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# Modelagem Dinâmica do Processamento Primário de Petróleo

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```s
K
x
h
p
p
L
L
\u3c4 ,
onde :
158
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
+\u2212
\u239f\u239f\u23a0
\u239e
\u239c\u239c\u239d
\u239b
=
L
L
L
L
L
L
p
dh
dL
dL
dt
dh
dh
dt
dh
dx
dL
dL
dt
dh
K
0
0
0
0
2
.
.
e
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
+\u2212
=
L
L
L
L
p
dh
dL
dL
dt
dh
dh
dt
dh
0
0
2
.
1\u3c4

13
3
'
' += s
K
P
h
p
pL
\u3c4 ,
onde :
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
+\u2212
\u239f\u23a0
\u239e\u239c\u239d
\u239b
=
L
L
L
L
L
p
dh
dL
dL
dt
dh
dh
dt
dh
dP
dL
dL
dt
dh
K
0
0
0
0
2
.
.
e
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
+\u2212
=
L
L
L
L
p
dh
dL
dL
dt
dh
dh
dt
dh
0
0
2
.
1\u3c4

A resposta linear será dada pela soma das funções de transferência acima.

\u2022 Pressão (P)
).().().( ,, Eii
i
Eii
i
E
E
LIN
GG
dG
dt
dP
LL
dL
dt
dP
PP
dP
dt
dP
dt
dP
dt
dP \u2212+\u2212+\u2212+\u239f\u23a0
\u239e\u239c\u239d
\u239b=
).().().( ,,00
0
,00
0
ELL
L
EE VVdV
dt
dP
GG
dG
dt
dP
LL
dL
dt
dP
\u2212+\u2212+\u2212+
Com:
ELT
EEEiEiE
E VV
GLGLP
dt
dP
,
,0,0,, )(
\u2212
\u2212\u2212+=\u239f\u23a0
\u239e\u239c\u239d
\u239b
Definindo-se em forma de variável desvio:
159
''
0
0
'
0
0
'''
'
...... L
L
i
i
i
i
V
dV
dt
dP
G
dG
dt
dP
L
dL
dt
dP
G
dG
dt
dP
L
dL
dt
dP
P
dP
dt
dP
dt
dP +++++=
Como:
'0'0'0
,00
'
0 ... L
L
L
L
E hdh
dL
P
dP
dL
x
dx
dL
LLL ++=\u2212=
'0'0'0
,00
'
0 ... TdT
dG
P
dP
dG
x
dx
dG
GGG G
G
E ++=\u2212=
'
,
' . L
L
L
ELLL hdh
dVVVV =\u2212=
+\u239f\u239f\u23a0
\u239e
\u239c\u239c\u239d
\u239b +++++= '0'0'0
0
'''
'
....... L
L
L
L
i
i
i
i
h
dh
dLP
dP
dLx
dx
dL
dL
dt
dP
G
dG
dt
dP
L
dL
dt
dP
P
dP
dt
dP
dt
dP
\u239f\u239f\u23a0
\u239e
\u239c\u239c\u239d
\u239b+\u239f\u239f\u23a0
\u239e
\u239c\u239c\u239d
\u239b +++ ''0'0'0
0
...... L
L
L
L
G
G
h
dh
dV
dV
dt
dP
T
dT
dGP
dP
dGx
dx
dG
dG
dt
dP

Separando-se as variáveis e aplicando-se a transformada de Laplace:

++=\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212 ''0
0
0
0
''
....... i
i
i
i
G
dG
dt
dP
L
dL
dt
dP
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dP
PsP
\u239f\u239f\u23a0
\u239e
\u239c\u239c\u239d
\u239b+\u239f\u239f\u23a0
\u239e
\u239c\u239c\u239d
\u239b ++\u239f\u239f\u23a0
\u239e
\u239c\u239c\u239d
\u239b ++ ''0'0
0
'0'0
0
........ L
L
L
L
G
G
L
L
L
L
h
dh
dV
dV
dt
dP
T
dT
dG
x
dx
dG
dG
dt
dP
h
dh
dL
x
dx
dL
dL
dt
dP

14
4
'
'
+= s
K
L
P
p
p
i
\u3c4 ,
160
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dP
dL
dt
dP
K ip
0
0
0
0
4
..
,
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dPp
0
0
0
0
4
..
1\u3c4

15
5
'
'
+= s
K
G
P
p
p
i
\u3c4 ,
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dP
dG
dt
dP
K ip
0
0
0
0
5
..
,
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dPp
0
0
0
0
4
..
1\u3c4

16
6
'
'
+= s
K
x
P
p
p
L
\u3c4 ,
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dP
dx
dL
dL
dt
dP
K Lp
0
0
0
0
0
0
6
..
..
,
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dPp
0
0
0
0
6
..
1\u3c4

17
7
'
'
+= s
K
h
P
p
p
L
\u3c4 ,
161
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
+
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dP
dh
dV
dV
dt
dP
dh
dL
dL
dt
dP
K
L
L
LL
p
0
0
0
0
0
0
7
..
.
,
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dPp
0
0
0
0
7
..
1\u3c4

18
8
'
'
+= s
K
x
P
p
p
G
\u3c4 ,
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dP
dx
dG
dG
dt
dP
K Gp
0
0
0
0
0
0
8
..
.
,
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dPp
0
0
0
0
8
..
1\u3c4

19
9
'
'
+= s
K
T
P
p
p
\u3c4 ,
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dP
dT
dG
dG
dt
dP
K p
0
0
0
0
0
0
9
..
.
,
\u239f\u239f
\u239f
\u23a0
\u239e
\u239c\u239c
\u239c
\u239d
\u239b
++\u2212
=
dP
dG
dG
dt
dP
dP
dL
dL
dt
dP
dP
dt
dPp
0
0
0
0
9
..
1\u3c4
162

A resposta linear será dada pela soma das funções de transferência acima.

14.4.1 Simulação de Modelo Linear de Separador Bifásico

A Figura 14.20 mostra a interconexão entre as funções de transferência relacionadas a h
(FT h) e as funções de transferência relacionadas a P (FT P). Os blocos FT h e FT P estão
detalhados nas Figuras 14.21 e 14.22, respectivamente.

na Figura 14.23. Os resultados da comparação estão mostrados na Figura 14.24. A
simulação foi conduzida com a sintonia obtida no item 14.2, com o controle por bandas e
vazões de gás e óleo constantes. Ressalta-se que a cada modelo estava associado o seu
próprio conjunto de controladores, apesar dos conjuntos trabalharem com a mesma
sintonia.

163
Falta Calcular G0, L0 e Volumes
h sat
P sat
2
Out2
1
Out1
Pe
T6
hle
T5
Bp
T4
Gie
T3
Lie
T2
Bl
T1
0
T
Saturation1
Saturation
In1
In2
In3
Out1
FT hl
In1
In2
In3
In4
In5
In6
Out1
FT P
4
Gi
3
Li
2
xG
1
XL
P
hl

Figura 14.20: Interconexão das Funções de Transferência do Separador Bifásico

1
Out1
Bl
xl inicial
-(c2*c4)/(c2*c6+c3)
-1/(c2*c6+c3)s+1
hl/xl
-(c2*c5)/(c2*c6+c3)
-1/(c2*c6+c3)s+1
hl/P
-c1/(c2*c6+c3)
-1/(c2*c6+c3)s+1
hl/Li
In1
In2 Out1
Switch
3
In3
2
In2
1
In1
hl

Figura 14.21: Funções de Transferência Relacionadas Diretamente ao nível: FT h

164
1
Out1
Bl
xl em t=0
Bp
xg em t=0
-(C5*C7)/(C1+C4*c5+C5*C8)
-1/(C1+C4*c5+C5*C8)s+1
p/xg
In1
In2 Out1
Switch1
In1
In2 Out1
Switch
-(C4*c4)/(C1+C4*c5+C5*C8)
-1/(C1+C4*c5+C5*C8)s+1
P/xl
-(C4*c4+C6*C10)/(C1+C4*c5+C5*C8)
-1/(C1+C4*c5+C5*C8)s+1
P/hl
-(C5*C9)/(C1+C4*c5+C5*C8)
-1/(C1+C4*c5+C5*C8)s+1
P/T
-C2/(C1+C4*c5+C5*C8)
-1/(C1+C4*c5+C5*C8)s+1
P/Li
-C3/(C1+C4*c5+C5*C8)
-1/(C1+C4*c5+C5*C8)s+1
P/Gi
6
In6
5
In5
4
In4
3
In3
2
In2
1
In1
P

Figura 14.22: Funções de Transferência Relacionadas Diretamente à Pressão: FT P
Instrumentação Analógica
Válvulas Falha Aberta,
hNL (m)
hLinear (m)
VAZÔES CONSTANTES (GL)
Li, Wi, Gi (PERTURBAÇÕES
SENSORES1
SENSORES
SAIDA DO POÇO (GL):
Li, Gi (PERTURBAÇÕES)
PNL (bar)
PLinear (bar)
Gc-P
PIC1
Gc-P
PIC
Gc-L
LIC1
Gc-L
LIC
ERRO1```