Dynamic simulation of fluid filled vessels
View Patent ↗A system is provided. The system comprises a computer system comprising at least one processor, a thermodynamic state solver application, and a thermodynamic system solver application. When executed by the at least one processor, the thermodynamic state solver application computes a flash equilibrium state solution for each of a plurality of nodes in a thermodynamic network and determines for each of the plurality of nodes at least one sensitivity of a first thermodynamic property with reference to at least one second thermodynamic property. When executed by the at least one processor, the thermodynamic system solver computes a pressure at each of the nodes and flows between the nodes based at least in part on the sensitivities, wherein a result based on the pressures and flows is determined.
1. A system, comprising:
a computer system comprising at least one processor;
a thermodynamic process simulation application executes for the duration of a time period, the time period comprising a plurality of time steps;
wherein the thermodynamic process simulation application executes on the at least one processor, iteratively invoking a pressure flow solver application to determine for each time step a plurality of pressures and flows for a thermodynamic network comprising a plurality of nodes,
wherein the thermodynamic process simulation application executes on the at least one processor, invoking a flash solver application for each of the plurality of nodes, the flash solver application performing a flash equilibrium calculation to obtain in part at least one sensitivity associated with a first thermodynamic variable and performing for each of the plurality of nodes a Taylor series expansion of a thermodynamic property associated with the first thermodynamic variable, wherein the expansion is based on the at least one sensitivity, to produce at least one residual,
wherein a result is determined,
wherein the Taylor series comprises an expansion of
ⅆ
V
ⅆ
t
,
where
ⅆ
V
ⅆ
t
indicates the rate of change over time t of the volume V of a fluid associated with a node, wherein
ⅆ
V
ⅆ
t
comprises
(
∂
V
∂
p
)
ⅆ
P
ⅆ
t
+
(
∂
V
∂
U
)
ⅆ
U
ⅆ
t
+
∑
i
(
∂
V
∂
n
i
)
ⅆ
n
i
ⅆ
t
,
wherein
∂
V
∂
P
is the sensitivity of the volume V with respect to a pressure P, wherein
∂
V
∂
U
is the sensitivity of the volume V with respect to an internal energy U, wherein
∑
i
indicates a summation over the plurality of chemical species associated with the node, wherein the index i ranges from 1 to M, wherein
∂
V
∂
n
i
is the sensitivity of the volume V with respect to n i , wherein n i is the number of moles of the i-th chemical species, wherein
∂
V
∂
P
,
∂
V
∂
U
and
∂
V
∂
n
i
are evaluated at the flash equilibrium solution point, wherein
ⅆ
P
ⅆ
t
=
Δ
P
Δ
t
,
where ΔP is the difference between the pressure at the current time step and the pressure at the previous time step and where Δt indicates the duration of a time step, wherein
ⅆ
U
ⅆ
t
=
1
n
[
F
f
H
f
-
F
v
H
v
-
F
l
H
l
+
Q
imp
+
Q
r
-
U
(
F
f
-
F
v
-
F
l
+
∑
r
i
)
]
,
wherein the superscripts “f”, “l” and “v” indicate properties associated with a feed, a mixed or liquid phase or a vapor phase, respectively, wherein the subscripts “imp” and “r” indicates a value imposed externally or via a reaction, respectively, wherein n indicates the number of moles associated with the node, wherein F indicates a molar flow, wherein H indicates an enthalpy, wherein Q indicates a heat flow, wherein
∑
i
indicates a summation over the plurality of chemical species associated with the node, wherein the index i ranges from 1 to M, wherein r i is the change in the number of moles of the i-th chemical species due to a reaction, wherein
ⅆ
n
i
ⅆ
t
is
ⅆ
n
i
ⅆ
t
is
ⅆ
n
i
ⅆ
t
=
F
f
x
i
f
-
F
v
y
i
-
F
l
x
i
+
r
i
,
wherein x f i is the molar fraction of the i-th chemical species in the feed, wherein x i is the molar fraction of the i-th chemical species in mixed or liquid phase and wherein y i is the molar fraction of the i-th chemical species in vapor phase.
2. The system of claim 1 , further comprising the computation of a volume residual R associated with a vessel associated with the node, wherein R comprises
(
V
o
-
V
drum
)
+
ⅆ
V
ⅆ
t
Δ
t
,
where V 0 is the volume of a fluid in the vessel, wherein the volume is calculated by a flash equilibrium calculation, where V drum is the volume of the vessel containing the fluid, where
ⅆ
V
ⅆ
t
is the rate of change rate of change over time t of the volume V of a fluid associated with the node, wherein V is calculated by the thermodynamic state solver application, and wherein Δt indicates the duration of a time step, and wherein R is compared to a stopping criterion.