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Modlado y asegurameinto de flujo de fluidos pesados Modelado de crudo pesado:
desde la físico-química básica hasta el aseguramiento de flujo.
Sergio E. Quiñones-Cisneros (UNAM) Institutio de Investigaciones en Materiales – UNAM
Grupo SSC
(Resumen de avance proyecto Banco de Pruebas PEMEX - Dos Bocas)
Equipo Multidisciplinarlo de Teabajo Facultad de Ingeniería – UNAM
• Teoría de fricción (antecedentes)
• Modelado de fluidos Newtonianos
• Modelo reológico para petróleo pesado
• Aseguramiento de flujo
• Conclusiones
Temario
NF kk µ=ar ppp +==σ
arf τττ +=
∑=
=1
,i
irirr pµτ ∑
==
1,
i
iaiaa pµτ
N
U F Fk u
uu δ+uu δ2+ hδ
hδhδ
τ
fτττ += 0
σ
σ
ff ηηητττ +=⇒+= 00
huδ
δτη =
Van der Waals: Amontons-Coulomb:
The Friction Theory
• The general model depends on one scaling parameter:
η = η0 +η f
η f = ηc κ̂ apapc
⎛⎝⎜
⎞⎠⎟+ κ̂ r
prpc
⎛⎝⎜
⎞⎠⎟+ κ̂ rr
prpc
⎛⎝⎜
⎞⎠⎟
2⎡
⎣⎢⎢
⎤
⎦⎥⎥
�
ηc,i = KcMWi Pci
2 / 3
Tci1/ 6 (Uyehara & Watson, 1940)
The FT one-parameter model
ηc
n-Alkanes Results
hc (mP) SRK PR
C H4 152.930 3.98% 3.53%
C3 H8 249.734 1.41% 1.40%
n-C5 258.651 3.18% 2.81%
n-C8 256.174 1.54% 1.56%
n-C10 257.928 1.40% 1.36%
n-C15 229.852 1.44% 1.06%
n-C18 206.187 2.32% 1.91%
Overall 2.19% 2.02%
Vogel’s propane data
Original mixing rules
fηηη += 0 ( )⎥⎦
⎤⎢⎣
⎡= ∑
=
n
iiix
1,00 lnexp ηη
2rrrrraaf ppp κκκη ++=
∑∑∑===
===n
iirrirr
n
iiaia
n
iirir zzz
1,
1,
1, κκκκκκ
∑=
==n
i i
i
i
ii
MWxMM
MMMWxz
1εε 30.0=ε
Mixtures Results
AAD/%f -SRK f -PR f -PRSV
C1 + C3 2.28 2.06 2.37C1 + n-C4 3.38 2.88 2.55C1 + n-C6 4.43 4.07 4.27C1 + n-C10 7.6 6.94 6.37n-C5+n-C8 4 4.02 4.19n-C5+n-C10 3.8 3.7 3.69n-C6 + n-C7 1.91 2.11 1.78n-C7+n-C8 3.41 3.5 3.62n-C7+n-C9 1.66 2.09 2.14n-C8+n-C10 2.14 1.91 1.75n-C10+n-C16 4.84 5.26 3.94n-C5+n-C8+n-C10 3.85 3.74 3.76n-C10+n-C12+n-C14+n-C16 1.39 1.56 1.63
Modeling Newtonian oils
Pseudocomponents
�
ηc,i = KcMWi Pci
2 / 3
Tci1/ 6
(Uyehara & Watson, 1940)
To be tuned (Kc=7.95 n-alkanes)
η c [µP]N2 174.179CO2 376.872Methane 152.930Ethane 217.562Propane 249.734i-Butane 271.155n-Butane 257.682i-Pentane 275.073n-Pentane 258.651Hexane 257.841
Light Components Based on regular EOS
characterization
⇒η = ηL + KcηH
CS(n) Distribution
0
0.05
0.1
0.15
0.2
0
s
fdis
Heavy Fraction Characterization
Mass Distribution Function: Chi-Squared (CS)
∫−
=i
i
disi
s
sdsffm
1
∫−
=i
i
disi
i
s
sdsfs
fms
1
1ˆ
ii sMWMW ˆ=
Light Components (Excluded Mass)
The CS(n)
The CS(n)
The CS(n)
The CS(n)
Mass Characterization
Mass Characterization
Mass Characterization
Mass Characterization
Pc & Tc Scaling Equations
After n-alkanes
05
101520253035404550
0 200 400 600 800 1000 1200MW
Pc (b
ar)
020040060080010001200140016001800
Tc (K
)
Pc (Emp. Eqn.)Pc (KAP & EHS)Tc (Emp. Eqn.)Tc (KAP & EHS)
KAP & EHS: K. Aasberg-Petersen and E. H. Stenby
�
Tc = -423.587 +210.152 ln(MW )
�
Pc = fc exp 9.67283− 4.05288MW0.1( )
w Scaling Equation
After n-alkanes
0
0.5
1
1.5
2
2.5
10 100 1000MW
ω(Emp. Eqn.)
(KAP & EHS)
KAP & EHS: K. Aasberg-Petersen and E. H. Stenby
⎟⎠⎞⎜
⎝⎛= 0.1MW
15.1665-8.50471expω
Scaling Equations
�
Tc = -423.587 +210.152 ln(MW )
�
Pc = fc exp 9.67283− 4.05288MW0.1( )
⎟⎠⎞⎜
⎝⎛= 0.1MW
15.1665-8.50471expω
After n-alkanes
Tuned to match the saturation pressure.
(Only applies to the C7+ fractions)
05
101520253035404550
0 200 400 600 800 1000MW
Pc (b
ar)
n-AlkanesBasic EqnTuned Pc
HP/HT FT Viscosity Results
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 200 400 600 800 1000
Pressure (bar)
Vis
cosi
ty (
cP)
Viscosity Tuning: Based on data above
saturation
η = ηL + KcηH
Heavy Oil 1
T = 72.8°C
MW = 240.2 g/mol.
05
101520253035
0 50 100 150 200Pressure (bar)
Vis
cosi
ty (c
P)
Experimental
f-theory
T = 68.3°C
MW = 430.4 g/mol
0
200
400
600
800
1000
1200
0 50 100 150
Pressure (bar)
Vis
cosi
ty (
cP)
Experimental
f-theory
Heavy Oil 2
T = 35°C
MW = 316.6 g/mol
0500
10001500200025003000350040004500
0 50 100 150
Pressure (bar)
Vis
cosi
ty (c
P)
Experimentalf-theory
Heavy Oil 3
T = 47.8°C MW = 422.9 g/mol
0.95
0.96
0.97
0.98
0.99
1
0.0 50.0 100.0 150.0
Pressure (bars)
Den
sity
(g/c
c)
DataCalculated
1000
1500
2000
2500
3000
3500
0 50 100 150
Pressure (bar)
Vis
cosi
ty (c
P)
Experimental
f-theory
Heavy Oil 4
Blending
0
200
400
600
800
1000
1200
0.00% 1.00% 2.00% 3.00% 4.00% 5.00%Mass% NG
Vis
cosi
ty (m
Pa.
s)
Experimentalf-theory
Heavy Oil + NG
341.5 K
0
200
400
600
800
1000
1200
0 50 100 150 200 250Sat. Pressure (bar)
Vis
cosi
ty (c
P)
Experimentalf-theory
Heavy Oil + NG
Rheological model for crude oils
Linear FT model
η f = ηL + KcηH
Kc = K0 +
11+ γ 0 γ
0.7( ) exp 1+ s0 Tr − Ts( )( )6( ) s1 Tr − Ts( )( )3 + s2Tr − Ts( )0.5
⎡
⎣⎢⎢
⎤
⎦⎥⎥
s0 = 0.534555 K0 + 22.0187s1 = 0.045992 K0 −1.40495s2 = 2.51409 γ 0 +1.72677
(Quiñones-Cisneros et al., Energy & Fuels 2008, 22, 799-804)
Kc γ −>0⎯ →⎯⎯ K0 + ΔK
Rheological model for crude oils
Linear FT model
η f = ηL + KcηH
Kc = K0 +
11+ γ 0 γ
0.7( ) exp 1+ s0 Tr − Ts( )( )6( ) s1 Tr − Ts( )( )3 + s2Tr − Ts( )0.5
⎡
⎣⎢⎢
⎤
⎦⎥⎥
s0 = 0.534555 K0 + 22.0187s1 = 0.045992 K0 −1.40495s2 = 2.51409 γ 0 +1.72677
(Quiñones-Cisneros et al., Energy & Fuels 2008, 22, 799-804)
Rheological model for crude oils
Linear FT model
η f = ηL + KcηH
Kc = K0 +
11+ γ 0 γ
0.7( ) exp 1+ s0 Tr − Ts( )( )6( ) s1 Tr − Ts( )( )3 + s2Tr − Ts( )0.5
⎡
⎣⎢⎢
⎤
⎦⎥⎥
s0 = 0.534555 K0 + 22.0187s1 = 0.045992 K0 −1.40495s2 = 2.51409 γ 0 +1.72677
(Quiñones-Cisneros et al., Energy & Fuels 2008, 22, 799-804)
Kc γ −>∞⎯ →⎯⎯ K0
Rhelogical f-theory model results (Pedersen & Rønningsen, Energy & Fuels 2000, 14, 43–51)
2°C ≤ T ≤ 50°C
Oil 4
Phase Envelope (Oil 4 + 40% methane)
285 K 150 bar
110 bar
Oil 4
Dilution
Viscosity Thinning (Dilution: Oil 4 + 40% methane)
285 K 150 bar
110 bar
Oil 4
Shear thinning
Viscosity Thinning (Shear)
285 K 150 bar
110 bar
Oil 4
Shear thinning
Viscosity Thinning (Shear)
Propiedades fluidos mexicanos
• Fluido Maya de referencia 21° API.
L1�Llegada
20�C
25�C
30�C
40�C
50�C60�C
1 2 5 10 20 50 100200 500
50
100
200
500
Γ� �s�1�
Η�mPa
s�
Propiedades fluidos mexicanos
• Fluido Ku extra pesado (modelo corregido).
Fluid 12.2�API20�C
30�C
40�C
50�C60�C70�C80�C
113.5�C
0.01 0.1 1 10 100
100
200
500
1000
2000
50001� 1042� 104
Γ� �s�1�
Η�mPa
s�
Propiedades fluidos mexicanos
• Predicción Fluido de 15° API.
Fluid 15�API20�C
30�C
40�C
50�C60�C70�C80�C
0.01 0.1 1 10 100
100
200
500
1000
2000
50001� 1042� 104
Γ� �s�1�
Η�mPa
s�
Propiedades fluidos mexicanos
• Predicción Fluido de 17° API.
Fluid 17�API20�C
30�C
40�C
50�C60�C70�C80�C
0.01 0.1 1 10 100
100
200
500
1000
2000
5000
1� 104
Γ� �s�1�
Η�mPa
s�
Simulación Fluido 21° API 30° C L1�Llegada
20�C
25�C
30�C
40�C
50�C60�C
1 2 5 10 20 50 100200 500
50
100
200
500
Γ� �s�1�
Η�mPa
s�
Simulación Fluido 21° API 30° C L1�Llegada
20�C
25�C
30�C
40�C
50�C60�C
1 2 5 10 20 50 100200 500
50
100
200
500
Γ� �s�1�
Η�mPa
s�
Simulación Fluido 12.2° API 30° C
Simulación Fluido 12.2° API 20% mol CH4 30° C
Conclusiones
• La correcta caracterización y modelado de los fluidos es fundamental.
• La viscosidad de los fluidos puede ser adelgazada efectivamente medinate: – Dilución
– Mecánicamente.
• Esto podría permitir un diseño novedoso y eficiente de lineas de transporte.
El desarrollo de un banco de pruebas para PEMEX es fundamental.
Conclusiones