive a relation which would hold over a reasonable dilution range commonly encountered in commercial practice. A large number of blends involving various types of commercial products and solvents was prepared and tested:
Oil A
dewaxed mid-continent distillate of 160-second S.U.V.
at 100° F.
solvent-treated and dewaxed mid-continent, neutral of 105-second S.U.V. at 100° F.
solvent-treated and dewaxed mid-continent residual oil of 103-second S.U.V. at 210° F.
solvent-treated and dewaxed mid-continent residual oil of 98-second S.U.V. at 210° F.
solvent-treated and dewaxed mid-continent neutral of 150-second S.U.V. at 100° F. Figure 2. Paraffinic Oil M ixtures with Low V iscosity D iluents at
2 0 4 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 39, No. 2 terms of viscosity of undiluted oils (S).
Validity of Equation 4 was verified further by employing data already available in the literature ( f ). Some of these data are presented in Tables IV and V and Figures 4 and 5.
The use of Equation 4 permits elimination of the viscosity fac
tor from Equation 3, which is reduced to the following form:
1 _ F y r ß a / W \ ß r l
R 1 - F [_ 2 P \ R / + P j (5) Equation 5 can be used for determining the optimum dilution by differentiating R with respect to F and equating the resulting derivative to zero to find the maxima of the function. The first
When equating Equation 6 to zero the only equation of interest is
February 1947 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 20 5 the maximum point. These points are
F =
+ x (9)
( 1 0 )
The optimum quantity of solvent is determined by substituting this value of 7 in Equation 8:
F = -4 .4 8
0.818 7 - 1 - 4 . 4 8 - 1
Optimum composition of the filtrate is, therefore,
(12)
S olvent, vol. % Oil, vol. %
81.8 18.2
In actual plant operations, dilutions are not based on wax-free filtrate, but on oil charge. Correction for the wax fraction is therefore important and can be made by using the relation
S = F
Thus, optimum filter charge composition is
S olven t, v o l. %
tion 9 is negative, and that determined by Equation 10 is positive.
This change in the slope of the curve defined by Equation 5 defi
nitely proves the existence of a maximum.
The use of Equation 8 for solution of practical problems is dem
onstrated by the following example; the laboratory data were
Substituting these data in Equation 4 the value of the constant y is
7 = - 4 . 4 8 (1 1 )
The recommended method was tested in commercial practice and found to be satisfactory for establishing operating condi
tions at dewaxing units. Calculated and observed optimum dilutions for various lubricating oil fractions are shown in the following table;
O ptim u m D ilu tion L u bricating Oil Fraction
M id -con tin en t distillate 145-sec. S .U .V . at 100° F.
S olvent-treated, m id-contin ent neutral 105-sec.
S .U .V . at 100° F .
S olvent-treated, m id-contin ent neutral 185-sec.
S .U .V . at 100° F.
S olven t-treated, m id-contin ent residual 96-sec.
S .U .V . at 210° F.
S olven t-treated, m id-contin ent residual 120-sec S .U .V . at 210 ° F.
A cid-treated, m id-contin ent residual 190-sec.
S.U .V . at 210° F.
206 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 39, No. 2 N O M E N C L A T U R E
A — area of filtering surface
F — fraction of solvent in total filtrate
P = pressure drop through filter medium and cake r — filter medium resistance
R = solvent-free liquors rate per unit area S = fraction of solvent in waxy oil charge v — volume per cent wax in oil charge V = volume of filtrate
IF = weight of dry cake solids a = average specific cake resistance /3 = viscosity of diluent
y = slope of viscosity-solvent fraction curve 0 = time
n — viscosity of filtrate X = incremental value of F
A C K N O W L E D G M E N T
The writer would like to express his appreciation to J. W. New
ton, W. W. Leach, P. L. Smith, and V. A. Kalichevsky for per
mission to publish this manuscript.
L IT E R A T U R E C ITE D
(1) Ira n y , E rn est P ., J . A m . Chem. Soc., 60, 2 1 0 6 -1 5 (1 9 3 8 ); 61, 17 3 4 -9 (1 9 3 9 ); 6 3 ,2 6 1 1 -1 7 (1 941).
(2) P erry, J oh n H ., C h em ical E ngineers' H a n d b o o k , 2nd ed., p.
1654, N e w Y o rk , M cG ra w -H ill B o o k C o ., In c ., 1941.
(3) T au sz et ed., Petroleum Z ., 26, 1117-2 4, 1 1 29-4 0 (1 9 3 0 ); 26, 4 1 -3 (1 9 3 1 ); 28, N o . 45, 1 -1 0 (1 9 3 3 ); 29, N o . 24, 1 -3 (1933);
Erdöl u . Tecr, 8, 3 9 6 -8 (1 9 3 2 ); Z . angew. Chem., 44, 884-6 (1 9 3 1 ); R oegiers, Ibid ., 45, 3 2 0 -3 (1932).
P r e s e n t e d b efore the D iv ision o f P etroleum C hem istry a t the 110th Meet
ing o f tho A m e r i c a n C h e m i c a l S o c i e t y , C h ica go, 111.