Optimum Dilution in Viscous I
Liquid Filtration E. J. REEVES Magnolia Petroleum Company, Beaumont, Texas
A useful relation is derived for calculating optimum dilution i n viscous liquid filtration. This relation is based on an empirical equation which was developed for expressing viscosity of filtrate as a function of solvent dilution. By using pertinent mathematical equations, the method can be adapted to dilution filtration of any viscous liquid. Observed and calculated data are shown to be in good agreement.
Integration of Equation 1 for constant pressure filtration gives tlhe 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
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 suggests dilution of viscous liquids with nonviscous solvents in order to increase the filter output.
50
100 50 100 Diluent, Volume Per Cent
50
Figure 1. Paraffinic Oil Mixtures with Low Viscosity Diluents at 54.4" C.
The solvent fraction and viscosity of the total filtrate in Equation 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 tlyo 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. a t 100" F. Oil B = solvent-treated and dewaxed mid-continent neutral of 105-second S.U.V. a t 100' F. Oil C = solvent-treated and dewaxed mid-continent residual oil of 103-second S.U.V. a t 210" F. Oil D = solvent-treated and dewaxed mid-continent residual oil of 98-second S.U.V. a t 210" F. Oil E = solvent-treated and dewaxed mid-continent neutral of 150-second S.U.V. a t 100' F. Oil F = solventtreated and deuaxed mid-continent neutral 6.0 of 150-second S.U.V. a t 100" F. v) 4.0 Oil , G = solvent.-$5 treated and dewaxed 2 mid-continent residual + 2.0 oil of 98-second S.U.V. 8 a t 210" F. 1.0 Oil H = solvent2 0.8 treated and dewaxed mid-continent residual 2 oil of 125-second S.U.V. ca t 210" F. b 2.0 On the basis of this 8 information, the most .$ 1.0 pertinent portions of xhich are presented 0.5 in Tables I, 11, and 50 100 50 100 111, and Figures 1, 2, and 3, the following Diluent, Volume Per Cent relation was found to Figure 2. Paraffinic Oil RIixtures hold for the values with Low Viscosity Diluents at of F ranging from 37.8" c.
100 "
Curve numbers on all figures refer to system numbers in corresponding- tables.
In applying this procedure to practical problems, the major consideration is not an increase in the total quantity of filtrate, 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 optimum dilution is determined normally on the basis of plant experience; however, it can be calculated mathematically from the known properties of the involved materials. The method described in this paper applies to filtration of petroleum oils in dewaxing operations but may be easily adapted t o other engineering problems of a similar nature by employing pertinent mathematical relations. The general Poiseuille equation ( g ) for 'homogeneous sludges may be presented in the following form:
dV
Ade
P
+
= ,U[a(W/A)
E
.3
TI
203
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
204
Vol. 39, No. 2
TABLEI. PARAFFINIC OIL MIXTURESWITH Lorn VI~COSITY TABLEIT. PARAFFINIC OIL MIXTURESWITH LOWVISCOSITY DILCENTS m 84.4 a C. DILUENTB AT 20" C. ( 1 ) 1. Oil A
2.
Oil B
Diluents, Vol. So 90 SO 70 60 50 90 80 70 60
+ methyl ethyl ketone + toluene
Viscosity, Centipoises 0 63 0 77 0 52 1 20
1.54
0 0 0 0
54 60 73 92
1. Oil No. 1 2.
Oil S o . 1 $. benzene
3.
011 S o . 2
4. Oil No. 3
4. Oil D
6. Oil A
+ toluene
90 80 70 60 50 90 80 70
+ toluene
50
0.56 0.75 1,lO P.55 2.16
+ heptane
TABLEv.
+ kerosene + ligroin
1. Oil D
2.
Oil D
+ methyl ethyl ketone + naphtha
Diluents, Vol. % 90 SO 70 60 50
Viscosity, Centipoises 0.50 0.69
90 80 60 50
0.58 1.51 2.21 3.31 5.84
90 80 70 60 50
0 52 0.63 0.81 1.04 . 1.43
70
3
Oil E
+ 50% methyl ethyl ketone-6OC/( toluene
VOL
1. Oil No. 5
+ heptane
3.
Oil KO.6
+ heptane
2,
Oil KO.5
+ heptane
At 00
ben-
100 90 SO
70
3.
60 50
+
Oil H 40% methyl ethyl ketone-40% benEene-ZO% toluene
6. 011G 4- 40% methyl ethyl ketone-405 benzene-20% toluene
2.
4.
At 15 5' C . 011F 40% methyl ethyl ketone-40% beneene-20% toluene
+
+ 40% methyl ethyl ketone-40% mqe-ZO% toluene Oil H
100
50 80 70 60 100 90 80 70 60
100 90 80 70 60
50 ben-
100
90
80
70 60
6. Oil G + 40% methyl ethyl ketone-40% benrene-20% toluene
100
90
80 70 60
100 74.9 49.9
0.57 1.39 4.56 0.57 1.54 6.35
100 75.2 50.2
0.47 1.01 2.98
100 75.1 50.2
0.47 1.09 3.66 0.47 1.00 2.72
ltfl ,5.0 50.0
c.
+ heptane
100 95.1 50.1
i:ig
Viscosity, Centipoises
4t 37 8' C2.
+ 40% methyl ethyl ketone-40yc ~ e n e - 2 0 7toluene ~
1. Oil F
Oil No. 7
Viscosity Centipoisis
c.
4. Oil No. 6 f heptane 6.
%
1.68
OIL MIXTURESWITH Loa. VISCOSITY TABLE111. PARAFFINIC DILCESTS AT 37.8" c. AK'D IS.5' c. Diluents, Vol. %
0.47 1.15 3.41 0.65 1.26 3.26 1.92 0 15 12 47 14 01 0.66 2.69 8.35
Diluents,
PAR.4FFIXIC OIL MIXTURES WITH LOW \-ISCOSITY
DILUENTS AT 37.8" C.
100 74.7 54.2 100 74.8 49.6
N.4PHTHENIC O I L MIXTCRES WITH LOTV VISCOSITY DILCEKTS AT 0 " A44ND20" 6. ( 1 )
At 200
TABLE11.
Viscosity, Centipoises
100 74 4 61 3 59 8 100 69.3 50.4
0.52
0.61 0.75 0.99 1.27
Diluents, Vol.
0 42 0'66 0 85 1.21 1.74 0 42 0.59 0.83 1.22 1.90 0.42 0.58 0.82
1.20 1.81
0.5 to 1.0-that curve :
is, for the most important fraction of the (4)
p = $ F y
This equation is somewhat similar in form t o the one developed by Tausz and Roegiers expressing viscosity of diluted oils in terms of viscosity of undiluted oils (3). Validity of Equation 4 was verified further by employing data already available in %heliterature (1). 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 factor from Equation 3, which is reduced to the following form:
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 derivative is equal to
0.64
0:ss
1.17 1.77 2.68 0.54 0.78 1.14
1.77 2.98 0.54 0.76 1.12 1.73 2.80
When equating Equation 6 to zero the only equation of interest is (y
- 1) - Y F - i
==
0
(7)
From this equation it follows thst the optimum dilution is equal to
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
February 1947
VI
205
The optimum quantity of solvent is determined by substituting this value of y in Equation 8:
3.0
.8 2.0 0
1,
+
. 3
8 1.0
u
Optimum composition of the filtrate is, therefore,
$0.5
%
Rolvent, vol. % Oil, vol. %
3
g 2.0
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
h
3
2 1.0
::
6
81.8 18.2
0.5
S =
F+50
100 50 100 Diluent, Volume Per Cent
50
F 1-F
100
1 - v
Assuming 14 volume 7 0 wax in the oil charge, the optimum dilution of the oil charge is
Figure 3. Paraffinic Oil Mixtures with Low Viscosity Diluents at 37.8" and 15.5' C.
S =
0.818 1 - 0.818 = 0.794 0.81' + 1 0.14
(14)
-
Thus, optimum filter charge composition is Solvent, vol. % W a s y oil, vol. %
79.4 20.6
6.0
g 4.0
." B '3 2.0 u3 v)
- 1.0
21
4 13
Diluent, Volume Per Cent
0.5
Figure 4. Paraffinic Oil Mixtures with Low Viscosity Diluents at 20" C.
%.
.e 0
3.0 2.0
3
The proof that Equation 6 gives a maximum of the function when equated to zero is obtained by determinfng the partial derivative of R with respect to F a t values of F above and below the maximum point,. These points are
8 6 1.0 0.5
50
100
50
50 100 Diluent, Volume Per Cent
100
Figure 5. Naphthenic Oil Mixtures with b w Viscbsity Diluents at 0' and 20' C.
The first partial derivative at the point determined by Equation 9 is negative, and that determined by Equation 10 is positive. This change in the slope of the curve defined by Equation 5 definitely proves the existence of a maximum. The use of Equation 8 for solution of practical problems is demonstrated by the following example; the laboratory data were secured on diluting a wax-free oil with solvent. The table presents the properties of a dewaxed lubricating oil of 126-second Saybolt Universal Viscosity (S.U.V.) a t 210' F. diluted with methyl ethyl ketone-benzene-toluene mixture: Solvent fraction, vol. % Viscosity a t filtering temp., centipoises
y
0.60 6.26
0.90 102
Substituting these data in Equation 4 the value of the constant is
.
y =
-4.48
(11)
The recommended method was tested in commercial practice and found to be satisfactory for establishing operating oonditions at dewaxing units. Calculated and observed optimum dilutions for various lubricating oil fractions are shown in the following table : Lubricating Oil Fraction Mid-continent distillate 145-seo. S.U.V. a t looo F. Solvent-treated, mid-continent neutral 105-sec. S.U.V a t 100' F. Solvent-treated, mid-continent neutral 185-seo. S.U.V. a t 100" F. Solvent-treated, mid-continent residual 96-sec. S.U.V. a t 210 Solvent-treated,Ozd-continentresidual 120-seo S.V.V. a t 210". F. Acid-treated, mid-continenc residual 190-sec. S.U.V. a t 210' 17.
Optimum Dilution 0bsvd.a Calcd. 67 67 66
87
68
68
76
76
78
79
a2
82
Observed dilutions were determined in commeroirtl operation of s methyl-ethyl-ketone dewaxing unit.
INDUSTRIAL AND ENGINEERING CHEMISTRY
206
A = area of filtering surface F = fraction of solvent in total filtrate P = pressure drop through filter medium and cake
r
Vol. 39, No. 2
QCKNOWLEDGMENT
NOMENCLATURE
The writer would like to express his appreciat,ionto J. W. Ncwt'on, W. W. Leach, P. L. Smith, and T'. A. Kalichevsky for permission to publish this manuscript.
= filter medium resistance
R = solvent-free liquors rate per unit area S = fraction of solvent in ryasy oil charge
LITERATURE CITED
v
(1) I r a n y , E r n e s t P., J . Am. Chem. SOC..60, 2106-16 ( 1 9 3 8 ) ; 61, 1734-9 ( 1 9 3 9 ) ; 63, 2611-17 ( 1 9 4 1 ) . (2) Perry, J o h n H., C h e m i c a l E n g i n e e r s ' H a n d b o o k , 2 n d e d . , p. 1684. New York, McGraw-Hill Book Co., Inc., 1941. (3) Tausz et al., Petroleum Z . , 26, 1117-24, 1129-40 ( 1 9 3 0 ) ; 26, 41-3 ( 1 9 3 1 ) ; 28, NO. 45, 1-10 (1933); 29, NO,24. 1--3 (1933); Erdol u. Teer, 8, 396-8 ( 1 9 3 2 ) ; 2. angew. Chem., 44, 8844 ( 1 9 3 1 ) ; Roegicrs, Ibid., 45, 320-3 (1932).
= volume per cent wax in oil charge V = volume of filtrate W = w i g h t of dry cake solids = average specific cake resistance p = viscosity of diluent y = slope of viscosity-solvent fraction curve e = time p = viscosity of filtrate x = incremental value of E'
PRESEKTED before the Division of Petroleum Chemistry a t the 110th Meet,i n s of the A M E R I C A N CHEMICAL SOCIETY,Chicago, Ill.
J
IER, Id. J. ICCbRPK,
,AND w. N. LACEY Ca'ali$ornia Institute of Technology, Pasadena, Calif-
PRESSilRE
L P PER
Sa. IN.
Figure 1. Compressibility Factor a s Affected b y Pressure at 460' F. for Four Mixtures of NLethane and n - B u t a n e
HE voluinetric behavior of the nietharle-nbutane system was studied earlier in this laboratory a t temperatures hetn-een 70 : ~ n d 250' F. and a t pressures up to 3000 {munds per square inch for a number oi experimental compositions in the one- arid two-phaee regions (9, IO). Beat,tie el al. (2) inve3tiguted three mixt,ures approximating 0.25, 0.50, and 0.76 niole fraction methane in the sii~:;Ie-phase area from 167" t,o 573" F. a r i d lip to 5300 pounds per square inch. The p r e ~ s u ~ e - v o l ~ i m e temperature properties of the sepanite components, mcthanc (4-7) and n-hiitnnc ( 1 , J , 8 ) , were determined by several investig:ttors. Since this binary system i: o f importance industrially and constitutes a p r i , of the t e r n a r y methane-n-butane-decanc s y s t e m which is under investigation, the expcrimcntal data on four rnktures m r e extended to include temperat,uresfrom 100' t o -260 O F. ,It pressures up t o 10,000 pounds per square inch, the measurements being confined t o the singlephase region.
