Chemical Engineering September 2020 - 37

H
€ / kWh
Q
€ / m3/s
H
BEP
Pump model
adaptation
Q
Figure 8. Shown here is a multiple-target optimization
problem of a pump system. Underlying performance
models are adapted to represent latest equipment
behavior
Pipeline model
adaptation
sumption is
increased.
P h y s i ca l
modeling of
every component
is similarly
used as in the
data reconciliation
step.
The modeling
equations
describe conservation
laws
and the equipment's
performance.
In
comparison to
data reconciliation, where an overdetermined system is
resolved, in simulation, the number of unknowns matches
exactly the available equations. This requirement dictates
the necessary number of parameters that need to be
specified in advance as system boundary conditions (in
this example, it is equal to three). An approach for solving
nonlinear equations is employed [3], by iteratively solving
a system of linear equations:
Solve per iteration:
Az ∙ δz = -F
Apply corrections:
ẑ = z + δz
(3)
(4)
Where, z are the original unknown parameters and ẑ
are the calculated parameters by applying the respective
corrections δz, Az
is the Jacobian and F the residual
matrices.
Following the proposed methodology, complex
pump systems can be simulated. Where the performance
characteristics of each component shall be
adapted in advance, according to recent sensor values
and data reconciliation results. This approach
offers a great number of what-if scenarios for evaluating
the current performance of the pump system.
The operator shall test the operating requirements
by performing system simulations, reflecting the different
operating scenarios available. Due to the nature
of the approach, boundary parameters can be
specified according to the desired operating conditions.
In case the throughput is of major interest, the
volumetric flow is provided as a boundary condition
and the system should resolve the other parameters.
Similarly, if discharge head or pump operation close
to BEP are of interest, these are defined as boundary
conditions.
Concerning reliability predictions, the target of the
proposed approach alerts the user with sufficient notice,
in order to prevent an imminent failure. A clear
benefit is gained through applying corrective measures
before the failure even occurs. It can reduce
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