Modlado y asegurameinto de flujo de fluidos pesados Modelado de crudo pesado: desde la físico-química básica hasta el aseguramiento de flujo.

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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

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•  Teoría de fricción (antecedentes) •  Modelado de fluidos Newtonianos

•  Modelo reológico para petróleo pesado •  Aseguramiento de flujo

•  Conclusiones

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N F_k = µ_k a r p p p = + = σ a r f τ τ τ = + ∑ = = 1 , i i r i r r µ p τ ∑ = = 1 , i i a i a a µ p τ N U F F_k u u uu+δ u+2δ δh h δ h δ τ f τ τ τ = ₀+ σ σ f f η η η τ τ τ = 0 + ⇒ = 0 + h u δ δ τ η =

Van der Waals: Amontons-Coulomb:

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•  The general model depends on one scaling parameter: η = η₀ + η_f η_f = η_c κˆ_a pa p_c ⎛ ⎝⎜ ⎞ ⎠⎟ + ˆκr p_r p_c ⎛ ⎝⎜ ⎞ ⎠⎟ + ˆκrr p_r p_c ⎛ ⎝⎜ ⎞ ⎠⎟ 2 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ η_c,i = K_c MWi Pci 2 / 3

Tc_i1/ 6 (Uyehara & Watson, 1940)

The FT one-parameter model η_c

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n-Alkanes Results h_c (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%

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Original mixing rules f η η η = ₀ +

_{( )}

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ =

∑

= n i i i x 1 0, 0 exp ln η η 2 r rr r r a a f κ p κ p κ p η = + +

∑

= = = = = = n i i rr i rr n i i a i a n i i r i r z z z 1 , 1 , 1 , κ κ κ κ κ κ

∑

= = = n i _i i i i i MW x MM MM MW x z 1 ε ε ε = 0.30

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Mixtures Results AAD/% f -SRK f -PR f -PRSV C1 + C3 2.28 2.06 2.37 C1 + n-C4 3.38 2.88 2.55 C1 + n-C6 4.43 4.07 4.27 C1 + n-C10 7.6 6.94 6.37 n-C5+n-C8 4 4.02 4.19 n-C5+n-C10 3.8 3.7 3.69 n-C6 + n-C7 1.91 2.11 1.78 n-C7+n-C8 3.41 3.5 3.62 n-C7+n-C9 1.66 2.09 2.14 n-C8+n-C10 2.14 1.91 1.75 n-C10+n-C16 4.84 5.26 3.94 n-C5+n-C8+n-C10 3.85 3.74 3.76 n-C10+n-C12+n-C14+n-C16 1.39 1.56 1.63

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Modeling Newtonian oils

Pseudocomponents

η_c,i = K_c MWi Pci

2 / 3

Tc_i1/ 6

(Uyehara & Watson, 1940)

To be tuned (Kc=7.95 n-alkanes) η c [µP] N2 174.179 CO2 376.872 Methane 152.930 Ethane 217.562 Propane 249.734 i-Butane 271.155 n-Butane 257.682 i-Pentane 275.073 n-Pentane 258.651 Hexane 257.841

Light Components Based on regular EOS _{characterization}

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CS(n) Distribution 0 0.05 0.1 0.15 0.2 0 s fdi s

Heavy Fraction Characterization

Mass Distribution Function: Chi-Squared (CS)

∫ − = i i dis i s s ds f fm 1

∫

− = i i dis i i s s s f ds fm s 1 1 ˆ i i MW s MW = ˆ Light Components (Excluded Mass)

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Pc & Tc Scaling Equations After n-alkanes 0 5 10 15 20 25 30 35 40 45 50 0 200 400 600 800 1000 1200 MW Pc (ba r) 0 200 400 600 800 1000 1200 1400 1600 1800 T c (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 )

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w Scaling Equation After n-alkanes 0 0.5 1 1.5 2 2.5 10 100 1000 MW ω (Emp. Eqn.) (KAP & EHS)

KAP & EHS: K. Aasberg-Petersen and E. H. Stenby

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = _0.1 MW 15.1665 -8.50471 exp ω

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Scaling Equations Tc = -423.587 +210.152 ln(MW ) Pc = f_c exp 9.67283

(

− 4.05288 MW 0.1

)

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = _0.1 MW 15.1665 -8.50471 exp ω After n-alkanes

Tuned to match the saturation pressure.

(Only applies to the C₇₊ fractions)

0 5 10 15 20 25 30 35 40 45 50 0 200 400 600 800 1000 MW Pc (ba r) n-Alkanes Basic Eqn Tuned Pc

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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) V iscosity (cP) Viscosity Tuning:

Based on data above saturation

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Heavy Oil 1 T = 72.8°C MW = 240.2 g/mol. 0 5 10 15 20 25 30 35 0 50 100 150 200 Pressure (bar) V is cos it y (c P ) Experimental f-theory

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T = 68.3°C MW = 430.4 g/mol 0 200 400 600 800 1000 1200 0 50 100 150 Pressure (bar) V iscosity (cP) Experimental f-theory Heavy Oil 2

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T = 35°C MW = 316.6 g/mol 0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 50 100 150 Pressure (bar) V is cos it y (c P ) Experimental f-theory Heavy Oil 3

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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) D ens it y (g/ cc ) Data Calculated 1000 1500 2000 2500 3000 3500 0 50 100 150 Pressure (bar) V is cos it y (c P ) Experimental f-theory Heavy Oil 4

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Blending 0 200 400 600 800 1000 1200 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% Mass% NG Vi s c o s ity (m Pa .s ) Experimental f-theory Heavy Oil + NG 341.5 K 0 200 400 600 800 1000 1200 0 50 100 150 200 250

Sat. Pressure (bar)

Vi s c o s ity (c P) Experimental f-theory Heavy Oil + NG

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Rheological model for crude oils Linear FT model η_f = η_L + K_cη_H K_c = K₀ + 1 1+ γ ₀γ0.7

(

)

exp 1

(

+ s

(

₀ (T_r − T_s)

)

6

)

(

s₁(T_r − T_s)

)

3 + s2 T_r − T_s ( )0.5 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ s₀ = 0.534555 K₀ + 22.0187 s₁ = 0.045992 K₀ − 1.40495 s₂ = 2.51409 γ ₀ + 1.72677

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K_c ⎯_γ⎯⎯ K__−>0→ ₀ + ΔK

Rheological model for crude oils

Linear FT model η_f = η_L + K_cη_H K_c = K₀ + 1 1+ γ ₀γ0.7

(

)

exp 1

(

+ s

(

₀ (T_r − T_s)

)

6

)

(

s₁(T_r − T_s)

)

3 + s2 T_r − T_s ( )0.5 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ s₀ = 0.534555 K₀ + 22.0187 s₁ = 0.045992 K₀ − 1.40495 s₂ = 2.51409 γ ₀ + 1.72677

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Rheological model for crude oils Linear FT model η_f = η_L + K_cη_H K_c = K₀ + 1 1+ γ ₀γ0.7

(

)

exp 1

(

+ s

(

₀ (T_r − T_s)

)

6

)

(

s₁(T_r − T_s)

)

3 + s2 T_r − T_s ( )0.5 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ s₀ = 0.534555 K₀ + 22.0187 s₁ = 0.045992 K₀ − 1.40495 s₂ = 2.51409 γ ₀ + 1.72677

(Quiñones-Cisneros et al., Energy & Fuels 2008, 22, 799-804)

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Rhelogical f-theory model results

(Pedersen & Rønningsen, Energy & Fuels 2000, 14, 43–51)

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Oil 4

Phase Envelope

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285 K 150 bar 110 bar Oil 4 Dilution Viscosity Thinning

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285 K 150 bar 110 bar Oil 4 Shear thinning Viscosity Thinning (Shear)

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285 K 150 bar 110 bar Oil 4 Shear thinning Viscosity Thinning (Shear)

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Propiedades fluidos mexicanos •  Fluido Maya de referencia 21° API.

L1�Llegada 20�C 25�C 30�C 40�C 50�C 60�C 1 2 5 10 20 50 100 200 500 50 100 200 500 Γ� �s�1� Η �mPa s�

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Propiedades fluidos mexicanos

•  Fluido Ku extra pesado (modelo corregido).

Fluid 12.2�API 20�C 30�C 40�C 50�C 60�C 70�C 80�C 113.5�C 0.01 0.1 1 10 100 100 200 500 1000 2000 5000 1 � 104 2 � 104 Γ� �s�1� Η �mPa s�

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•  Predicción Fluido de 15° API.

Fluid 15�API 20�C 30�C 40�C 50�C 60�C 70�C 80�C 0.01 0.1 1 10 100 100 200 500 1000 2000 5000 1 � 104 2 � 104 Γ� �s�1� Η �mPa s�

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•  Predicción Fluido de 17° API.

Fluid 17�API 20�C 30�C 40�C 50�C 60�C 70�C 80�C 0.01 0.1 1 10 100 100 200 500 1000 2000 5000 1 � 104 Γ� �s�1� Η �mPa s�

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Simulación Fluido 21° API 30° C L1�Llegada 20�C 25�C 30�C 40�C 50�C 60�C 1 2 5 10 20 50 100 200 500 50 100 200 500 Γ� �s�1_� Η �mPa s�

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Simulación Fluido 21° API 30° C L1�Llegada 20�C 25�C 30�C 40�C 50�C 60�C 1 2 5 10 20 50 100 200 500 50 100 200 500 Γ� �s�1_� Η �mPa s�

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Simulación Fluido 12.2° API 30° C

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Simulación Fluido 12.2° API

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•  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.