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Annals of Operations Research 82(1998)251 – 267 251 .

Modeling Norwegian petroleum production and

transportation★

Bjørn Nygreenc, Marielle Christiansen

a, Kjetil Haugen

a,b, Thor Bjørkvoll

c

and Øystein Kristiansend

aSection of Managerial Economics and Operations Research, The Norwegian

University of Science and Technology, N-7034 Trondheim, Norway

b Molde Regional College, N- 6400 Molde, Norway

E-mail: [email protected]

cThe Foundation for Scientific and Industrial Research at NTNU – SINTEF, Trondheim,

Norway

d Norwegian Petroleum Directorate, Stavanger, Norway

In memory of Åsa Hallefjord

In the continental shelf off the coast of Norway, there are several petroleum fields contain-ing a mixture

of oil and gas. A multiperiod mixed integer programming model for investment planning for these fields

has been used by The Norwegian Petroleum Directorate for more than fifteen years. In practical use, the

production from each field has mostly been declared to follow profiles given by the user, but the user may

also declare that the production can vary from the given profile. This paper describes the model and

comments on some of the real problems the model has been used to analyze and the modeling process

involved.

Keywords: mixed integer programming, petroleum field scheduling

1. Introduction

This paper reports on an MIP model used by the NPD (Norwegian Petroleum

Directorate) and other major Norwegian oil companies for more than fifteen years. The

model deals with long-term planning of Norwegian petroleum production and

transportation–with emphasis on scheduling of projects. This involves decisions on

★ Financial support form The Norwegian Petroleum Directorate is gratefully acknowledged.

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© J.C. Baltzer AG, Science Publishers

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252 B. Nygreen et al. / Producing and transporting petroleum

when various fields should be initiated and simultaneous design of pipeline systems. The

model objective is to maximize the total net present value for all involved fields includingtransportation costs.

This model is interesting due to the fact that it has been in practical use for more than fifteen

years. During this time, the model has been under almost continuous development. The

original version of the model was a pure discrete one, while the current one has both discrete

and continuous decision variables. The model has also been moved from mainframes to

workstations. In this process, also the model language and the solver were changed. Today,

the model also runs on PCs.

1.1. Modeling issues

The planning task described above involves interesting modeling issues. Some

important keywords involved in an efficient OR-modeling process are:

• reality representation,

• ease of communication,

• solution speed.

The terms reality representation and solution speed are classical “trade-offs” in OR-

modeling, and refer to the simple fact that an “increase” in a model’s reality repre-sentation

will almost always lead to a decrease in solution speed. As both normally are seen to be

positive from a users’ point of view, they introduce a difficult “trade-off” in practical

modeling. The term ease of communication relates to the fact that models must correspond

with the users’ intuition. A model without such an ability

– for instance, a stochastic optimization model which may give both a better reality

description and faster solutions than an alternative deterministic model – may fail, as the

user may lack the necessary understanding of stochasticity to fully exploit the model’s

impact on real-world decisions. As a consequence, all three elements described above should

be taken fully into consideration and as they may conflict, in all dimensions, the process of

efficient “OR-modeling” is indeed complex.The process of modeling and solving production and transportation planning problems

for Norwegian oil companies has fully shown the degree of complexity along the above

described dimensions. One way of separating the problem involved is to look at the various

tasks involved in the modeling process and assign them to various academic disciplines. One

way of doing this may be summed up by the points below:

• economic theoretic content,

• reservoir description,

• transport description.

The term economic theoretic content refers to the fact that the model judges eco-nomicdecisions – maximal total net present value is used as the objective. Obviously,

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B. Nygreen et al. y Producing and transporting petroleum 253

there are a lot of interesting problems that could be discussed in this context; we will merely

state a few.

Using net present value as an economic value measure implies acceptance of many

assumptions. Among these, the most crucial are probably those of deterministic cash-flows

and the existence of a frictionless capital market. The assumption of deterministic cash-

flows is obviously incorrect. As the model is used for planning horizons up to and above 40

years, such an assumption directly implies that the user has to be able to predict all resource

prices perfectly more than 40 years into the future. This is surely impossible. Hence, a

stochastic optimization model may be a better choice than the reported model. However, in

the mid-eighties, during a very erratic period in the world market price on crude oil, weoffered the oil companies an alternative model, somewhat simpler in some of the

deterministic parts, but with uncertainty in both prices and reservoir volumes [7]. Even

though this model may be seen as a better reality description, and not necessarily very much

harder to solve, the users chose to abandon such a model concept – maybe as a result of

mismatch between user and model-maker intuition.

The assumption of frictionless capital markets is also interesting to assess in this context.

One of the main assumptions in the model is that a project can either be chosen to start or

not to start (see equation (1)). Therefore, a solution involving a 50% project start in a certain

year is not allowed. From a “combinatorial optimization point of view”, such an assumption

may be plausible. However, given the existence of frictionless capital markets, such asolution merely implies that you should finance half the project yourself and sell the other

half in the market. Hence, if this assumption were relaxed, the model would surely be a

better reality description, and it would solve much faster – an MIP problem would be

changed to an LP problem. The users did not like the idea of starting fractions of projects. At

best, such decisions may be taken elsewhere in the organization.

The reservoir description – referenced in section 3.4 – shows another set of crude

approximations used in this model. Anyone somewhat familiar with the oil business should

be aware of the enormous time spent on “reservoir simulations”. A reservoir simulation is

the oil business’ name of the numerical solution of a coupled set of partial differential

equations describing flow from a petroleum reservoir. This model mimics the partialdifferential equation description with a simple set of equations which at best may look like

reservoir simulation results in an empirical way.

1)This is not the whole truth. As the model contains precedence constraints, the transformation from an

MIP to an LP model is not as straightforward as described in the text. Additionally, the notion of

selling parts of a producing project in the market is plausible. However, such a mechanism is harder to

imagine for a pipe. Suppose that 50% of a pipe capacity is utilized in the continuous optimal solution.

Does this imply that the other half of the pipe could be sold in a market? Obviously, this is not the case.

Additionally, choosing “half the pipe” as the solution assumes that the cost structure of pipes is linear

which does not necessarily have to be the case.

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254 B. Nygreen et al. y Producing and transporting petroleum

The transport description in the model, mainly shown in equations (11), (12) and(13), plays a similar role. This model assumes a free mass balance type description without

any friction due to pressure, temperature or volume structures in the actual pipes.

Obviously, this is a rough approximation of the real-world situation.

To sum up, the model is certainly composed of a set of very crude approxi-mations.

Economists and petroleum engineers are notorious for criticizing it for its lack of real-world

description abilities. Still, the model is very popular and – as noted – it has been heavily

used for more than fifteen years. As such, this model may be seen as

a typical successful example of how an efficient modeling process may be conducted. The

basic aim of the model is, of course, to judge decisions at a high level, which is of critical

importance for the oil companies. In such a case, the possibility of capturing the main

forces driving such decisions is more important than the descriptive power of the model in

various sub-fields.

Hence, the main issue of this paper is neither to report on a model with special

modeling issues nor to report on special solution procedures, but merely to report on a

model concept or a model process which have proven successful.

1.2. Some historic remarks

At the end of the 1970’s, it became more and more evident that the petroleum sector

in Norway had the potential to become a long-term growth sector. The need for a more

detailed analysis of the future potential became clear. At that time, the NPD (Norwegian

Petroleum Directorate) started actively predicting the number of wells drilled, investments,

operating costs, man-hours, utilization of installed processing and transport capacities, etc.

As long as NPD worked with the developed fields, obtain-ing predictions was

unproblematic. But at that time, NPD also started systematically generating profiles for

fields under planning, new discoveries and prospects.

This task involved a detailed analysis of a large number of projects, both fields and

transportation systems. It required the development of alternative solutions for each project

and strategies for the development of larger petroleum provinces. In the end, NPD

generated very large quantities of data which required the development of new planning

tools to handle and analyze it.

1.3. Similar models in the literature

Bodington and Baker [5] wrote a history of mathematical programming in the

petroleum industry, but they excluded all papers about development planning. Aboudi et al.

[1] describe a model similar to ours. This model, although attempting to solve a similar

type of problem, has not been in practical use as far as these authors know. Beale [2]

describes the nonlinear parts of a model with a similar purpose. The main focus of this

model (an NLP model) is to do a more thorough description of the physics in the problem –

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pipe flows are more thoroughly modeled. As a consequence, the

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number of practical problems it can handle is somewhat more limited than in our model.

Haugland et al. [8] include a model of the reservoirs. As this model also in-cludes

nonlinear elements, its main application area is more limited than ours. These models are

usually formulated and solved as mixed integer programming problems.

2. The main model assumptions

The decision problem analyzed here is a deterministic problem in which the discrete

decisions, when to develop the fields, are the most important ones.

There is a given number of projects which can be started in any one of several years,

or some of them do not need to be started at all. Some projects produce oil and yor gas,

while other projects have the capacity for processing or transportation of the products.

When it is decided to start a project in a given period, this will often decide the amount of

oil and gas produced by the project in all future years. All resources needed by the project

in all future years are also decided by the start year. Typical production and resource

profiles are illustrated in figure 1.

Figure 1. Production and resource profiles for different start periods.

For some projects, the user may declare that the production can vary in the following

way: The cumulative production can never be greater than the amount given by the input

profile and the production can never be greater than the maximum capacity

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Figure 2. Variable production.

or a given fraction of what is left in the reservoir. This is illustrated in figure 2. In such

cases, it is possible for the user to specify that some parts of the resource usage will vary

with the production. The user is also able to specify that the production must be above a

user-defined fraction of the user-given profile.

Some products are transported through a network of pipelines, so that it is physicallyimpossible to say which fields deliver to which markets. The model can handle different

prices in different markets correctly, but it has no unique logical way to divide the profit

from different markets between the producing fields.

3. The model

We have chosen to use a notation similar to that introduced by Beale et al. [3]. Lower

case letters are used to represent subscripts and variables, and capital letters to represent

constants and parts of the constant names written as literal subscripts.

Only the essential parts of the model implemented will be described here. We have

chosen not to comment on whether the constants are given directly or not.2)

For simplicity, many variables and constraints will be defined for all the possible

combinations of their subscripts, even if they are used for only some of the possible

combinations. This means that the exclusion tests for variables and constraints are omitted.

Sets describing which subscripts to sum over in various constraints are also omitted.

2) Some constants are calculated from other constants.

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B. Nygreen et al. y Producing and transporting petroleum 257 .

3.1. Start of projects

If project j starts in period u, then variable x ju is set equal to one. A project that does

not start at all has its non-start variable, y j , set equal to one. The user can set individual

start periods for each project and force some projects to start. This is not shown explicitly

in the formulation. All projects may start at most once. This can be modeled either by

declaring the mentioned variables as binary, or by declaring that the variables for project j

belong to a special ordered set of type 1. Our experience is that branching on sets in this

model is better than branching on binary variables. We have therefore chosen to use sets.

The mentioned variables can only take the values 0 and 1. Special ordered sets are

implemented in different ways in different solvers. Our code uses the original definition by

Beale and Tomlin [4], where at most one variable can be non-zero. This value does not

need to be equal to one. For this reason, we need to use an explicit slack, y j , in constraint

type (1):

∑u

x ju+ y j=1,∀ j .(1)

3.2. Alternatives

The user can define several different ways to develop a given petroleum field by

defining each possible development as a project and all these projects as an alternative. An

alternative is a set of projects where at most one is allowed to start. The following

constraint type is the least dense way to formulate this:

∑ j

y j ≥ N ALTa−1,∀ a .(2)

where N ALTa is the number of projects in alternative a. The summation over j above is only

for projects that belong to alternative a.

3.3. Precedence constraints

Some projects are dependent on the start of other projects. We have modeled this via

precedence constraints. In each such constraint, we call the dependent project the successor

and the other project the predecessor . For some constraints, the time between the start of

the successor and the predecessor projects is critical. This means that for each possible start

period for the successor project, there is a specified interval (time windows) for start of the

predecessor project.

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Constraints with and without time windows are modeled differently. Constraints (3) are

without and constraints (4) are with time windows. The definitions of the windows are not

shown explicitly. We use d as subscript for the precedence constraints without time

windows and e is used for the constraints with time windows. In both constraint types, j is

always the successor project, while i is the predecessor project:

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y j−v j ≥0,∀d ,(3)

x ju−∑u

x jv ≤0 ,∀ e , u .(4)

For each value of d in (3), there are corresponding values of j and i, such that we

could have written y j(d ) – yi (d ) instead of y j – yi , and similarly for the x’s in (4). The

summation over υ in (4) is only for such υ that the time window for constraint e is satisfied

when the successor project is stated in u.

3.4. Variable production

Since the production from each project is forced to follow the profile given by the

user, it is difficult to get the production to fit the capacities of the pipes and the markets.

Since the profiles are uncertain, this means that some constraints are too hard. One way of

changing this will be to make the constraints soft by introducing surplus variables with

penalties in the objective.

Another way to make the capacity constraints less hard is to allow the production to

differ from the given profiles. Sullivan [12] interpolates between two different

developments of a field. Beale [2] used variables for pressure both in the reservoir and in

the pipes instead of profiles.

In a simple way, we may say that we have chosen the possibility of saving some

product for a later period as long as the maximal production in the profile given by the user

is not exceeded. All projects j referenced in section 3.4 are projects with variable

production.

3.4.1. Maximal production

The user gives data for projects with fixed and variable production in the sameway.

Project j, which is started in period u, will produce P Rjstu of product s in period t , if the

production is fixed. From this profile, a “lifted’’ profile PLjstu is calculated as the

maximum of P Rjstu and P Ljs(t –1)u . The variable production pjst of product s from project j in

period t cannot be greater than that given by the “lifted’’ profile:

p jst −∑u

P Ljstu x ju ≤0 ,∀ j , s , t . (5 )

3.4.2. Minimal production

To reduce the possibility of production varying too much over time, the user may

specify that it must stay above a given ratio R ALjs of the given profile:

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p jst −∑u

R ALjs P Rjstu x ju ≥0 ,∀ j , s , t .(6)


3.4.3. Decline of production

When a project is defined to have variable production, we assume an exponential

decline rate. From the data given by the user, this rate D ECLjs is estimated for project j and

product s. The total amount of product s in the field j is called T Pjs:

p jst D ECLjs q js(t −1)≤ D ECLjs T Pjs , ∀ j , s , t .(7)

The cumulative productionq jst is defined by

q jst = p jst +q js (t −1) , , j , s , t .

3.4.4. Production stop

For each project j with variable production of product s, there is a ratio R ATjs between

the maximal recoverable amount of the product and the total amount in the field. R ATjs and

T Pjs are estimated so that their product is equal to the sum of the input profile values:

q jst ≤ R ATjs T Pjs ,∀

j , s , t . (8)

So far in section 3.4, we have assumed that the production of each product within a

project can be planned in isolation. Often this is not true. Therefore, the user may declare

some products from a project to be associated. For such projects, one has to declare one of

the products as the leader . For the leader, the constraints given in this section are valid. For

the other associated products, constraints (5) – (8) will be re-placed by constraints saying

that the ratio between the amount of leader product and the amount of associated product is

constant over time. This constant ratio is calculated as the ratio between the total amount of

the products in the profiles provided by the user.

3.5. Global profile constraints

Occasionally, the users of the model have been interested in constraints on total

production of a particular product or total use of a particular resource in a specified period.

In other cases, the interest has been devoted to the bounds for weighted production or

resource usage. The user must specify aggregation factors for products and resources in

order to be able to use aggregates. The model is formulated so that the user can specify

upper andyor lower bounds on pure or aggregated profile values in some or all periods.

This is shown here only for resources.

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3.5.1. Resource balances

For each project j, the user has given data Rjbtu for the usage of resource b in period t

given that the project starts in period u. If project j has variable production, a constant RPjsb

is needed which gives the amount of resource b for each unit of product s produced from

the project. We define a variable rbt which is equal to the total amount of resource b

required in period t :

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∑ j

∑u

R jbtu x ju+∑ j

∑s

R Pjsb p jst −rbt =0 , ∀b , t .(9)

The last summation over j is only for projects with variable production.

3.5.2. Bounds on the resource usage

R MXbt and R MNbt are upper and lower bounds on the usage of resource b in period t :

R MNbt ≤r bt ≤ R MXbt ,∀b ,t (10)

The resource variable, the resource balance and the bounds are only defined for periodswhere there is at least one bound on the resource variable.

3.6. Transportation and market constraints

If two or more pipes are built between the same nodes, we cannot account for different

flows in the different pipes. This means that it is the pipe arcs k which really matter here.

3.6.1. Pipe arc capacities

When the planning period starts, there is a capacity C Akst for product s along arc k in

period t . Project j, started in period u, has a new capacity C jstu for product s in period t . Theseconstants will be used for other projects for new processing capacities in nodes. With these

constants and a new variable fkst for the flow of product s along arc k in period t , the pipe arc

capacities may be written:

f kst −∑ j

∑u

C jstu x ju ≤C Akst ,∀ k , s , t .(11)

The constraints are only defined from the first period where it is possible to send

product s along arc k . The summation over j is only for projects that expand the capacity

along arc k for product s. If no such j exists, the constraint is implemented as an upper bound.

3.6.2. Node balances

Normally, there are few markets compared with the number of nodes, but even so, the

model is written such that it is possible to have a market in every node. The variable for the

amount of product s delivered to the market at node n in period t is written as mnst . This is

modeled as a delivery from the node. The amount of the same product delivered to the same

node in the same period caused by decisions taken before the planning period starts is the

constant DPnst . S Ink is equal to +1 ( –1) if node n is an end node (a start node) for arc k :

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∑ j

∑u

P Rjstu x ju+∑ j

p jst +∑k

!"k f kst −#"st = D P"st ,∀ " , s , t .(12)


These constraints say that the flow into a node is equal to the flow out of the same node

in every period. The summation over j is only for projects that deliver their product directly

to node n. The first term accounts for the fixed production projects, while the second term

accounts for the variable production projects. The flow variables account for the flow from

and to other nodes, while the market variables account for product leaving the transportation

system.

3.6.3. Node processing capacities

When the planning period starts, there is a capacity C Nnst that has been determined for

product s through node n in period t :

∑k

f kst +#"st −∑ j

∑u

C jstu x ju ≤ C N"st , ∀" , s , t .(13)

These constraints say that the flow out of a node can not exceed the processing capacity of

the node. The constraints are only defined for such combinations of n and s where capacity

shortage might occur. The summation over k is only for arcs that start at node n. The

summation over j is only for projects that give new capacity to node n.

3.6.4. Market delivery constraints

The upper and lower bounds for delivery of product s to market n in period t , M MXnst and

M MNnst , are given by the user for individual time periods, and modeled as bounds:

M MNnst ≤ mnst ≤ M MXnst , ∀n, s, t .(14)

3.7. The objective

The model is written in such a way that the user can choose between two objectives. It

is possible to either minimize a weighted sum of deviations from a given goal on production

or resource usage, or to maximize the total net present value from all the projects. Only the

maximization of the net present value will be discussed here. From the original data such as

production profiles, cost profiles, product prices and interest rates, we can calculate the

contribution to the net present value from each project, but this calculation is not described

here.

The net present value N Xju for project j started in period u is calculated without taking the

contribution from any variable production into account. The net present value N Pjst of one unit

of variable product s produced from project j in period t is calculated in the same way. For all

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markets, the user needs to specify a unit price for all products in every period. The price

profiles for one of the markets (for all products) are called reference prices, and these are

used in the net present value calculations mentioned above. To get the correct total net

present value, we also need to calculate the change in the total net present value N Mnst for

delivering a unit of product s to

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market n in period t , caused by the difference in prices between this market and the reference

market.This means that the objective can be written in the following way:

Max $=∑ j

∑u

N Xju x ju+∑ j

∑s

∑t

N Pjst p jst x ju+∑"

∑s

∑t

N M"st #"st .(15)

The first summation over j is for all j, because all projects are expected to have at least

some of their costs fixed at the start of the project. The next summation over j is only for

projects with variable production.

4. Implementation

We have implemented the model using MGG from EDS [11]. MGG produces FORTRAN

code that has to be compiled and linked. We wrote our own routines to read the data as

specified by NPD. This code was then linked with the MGG code to give a matrix generator.

After the numerical data has been read, a routine is called that tries to strengthen some

constraints in the model before the matrix is generated.

The normal way of using the system is to generate the matrix in demand mode before

the optimization is done in batch mode via SCICONIC [10]. After the optimiza-tion is

completed, the user generates a report in demand mode. The MGG system generates FORTRAN

code that reads the solution file from SCICONIC into common, where the model builder canaccess it. The report writer has been written in FORTRAN and linked with the code that reads

the solution file. The user can choose which parts of the report to generate. Most of the

resulting production and resource profiles can also be reported graphically.

The model was first installed on Vax machines to run under VMS, but was later moved

to Alpha (VMS), SUN (Unix) and PC (DOS). Outside NPD, the model is used by Saga

Petroleum, Norsk Hydro and for teaching purposes by The Norwegian Uni-versity of Science

and Technology. Statoil use a similar model, which NPD also has access to.

5. Some computational results

An old version of the model has been in use since the early eighties, while this version

has been used by NPD since the end of 1990. There, this version is run on a Micro-Vax 3400

under VMS 5.3. The run times in demand mode for generating matrices and reports are fairly

small compared with the CPU time needed for the optimization.

NPD run many cases to analyze the effect of small changes in particular types of data.

They try to solve both easy and hard problems and the CPU time for the optimization varies

from some minutes to more than ten hours. To give a better idea of normal optimization

times, table 1 lists three actual cases that NPD has used.

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Table 1

Some practical problem sizes together with running times (Micro-Vax 3400 under VMS5.3).

Cases Case 1 Case 2 Case 3

Rows 2248 2240 2222

Columns 1499 1617 147

S1-sets 25 36 35

Set members 197 299 279

Continuous objective 209.4 261.3 281.8

Integer objective 208.6 259.5 277.3

CPU sec. to cont.opt. 420 588 408

CPU sec. to int. opt. 623 1441 1313

CPU sec. to search compl. 899 2238 4207

Nodes to integer opt. 18 61 142

Nodes to search complete 40 198 613

In the table, we give information about the problem sizes and the values of both the

continuous and the integer optima which normally say something about how hard the

problems are to solve. In the same table, we give information both about CPU times in

seconds and node numbers, and for finding the optimal solution and com-pleting the branch

and bound search.

If a problem is too hard to solve, the NPD does some sort of a manual branching. Aproblem is too hard to solve if the solution time is too long. In some cases, they use the night

as an upper bound on the solution time, while in other cases, they only use a couple of hours.

Then, they reduce the possible start interval for one or more projects and yor remove the

possibility for a project to have variable production. They generate several new problems

this way, but they do not do a complete branching. The NPD feels that the solutions for

these new problems together give the essential results for the original problem, even if the

resulting solution is not necessarily the optimal solu-tion of the original problem.

6. Practical use of the model

Over time, different investment planning issues have been addressed by the NPD and

this model has been a helpful tool in finding good solutions. Broadly, the issues fall into

three different categories:

• the size of the petroleum sector;

• development alternatives for major projects – area planning;

• sequencing due to technical or market constraints.

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6.1. The size of the petroleum sector

It is interesting to note that the political discussion over time has mainly focused onproduction level and to some extent on the level of annual capital investment in the

petroleum sector. The focus has, to a limited extent, also been on income generation.

The discussion on whether to plan for 40, 60 or 90 mill tons of annual petroleum

production was raised mainly due to concern about the impact on the rest of the society and

due to concern about the depletion rate of an exhaustible resource.

Looking back on NPD’s investment planning, NPD also tended to focus on the use of

input factors such as annual spending on capital goods, the demand for construc-tion and

engineering man-hours and the use of other skilled personnel. With the new modeling

capabilities, NPD had ample possibilities to experiment with different con-straints regarding

input factors.

The model also gave NPD the possibility to choose an objective for the model where

the weighted sum of deviations from a given goal was minimized. In this way NPD could

find potential sequences of fields which gave low annual variations in the use of specific

input factors, thereby reducing the shocks on other sectors of the economy. By comparing

the net present value of such solutions with solutions optimized under normal constraints for

the same input factor and with the objective of maximizing net present value, it was possible

to calculate the cost for obtaining a more even level of demand for particular input factors.

In a report to the Norwegian government [13] in 1983 about the future of the

Norwegian petroleum industry, it was suggested that the petroleum activity should be

planned so that the ratio between the state revenue from this sector and the GNP, less

investments in the petroleum sector and corrected for the exportyimport balance, should bekept at a desired level. In [6], NPD made calculations of this ratio based on scenarios

developed by this model, showing variations between 0.08 and 0.25 depending on

assumptions regarding production and oil price. As many Norwegians remember, the

discussion died out together with the question of creating an oil-revenue-fund.

More recently, NPD used the model to calculate the total value of the petroleum

resources. In this calculation, it was necessary to find a sequence for the development of

future fields and prospects, and to calculate the value of the cash flows.

6.2. Development alternatives for major projects – area planning

Frequently, the operator has many alternatives under consideration. By maintain-ing anactive dialogue throughout the planning process, it is also possible to influence the licensees

in their final decisions.

NPD has experienced various issues of discussion, particularly the question of

establishing its own processing capacity or to go for a less expensive satellite develop-ment,

usually at the cost of delaying the project. Another frequent issue is how

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to transport the oil or gas from the field. The NPD has all the relevant technical information

of the existing installations and information of the proven or expected resource potential in

the area. Therefore, NPD is sometimes in a better position than others to evaluate theavailable options. If NPD finds an attractive solution the licensees have not analyzed

themselves, it requires the licensees to analyze this solu-tion before a final decision is made.

It is a fact that the commercial terms offered between the different groups of licensees

sometimes prohibit the selection of otherwise good solutions. The Ministry has the power to

reject tariffs if the profit element is too high, but this right is usually not exercised.

To be able to perform this kind of investment analysis, it is necessary to possess and

maintain very good data. In NPD, this model is connected to databases to facilitate easy

access to the relevant information. NPD usually has data for many different development

options on each field or transport systems under planning. A particular field may sometimes

be developed by quite different reservoir strategies, particularly if the field contains a mix of

different hydrocarbons, consists of separate reservoirs, needs pressure support, etc. One field

could start as a gas importer in one case or as a gas exporter in another case. The possibility

to handle a large number of alternatives for each project is therefore an important

characteristic with this model.

For NPD, it is frequently not satisfactory to analyze the different projects separately. It

is usually necessary to include other projects in the same area, which in some way or another

represent technical constraints or compete for the use of the same services offered by the

infrastructure in the area. The analysis usually has to be carried out under different sets of

constraints, and so the number of model-runs can be quite high.

NPD usually works out, at regular intervals, preferred long-term development plans

covering the most important geographic areas on the shelf. That way, they are able torespond very quickly if a certain project is becoming hot on the agenda. Over time, NPD has

seen that the planning picture is becoming more and more complex. The number of fields in

production is increasing (26 as of today), and many of them have several platforms with full

processing facilities. Another 14 fields are under construction or have been marked for

development. If we look at fields in an active planning process, the number is 12 and more

than 50 other discoveries are candidates for future development. The potential for future

discoveries is bright; some people at NPD would not be surprised if another 100 oil and gas

fields are discovered.

The number of fields in the less mature classes is high, but the associated reserve

figures are on average far lower than NPD is used to. Development of satellites will

therefore most probably be more frequent in the future than today. A further compli-cating

factor is that these new satellites compete for the same processing and transport capacities,

as do Increased Oil Recovery (IOR) projects at existing fields. But the latter group of

projects have usually a limited time window if they are going to be carried out.

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NPD thinks that the model’s ability to handle technical constraints, precedence

constraints and time windows makes it very well suited to handle these very complex issues.

6.3. Sequencing due to technical or market constraints

One issue in particular has frequently been addressed and that is the selection of new

gas fields to be developed when new gas contracts have been signed. All new contracts

established in the last decade have been supply-type contracts, not depletion contracts

assigned to particular fields. To a varying degree, the sellers have an extensive freedom to

choose the source fields to fulfill the contract. Sometimes the source fields contractually

have to be backed up by larger fields which guarantee the deliveries.

The sellers of the gas, at the moment the GFU (the gas negotiating committee),

nominate the source fields but need the final approval from The Royal Ministry of Industry

and Energy (MIE). The NPD acts as an advisor to the MIE in these matters. NPD uses the

model for this purpose and its ability to handle different markets (contracts) at the end of

each transport node is an important quality. NPD has also defined several pipes along the

same path to be activated by the model if new capacities are required.

7. Conclusion

The model has been heavily used for more than fifteen years. Even so, it is hard to say

how large its impact on the decisions has been. We feel that most of the impor-tant decisions

have been taken on a political basis, but we are sure that the model has influenced the

thinking of possible ways to develop the continental shelf.

When the old model had been in use for six years, Müller [9] analyzed the

organizational impact of the model’s use. His main conclusion was that the model had been

very useful to the organization.

We feel that the best proof of the model’s usefulness is that several companies have

been willing to pay for moving the mathematical model to new modeling and optimization

software several times during a period of fifteen years.

Together with building a useful model in the first place, we think that an essential

reason for the model’s continuous use over many years is that the users have always had

access to people that have been able to change the model when needed.

Even if the model is regarded as simple by the people who wrote it, the actual users of

the model regard it as complex. From time to time, the users have needed to discuss the use

of the model with people who fully understand all aspects of it. For this reason, we have the

impression that the users of the model have benefited from continuously having access to all

the people who wrote major parts of both the mathematics and the code. We believe this to

be the main reason for the long life of the model discussed.

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References

[1] R. Aboudi, Å. Hallefjord, C. Helgesen, R. Helming, K. Jørnsten, S. Pettersen, T. Raum and P. Spence,

A mathematical programming model for the development of petroleum fields and trans-portation

systems, European Journal of Operational Research 43(1989)13 – 25.

[2] E.M.L. Beale, A mathematical programming model for the long-term development of an off-shore gas

field, Discrete Applied Mathematics 43(1983)1 – 9.

[3] E.M.L. Beale, G.C. Beare and P.Bryam-Tatham, The doae reinforcement and redeployment study: A

case study in mathematical programming, in: Mathematical Programming in Theory and Practice, eds.

P.L. Hammer and G. Zoutendijk, 1974, pp. 417 – 442.

[4] E.M.L. Beale and J.A. Tomlin, Special facilities in a general mathematical programming system for

non-convex problems using ordered sets of of variables, in: Proceedings of the 5th International

Conference on Operations Research, ed. J. Lawrence, Tavistock, London, 1969.[5] C.E. Bodington and T.E. Baker, A history of mathematical programming in the petroleum industry,

Interfaces 20(1990)117 – 127.

[6] The Norwegian Petroleum Directorate, NPD: Petroleum Outlook – 84, Stavanger, Norway, 1984.

[7] K.K. Haugen, Possible computational improvements in a stcochastic dynamic programming mode for

scheduling of off-shore petroleum fields, Ph.D. Thesis, Norwegian Institute of Technology, 7034

Trondheim, Norway, August 1991.

[8] D.Haugland, Å. Hallefjord and H. Asheim, Models for petroleum field exploitation, European Journal

of Operational Research 36(1988)58 – 72.

[9] F. Müller, Decision support and organizational change, Norwegian Report STF83 A88006 from The

foundation for Scientific and Indstrial Research at the Norwegian Institute of Technology, 1988.

[10] Scicon, Sciconic User Guide, Version 2.11, Milton Keynes, England, 1990.

[11] Scicon, Mgg User Guide, Version 3.1, Milton Keynes, England, 1991.

[12] J. Sullivan, The application of mathematical programming methods to oil and gas field development

planning, Mathematical Programming 42(1988)189 – 200.

[13] Norges Offentlige Utredninger, The Future of the Petroleum Activity, NOU 1983:27, Universitets-

forlaget, Oslo, Norway, 1983 (in Norwegian).

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