A Mixed Integer Linear Programming Model for the Optimal

Operation of a Network of Gas Oil Separation Plants

Songsong Liua, Ishaq Alhasana,b, Lazaros G. Papapgeorgioua,*

a
Centre for Process Systems Engineering, Department of Chemical Engineering, University
College London, Torrington Place, London WC1E 7JE, UK
b
South Ghawar Producing Department, Saudi Aramco, Dhahran, Saudi Arabia

Abstract
Inspired from a real case study of a Saudi oil company, this work addresses the optimal
operation of a regional network of gas-oil separation plants (GOSPs) in Arabian Gulf Coast
Area to ultimately achieve higher savings in operating expenditures (OPEX) than those
achieved by adopting single-surface facility optimisation. An originally tailored and
integrated mixed integer linear programming (MILP) model is proposed to optimise the crude
transfer through swing pipelines and equipment utilisation in each GOSP, to minimise the
operating costs of a network of GOSPs. The developed model is applied to an existing
network of GOSPs in the Ghawar field, Saudi Arabia, by considering 12 different monthly
production scenarios developed from real production rates. Compared to rule-based current
practice, an average 12.8% cost saving is realised by the developed model.

Keywords: upstream oil and gas industry, gas oil separation plant, operating expenditures,
mixed integer programming

1. Introduction
In the upstream oil and gas industry, a surface separation facility is called a gas-oil separation
plant (GOSP). Every GOSP receives its feed from several wells located municipally around
the GOSP (Abdel-Aal et al., 2003). Some of these wells are dry and some are wet (contain
associated water). Figure 1 shows a holistic view of a complete single upstream field where
the GOSP is located in the middle, and crude wells are connected to it through pipelines.
Also, the GOSP is connected to disposal wells, which receive treated gas and/or water from
the GOSP to boost up the reservoir pressure and enhance oil production and sweep in the
subject area (Raju et al., 2005).

* Corresponding author. Tel: +44-20-76792563. Fax: +44-20-76797092. Email:

l.papageorgiou@ucl.ac.uk.
 Figure 1. Schematic Layout of a GOSP and its Wells

In rich oil areas, such as the Arabian Gulf coast countries, large numbers of GOSPs exist near
each other within the same geological area to serve the high demands of production.
Typically, each well serves only one GOSP due to the high cost of pipelines that would be
required to connect the wells to more than one GOSP. Some of these GOSPs are connected
together laterally through swing pipelines, which allow the transfer of production from GOSP
wells to be treated in another GOSP. The purpose of these swing pipelines is to provide a
backup route of production from all wells in case of any breakdown or during the planned or
unplanned shutdown of a GOSP to avoid any intermittent production. These pipelines are
constructed only between nearby GOSPs where wells can free flow naturally based on excess
reservoir pressure without the need to use any artificial surface boosting or subsurface lifting.
Thus, no pump is required and no cost occurs for the production transfer. Figure 2 shows an
example of a network of GOSPs connected by swing pipelines. The production from the
wells of a GOSP can be produced through the same GOSP or diverted partially/completely to
one of the connected GOSPs for processing. It is worth noting that the existence of these
swing pipelines is rare and they are found in only a few applications, as shown in the case

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study of this paper. Consideration of these swing pipelines for new projects is increasing due
to their added flexibilities and tangible benefits in many aspects.

Figure 2. Example of a network of GOSPs

At an area containing several GOSPs, the network of swing pipelines may be used for an
additional purpose, which is integrating production rates laterally between the facilities to
optimise chemicals consumption and equipment power consumption, while maintaining the
assets in their best mode of operation. Finding the optimum allocation strategy utilising the
swing pipelines is very complicated and requires the careful consideration of thousands of
variables. These GOSPs contain hundreds of equipment with different flow vs. power curves
and different chemicals consumption relationships and costs, not to mention the various
constraints from all aspects. An opportunity was spotted for the potential optimisation of the
whole network as a single node by developing an integrated optimisation model with an
objective function targeting a combined reduced operating expenditure (OPEX) of GOSPs.

The OPEX of the upstream sector in the oil and gas industry has been consistently rising over
the past years, and will continue to rise in a trend (HIS, 2012). In addition, the fluctuation and
uncertainty of oil prices put more pressure on the upstream sector to find effective means to
cut down their OPEX and increase their profit margin. Power and chemical consumption
costs of GOSPs are considered one of the major cost contributors to the upstream OPEX. A
saving of even 1% of these costs could represent a 7 figure USD value for a company as big

3
as the one considered for this paper’s case study. Therefore, it is very critical for the upstream
sector to find innovative approaches such as the model presented by this paper, and adapt
them to face their challenges. In order to accurately calculate the OPEX, especially the power
consumption cost, it is important to consider the details of individual equipment, such as
pumps and compressors. Given that each equipment has its own unique power vs. flow curve,
and the flow rate for each equipment is not only determined by production transfer decisions,
but also by the number of selected running equipment units, it is critical to consider
equipment specific details to achieve the optimal power consumption.

The aim of this work is to develop an original and integrated mathematical model for the
optimal operation of an existing network of GOSPs in Arabian Gulf Coast Area to minimise
its OPEX. To the best of our knowledge, it is the first work focuses on the optimisation of
operational decisions with the lateral integration among multiple upstream surface separation
facilities to achieve the minimum OPEX.

The structure of this paper is organised as follows: Section 2 discusses the major optimisation
work on the oil and gas upstream sector with a focus on GOSPs optimisation. Section 3
presents a mixed integer linear programming (MILP) model. Then a case study of a
production area in Saudi Arabia is presented in Section 4, followed by the results presentation
and discussion in Section 5. Finally, the conclusion is given in Section 6.

2. Literature Review
The petroleum industry has been given huge attention academically and industrially for its
dominance and effect on the global economy. The optimisation literature covers a wide range
of subjects, from short-term scheduling to strategic supply chain planning (Shah, 1996; Moro
and Pinto, 2004; Neiro and Pinto, 2004; Relvas et al., 2006; Fernandes et al., 2013; Tavallali
and Karimi, 2014; Sahebi et al., 2014). Given the maturity of the industry, applications of
mathematical programming have been employed since 1940s (Bodington and Baker, 1990).
Schlumberger (2005) classified the optimisation problems in the upstream sector to four
groups, including operator optimisation, production optimisation, field optimisation and
reservoir recovery optimisation, with time scales from seconds to years. This work will
address the production optimisation for one day to a few months, which is also called real-
time production optimisation (RTPO) (Gunnerud and Foss, 2010). Another grouping, based

4
on the scope and function, was suggested by Wang (2003). The author reviewed optimisation
problems in the upstream sector and classified them into three main categories: lift gas and
production rate allocation; optimisation of production system design and operations; and
optimisation of reservoir development and planning. Ulstein et al. (2007) divided the
upstream optimisation planning problems to operational, tactical and strategic problems,
which, to a certain degree, is also compatible with that of Wang (2003) and Schlumberger
(2005).

In the literature, there are lots of literature work focusing on the optimisation of design and
planning of production networks in oil fields, including subsurface and/or surface facilities.
Iyer et al. (1998) developed an mixed integer nonlinear programming (MINLP) model for the
planning and scheduling of investment and operation in offshore oil field facilities, including
the selection of reservoirs, well sites, well drilling, and platform installation schedule and
capacities of well and production platforms. van den Heever et al. (2001) proposed an
MINLP optimisation model for the design and planning of offshore hydrocarbon field
infrastructures and developed a Lagrangean decomposition solution procedure. Goel and
Grossmann (2004) addressed the optimal investment and operational planning of gas field
developments under uncertainty in gas reserves using stochastic programming. Cullick et al.
(2004) developed an framework for the optimal reservoir planning and management under
the uncertainty of associated risks. Kosmidis et al. (2005) proposed an MINLP optimisation
model and a solution procedure for the well scheduling problem considering the optimal
connectivity of wells to manifolds and separators, as well as the optimal well operation and
gas lift allocation. Foss et al. (2009) proposed a Lagrangian decomposition method for a well
allocation and routing optimisation problem. Gunnerud and Foss (2010) presented an MILP
model for the real-time optimisation of process systems with a decentralized structure, which
was solved using Lagrangian decomposition and Dantzig-Wolfe decomposition. These work
was extended to the use of parallelization of Dantzig-Wolfe decomposition (Gunnerud et al.,
2010; Torgnes et al., 2012) and Brach & Price decomposition (Gunnerud et al., 2014).
Rahmawati et al. (2012) addressed the integrated field operation and optimisation by
developing an optimisation framework integrating reservoir, well vertical-flow, surface-
pipeline and surface-process, thermodynamic and economic models. Codas et al. (2012) used
piecewise linearisation to develop an MILP model integrating simplified well deliverability
models, vertical lift performance relations, and the flowing pressure behavior of the surface
gathering system. Tavallali et al. (2013) developed an optimisation model for the optimal

5
producer well placement and production planning in an oil reservoir, and extended for
multireservior oil fields with surface facility networks (Tavallali et al., 2014). Silva and
Camponogara (2014) developed an integrated production optimisation model for complex oil
fields, considering the production network structure.

However, in the literature, the operational decisions of GOSP network, as focused in this
work, was given little attention, possibly due to the unconventional nature of the project, as
surface facilities usually stand solo with no connections or integration with nearby similar
purpose facilities. Figure 3 shows the common boundaries in the upstream real-time
optimisation problems related to surface facilities (dash line). The objective of the literature
model is either oil production maximisation, single facility OPEX minimisation, or NPV
maximisation. None of the literature work has considered multiple production trains in a
single model to optimise combined OPEX. The optimisation boundary targeted by this work
is illustrated by the solid line. It is important to highlight that this boundary does not overlap
with existing upstream real-time optimisation models. On the contrary, the proposed
optimisation model in this work could be applied sequentially after the optimisation within
any other boundaries in a complementary manner.

Figure 3. Research boundary comparison between this work and the literature work on the
upstream real-time production optimisation

3. Problem Statement
In this work, we address the optimal operation of a network of GOSP’s, considering the crude
transfer via swing pipelines and operation mode of the equipment in the process of each

6
GOSP. A GOSP is considered to be the first crude treatment process to provide preliminary
separation of the crude to gas, oil and water. Its objective is mainly to separate gas, water and
contaminants from the oil and treat the three products to the required specifications. Then, oil
and gas are streamed to oil refineries and gas processing plants, respectively, for further
processing. Water, and sometimes part of the gas, is injected back in the reservoir, depending
on the oil recovery enhancement strategy of the production field. The main operations within
a GOSP can be summarised as follows:
 Separation; separating the gas, oil and water from produced wellhead streams through
multiple tasks
 Dehydration; removing water droplets emulsified within the oil
 Desalting; reducing the salt content of the crude by diluting associated water and then
dehydrating

Beside the crude received from the wells, GOSPs consume chemicals as raw materials for
different purposes. The main chemicals consumed are:
 Demulsifier; to enhance the separation between oil and water in highly emulsified
mixtures
 Corrosion inhibitor; mainly to prevent corrosion development in metal pipelines
 Scale inhibitor; to prevent any scale build-up in the containers.

GOSP capacities vary greatly from approximately 20 thousand barrels per day (kbd) to 400
kbd of oil. The capacity of a GOSP is designed based on the the forecasted production rates
for the associated field wells. A standard GOSP size in our case study is around 330 kbd.
These facilities require intensive power supply to run the various rotating equipment
contained. The major sets of power equipment are:
 Charge pumps (two-phase pumps, oil and water)
 Injection pumps (water)
 Boosting pumps (oil)
 Shipper pumps (oil)
 High pressure (HP) compressors (gas)
 Low pressure (LP) compressors (gas)

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Every GOSP has the same set of equipment but varies greatly when it comes to capacity,
efficiency and number of equipment items depending on the age, design parameters and
philosophy. In each GOSP, the number of operating equipment items and their operation
modes has significant effects on power consumption, which can represent a large portion of
the OPEX in the upstream.

The GOSPs considered here are connected by swing pipelines. Although the production rates
of each GOSP are originally determined by its wells’ production, its actual production rates
can be reallocated by transferring crude to the nearby GOSPs through swing pipelines. The
final inlet feed of each GOSP, after crude transfer, can determine the amount of chemicals for
the separation and the flow rates of operating equipment. Therefore, in this work, we aim to
find the optimal production transfer between GOSPs and the equipment operation modes
within each GOSP, with a minimum total OPEX of the network of GOSPs considered.

There are some assumptions made for the optimisation problem in this work, as listed below:
 Crude can be transferred from selected wells of one GOSP to another using the swing
pipelines without any back-effect on well productivity.
 Temperature drops in the crude when it is transferred from one GOSP to another are
ignored here due to the fact that all transfer pipelines are internally coated and buried
underground, which preserves the temperature with very minimal loss.
 Given that all nearby GOSPs have very similar crude characteristics, the effect of
crude mixing on the chemicals consumption was ignored.
 Component separation fractions from the vessels were assumed to be constant. For
gas-oil separation, it is highly dependent on separator pressure, which is fixed. For
water-oil separation, the automated demulsifier injection system at these GOSPs
maintains the separation of water and oil at steady fractions.
 The flow vs. power curve of each equipment item can be represented by quadratic
polynomials.
 All parallel equipment for the same task has identical characteristics.
 Equipment serving the same task shares a common suction and so the load is equally
shared among the operated ones.
 Discharge pressure requirements are not considered directly. The equipment
minimum and maximum flow rates take into account the system required pressure,

8
 and ensure that the equipment can always overcome the discharge pressure if it
operates within a certain window of flow rates.
 A recycle mode of operations is not allowed. The assigned minimum flow rate for
each piece of equipment is actually its minimum recycle flow rate to avoid any
recycle operations.
 The reservoir effects in terms of variations in GOSP injected water are ignored. The
GOSP injected water serves as a secondary source of the injected water in the
reservoir, while the main source comes from treated seawater plants.
 Only power consumption costs of the liquid pumps and gas compressors are
considered, as they contribute most of the operating cost. Common and trivial power
consuming items, such as air conditioning and lighting, are ignored in power cost, and
are considered under fixed operating cost, which also includes the manpower cost and
maintenance and service cost.
 As demulsifier accounts for over 90% of the total chemicals cost; other chemicals cost
is ignored in this problem.
 The added freshwater and salty water are mixed and considered as water, one of the
final products.

Based on the above assumptions, the considered optimisation problem is described as follows:
Given are:
 A network between GOSPs with swing pipeline connections;
 GOSP capacities for each component;
 daily initial designated flow rate for each GOSP;
 capacities of the swing pipelines connecting any two GOSPs;
 fixed operating cost and operating time of each GOSP;
 process flow sheet within each GOSP;
 available equipment, their minimum/maximum capacities, power consumption curves,
and the separation fractions of all components;
 chemicals consumption equations based on treated production rates; and
 chemical and electricity prices;
to determine:
 GOSP selection;
 swing pipeline selection;

9
  transferred flow rates through swing pipelines;
 final inlet crude flow rates of each component; and
 equipment selection and operating rates;
so as to
 minimise the total OPEX, including power and chemicals consumption costs, and
fixed operating cost.

4. Mathematical Formulation
In this section, we present a static MILP model for the OPEX minimisation of a network of
GOSPs in a fixed planning horizon. The notation used in the model is presented below:

Indices
𝑔, 𝑔′ Gas-oil separation plant, GOSP
𝑐 Component = {oil, water, gas, demulsifier, freshwater}
𝑗 Operating equipment/unit
𝑖 Task
𝑠 Produced and consumed states
𝑘 Break point in piecewise linearisation

Sets
𝐽𝑔𝑖 Equipment performing the task i in GOSP g
𝐼𝑅 Tasks by rotating equipment (pumps + compressors)
𝐼𝑃 Tasks by pumps
𝐺𝑔 GOSPs connecting GOSP 𝑔 through swing pipelines
𝑆𝑖 State produced or consumed by task i
𝑆 𝐼𝑁 Intermediate state
𝑆 𝑅𝑀 Raw material state
𝑆𝑃 Product state

Parameters
𝑎𝑔𝑖 second order coefficient in flow vs. power curve for task i in GOSP 𝑔
𝑏𝑔𝑖 first order coefficient in flow vs. power curve for task i in GOSP 𝑔
𝑐𝑔𝑖 constant coefficient in flow vs. power curve for task i in GOSP 𝑔
𝑚𝑎𝑥
𝐶𝐶𝑔𝑐 Maximum component capacity in GOSP 𝑔
𝑚𝑖𝑛
𝐶𝐶𝑔𝑐 Minimum component capacity in GOSP 𝑔
𝐶ℎ𝑒𝑚𝐶𝑔 Chemicals market price for GOSP 𝑔
𝐹𝑂𝐶𝑔 Fixed operating cost for GOSP 𝑔
𝐹𝑊𝑔 Freshwater consumption in GOSP 𝑔
𝐼𝐹𝑔𝑐 Initial designated flow rate of component c for GOSP 𝑔
𝑂𝑇 Operating time
𝑃𝑐 Power market price
𝑃𝑖𝑘𝑔𝑖𝑘 Power at breakpoint k for task i in GOSP 𝑔

10
 𝑚𝑎𝑥
𝑃𝑗𝑔𝑖𝑗 Maximum power consumption of equipment j for task i in GOSP 𝑔
𝑚𝑎𝑥
𝑅𝑗𝑔𝑗 Maximum capacity rate for equipment j in GOSP 𝑔
𝑚𝑖𝑛
𝑅𝑗𝑔𝑗 Minimum capacity rate for equipment j in GOSP 𝑔
𝑅𝑖𝑘𝑔𝑖𝑘 Operating rate at breakpoint k for task i in GOSP 𝑔
𝑚𝑎𝑥
𝑆𝑃𝐶𝑔𝑔 ′ Maximum swing pipeline capacity from GOSP 𝑔 to 𝑔′
𝑚𝑖𝑛
𝑆𝑃𝐶𝑔𝑔 ′ Minimum swing pipeline capacity from GOSP 𝑔 to 𝑔′
+
𝜓𝑔𝑠𝑖𝑐 Fraction of components in each produced state s for task i in GOSP 𝑔
−
𝜓𝑔𝑠𝑖𝑐 Fraction of components in each consumed state s for task i in GOSP 𝑔

Continuous Variables
𝐶𝐶 Chemicals consumption cost
𝐹𝐶 Fixed operating cost
𝐹𝐹𝑔𝑐 Final inlet flow rate of component c in GOSP 𝑔
𝑂𝑃𝐸𝑋 Total OPEX for all GOSPs
𝑃𝑔𝑠 Final products (gas, oil and water) for GOSP 𝑔
𝑃𝐶 Power consumption cost
𝑃𝑖𝑔𝑖 Power consumption for a single unit for task i in GOSP 𝑔
𝑃𝑗𝑔𝑖𝑗 Power consumption for equipment j for task i in GOSP 𝑔
𝑄𝑔𝑔′ Total transferred flow rate from GOSP 𝑔 to 𝑔′
𝑅𝑔𝑖𝑐 Rate of component c for task i in GOSP 𝑔
𝑅𝑖𝑔𝑖 Processing rate for a single unit for task i in GOSP 𝑔
𝑅𝑗𝑔𝑖𝑗 Processing rate for equipment j for task i in GOSP 𝑔
𝑅𝑀𝑅𝑔𝑠𝑐 Inlet rate of component c for raw materials state s for GOSP 𝑔
𝑊𝑔𝑖𝑘 SOS2 variable at break point k for task i in GOSP 𝑔

Binary Variables
𝑋𝑔 1 if GOSP 𝑔 is selected for process; 0 otherwise
𝑌𝑔𝑔′ 1 if transfer from GOSP 𝑔 to 𝑔′ is selected; 0 otherwise
𝑍𝑔𝑖𝑗 1 if equipment j is selected to perform task i at equipment 𝑔; 0 otherwise

In the MILP model presented below, the gas flow rates in = (mscfd) are converted to
thousand barrels per day of oil equivalent (kbdoe) to improve numerical stability.

4.1 Production Designation through GOSPs

The crude production is initially designated for the wells connected to a GOSP based on the
reservoir strategy and production demands. This gives us the initial production flow rates for
each GOSP. By utilising the swing pipelines, the crude can be reallocated to other GOSPs for
process. Therefore, the mass balance for determining the final inlet component flow rates
entering the GOSPs can be expressed as:
𝐹𝐹𝑔𝑐 = 𝐼𝐹𝑔𝑐 + ∑𝑔′ ∈𝐺𝑔 𝐶𝐹𝑐𝑔′ ⋅ 𝑄𝑔′ 𝑔 − ∑𝑔′ ∈𝐺𝑔 𝐶𝐹𝑐𝑔 ⋅ 𝑄𝑔𝑔′ , ∀𝑔, 𝑐 (1)

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where 𝐼𝐹𝑔𝑐 and 𝐹𝐹𝑔𝑐 are the initial designated and final inlet rates of component 𝑐 for GOSP
𝑔, respectively; 𝑄𝑔′𝑔 is the combined flow rate from GOSP 𝑔′ to 𝑔; 𝐶𝐹𝑐𝑔 is the component
fraction based on the initial designation for each 𝑔; and 𝐺𝑔 is the set of GOSPs connecting 𝑔
through swing pipelines. Note that to avoid the difficulty in tracking the components in the
crude through transfer, it is assumed that the crude can only be transferred to the GOSPs
directly connected to its originally designated ones for processing, and cannot go to further
GOSPs. Therefore, for each GOSP, its total flow rate transferred to other GOSPs cannot
exceed its originally designated flow rate.

The transfers between GOSPs are constrained by the capacities of the swing pipelines
connecting them. Therefore, Eq. (2) is introduced to maintain the transferred flow rates
between the maximum and minimum capacities of the pipelines accordingly:
𝑚𝑖𝑛 𝑚𝑎𝑥
𝑇𝑃𝐶𝑔𝑔 ′ ∙ 𝑌𝑔𝑔′ ≤ 𝑄𝑔𝑔′ ≤ 𝑇𝑃𝐶𝑔𝑔′ ∙ 𝑌𝑔𝑔′ , ∀𝑔, 𝑔′ ∈ 𝐺𝑔 (2)
𝑚𝑖𝑛 𝑚𝑎𝑥
where 𝑇𝑃𝐶𝑔𝑔 ′ and 𝑇𝑃𝐶𝑔𝑔′ are the minimum and maximum swing pipeline capacities
between 𝑔 and 𝑔′ , respectively; and 𝑌𝑔𝑔′ is a binary variable to indicate whether the transfer
from 𝑔 to 𝑔′ is selected.

Physically, there is only a single swing pipeline connecting any two GOSPs; therefore, the
transfers through any swing pipeline should be limited to one direction, if both directions are
available, as defined by the constraint below:
𝑌𝑔𝑔′ + 𝑌𝑔′𝑔 ≤ 1, ∀𝑔 ∈ 𝐺𝑔′ , 𝑔′ ∈ 𝐺𝑔 , 𝑔 < 𝑔′ (3)

For each GOSP, its final inlet component flow rates must be maintained within the minimum
and maximum capacities, if the GOSP is selected (binary variable 𝑋𝑔 = 1):
𝑚𝑖𝑛 𝑚𝑎𝑥
𝑆𝑃𝐶𝑔𝑐 ∙ 𝑋𝑔 ≤ 𝐹𝐹𝑔𝑐 ≤ 𝑆𝑃𝐶𝑔𝑐 ∙ 𝑋𝑔 , ∀𝑔, 𝑐 (4)

4.2 Process in a GOSP

The representation of a process can either be aggregated, short-cut or rigorous depending on
the complexity and details included. Adding too much detail may result in computational
challenges and rigidness to find the optimal solution. Simplifying the flow sheet could result
in overlooking critical details that could render the model unpractical. In this work, the
process within the GOSPs was formulated by the state-task network (STN) framework

12
(Kondili et al., 1993), due to its capability to cover all the process features and the modelling
requirements. The component fractions for the separation tasks (T1, T2, T4 and T6) are
assumed to be known parameters. Figure 4 shows the developed STN representation for a
standard GOSP in the oil and gas industry. In this framework, we represent all GOSP
processes in a unified representation that segregate the states, tasks and units so that they can
be easily utilised for the required purposes in the model. Every state consists of five
components: gas, oil, salty water associated with crude, chemicals demulsifier and added
freshwater. The fraction of these components is different from state to another and from a
GOSP to another. The tasks represent the different separation, pumping and compressing
tasks within the GOSP. All equipment is linked to one specific task only and there is no
+ −
multitasking equipment in our problem. In each GOSP 𝑔, we have 𝜓𝑔𝑠𝑖𝑐 (> 0)/𝜓𝑔𝑠𝑖𝑐 (< 0)
for the fraction of component c that is produced/consumed in state 𝑠 for the processing task i
within GOSP 𝑔.

Figure 4. STN representation of a GOSP

The STN process flow is initiated by linking the raw materials 𝑅𝑀𝑅𝑔𝑠𝑐 to the task rates 𝑅𝑔𝑖𝑐 ,
so that the consumed task rate is equal to the raw materials added.

13
 −
𝑅𝑀𝑅𝑔𝑠𝑐 + ∑(𝜓𝑔𝑠𝑖𝑐 ∙ 𝑅𝑔𝑖𝑐 ) = 0, ∀𝑔, 𝑐, 𝑠 ∈ 𝑆 𝑅𝑀 (5)
𝑖∈𝑆𝑖

In the GOSP operation, usually there are five raw materials that enter the GOSP (oil, gas and
salty water from the crude received from the wells, chemicals and added freshwater). Eqs.
(6)-(8) define the five raw materials.

Eq. (6) bridges the network outside the GOSPs with the internal process flow sheets by
equating the GOSPs final inlet component flow rate, 𝐹𝐹𝑔𝑐 , with the state of STN crude raw
materials.
𝑅𝑀𝑅𝑔𝑠𝑐 = 𝐹𝐹𝑔𝑐 , ∀𝑔, 𝑐 ∈ {𝑜𝑖𝑙, 𝑔𝑎𝑠, 𝑤𝑎𝑡𝑒𝑟}, 𝑠 = 𝑠1 (6)

The demulsifer is the main chemical raw material considered, and its consumption is
determined by the inlet oil and water rates:
𝑅𝑀𝑅𝑔𝑠,𝑑𝑒𝑚𝑢𝑙𝑠𝑖𝑓𝑒𝑟 = 𝐶ℎ𝑒𝑚𝑅𝑔 ∙ (𝐹𝐹𝑔,𝑜𝑖𝑙 + 𝐹𝐹𝑔,𝑤𝑎𝑡𝑒𝑟 ) ∀𝑔, 𝑠 = 𝑠2 (7)
where chemicals consumption rate, 𝐶ℎ𝑒𝑚𝑅𝑔 , is a function of the crude temperature, liquid
flow rate and GOSP characteristics obtained experimentally.

The consumed freshwater for each GOSP is assumed to be a fixed value.

𝑅𝑀𝑅𝑔𝑠,𝑓𝑟𝑒𝑠ℎ𝑤𝑎𝑡𝑒𝑟 = 𝐹𝑊𝑔 ∙ 𝑋𝑔 , ∀𝑔, 𝑠 = 𝑠6 (8)

The intermediate states and tasks are modelled in the STN in the following format:
+ −
∑𝑖∈𝐼𝑠 (𝜓𝑔𝑠𝑖𝑐 + 𝜓𝑔𝑠𝑖𝑐 ) ∙ 𝑅𝑔𝑖𝑐 = 0, ∀𝑔, 𝑐, 𝑠 ∈ 𝑆 𝐼𝑁 (9)

Then, the mass balance for the final products is formulated as follows:
+
∑𝑖∈𝐼𝑠 ∑𝑐 𝜓𝑔𝑠𝑖𝑐 ∙ 𝑅𝑔𝑖𝑐 = 𝑃𝑔𝑠 , ∀𝑔, 𝑠 ∈ 𝑆 𝑃 (10)
where 𝑃𝑔𝑠 denotes the final products (gas, oil and water) production from GOSP g treated for
the targeted specifications, noting that fresh water and salty water are combined as produced
water in the final product. Demulsifier will be dissolved in the oil and therefore it is added to
the oil rate in the final quantity. Therefore, we have five raw materials but three final
products.

So far, the process flow rates are defined through tasks. For the tasks that involve rotating
equipment, i.e., pumps and compressors (T3, T5, T7, T8 and T9 in Figure 4), the flow rates

14
must also be associated with the equipment rates to calculate power consumption. For
example, if a task is coupled to multiple pumps, the number of pumps would be required to
process the task rate and the flow rate for each pump need to be optimised. As a result, Eq.
(11) is defined to link the task flow rates with their associated equipment flow rates, in which
the total rate for all equipment is equal to the summation of all components and streams
produced from a task.
+
∑𝑐 ∑𝑠 𝜓𝑔𝑠𝑖𝑐 ∙ 𝑅𝑔𝑖𝑐 = ∑𝑗∈𝐽𝑔𝑖 𝑅𝑗𝑔𝑖𝑗 , ∀𝑔, 𝑖 ∈ 𝐼 𝑅 (11)

where 𝑅𝑗𝑔𝑖𝑗 is the processing flow rate of equipment 𝑗 for task 𝑖 within GOSP 𝑔. The above
equation is valid in our case given that all pumping and compression tasks are modelled
through the STN independently with only a single state consumed and a single state
produced. If there are multiple produced states and only one goes to the set of equipment
associated, then this equation needs to be modified accordingly.

Every equipment has an upper and lower operating range that must be maintained. So, the
equipment rates are limited within given bounds, if it is selected within their specific
operating windows:
𝑚𝑖𝑛 𝑚𝑎𝑥
𝑅𝑗𝑔𝑗 ∙ 𝑍𝑔𝑖𝑗 ≤ 𝑅𝑗𝑔𝑖𝑗 ≤ 𝑅𝑗𝑔𝑗 ∙ 𝑍𝑔𝑖𝑗 , ∀𝑔, 𝑖 ∈ 𝐼 𝑅 , 𝑗 ∈ 𝐽𝑔𝑖 (12)
𝑚𝑖𝑛 𝑚𝑎𝑥
where 𝑅𝑗𝑔𝑗 and 𝑅𝑗𝑔𝑗 are the minimum and maximum rate of equipment 𝑗 within GOSP 𝑔,
respectively; and 𝑍𝑔𝑖𝑗 is a binary variable to indicate whether equimpent 𝑗 is selected to
perform task 𝑖 within GOSP 𝑔.

If GOSP 𝑔 is not selected for operation, then no equipment inside this GOSP should operate:
𝑍𝑔𝑖𝑗 ≤ 𝑌𝑔 , ∀𝑔, 𝑖 ∈ 𝐼 𝑅 , 𝑗 ∈ 𝐽𝑔𝑖 (13)

Typically, all equipment within the same set shares a common suction pipeline and a
common discharge pipeline, as shown in Figure 5. Therefore, the flow rates of each pump
within one set must stay the same to prevent the pumps from affecting the performance of the
other pumps. The compressors can be allowed to have variable equipment flow rates, but the
current practice in the industry shares also the load equally to maintain a similar distance for
all compressors from their minimum flow rate limit (known as a surge line).

15
 Figure 5. Common suction and discharge pipelines for a set of pumps

Since all equipment in a set is linked to a single task, a unified rate can be enforced for all
running equipment by equating their rates to a single auxiliary variable associated with the
containing task, 𝑅𝑖𝑔𝑖 . To avoid enforcing all equipment to have a positive value, the flow rate
of each running equipment j must be equal to 𝑅𝑖𝑔𝑖 . .
𝑅𝑗𝑔𝑖𝑗 ≤ 𝑅𝑖𝑔𝑖 , ∀ 𝑔, 𝑖 ∈ 𝐼 𝑅 , 𝑗 ∈ 𝐽𝑔𝑖 (14)
𝑚𝑎𝑥
𝑅𝑗𝑔𝑖𝑗 ≥ 𝑅𝑖𝑔𝑖 − 𝑅𝑗𝑔𝑗 ∙ (1 − 𝑍𝑔𝑖𝑗 ), ∀ 𝑔, 𝑖 ∈ 𝐼 𝑅 , 𝑗 ∈ 𝐽𝑔𝑖 (15)

Note that if different operating flow rates for the parallel compressors are allowed, the above
equations can be only valid for tasks by pumps, i.e., 𝑖 ∈ 𝐼 𝑃 .

4.3 Equipment Power Consumption

The power consumption of each equipment can be calculated from its flow vs. power curve.
These curves can be represented by quadratic polynomials. To ease the computational load
and speed up the convergence, it is assumed that this curve of each equipment for the same
task remains the same. Therefore, the power consumption, considering motor efficiency and
gearbox efficiency of each equipment for task 𝑖 within GOSP 𝑔, 𝑃𝑖𝑔𝑖 , is calculated by 𝑅𝑖𝑔𝑖 as
follows:
2
𝑃𝑖𝑔𝑖 = 𝑎𝑔𝑖 ∙ 𝑅𝑖𝑔𝑖 + 𝑏𝑔𝑖 ∙ 𝑅𝑖𝑔𝑖 + 𝑐𝑔𝑖 , ∀𝑔, 𝑖 ∈ 𝐼 𝑅 (16)
Where 𝑎𝑔𝑖 , 𝑏𝑔𝑖 and 𝑐𝑔𝑖 are the polynomial equation parameters. The above nonlinear power
consumption curves can be approximated using piecewise linearisation technique. For a
reasonable accuracy, the linearisation was based on analytical approximation. If more
accuracy is required, Natali and Pinto (2008) provides a scientific linearisation approach that
may be followed. Based on Eq. (16), we can obtain the breakpoints of the power consumption
𝑇𝑃𝑘𝑔𝑖𝑘 and the flow rate 𝑅𝑘𝑔𝑖𝑘 , for each equipment of task i. Therefore, the power
consumption and flow rate can be formulated as:
𝑅𝑖𝑔𝑖 = ∑𝑘 𝑅𝑖𝑘𝑔𝑖𝑘 ∙ 𝑊𝑔𝑖𝑘 , ∀𝑔, 𝑖 ∈ 𝐼 𝑅 (17)
𝑃𝑖𝑔𝑖 = ∑𝑘 𝑃𝑖𝑘𝑔𝑖𝑘 ∙ 𝑊𝑔𝑖𝑘 , ∀𝑔, 𝑖 ∈ 𝐼 𝑅 , 𝑗 ∈ 𝐽𝑔𝑖 (18)

16
where 𝑊𝑔𝑖𝑘 is a SOS2 variable that takes at most two consecutive values to locate 𝑅𝑖𝑔𝑖 value
in any of the corresponding operating intervals of 𝑅𝑗𝑘𝑔𝑖𝑘 . Therefore, it follows:
∑𝑘 𝑊𝑔𝑖𝑘 = 1, ∀𝑔, 𝑖 ∈ 𝐼 𝑅 (19)

Thus, the power consumption for each equipment is calculated as follows:

𝑚𝑎𝑥
𝑃𝑗𝑔𝑖𝑗 ≤ 𝑃𝑗𝑔𝑖𝑗 ∙ 𝑍𝑔𝑖𝑗 , ∀𝑔, 𝑖 ∈ 𝐼 𝑅 , 𝑗 ∈ 𝐽𝑔𝑖 (20)
𝑚𝑎𝑥
𝑃𝑗𝑔𝑖𝑗 ≥ 𝑃𝑖𝑔𝑖 − 𝑃𝑗𝑔𝑖𝑗 ∙ (1 − 𝑍𝑔𝑖𝑗 ), ∀𝑔, 𝑖 ∈ 𝐼 𝑅 , 𝑗 ∈ 𝐽𝑔𝑖 (21)
𝑃𝑗𝑔𝑖𝑗 ≤ 𝑃𝑖𝑔𝑖 , ∀𝑔, 𝑖 ∈ 𝐼 𝑅 , 𝑗 ∈ 𝐽𝑔𝑖 (22)
where 𝑃𝑗𝑔𝑖𝑗 is the power consumption for equipment j for a task i in GOSP 𝑔.

4.4 Objective Function

The objective of the proposed model is to minimise OPEX for the complete network of
GOSPs. The three costs considered in this model are power consumption cost, 𝑃𝐶, chemicals
consumption cost, 𝐶𝐶, and fixed operating cost, 𝐹𝐶. Therefore, the total OPEX for all GOSPs
is calculated below with further detailed calculation for each term:
𝑂𝑃𝐸𝑋 = 𝑃𝐶 + 𝐶𝐶 + 𝐹𝐶 (23)
where 𝑃𝐶 is the combined power cost for running equipment in all GOSPs; 𝐶𝐶 is the
combined chemicals cost; 𝐹𝐶 is the total fixed operating cost which is independent of the
processed flow rates. It only depends on whether a GOSP is running or not.

Here, as discussed previously, we only focus on the power consumption by liquid pumps and
gas compressors in the power consumption calculation, due to their significate contribution,
and other small portion power consumption cost is considered in the fixed operation cost. The
power consumption cost is considered by the total power multiplied by the operating time,
OT, and power price, Pc.

𝑃𝐶 = 𝑂𝑇 ∙ 𝑃𝑐 ∙ (∑𝑔 ∑𝑖∈𝐼𝑅 ∑𝑗∈𝐽𝑔𝑖 𝑃𝑗𝑔𝑖𝑗 ) (24)

The chemicals consumption cost is given by the chemicals cost in each GOSP, 𝐶ℎ𝑒𝑚𝐶𝑔 , and
its consumed amount.
𝐶𝐶 = ∑𝑔 ∑𝑐 𝐶ℎ𝑒𝑚𝐶𝑔 ∙ 𝑆𝑇0𝑔,𝑠2,𝑐 (25)

17
The fixed operating cost of one GOSP, 𝐹𝑂𝐶𝑔 , is included in the objective function if the
GOSP operates.
𝐹𝐶 = ∑𝑔 𝐹𝑂𝐶𝑔 ∙ 𝑋𝑔 (26)

In summary, the proposed MINLP model consists of Eq. (23) as the objective function and
Eqs. (1)-(15), (17)-(22), (24)-(26) as the constraints.

5. Case Study
In this section, we apply the proposed model to a real case study. The Ghawar field in Saudi
Arabia is considered by far the largest conventional oil field in the world. We focus on a
production area of the Ghawar field containing multiple operating GOSPs. The characteristics
of the subject area are:
 It consists of 19 GOSPs extending across a distance of 200 km.
 Total oil production rate varies between 3-3.5 million barrel per day (MBD).
 The total number of wells serving all the GOSPs exceeds 1800 wells, and every
GOSP is fed by its own wells separately as a single production train from wells to
midstream.
 The GOSPs contain around 200 rotating equipment (liquid pumps and gas
compressors) varying in size, capacity, function, age and efficiency.

The inlet feed rates to the GOSPs are altered at monthly intervals in response to production
demands, reservoir strategy and other considerations. These rates are controlled and adjusted
by the choke valves of the feeding wells at the well pads to ensure that each GOSP receives
its targeted production rates. The controlling component in production is oil. Gas and water
are produced as associated products. Here, 12 monthly production scenarios for a one year
period (January to December) are developed from the actual productions. The initial
designated flow rate of each GOSP in January is shown in Table 5.

At the surface level, GOSPs are connected by a long chain of pipelines as illustrated in Figure
6. A total of 20 swing pipelines are available to create the lateral connections between all
GOSPs. Every GOSP is connected to at least a nearby GOSP. All swing pipelines allow for
bidirectional transfers except for three (GOSP7-GOSP6, GOSP16-GOSP3 and GOSP16-
GOSP14). These three swing pipelines are unidirectional due to certain restrictions in well
deliverability and receiving GOSP designs. Due to their low production rates and the spare

18
capacity in the receiving GOSPs, it has been decided that GOSP7 and GOSP16 are shut down
and their production is transferred to the connected GOSPs. This results in the binary variable
𝑚𝑖𝑛
𝑋𝑔 for the above two GOSPs being fixed to 0. The minimum (𝑆𝑃𝐶𝑔𝑔 ′ ) and maximum

𝑚𝑎𝑥
(𝑆𝑃𝐶𝑔𝑔 ′ ) flow rates allowed in the swing pipelines are 5 and 100 kbode, respectively. The

𝑚𝑎𝑥
monthly operating time (𝑂𝑇) is 720 hours. Additionally, the maximum capacity (𝐶𝐶𝑔𝑐 ) and
fixed operating cost (𝐹𝑂𝐶𝑔 ) for each GOSP are given in Table 1.

Figure 6. The network of GOSPs case study

19
 Table 1. Capacity of each GOSP and its fixed operating cost
Oil rate Water rate Gas rate
Fixed operating
capacity, capacity, capacity,
𝑚𝑎𝑥 𝑚𝑎𝑥 𝑚𝑎𝑥 cost, 𝐹𝑂𝐶𝑔
𝐶𝐶𝑔,𝑂𝑖𝑙 𝐶𝐶𝑔,𝑊𝑎𝑡𝑒𝑟 𝐶𝐶𝑔,𝐺𝑎𝑠
(million $)
(kbdoe) (kbdoe) (kbdoe)
GOSP1 330 150 30 0.024
GOSP2 330 150 30 0.026
GOSP3 330 165 30 0.039
GOSP4 330 150 30 0.024
GOSP5 330 375 30 0.016
GOSP6 330 300 30 0.019
GOSP7 330 300 30 0.019
GOSP8 330 165 30 0.031
GOSP9 330 165 30 0.040
GOSP10 330 375 30 0.040
GOSP11 330 375 30 0.058
GOSP12 330 165 30 0.030
GOSP13 330 165 30 0.046
GOSP14 330 165 30 0.035
GOSP15 330 165 30 0.049
GOSP16 330 165 30 0.019
GOSP17 330 165 30 0.055
GOSP18 330 165 30 0.055
GOSP19 330 165 30 0.055

The GOSPs in our application were built at different periods of time. Their ages, design
technologies, efficiencies, parameters and production forecast are different. Due to this, the
equipment characteristics (including power curves) are also different. Table 3 lists the
number and capacity of the major equipment in each GOSP, including charge pumps for task
T3, booster pumps for task T5, shipper pumps for task T5, injection pumps for task T7, LP
gas compressors for task T8, and HP gas compressors for task T9, which are the main sources
of power consumption. Note T1, T2, T4 and T6 are separation tasks, which are not
considered in the power consumption cost in this problem. The variances in characteristics
between the equipment provide an opportunity to utilise the developed optimisation models
for the optimum power consumptions while meeting the demands.

20
 𝑚𝑎𝑥
Table 2. Number and capacity (𝑅𝑗𝑔𝑗 ) of the major equipment in each GOSP
Charge Booster Shipper Injection LP gas HP gas
pump (T3) pump (T5) pump (T5) pump (T7) compressor (T8) compressor (T9)
Capacity Capacity Capacity Capacity Capacity Capacity
No No No No No No
(kbdoe) (kbdoe) (kbdoe) (kbdoe) (kbdoe) (kbdoe)
GOSP1 2 210 1 210 0 0 2 75 1 6.9 2 15
GOSP2 2 210 1 210 0 0 2 75 1 6.9 2 15
GOSP3 2 210 2 160 0 0 3 55 1 6.9 2 15
GOSP4 2 210 1 210 0 0 2 75 1 6.9 2 15
GOSP5 2 210 2 160 0 0 5 75 1 6.9 2 15
GOSP6 2 210 2 160 0 0 4 75 1 6.9 2 15
GOSP7 2 210 2 160 0 0 4 75 1 6.9 2 15
GOSP8 2 210 2 160 0 0 3 55 1 6.9 2 15
GOSP9 2 210 2 160 0 0 3 55 1 6.9 2 15
GOSP10 2 210 2 160 0 0 5 75 1 6.9 2 15
GOSP11 2 210 2 160 0 0 3 55 1 6.9 2 15
GOSP12 2 210 2 160 0 0 3 55 1 6.9 2 15
GOSP13 2 210 2 160 0 0 3 55 1 6.9 2 15
GOSP14 2 210 2 160 0 0 3 55 1 6.9 2 15
GOSP15 2 210 2 160 0 0 3 55 1 6.9 2 15
GOSP16 2 210 2 160 0 0 3 55 1 6.9 2 15
GOSP17 2 210 0 0 2 200 3 55 1 6.9 2 15
GOSP18 2 210 0 0 2 200 3 55 1 6.9 2 15
GOSP19 2 210 0 0 2 200 3 55 1 6.9 2 15

Compressor power curves of the existing applications were developed based on rated inlet
conditions. Some parameters, such as pressure and temperature, have changed greatly since
then. Therefore, we considered correction factors for the obtained power (Lapina, 1982). For
the pumps, we used Sulzer online database (Sulzer, 2014) to obtain several different curves
for the pumps based on similar design parameters. Therefore, we used three different curves
for every type of pumping set in the model and then distributed them randomly on the
GOSPs.

The proposed model was implemented in GAMS 24.4 (Brooke et al., 2014) on a 64-bit
Windows 7 based machine with 3.20 GHz six-core Intel Xeon processor W3670 and 12.0 GB
RAM. The computational time limit is 3600 seconds and the optimality gap is 1%.

6. Results and Discussion

In this section, the obtained optimal solutions of the models for the case study in the above
section are presented and discussed.

21
6.1. Model Statistics
We take the January scenario as an example, and the model statistics and computational
results are presented in Table 3. To investigate the accuracy of the piecewise linearisation, we
fix the variables values obtained by the MILP model, and the post-processed values of
variable 𝑃𝑖𝑔𝑖 and objective value. The obtained objective values show that the piecewise
approximation given by the MILP model provides a OPEX within less than 0.1% of the
actual OPEX. Similar results can be found for other scenarios as well.

Table 3. Model statistics for the January production scenario

No of No of continuous No of binary OPEX
Model Solver CPU (s)
equations variables variables (million $)
MILP 3192 1981 244 CPLEX 7.49a/7.50b 10
a
Optimal MILP solution; bpost-processed without approximation

6.2. Optimal Solutions

In this section, the optimal solution of the January production scenario is presented in details
here. Figure 7 shows a schematic map of optimal swing pipelines utilisation between the
GOSPs. Out of a total of 20 swing pipelines, 18 ones are utilised, while only the ones
between GOSP4 and GOSP5, as well as between GOSP14 and GOSP16, are not utilised. The
optimal transfer amount in each pipeline is presented in Table 4.

22
Figure 7. Schematic map of swing pipelines utilization for the January production scenario

23
 Table 4. Optimal transfer through swing pipelines for the January production scenario
Transfer
Oil Water Gas
From To amount
(%) (%) (%)
(kbdoe)
GOSP1 GOSP6 52.4 60.0 34.4 5.7
GOSP2 GOSP5 39.0 53.9 41.0 5.1
GOSP3 GOSP12 48.0 73.2 19.8 6.9
GOSP7 GOSP6 16.4 91.5 0.0 8.5
GOSP8 GOSP10 39.3 68.2 25.3 6.5
GOSP9 GOSP8 76.9 53.4 41.5 5.0
GOSP9 GOSP10 100 53.4 41.5 5.0
GOSP9 GOSP11 92.7 53.4 41.5 5.0
GOSP10 GOSP3 5.0 55.0 39.8 5.2
GOSP11 GOSP10 100 65.0 28.8 6.2
GOSP11 GOSP12 100 65.0 28.8 6.2
GOSP13 GOSP11 68.5 62.6 31.5 5.9
GOSP13 GOSP14 5.8 62.6 31.5 5.9
GOSP15 GOSP14 81.4 79.8 12.6 7.6
GOSP15 GOSP17 64.8 79.8 12.6 7.6
GOSP16 GOSP3 16.4 91.5 0.0 8.5
GOSP18 GOSP17 100.0 74.4 18.5 7.1
GOSP18 GOSP19 60.4 76.8 15.9 7.3

 Due to their low production rates and the spare capacity in the receiving GOSPs, it has been decided that GOSP7 and GOSP16
are shut down and their production and transferred to the connected GOSPs. This results in 𝐹𝐹𝑔𝑐 for the two GOSPs being fixed
𝑚𝑖𝑛 𝑚𝑎𝑥
to 0. The minimum and maximum flow rates allowed in the swing pipelines are 𝑆𝑃𝐶𝑔𝑔 ′ =5 kbdoe and 𝑆𝑃𝐶𝑔𝑔′ =100 kbdoe,

respectively.

The initial designated and final inlet rates after transfer are given in Table 5. Besides the
shutdown GOSP7 and GOSP16, GOSP9 also transfers all its designated rates to other
GOSPs, and does not operate in January.

24
 Table 5. Initial designated rates and optimal final inlet rates for the January production
scenario
Initial rate (kbdoe) GOSP Final inlet rate (kbdoe)
Oil Water Gas Selection Oil Water Gas
GOSP1 110 63 10.4 Yes 78.6 45.0 7.4
GOSP2 92 70 8.7 Yes 71.0 54.0 6.7
GOSP3 170 46 16.1 Yes 152.6 38.5 14.4
GOSP4 156 67 14.8 Yes 156.0 67.0 14.8
GOSP5 113 54 10.7 Yes 134.0 70.0 12.7
GOSP6 205 127 19.4 Yes 251.4 145.0 23.8
GOSP7 15 0 1.4 No - - -
GOSP8 143 53 13.6 Yes 157.3 75.0 14.9
GOSP9 144 112 13.6 No - - -
GOSP10 174 126 16.5 Yes 316.5 204.3 30.0
GOSP11 196 87 18.6 Yes 158.4 89.4 15.0
GOSP12 216 99 20.5 Yes 316.6 154.1 30.0
GOSP13 205 103 19.4 Yes 158.5 79.6 15.0
GOSP14 248 142 23.5 Yes 316.6 154.1 30.0
GOSP15 266 42 25.2 Yes 149.3 23.6 14.1
GOSP16 15 0 1.4 No - - -
GOSP17 233 58 22.1 Yes 316.3 72.8 30.0
GOSP18 236 49 22.4 Yes 158.0 32.9 15.0
GOSP19 270 37 25.6 Yes 316.4 46.6 30.0

The optimal OPEX in January production scenario is $7.49 million, in which power
consumption cost is $5.99 million (80%); chemicals consumption cost is $0.60 million
(12%); and the fixed operating cost is $0.60 million (8%). As a result, most OPEX results
from power consumption cost, which can be further analysed. In Figure 8, most of the power
is consumed by HP compressors and power injection pumps, which represents a total of 86%
of the power consumption cost. The details of the operation of liquid pumps and gas
compressors are given in Table 6. There are 109 equipment items out of 190 available items
utilised as follows:
 22/35 charge pumps (oil + water);
 17/29 booster pumps (oil + injected demulsifier);
 5/6 shipper pumps (oil + injected demulsifier);
 27/60 injection pumps (salty water + injected freshwater);
 16/19 LP gas compressors (gas); and
 22/38 HP gas compressors (gas).

25
 Chemicals consumption cost Fixed operatng cost
Charge pumps power cost Boost/shipper pumps power cost
Injection pumps power cost LP compressors power cost
HP compressors power cost

$0.60 39%
million 1%

$0.90 $5.99 million 8%

million
5% 47%

Figure 8. Cost breakdowns of the January production scenario

Table 6. Optimal operation of equipment in the January production scenario

HP gas
Charge pumps Booster pump Shipper pump Injection pump LP gas compressor
compressor
Powe
No Rate Power No Rate Power No Rate Power No Rate Power No Rate Power No Rate
(kbdoe) (kW) (kbdoe) (kW) (kbdoe) (kW) (kbdoe) (kW) (kbdoe) (kW) (kbdoe) r (kW)
GOSP1 1 101 273 1 80 688 - - - 1 50 3742 1 0.7 138 1 7 3837
GOSP2 1 98 269 1 71 675 - - - 1 59 3977 1 6.7 134 1 7 3431
GOSP3 1 173 380 1 153 513 - - - 1 43 1988 1 1.4 176 1 14 4699
GOSP4 1 190 407 1 156 801 - - - 1 72 4359 1 1.5 178 1 15 4649
GOSP5 1 170 375 1 135 492 - - - 1 75 4448 1 1.3 167 1 13 4933
GOSP6 2 162 364 2 126 481 - - - 2 75 4448 1 2.4 225 2 12 4897
GOSP8 1 194 415 1 157 518 - - - 2 40 1916 1 1.5 179 1 15 4631
GOSP10 2 210 439 2 159 428 - - - 3 70 2532 1 3.0 255 2 15 4622
GOSP11 1 203 429 1 159 520 - - - 2 47 2066 1 1.5 180 1 15 4622
GOSP12 2 193 411 2 158 520 - - - 3 47 2071 1 3.0 255 2 15 4622
GOSP13 1 199 421 1 159 520 - - - 2 42 1964 1 1.5 180 1 15 4622
GOSP14 2 197 419 2 159 520 - - - 3 53 2187 1 3.0 255 2 15 4622
GOSP15 1 161 363 1 150 509 - - - 1 29 1674 1 1.4 175 1 14 4737
GOSP17 2 177 387 - - - 2 159 1035 2 39 1892 1 3.0 255 2 15 4622
GOSP18 1 174 383 - - - 1 159 1035 1 38 1870 1 1.5 180 1 15 4622
GOSP19 2 171 377 - - - 2 159 1034 1 52 2158 1 3.0 255 2 15 4622

6.3. Optimal Solution vs. Current Practice

To evaluate the optimal solution achieved, we compare the optimal results for all the 12
monthly production scenarios with the current practice, i.e., each GOSP only processes its

26
initial designated rate only, except the shutdown GOSP7 and GOSP16, to get an insight of
the added value from the model.

The OPEX between the two solutions for all 12 months are compared in Figure 9, in which
the optimal solutions have consistent savings of 8% to 15% in all 12 months. In Figure 10, it
can be observed that in some months, the difference in chemicals consumption cost and fixed
operating cost is not very significant. In particular, in March and August, the chemicals
consumption cost in the current practice is even lower than the optimal solution. The power
consumption cost in the optimal solutions, which represents about 80% of the total OPEX,
has 10-20% advantage than the current practice. As a result, the total OPEX in the optimal
solutions shows significant savings.

Optimal solution Current practice Difference

10 20%
18%
OPEX (million $)

8 16%
14%

Difference
6 12%
10%
4 8%
6%
2 4%
2%
0 0%
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month

Figure 9. OPEX of the optimal solution and current practice in all monthly production
scenarios

27
 Power consumption cost Chemicals consumption cost
Fixed operating cost
20%

15%
Difference

10%

5%

0%

-5%
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month

Figure 10. Cost saving of the optimal solution compared to the current practice in all monthly
production scenarios

Figure 11 presents the OPEX comparison for each GOSP between optimal solution and
current practice in the January production scenario. It shows that the optimal solution cannot
guarantee that all GOSP can obtain OPEX savings compared to the current practice. In the
January scenario, the OPEX of only nine GOSPs in the optimal solution is lower than that in
the current practice, while there are eight GOSPs that have higher OPEX in the optimal
solution. The optimisation model considers the whole network of GOSP’s and reallocates the
process rates among all GOSPs, to achieve a better overall saving rather than the saving of
each GOSP. In other words, some GOSPs must experience an increase in their OPEX in
order to achieve a better overall OPEX for the whole network.

28
 Optimal solution Current practice
0.80
OPEX (million $)

0.60

0.40

0.20

0.00
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
GOSP

Figure 11. OPEX of the optimal solution and current practice for each GOSP in the January
production scenario

Now, we compare the annual total OPEX between the optimal solution and current practice
to show the benefit of the proposed optimisation models. Figure 12 shows that a total annual
OPEX of $92.28 million in the optimal solution, compared to $105.85 million for the current
practice, with a saving of $13.57 million representing 12.8% difference. Most of the savings
results from the power consumption cost, which has a 14.5% difference.

Power consumption cost Chemicals consumption cost Fixed operating cost

120
100 7.70
11.96
OPEX (million $)

7.12
80 11.50
60
40 86.19
73.65
20
0
Optimal solution Current practice
Scenario

Figure 12. Annual OPEX of the optimal solution and current practice

29
7. Conclusions
In this work, we have integrated GOSP well production at the surface facilities to achieve a
combined optimal OPEX for a network of GOSPs connected laterally through swing
pipelines. A MILP model has been developed to optimise the operating costs of these GOSPs
while maintaining all equipment in the best mode of operation. The developed models were
applied to a real case study in Ghawar field, Saudi Arabia, by considering 12 monthly
production scenarios. The benefits of the proposed optimisation model was demonstrated by
comparing the optimal solutions with the current practice without swing pipelines transfer.
The computational results showed an average of more than 10% OPEX reduction, which
leads to an annual OPEX savings of about $14 million.

This work also provides the basis for further optimisation opportunities by possibly coupling
the proposed models with existing upstream and downstream sections, to expand the area of
interest and obtain even higher combined savings.

Acknowledgements
I.A. gratefully acknowledges the financial support from Saudi Aramco.

References
Abdel-Aal, H.K., Aggour, M., and Fahim, M.A., 2003. Petroleum and Gas Field Processing.
Marcel Dekker, Inc. New York.

Bodington, C. and Baker, T., 1990. A history of mathematical programming in the petroleum
industry. Interfaces, 20(4), 117-127.

Brooke, A., Kendrick, D., Meeraus, A., and Raman, R., 2014. GAMS - A User's Guide.
GAMS Development Corporation, Washington, D.C.

Codas, A., Campos, S., Camponogara, E., Gunnerud, V., and Sunjerga, S., 2012. Integrated
production optimization of oil fields with pressure and routing constraints: The Urucu field.
Computers & Chemical Engineering, 178-189.

Cullick, A.S., Heath, D., Narayanan, K., April, J., and Kelly, J., 2004. Optimizing multiple-
field scheduling and production strategy with reduced risk. Journal of Petroleum Technology,
56, 77-83.

Dzubur, L. and Langvik, A.S., 2012. Optimization of Oil Production - Applied to the Marlim
Field. Master Thesis. Norwegian University of Science and Technology, Norway.

30
Fernandes, L.J., Relvas, S., and Barbosa-Póvoa, A.P., 2013. Strategic network design of
downstream petroleum supply chains: Single versus multi-entity participation. Chemical
Engineering Research and Design, 91, 1577-1587.

Foss, B., Gnnerud, V., and Diez, M.D., 2009. Lagrangian decomposition of oil production
optimization - applied to the troll west oil rim. SPE Journal, 12, 646-652.

Goel, V., Grossmann, I.E., 2004. A stochastic programming approach to planning of offshore
gas field developments under uncertainty in reserves. Computers & Chemical Engineering,
28, 1409–1429.

Gunnerud, V., and Foss, B., 2010. Oil production optimization—A piecewise linear model,
solved with two decomposition strategies. Computers & Chemical Engineering, 34, 1803-
1812.

Gunnerud, V., Foss, B., Torgnes, E., 2010. Parallel Dantzig–Wolfe decomposition for real-
time optimization—applied to a complex oil field. Journal of Process Control, 20, 1019–1026.

Gunnerud, V., Foss, B.A. McKinnon, K.I.M. and Nygreen, B., 2012. Oil production
optimization solved by piecewise linearization in a Branch & Price framework. Computers &
Operations Research, 39, 2469-2477.

Haugland, D., Hallefjord, A., and Asheim, H., 1998. Models for petroleum field expolitation.
European Journal of Operational Research, 37(1), 58-72.

IHS: Upstream, capital operating costs rise, 2012. Oil and Gas Journal. Retrieved from
http://www.ogj.com/articles/2012/12/ihs-upstream-capital-operating-costs-rise.html.

Iyer, R.R., Grossmann, I.E. Vasantharajan, S. and Cullick, A.S., 1998. Optimal planning and
scheduling of offshore oil field infrastructure investment and operations. Industrial &
Engineering Chemistry Research, 37, 1380−1397.

Kondili, E., Pantelides, C.C., and Sargent, R.W.H., 1993. A general algorithm for short-term
batch operations. 1. MILP formulation. Computers and Chemical Engineering, 17, 211-217.

Kosmidis, V.D., Perkins, J.D., and Pistikopoulos, E.N., 2005. A mixed integer optimization
formulation for the well scheduling problem on petroleum fields. Computers & Chemical
Engineering, 29, 1523–1541.

Lapina, R.P., 1982. How to use the performance curves to evaluate behavior of centrifugal
compressors. Chemical Engineering, 89(1), 86

Moro, L.F.L. and Pinto, J.M., 2004. Mixed-integer programming approach for short-term
crude oil scheduling. Industrial & Engineering Chemistry Research, 43, 85-94.

Neiro, S. and Pinto, J. M., 2004. A general modeling framework for the operational planning
of petroleum supply chains. Computers and Chemical Engineering, 28(6), 871-896.

Rahmawati, S.D., Whitson, C.H. Foss, B., and Kuntadi, A., 2012. Integrated field operation
and optimization. Journal of Petroleum Science and Engineering, 81, 161-170.

31
Raju, K. U., Nasr-El-Din, H. A., Hilab, V., Siddiqui, S., and Mehta, S., 2005. Injection of
aquifer water and GOSP disposal water into tight carbonate reservoirs. SPE Journal, 10, 374-
384.

Relvas, S., Matos, H.A., Barbosa-Póvoa, A.P.F.D., Fialho, J., and Pinheiro, A.S., 2006.
Pipeline scheduling and inventory management of a multiproduct distribution oil system.
Industrial & Engineering Chemistry Research, 45, 7841-7855.

Sahebi, H., Nickel, S., and Ashayeri, J., 2014. Strategic and tactical mathematical
programming models within the crude oil supply chain context—A review. Computers &
Chemical Engineering, 56-77.

Schlumberger, 2005. Acting in tme to make the most of hydrocarbon resources. Oilfield
Review, 17, 4-13.

Shah, N., 1996. Mathematical programming technique for crude oil scheduling. Computers
and Chemical Engingeering, 20, S1227-S1232.

Silva, T.L., and Camponogara, E., 2014. A computational analysis of multidimensional

piecewise-linear models with applications to oil production optimization. European Journal
of Operational Research, 232, 630-642.

Sulzer, 2014. Online tools. URL:http://www.sulzer.com/en/Resources/Online-Tools, [1 July

2014]

Tavallali, M.S., Karimi, I.A., Teo, K.M., Baxendale, D., and Ayatollahi, S., 2013. Optimal
producer well placement and production planning in an oil reservoir. Computers & Chemical
Engineering, 5, 109-125.

Tavallali, M.S., Karimi, I.A., Halim, A. Baxendale, D., and Teo, K.M., 2014. Well
placement, infrastructure design, facility allocation, and production planning in multireservoir
oil fields with surface facility networks. Industrial & Engineering Chemistry Research, 53,
11033-11049.

Tavallali, M.S., and Karimi, I., 2014. Perspectives on the design and planning of oil field
infrastructure. In: Mario, R., Eden, J.D.S., Gavin, P.T. (eds) Computer Aided Chemical
Engineering, vol. 34, pp. 163-172.

Torgnes, E., Gunnerud, V., Hagem, E., Ronnqvist, M., and Foss, B., 2012. Parallel Dantzig–
Wolfe decomposition of petroleum production allocation problems. Journal of the
Operational Research Society, 63, 950-968.

van den Heever, S.A., Grossmann, I.E., Vasantharajan, S., and Edwards, K., 2001
Lagrangean decomposition heuristic for the design and planning of offshore hydrocarbon
field infrastructures with complex economic objectives. Industrial & Engineering Chemistry
Research, 40, 2857-2875.

Wang, P., 2003. Development and Applications of Production Optimization Techniques for
Petroleum Fields.PhD Thesis. Standford University, UK.

32
Ulstein, N.L., Nygreen, B., and Sagli, J.R., 2007. Tactical planning of offshore petroluem
production. European Journal of Operations Research, 176, 550-564.

33