Ciencia  y  Tecnología,  27(1  y  2):  78-­‐‑83,  2011  
ISSN:  0378-­‐‑0524  
 
  
VISCOUS-­‐‑FLOW  MECHANISM  OF    #6  FUEL  OIL  –  PALM  OLEIN  MIXTURES  
  
Ritzela  E.  Lezcano-­‐‑González1  and  Julio  F.  Mata-­‐‑Segreda2  
  
Laboratory  of  Bio-­‐‑organic  Chemistry,  School  of  Chemistry,  University  of  Costa  Rica,  11501-­‐‑2060  Costa  Rica.  
  
Recibido  23  de  mayo,  2010;  aceptado  10  de  diciembre,  2010  
  
  
Abstract  
   The   viscosities   of  mixtures   of   #6   fuel   oil   and   palm   olein   at   60   °C   do   not   obey  
Kendall-­‐‑Monroe   equation.      Molecular   considerations   predict   deviation   from  
ideal-­‐‑mixture  behaviour  for  this  kind  of  “binary”  material.    It  is  proposed  that  the  
observed  positive  deviations  are  mainly  due   to   looser  molecular  packing   in   the  
mixtures  than  in  the  “pure”  components.    Thus,  mixing  results  in  a  lesser  degree  
of   hindrance   for   the   viscous-­‐‑flow   process.      The   empirical   fit   of   fluidity   as   a  
function  of  olein  mass   fraction   (x)   is   ln   [Φmix/Φolein]   =   -­‐‑   (2,72±0,05)  +   (5,6±0,3)  x   -­‐‑  
(2,9±0,3)  x2;    r2  =  0,992,    p  <  0,01.  
  
Resumen  
   Las   viscosidades   a   60   °C   de  mezclas   de   aceite   bunker  C   y   oleína   de   palma   no  
muestran   conformidad   con   la   ecuación   de   Kendall-­‐‑Monroe.      Consideraciones  
moleculares   predicen   la   desviación   del   comportamiento   de   mezcla   ideal,   para  
este  caso  de  material  “binario”.    Se  propone  que  las  desviaciones  positivas  de  la  
fluidez   se   deben   a   un   menor   grado   de   empacamiento   molecular   de   los   dos  
componentes  “puros”  de  las  mezclas,  resultando  así  en  una  menor  resistencia  al  
flujo.     El   ajuste   empírico  de   la   fluidez   como   función  de   la   fracción  ponderal  de  
oleína  (x)  es  ln  [Φmix/Φolein]  =  -­‐‑  (2,72±0,05)  +  (5,6±0,3)  x  -­‐‑  (2,9±0,3)  x2;    r2  =  0,992,    p  <  
0,01.  
 
  
Key  words:  #6  fuel  oil,  palm  olein,  viscous  flow,  Kendall-­‐‑Monroe  equation.  
  
Palabras  claves:  búnker  C,  oleína  de  palma,  flujo  viscoso,  ecuación  de  Kendall-­‐‑Monroe. 
 
 
I   INTRODUCTION  
  
It   is   widely   accepted   that   climate   change   is   an   urgent   problem   that   requires   globally  
concerted  actions.    Atmospheric  CO2  accounts  for  63  %  of  the  gaseous  radiative  forcing  responsible  
for  anthropogenic  climate  change  [1].     From  the  so-­‐‑called  Keeling  curve,  we  have  calculated  that  
atmospheric  CO2  has  been  increasing  at  an  annual  rate  of  0,4  %  during  the  last  five  decades.    This  
growth   is   mainly   due   to   two   sources   of   this   greenhouse   gas:   a)   emissions   from   fossil-­‐‑fuel  
                                                
1 Current  address:  Department  of  Physical  Chemistry,  School  of  Chemistry,  University  of  Panama,  Panama  City.  
2  Corresponding  author,  e-­‐‑mail:  julio.mata@ucr.ac.cr  
 
R.E.  LEZCANO-­‐‑GONZÁLEZ  –  J.F.  MATA-­‐‑SEGREDA  
Ciencia  y  Tecnología,  27(1  y  2):  78-­‐‑83,  2011  -­‐‑  ISSN:  0378-­‐‑0524   79 
combustion   and   industrial   processes   (23   Gt   CO2   per   year)   and   b)   production   due   to   land-­‐‑use  
change,  mainly  land  clearing  (5,5  Gt  CO2  per  year).    The  first  source  has  been  growing  rapidly  over  
recent  years,  and  the  latter  remaining  nearly  steady  [1].  
 
 
FIGURE  1.    Keeling  curve.    The  proportional  rate  of  CO2  enrichment  is  0,40  %  y-­‐‑1  during  the  last  five  
decades  [2].  
 
 Different   actions   make   possible   the   lessening   of   enviromental   impacts   due   to   CO2  
accumulation  in  the  atmosphere.     One  is   the   improvement   in  the  use  of   thermal  energy  and  also  
the  partial  substitution  of  fossil  fuels  used  in  industrial  activities  such  as  cement  production,  and  
the   operation   of   thermoelectrical   units   or   boilers.      These   fuel  materials   should   be   derived   from  
renewable  sources,  such  as  the  case  of  vegetable  oils  or  animal  fats.  
   It  was  brought  to  our  attention  the  possibility  of  using  mixtures  of  palm  olein  and  #6  fuel  
oil   (bunker   C)   as   fuel   for   the   operation   of   thermoelectrical   generators.      Three   aspects   must   be  
considered  in  assessing  the  feasibility  of  the  proposal.  
The   first   is   the   calorific   value   of   this   vegetable   oil,   which   is   38  MJ/kg.      This   quantity   is  
similar   to   the  observed  value  of     40  MJ/kg   for  #6   fuel  oil.     The  second  aspect   to  be  considered   is  
price   and   availability   of   palm   olein,   situations   that   need   be   analysed   in   specific   scenarios.      The  
third  aspect   is   the  resulting  viscosities  of  #6  fuel  oil-­‐‑olein  mixtures.      If  viscosities  are  higher  than  
values  expected  from  linear  dependence  of  the  logarithm  of  viscosity  with  composition  (vide  infra),  
higher  energy  costs  would  be  involved  in  the  pumping  of  the  fuel  mixture  due  to  friction  loss.  
Binary  liquid  ideal  mixtures  of  xi  mole-­‐‑fraction  composition  obey  Kendall-­‐‑Monroe  equation  
[3]:  
 
ln Φmix = x1 ln Φ1 + x2 ln Φ2         (1) 
 
where  Φ   refers   to   fluidity.  The   ideal-­‐‑mixture  condition   is  approached  when  the  molecules  of   the  
components  are  similar  in  polarity,  shape  and  size  [4].     This  condition  assures  microscopic   laminar  
flow  due  to  independence  of  the  sliding  process  of  the  molecular  layers,  from  the  chemical  identity  
of  the  constituents.  
Viscous-­‐‑flow  mechanism  of  #6  fuel  oil  –  palm  olein  mixtures. 
Ciencia  y  Ciencia  y  Tecnología,  27(1  y  2):  71-­‐‑76,  2011  –  ISSN:  0378-­‐‑0524 80 
   The  proposal   can   be   stated   that   non-­‐‑linear  dependency   of   ln  Φmix   on  x   is   expected  when  
either   positive   or   negative   deviations   from   ideal   behaviour   occurs.      Experimental   observation  
supports   the   proposal   [3].      For   example,   C6H6-­‐‑EtOH   mixtures   show   positive   deviations   from  
Raoult’s  law,  and  this  suggests  the  same  mathematical  result  on  equation  (1),  a  result  borne  out  by  
experiment.    The  opposite  is  observed  for  Cl3CH-­‐‑Et2O  mixtures.  
   We   present   the   rheological   behaviour   of  mixtures   of   #6   fuel   oil   and   palm   olein   and   the  
compatibilty  of  the  mixtures.  
 
II   MATERIALS  AND  METHODS  
 
Materials.    Palm  olein  was  obtained  as  a  gift  from  Palma  Tica®  (Costa  Rica)  and  the  #6  fuel  
oil  sample  used  in  this  study  was  from  the  state-­‐‑owned  petroleum  company  Recope  (Costa  Rica).    
All  mixtures  of  mass  fraction  x  were  prepared  gravimetrically.  
Viscometric   measurements   and   compatibility.      A   Saybolt   Furol   viscometer   was   used,  
according   to  procedure  ASTM-­‐‑D88.  The  measurements  were  done  at   60,0   °C.     The   compatibility  
test  was  carried  out  as  indicated  by  ASTM-­‐‑D2781.  
Data   treatment.     The  1/(kinematic  viscosity)  –   composition  data  were  subjected   to  Anova  
analysis   in   the   Kendall-­‐‑Monroe   equation   form   jjmix xaitycosviskinematic ∑=
0
)/1ln(    for   linear   and  
quadratic  fits,  by  using  polynomial-­‐‑regression  analysis  with  the  Excel  package.  
 
III   RESULTS  AND  DISCUSION  
 
Macroscopic   properties.      Table   1   gives   the   kinematic   viscosities   of   the   mixtures   studied.      The  
measurements  were  carried  out  at  60,0  °C.  
  
TABLE 1  
KINEMATIC VISCOSITIY OF MIXTURES OF  #6 FUEL OIL AND PALM OLEIN AT 60,0 °C. 
 
Mass  fraction  of  palm  olein   Kinematic  viscosity  /  SSF  
0,000   290,1  
0,051   191,1  
0,100   152,0  
0,199   90,6  
0,301   65,0  
0,399   41,4  
0,500   36,6  
1,000   17,5  
 
Figure  1   shows   the   correlation  of   ln   [Φmix/Φolein]  vs.  x   is  nonlinear.     Anova  analysis   shows  
that  both  linear  and  quadratic  terms  are  statistically  significant  to  at  least  p  <  0,01,    r2  =  0,992.  
In  analogy  to  Kendall-­‐‑Monroe  equation,  the  following  empirical  relationship  results:  
 
         ln [Φmix/Φolein] = - (2,72±0,05) + (5,6±0,3) x – (2,9±0,3) x2          (2) 
R.E.  LEZCANO-­‐‑GONZÁLEZ  –  J.F.  MATA-­‐‑SEGREDA  
Ciencia  y  Tecnología,  27(1  y  2):  78-­‐‑83,  2011  -­‐‑  ISSN:  0378-­‐‑0524   81 
 
Though  1/(kinematic  viscosity)  =  density/absolute  viscosity  =  density  ×  absolute  fluididty,  it  
is   clear   that   density   changes   with   x   much   less   than   absolute   fluididty   does,   as   seen   from   the  
density  values  for  the  two  components  at  60,0  °C:  0,89  g/cm3  for  palm  olein  and  0,97  g/cm3  for  #6  
fuel  oil.     Thus,  [∂ln(1/kinematic  viscosity)mix/∂x]T  ≈   [∂lnΦmix/∂x]T.     This  means  that  one  can  use  the  
inverse  of  the  kinematic  viscosity  in  place  of  exact  Φmix  values  for  the  analysis  of  the  results  of  this  
work.  
The   observed   positive   deviation   from   equation   (1)   indicates   that   no   additional   energy  
expenditure  should  be  expected  in  the  pumping  of  these  mixtures  than  what  is  required  for  fuel  oil  
alone,  a  favourable  mechanical  feature  of  the  system.  
It   is   important   to   determine   the   composition   at   which   one   has   the   greatest   difference  
between  the  real  system  and  the  situation  predicted  by  the  Kendall-­‐‑Monroe  equation.  
 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
FIGURE  2.    Effect  of  composition  on  the  fluidity  of  binary  mixtures  of  #6  fuel  oil  and  palm  olein  at  60,0  °C.    
 
yKendall = ln Φbunker + ln (Φolein/Φbunker) x 
yreal = -5,58 + 5,6 x -2,9 x2 
d(yreal – yKendall)/dx = 5,6 – 5,8 x - ln (Φolein/Φbunker) 
d(yreal – yKendall)/dx = 0 
xmax = 0,48 
 The   above   straightforward   exercise   shows   the   best   mixture   to   contain   ∼   50   %   (m/m)   of  
olein,  in  order  to  have  the  maximum  fluididty  relative  to  Kendall-­‐‑Monroe  rheology.  
   An  additional  aspect  to  be  considered  is  that  of  compatibility  of  the  two  components.    If  the  
components   are   compatible,   there   is   assurance   that  no  phase   separation  will   occur   after  mixing.    
ASTM-­‐‑2781  procedure  shows  good  compatibility  (degree  1  –  2)  for  all  mixtures  studied.  
 
x
-3
-2
-1
0
0 0,2 0,4 0,6 0,8 1
ln
[Φ
m
ix
/Φ
ol
ei
n]
Kendall-Monroe 
Viscous-­‐‑flow  mechanism  of  #6  fuel  oil  –  palm  olein  mixtures. 
Ciencia  y  Ciencia  y  Tecnología,  27(1  y  2):  71-­‐‑76,  2011  –  ISSN:  0378-­‐‑0524 82 
Microscopic  considerations.     The   thermal  coefficient  of  cubic  expansion  of  a  particular  material,  
pT
V
V
⎟
⎠
⎞
⎜
⎝
⎛
∂
∂
=
1
α ,  is  an  inverse  function  of  intermolecular  forces  and  of  how  well  molecules  are  packed  
in  supramolecular  lattices  [5]:  
H
C
vap
p
Δ
=
λ
α
72
7
                          (3)  
where  λ  is  related  to  the  packing  of  molecules  in  the  liquid.    The  α  values  of  palm  olein  [(7,0±0,2)  ×  
10-­‐‑4  K-­‐‑1]  and  of    #6  fuel  oil  [(6,90  ±0,09)  ×  10-­‐‑4  K-­‐‑1]  are  identical  [6].  
The  petro-­‐‑material   is  mainly  made  up  of   long-­‐‑chain  hydrocarbons   from  C20   to  C70.     Palm  
olein   triacylglyceride  molecules   (TAG)  are   smaller  objects   than   those   in      fuel  oil.      It   is   clear   that  
intermolecular  attractive  forces  in  the  latter  material  must  be  somehow  greater  than  those  between  
TAG,   because   the  Cn   are   long   coiled  molecules  with   large  molecular   surfaces,  whilst   TAG  have  
almost  cylindrical  compact  shapes,  as  shown  by  the  space  filling  model  below  [obtained  from  the  
internet  site  www.3dchem.com/molecules.asp?ID=320#].  
  
 
Figure  3.    Space  filling  model  for  triacylglycerols.  
  
The  qualitative  idea  agrees  with  the  difference  in  ΔvapH°  =  163±4  kJ/mol  (190  kJ/kg)  for  TAG  
in  general   [7]  and  values   in   the  range  101,8  kJ/mol  and  192,6  kJ/mol   for  C20   -­‐‑  C38   [8].     A  value  of  
apparent  ΔvapH°  =  220  kJ/kg  is  reported  for  #6  fuel  oil  [9].  
   We  give  the  following  interpretation  to  the  findings  discussed  in  this  work.    The  magnitude  
of  intermolecular  forces  does  not  seem  to  play  the  main  role  in  this  case.  
Packing  arrangement   influences  many  properties  of   liquids  such  as  density,  viscosity  and  
diffusivity  [10].    The  supramolecular  configuration  in  both  “pure”  components  is  similar,  as  can  be  
expected  from  the  α  values.    The  λ  parameters  are  calculated  from  equation  3  with  the  aid  from  Cp  
values  reported  in  the  literature:  1,9  kJ  K-­‐‑1/kg  for  #6  fuel  oil  [9]  and  1,96  kJ  K-­‐‑1/kg  for  palm  oil  [11].    
The  resulting  values  are  λfuel  oil  =  1,2  and  λolein  =  1,4.  
The  difference  in  molecular  sizes  and  shapes  between  the  molecular  objects  in  TAG  and  in  
#6   fuel   oil   results   in   greater   amount   of   excluded   volume   in   the   mixtures.      This   means   looser  
intermolecular   packing   in   the   mixtures   than   in   the   pure   components.      Though   intermolecular  
forces  are  somehow  greater  in  #6  fuel  oil,  the  looser  lattice  in  the  mixtures  renders  a  lesser  degree  
of  hindrance  to  the  viscous-­‐‑flow  process,  relative  to  the  situations  of  the  two  “pure”  components.  
   The   observed   compatibility   of   the   mixtures   can   be   understood   in   terms   of   the   similar  
dielectric  constants  and  Hildebrand  solubility  parameters  (
m
vap
H V
HΔ
≈δ )  [12]  of  these  two  materials.    
The  mean  dielectric  constant  of  vegetable  oils   is  3,1  and  a  value  of  2,6   is  accepted  for  #6   fuel  oil.  
From  the  ΔvapH  and  densities  indicated  above,  one  calculates  δH  =  13,0  MPa½  for  palm  olein  and  δH  =  
14,6  MPa½  for    #6  fuel  oil.  
  
R.E.  LEZCANO-­‐‑GONZÁLEZ  –  J.F.  MATA-­‐‑SEGREDA  
Ciencia  y  Tecnología,  27(1  y  2):  78-­‐‑83,  2011  -­‐‑  ISSN:  0378-­‐‑0524   83 
Conclusion.    The  fluidity  of  mixtures  of  #6  fuel  oil  and  palm  olein  shows  positive  deviations  from  
the   Kendall-­‐‑Monroe   equation   at   60,0   °C.      The  most   fluidal  mixture   contains   48%   of   palm   olein  
(m/m).    This  observation  indicates  that  use  of  this  type  of  mixtures  as  fuel  means  no  extra  energy  
requirement   for   pumping   the   fuel   mixture   from   storage   reservoirs   to   combustion   chambers.    
Mixtures  with  up  to  48  %  olein  (m/m)  are  compatible,  according  to  test  ASTM-­‐‑2781.  
This   rheology   feature   is   thought   to   be   the   result   of   looser   packing   of   molecules   in   the  
mixtures  than  in  the  “pure”  components.  
 
IV REFERENCES 
 
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Proc.  Natl.  Acad.  Sci.  (USA)  2007,  104,  10288-­‐‑10293.  
  
[2]   Briggs,   H.,   “50   years   on:   The   Keeling   Curve   legacy”,   BBC   News,   2   December   2007,  
www.news.bbc.co.uk/1/hi/sci/tech/7120770.stm,  Downloaded  on  18  December  2008.  
    
[3]    Glastone,  S.;  Laidler,  K.  J.;  Eyring,  H.,  The  theory  of  rate  processes,  McGraw-­‐‑Hill:  New  York,  1941,  
chapter  9.  
  
[4]    Pitzer,  K.  S.;  Brewer,  L.,  Gilbert  Newton  Lewis  and  Merle  Randall  Thermodynamics,  McGraw-­‐‑Hill:  
New  York,  1961,  pp  280-­‐‑282.  
  
[5]    Castellón-­‐‑Elizondo,  E.;  Lutz,  G.;  Mata-­‐‑Segreda,  J.  F.,  J  .  Phys.  Org.  Chem.  2006,  19,  744-­‐‑747.  
  
[6]    α  values  were  calculated  from  the  densities  (ρ)  at  different  temperatures  as  α  =  -­‐‑  (∂lnρ/∂T)p.  
  
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Acknowledgement.     The  authors  wish  to  thank  Alejandro  A.  Azofeifa  (Instituto  Costarricense  de  
Electricidad)  for  suggesting  this  study,  and  Bernardo  Aguilar  and  José  Duarte  (Recope,  Costa  Rica)  
for   their  help   in  measuring   the  viscosity  profile  of   the  mixtures  and   the  compatibility   tests.     The  
gift  of  oil-­‐‑palm  olein  from  Palma  Tica  is  recognised.