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OTC-28104-MS
Dynamic Model for Production Optimization to Offshore Platforms with
Short-Time Machine Failures
B. F. Vieira, Petrobras Cenpes; V. R. Rosa, F. F. Arraes, and A. F. Teixeira, Petrobras
Copyright 2017, Offshore Technology Conference
This paper was prepared for presentation at the Offshore Technology Conference Brasil held in Rio de Janeiro, Brazil, 24–26 October 2017.
This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of
the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any
position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written
consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may
not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.
Abstract
The objective of this paper is to give a support decision tool to help the engineer when main equipments,
especially compressors, fail for a short-period, that is to say, a few hours. This is a very complex problem
since, according to the transient period of the wells, an intertemporal component is included. Until a steady
state is reached again the operator must decide every period (typically every hour or every half an hour) on
which wells to close or open, how much gas lift should be injected, how much the chokes should open or
close in order to maximize oil production.
Introduction
This paper deals with the dynamic problem of how to cope with short-time failures of main machines in
offshore platforms with satellite wells that use gas lift injection. This is a common situation in Brazil.
For instance, a compressor goes down and about three hours will be necessary for the equipment to work
again. In this case some wells may need to be closed for lack of gas lift and others should have its production
reduced.
An optimization model will help decide which wells to restrict or to close so that oil production can be
maximized over the whole period.
Moreover it is taken into account the time a well needs to resume its best production if it is necessary to
close it, that is to say, its transient behavior if a well is closed and then reopened. This problem is similar than
Campos, Teixeira and Arraes (2014) but a time component is included increasing the size and complexity
of the problem.
Optimization Model
A pseudo-dynamic (differential equations are not used) optimization model is developed so that the engineer
can decide what to do when there is a temporary problem with important machines in the platform, be it
compressors or separators.
The objective function (f) is to maximize oil production from all the wells
over time:
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OTC-28104-MS
(1)
Furthermore the following constrainsts must be observed for every period:
(2)
For every period the total gas produced from all the wells is qgas-prod,t.
(3)
For every period the total gas lift from all the wells is qgas-lift,t.
(4)
For every period, the flow of gas follows a mass balance in which produced gas is distributed between
exportation, the flare and the turbines. Gas lift may be excluded because it is the same both ways.
(5)
This equation shows the maximum capacity for gas treatment every period.
(6)
There is a maximum positive amount of gas that can be exported per period and gas cannot be imported.
(7)
A similar equation for the gas burned in the flare.
Then two equations, about the maximum treatment capacities of liquids and water:
(8)
(9)
Another equation relating oil production from each well to its respective gas production through GOR :
(10)
Moreover the transient behavior of the wells is modeled as a piecewise linear model as shown in figure 1:
OTC-28104-MS
3
Figure 1
Where qo symbolizes the transient behavior of a well that was closed due to a reduction in compression
capacity (for example, 1 of 3 compressors in a platform goes down and this well had to be closed on period 3
and was reopened on period 5 when the compressor restarted working). It was assumed that the production
of the well would return linearly. This would simplify the model and based on the expertise of production
engineers it was a reasonable assumption.
Several binary variables were included in tne mathematical model to represent this transient behavior
figure 2:
Figure 2
4
OTC-28104-MS
•
•
•
•
Z1,t is 1 when the well is operating normally. This means that if the well is not closed, z1 remains
1 for all periods;
Z2,t is 1 only when a well is closed due to fails in a main equipment;
Z3,t is 1 only when a well is restarting production;
Z4,t is 1 only after it has been reopened and reached stady state production.
The figures below summarize the main inputs and restrictions and decision variables of the problem
figure 3 figure 4:
Figure 3
Figure 4
The optimization model is a MILP (Mixed Integer Linear Programming) in which binary and SOS2 (as
in Campos and Teixeira 2011) variables are created to linearize the model.
is considered a function of
gas lift injection and wellhead pressure.
OTC-28104-MS
5
In order to run properly, the model takes as input the periods when the machines will be shut down or
function with reduced capacity and the transient behavior of the wells from being closed until reaching
steady production (assumed linear).
The model is run on CPLEX (solver) and uses GAMS as an optimization language.
Results
This model insofar has been tested on simulated data and the results seem to be in accordance with what
is expected, as can be seen in the figures below figure 5:
Figure 5
Data on the graphics were normalized in order to make visualization easier.
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OTC-28104-MS
Conclusions
A complex model that should generate production gains has been successfully formulated. Minor
adjustments may still be necessary.
Next steps are:
•
•
•
•
quantifying gains in real examples by comparing with similar cases in the past;
create a friendly interface for the user;
include ESPs;
include manfolds.
Ackowledgments
We thank our colleagues in Petrobras and to our partners UFSC and Tecgraf that are working together with
us on this project. We also thank Petrobras for authorizing the publication of this work.
References
CAMPOS, M. C. M. M., TEIXEIRA, A. F. Os Benefícios e Desafios da Aplicação de Técnicas de Controle Avançado e
Otimização em Tempo Real em Unidades Marítimas de Produção, IBP, VI Congresso Rio Automação, Rio de Janeiro,
Brasil, 16-17 May 2011 (reference in portuguese).
CAMPOS, M. C. M. M., TEIXEIRA, A. F., VON MEIEN, O. F., SIMÕES, S., SANTOS, W., PIMENTA, A., STENDER,
A. Advanced Control Systems for Offshore Production Platforms, OTC 24286, 2013 Offshore Technology Conference
Brasil held in Rio de Janeiro, Brasil, 29-31 October 2013.
CAMPOS, M. C. M. M., TEIXEIRA, A. F., ARRAES F. F. Otimização da Produção de Plataformas Offshore, Rio Oil
Gas 2014 (IBP1216_14, reference in portuguese)
CODAS, A., and CAMPONOGARA, E. Mixed-Integer Linear Optimization for Optimal Lift-Gas Allocation with WellSeparator Routing. European Journal of Operational Research 212: 222–231, 2012.
GUNNERUD, V., FOSS, B. Oil Production Optimization – A Piecewise Linear Model, Solved with Two Decomposition
Strategies. Computers and Chemical Engineering 34: 1803–1813, 2010.
MISENER, R., GOUNARIS, C. E., FLOUDAS, C. A. Global Optimization of Gas Lifting Operations: A Comparative
Study of Piecewise Linear Formulations. Ind. Eng. Chem. Res. 48: 6098–6104, 2009.
TEIXEIRA, A. F. Otimização da Produção de Poços de Petróleo com Gas Lift Contínuo. Dissertação de Mestrado, UFRJDepartamento de Química, 2013 (reference in portuguese)
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