A Review of Mathematical Optimization AP

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International Journal of Energy and StatisticsVol. 1, No. 2 (2013) 143154c Institute for International Energy Studies

DOI: 10.1142/S2335680413500105

A REVIEW OF MATHEMATICAL OPTIMIZATION

APPLICATIONS IN OIL-AND-GAS UPSTREAM &

MIDSTREAM MANAGEMENT

MAJID SHAKHSI-NIAEI, SEYED HOSSEIN IRANMANESH

and SEYED ALI TORABI

Department of Industrial Engineering,

College of Engineering, University of Tehran, [email protected]

Received 27 May 2013Revised 2 June 2013

Accepted 3 June 2013Published 5 July 2013

The growth of demand in developing countries has given rise to a constant increase inconsumption of most non-renewable resources, including oil and gas. In this regard, theimportance of planning activities rises because of the limited availability of oil and gasresources. Optimization techniques are tools that help upstream and midstream man-agers to decide optimally. The purpose of this review article is to provide a summary ofthe scientific literature on optimization applications in oil-and-gas upstream and mid-stream management. The main problems are described within a classification schemeand the most important contributions are summarized.

Keywords: Mathematical optimization; Oil and gas; Upstream; Midstream.

1. Introduction

Economic development mainly relies on non-renewable resources [1]. The rapid

growth of demand in developing countries has given rise to a constant increase

in consumption of most non-renewable resources, including oil and gas [2]. Liquid

fuels are expected to remain the major source of energy and their total consumption

continues to increase despite rising prices [3]. Similarly, worlds total natural gas

consumption is expected to increase by 1.6 percent per year on average. Figure 1

shows the upward trend in consumption of all energy sources.A typical optimization problem consists of maximizing or minimizing

one/several objective function(s) by systematically choosing input values from

within allowed sets. The allowed sets of input variables are defined in forms of

several constraints. Figure 2 represents a general form of mathematical optimiza-

tion problems. As oil and gas resources have a limited availability, the importance

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144 M. Shakhsi-Niaei, S. H. Iranmanesh & S. A. Torabi

Fig. 1. World energy consumption by fuel, 19902035 (quadrillion Btu) [3].

Minimize / Maximize {One or more objective function(s)}

Subject to: Resource constraint(s)

Structural constraint(s)Other constraint(s)

Declaring variables and variable types

Fig. 2. A typical mathematical optimization problem.

of planning activities rises. Optimization techniques are important tools that help

upstream and midstream managers to decide optimally.

As an example, a basic form of exploration project selection problem can beformulated via the following equations:

Max z=n

i=1

fixi (1)

Subject to:n

i=1

cixi budget (2)

x3+ x4 1, (3)

x2 x1 1, (4)

xi {0, 1}, (5)

where, xi is the binary variable that denotes the selection (xi = 1) or not (xi = 0)

of the i-th project, n is the number of projects, and fi is the utility of the i-th

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A Review of Mathematical Optimization Applications 145

project, e.g. net present value of the i-th project. Equation (1) maximizes the total

utility achieved by selected projects.

Equation (2) applies the budget constraint where parameter budger repre-

sents the available budget. Equation (3) is an example of logical constraint whereprojects 3 and 4 are mutually exclusive. Equation (4) is another example of logi-

cal constraint denoting if project 2 is elected then project 1 must be also selected.

Finally, equation 5 declares the binary nature of variables x. Many researchers have

added different considerations to this basic problem to meet real-world needs, e.g.

considering interaction between projects, uncertainty, budget segmentation, poli-

cies, and so on.

The purpose of this paper is to provide a summary of the scientific literature

on optimization applications in oil-and-gas upstream and midstream management.

The rest of the paper is organized as follows. Upstream and midstream optimization

problems have been categorized in Sec. 2. The literature on strategic optimization

problems is reviewed in Sec. 3. Sections 4 and 5 review the literature on tactical

and operational optimization problems, respectively. Finally, Sec. 6 concludes this

paper.

2. Categorizing Upstream and Midstream Optimization Problems

Various researchers have tried to apply optimization tools and techniques in oiland gas planning area. Nygreen and Haugen [4] have surveyed applied mathe-

matical programming models in Norwegian petroleum field and pipeline develop-

ment. Hagem and Torgnes [5] have classified related optimization problems into four

groups according to their time scale, i.e. operator optimization, real-time produc-

tion optimization, field optimization, and strategic decisions as shown in Figure 3.

Wang [7] reviewed the applications of optimization techniques to petroleum

fields and categorized them into the following groups:

Lift gas and production rate allocation

Optimization of production system design and operations

Optimization of reservoir development and planning

Fig. 3. Time scale for exploration and production decisions (reproduced from [6]).

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Table 1. Taxonomy of upstream and midstream optimization problems.

Timeframe of

decisions

Scope

Exploration & Development Production Transportation

Strategic

Project portfolio selection

and scheduling

(exploration, new facilities,

pipelines, refineries,

petrochemicals, etc.)

Annual delivery planning

(ADP)

Vessel purchasing /leasing

/chartering decisions

Tactical Staffing Drilling optimization

Production planning Cargo planning

Operational

Job assignment Production optimization

and scheduling

Well optimization

Transport scheduling

Vehicle routing

Ulstein et al. [8] divided the related planning tools into operational, tactical, and

strategic tools. This classification seems compatible with that of Wang [7].

Herein, by adding production and planning scopes, we propose a mixed taxon-

omy for upstream and midstream optimization problems based on their timeframeand scope of planning, as shown in Table 1.

3. Strategic Optimization Problems

Walls [9] and Orman et al. [10] endeavoured to implement Markowitz optimization

method to exploration and production portfolio project selection, providing efficient

set of portfolios via minimizing risk subject to a particular level of return. Some

researchers have added some considerations to this problem, e.g. interdependencies

among projects [11] or scheduling of the selected projects, as an integral part ofproject selection model.

Bohannon [12] proposed a linear programming model for optimum drilling and

facility expansion schedules for multi-reservoir pipeline systems.

McFarland et al. [13] applied generalized-reduced gradient nonlinear program-

ming methods to solve optimal control models for petroleum reservoir development

planning and management. The decision variables include how many wells to drill

in each time period, the production rates, abandonment time, and platform size

while the objective function of their model is to maximize present value of profits.Aboudi et al.[14] proposed an integrated mathematical programming model for

the development of petroleum fields and transport systems. Their work was the

earliest integrated work which considers all of development, production, and trans-

portation planning scopes at a strategic level. They considered only one product and

fixed-production profiles for potential fields while later works have developed these

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considerations into multiple products and variable production profiles. Jrnsten

[15] proposed a model for sequencing offshore oil and gas field developments under

uncertainty where the emphasis is on the field sequencing decisions and the trans-

portation network is given in aggregate form. Haugen [16] and [17] tried to incor-porate uncertainties in filed development planning and used stochastic dynamic

programming as the solution approach where the transportation decisions are at

an aggregated level. Even some computational improvements in dynamic stochastic

programming formulation have been suggested; the computational burden is still

onerous. Johansen [18] discussed optimal development of an offshore natural gas

field. Nygreen et al. [19] proposed a mixed-integer-programming model for infras-

tructure planning. Although their model was formulated deterministically, it is used

more than fifteen years by the Norwegian Petroleum Directorate and other major

Norwegian oil companies. Nygreen and Haugen [4] pointed out that early stochas-

tic modelling attempts did not survive in the companies as operative models. It

is possibly because deterministic models are hard enough to solve while stochastic

models add (stochastic) informational needs to them. Compared to the full-scale

models, attempts to include uncertainty had to contain simplifications and signifi-

cantly reduce the number of possible projects, time periods, and etc.

Carvalho and Pinto [20] proposed an mixed-integer linear model and solution

technique for the planning of infrastructure in offshore oilfields as well as the timing

of extraction and production rates. Rahmawati et al.[21] evaluated optimal produc-tion strategies using several key control variables and field operational constraints

in an integrated optimization model. Their integrated model consists of reservoir,

surface facility, and economic models.

Dutta-Roy et al. [22] analysed the compressor installation costs and operating

strategy required to meet the production goals over the life of a gas field. Key ele-

ments of the objective function which have been optimized include a time-dependent

revenue stream based on the projected price of gas, capital costs associated with

adding incremental compression at periodic intervals, and compressor fuel consump-

tion costs that are typically a near-linear function of the operating horsepower.Lee and Aronofsky [23] proposed a linear programming model for scheduling

crude oil production from five sources over an eight-year period subject to certain

restrictions.

4. Tactical Optimization Problems

Dyer et al. [24] proposed a decision support system for prioritizing oil and gas

exploration activities and then assigning personnel to the most promising ones.Lasdon et al. [25] investigated optimal production strategies for several optimiza-

tion criteria and potential constraints on reservoir over 1 to 3 year(s) period. The

strategies considered include different aspects of production and storage operations.

Haugland et al. [26] proposed some models for an early evaluation of a petroleum

field which suggest decisions concerning platform capacity, drilling program, and

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Table 2. Several strategic optimization researches.

Author(s) Scope(s)

Exploration & Production Transportation RemarkableDevelopment consideration(s)

Walls [9] Orman et al. [10] Brashear et al. [11] Interdependencies

among projectsBohannon [12] McFarland et al. [13] One reservoirAboudi et al. [14] Fixed production

profiles, singleproduct system

Jrnsten [15] Uncertaintyin priceHaugen [16] Uncertainty in

price anddemand

Haugen [17] Uncertaintyin resource(field size)

Johansen [18] One offshorenatural-gas field

Nygreen et al. [19] Variable

productionCarvalho and Pinto [20] Pressure in eachreservoir

Rahmawati et al. [21] Surface facilitiesDutta-Roy et al. [22] Lee and Aronofsky [23]

well production plan. Carroll and Horne [27], and Ravindran [28] used multivariate

optimization to determine optimal recovery over a period of time while Fujii and

Horne [29] also considered network parameters in determining optimum production

rates, i.e. separator pressure, the diameters of tubing, pipeline, or surface choke, andthe length of pipeline. Owing to the nonlinearity of the model, they used Newton

derivative-based methods, the polytope function-value-based method, and a genetic

algorithm. Considering several test calculations, they suggested polytope method

for low dimension problems and genetic algorithm for large systems with many

variables. Zhang and Zhu [30] formulated a bi-level programming method for pipe

network optimization. Their problem consists of a given pipe network where several

available diameters can be selected for each pipe. Palke [31] proposed an integrated

nonlinear model to optimize the gas-lift configuration. The numerical methods canfind the combination of production parameters that maximizes the net present

value. The control parameters include tubing diameter, separator pressures, depth

of gas injection, and volume of gas injected. Polytope and genetic algorithm opti-

mization techniques have been used which are shown to be both stable and efficient.

Barua et al. [32] used a non-linear sequential-quadratic-based network optimizer to

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Table 3. Several tactical optimization researches.

Scope(s)

Author(s) Exploration & Production Transportation RemarkableDevelopment consideration(s)

Dyer et al. [24] Lasdon et al. [25] Hauglandet al.[26] Carroll and

Horne [27] Single-well system

Ravindran [28] Decision variables canvary with time

Fujii and Horne [29] Multi-well productionsystem

Zhang and Zhu [30] Palke [31] Barua et al. [32] Dutta-Roy

et al. [22] Compressor installation

cost and operatingstrategy

Bittencourt andHorne [33]

Ulstein et al. [8] Disruptions, flowcomponents, chemicalprocessing, markets

Hagem andTorgnes [5]

Atkinson andIsangulov [34]

Failure of a component

solve some of the typical problems in the oil and gas production including tactical

operation problems. Bittencourt and Horne [33] used a hybrid genetic algorithm for

reservoir development decisions including reservoir properties, well locations, and

production scheduling parameters. They applied their model on a real oil field devel-

opment project with 33 new wells. The wells were allowed to be placed anywhere in

the reservoir and could be vertical or horizontal. They reported a reduction of the

total number of new wells as a result. Ulstein et al. [8] proposed a mathematical

model to optimize a group of tactical decisions, i.e. Regulation of production levels

from wells, splitting of production flows into oil and gas products, and further pro-

cessing of gas and transportation in a pipeline network. They implemented their

model in Norwegian production network and also analyzed possible shut-downs in

one of its production fields. Hagem and Torgnes [5] proposed and evaluated different

mathematical models for a petroleum production allocation problem and investi-gated the computational performance of a parallel Dantzig-Wolfe algorithm and

Branch & Price applied to these problems. Atkinson and Isangulov [34] formulated

a mathematical model for development of an oil and gas field. They considered

completion of wells and production amounts as random processes.

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5. Operational Optimization Problems

Attra et al. [35] used linear programming to maximize daily income from a multi-

reservoir producing field on a day-to-day basis. Lo and Holden [36] proposed two

methods for maximizing field oil rate at every time step. In the first method, the

problem of well management is formulated as a linear programming problem and

solved by the standard Simplex method. The second method provides approximate

results in close agreement with the LP results (within 5%) for most cases. Chris-

tiansen and Nygreen [37] proposed a planning model for the management of approx-

imately 130 petroleum-producing wells in the North Sea including decisions about

which wells to produce from and which to shut down during a period. The well-

management model is solved by means of a standard mathematical programming

procedure. Nishikiori et al. [38] developed a new method to maximize the total oilproduction rate and to determine the optimum gas injection rates for a group of con-

tinuous gas lift wells. They used a quasi-Newton nonlinear optimization technique

to solve this problem. Fang and Lo [39] developed an integrated model to maximize

oil production which considers reservoir performance, wellbore hydraulics, surface

facility constraints, and lift-gas allocation. Dutta-Roy and Kattapuram [40] pro-

posed an approach for simulation and optimization of the overall gas-lift allocation

problem using pressure-balance-based multiphase flow network solving technique

integrated with a robust sequential quadratic programming approach.

Heiba et al. [41] formulated an integrated approach for management of cyclicstimulation programs. The approach combines the use of technologies to simulate

the flow of steam in networks and wellbores with an industrially tested variant of

the successive quadratic programming algorithm for process optimization. Vazquez

et al. [42] developed an optimization procedure combining artificial intelligence

techniques with operations research techniques to deal with oil production systems.

Yeten et al. [43] proposed a methodology for optimization of nonconventional wells

which are more complicated than other well optimization problems. Wang et al.

[44] developed an optimization technique for allocating production rates and lift-gas

rates to wells in large fields subject to multiple flow rate and pressure constraints.

Neiro and Pinto [45] developed a complex multi-period mixed-integer-non-linear

programming model for petroleum supply chain including some nodes representing

refineries, terminals, and pipeline networks. Decision variables consist of stream

flow rates, properties, operational variables, inventory, and facilities assignment.

Huseby and Haavardsson [46] optimized the problem of determining produc-

tion shares of different reservoirs in a multi-reservoirs field. Their model considers

uncertainty about key reservoir parameters. However, the optimization problem is

analysed deterministically.Gunnerud and Foss [47] proposed a mixed-integer-linear model for real-time

optimization of production network. They used and tested two decomposition meth-

ods in order to lower the computational complexity of the problem, i.e. Lagrange

decomposition and DantzigWolfe decomposition. Herran et al. [48] formulated a

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Table 4. Several operational optimization researches.

Scope(s)

Author(s) Exploration & Production Transportation Remarkable

Development consideration(s)

Attra et al. [35] Multiple reservoirsLo and Holden [36] Multiple flow rate

constraintsChristiansen and

Nygreen [37]

Nishikioriet al.[38] Fang and Lo [39] Lift gas and production

ratesDutta-Roy and

Kattapuram [40]

Flow interactions among

wellsHeiba et al. [41] Vazquez et al. [42] Yeten et al. [43] Wang et al. [44] Flow interactions among

wells when allocatingwell rates

Neiro andPinto [45]

Petroleum supply chain

Huseby andHaavardsson [46]

Multiple reservoirs withuncertain parameters

Gunnerud andFoss [47]

Herran et al. [48] Multiple petroleumproducts in amulti-pipeline system

mathematical model for optimizing transportation of multiple petroleum products

in a multi-pipeline system where multiproduct pipelines have been connected and

formed a complex system.

6. Conclusion

The study of oil-and-gas upstream & midstream optimization problems is a rela-

tively new and fast growing research area which should gain importance because

in many situations, decisions are irreversible and have a significant impact on the

industry. Moreover, it has been observed that optimization techniques, in a wide

variety of models, have helped upstream and midstream managers in making opti-

mal decisions.

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