Olatunji Adewale

8/19/2019 Olatunji Adewale

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The Pennsylvania State University

The Graduate School

Department of Energy and Mineral Engineering

OPTIMIZATION OF NATURAL GAS FIELD DEVELOPMENT USING

ARTIFICIAL NEURAL NETWORKS

A Thesis in

Petroleum and Mineral Engineering

by

Adewale Olatunji

© 2010 Adewale Olatunji

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

May 2010


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The thesis of Adewale Olatunji was reviewed and approved* by the following:

Luis F. AyalaAssistant Professor of Petroleum and Natural Gas EngineeringThesis Advisor

R. Larry GraysonProfessor of Energy and Mineral EngineeringGeorge H., Jr., and Anne B. Deike Chair in Mining Engineering

Graduate Program Officer of Energy and Mineral Engineering

Mku T. ItyokumbulAssociate Professor of Mineral Processing and Geo-Environmental Engineering

Yaw D. YeboahProfessor and Department Head of Energy and Mineral Engineering

*Signatures are on file in the Graduate School.


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Abstract

Field development of natural gas reservoirs is one of the main aspects of

exploration and production of natural gas for oil and gas operators. After a natural gas

field is deemed economically viable for development, and the reservoir properties have

been determined, a field development plan will normally be put together as a blueprint

for producing the field. However, since the main objective of natural gas field operators

is to maximize profits, it is imperative to understand how to optimize recovery from the

field. In this study, a model that uses reservoir engineering concepts to determine the

optimum hydrocarbon that can be produced per dollar spent has been developed. The

model adopts an optimization-based systems approach to field development, which

begins with predicting reservoir performance, and subsequently incorporating economic

parameters to determine the number of wells that will yield the maximum monetary value

of the field.

Artificial neural network (ANN) technology as a tool is increasingly becoming

popular for use in reservoir engineering applications such as reservoir characterization

and prediction of enhanced oil recovery performance due to its relatively fast,

computationally cost-effective, and reliable delivery compared to other tools such as

reservoir simulators. In this study, ANN technology is applied to the field development

optimization model in order to reliably predict the optimum number of wells for any gas

field development project within the specified reservoir and economic parameters. In this

regard, an ANN expert system has been developed and several data sets containing

relevant parameters have been used to train and test the developed ANN system. At the


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end of the study, the ANN system showed considerable effectiveness and robustness in

being able to predict the optimized development pattern of a natural gas field.


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Table of Contents

List of Figures…………………………………….…………………..………………….vii

List of Tables…………………………………………………………..…..……………..ix

Nomenclature………………………………….……………………….……………….....x

Acknowledgements……………………………………………………………..………xiii

Chapter 1 Introduction………............................................................................................1

Chapter 2 Background..…..…................................................................……………........3

2.1 Gas Field Development from Initial Discovery to Abandonment………………..…...3

2.2 Reservoir Performance Prediction….…………………………………………………6

2.3 Optimization of the Field Development………………………………….………….21

2.4 Artificial Neural Networks……….………………………………………………….24

2.5 Artificial Neural Networks in Petroleum Engineering….……………………….…..34

Chapter 3 Problem Statement……………………………………………………...……39

Chapter 4 Natural Gas Field Development...………………..…….................................41

4.1 Reservoir Performance Prediction.…………………………..………………………41

4.2 Economic Considerations……………………………………………..……………..60

4.3 Optimization of Gas Field Development..…………………………………...………65

Chapter 5 Implementation of ANN Model………………………..…………..……..….70

5.1 Development of ANN Model………………………………………………………..70

5.2 Generation of Data Sets……………. …………………………………………….....725.3 Results……………….........………..………………………………………….……..78

Chapter 6 Conclusion and Recommendations………..…………………………………85

Bibliography ……………………………………………...……………………………..89


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Appendix A MATLAB® Program Codes………………….……….…………………..94

A.1 Bisection……………………………………………………….…………………….94

A.2 Bisection_Pz….……………………………….……………………………………..95A.3 CullSmith….………………………………….……………………………………..96

A.4 NPV.……….………………………………………………..……………………….98

A.5 Optimization….…………………………………………………………………….100

A.6 Performance_Prediction……………………………………….…………………...102

A.7 Viscosity………………………………………………………………………..…..105

A.8 Zfactor……………………..……...……………………………….………..……...106

Appendix B: ANN MATLAB® Code…......……………..……………………………107


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List of Figures

Figure 2.1: Life cycle of a typical natural gas field………………………………………4

Figure 2.2-1: Natural gas reservoir material balance plot.....................……………..….12

Figure 2.2-2: IPR curves for decreasing values of reservoir pressure, P r ……..……..…14

Figure 2.2-3: Typical TPR curves for two wellhead pressures based on the Cullender &

Smith Correlation…...……………………………………………………………………17

Figure 2.2-4: IPR curves showing reservoir depletion effects over time.……..…..……19

Figure 2.4-1: Basic components of a neuron ……..……………………………….....…27

Figure 2.4-2: Basic components of a perceptron……….……..…………………..….…28

Figure 2.4-3: Basic model of ANN…………….……….……..…………………..……29

Figure 2.4-4: Structure of a neuron, where inputs from one or more previous neurons are

individually weighted, then summed ………………………………..……………..……31

Figure 4.1-1a: Production rate, Q field as a function of time…….……………….………43

Figure 4.1-1b: Cumulative production, G p as a function of time…….…………………44

Figure 4.1-1c: Pressure drawdown as a function of time…….…………………………45

Figure 4.1-2: IPR curve at initial reservoir pressure, P i for hypothetical gas field...……49

Figure 4.1-3: TPR curve at minimum wellhead pressure, P wh_min for hypothetical gas

field………………………………………………………………………………………50Figure 4.1-4: IPR curves at P i = 3000 psia and P r |tp = 1511 psia…..……………………53

Figure 4.1-5: Performance prediction for hypothetical gas field showing field production

rate, Q field over time………………...………………………………………….…………58


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Figure 4.1-6: Performance prediction for hypothetical gas field showing cumulative gas

produced, G p over time…………..………………………………………….………...…59

Figure 4.1-7: Pressure drawdown of hypothetical gas field over time……….…………60

Figure 4.2: Flow rate vs. time plots for hypothetical gas field based on different number

of wells...............................................................................................................................61

Figure 4.3: Optimization of the hypothetical gas field………………….………………68

Figure 5.2-1: Sensitivity Analysis for N w_opt .…………………….…………..…………77

Figure 5.2-2: Sensitivity Analysis for NPV max..………………….…………..…………77Figure 5.3-1: Optimized network architecture...………………….…………..…………79

Figure 5.3-2: ANN results for N w_opt…..……………………….……….………………81

Figure 5.3-3: ANN results for NPV max…..……………………..……….………………82

Figure 5.3-4: Relevance of input parameters……………………...…….………………83


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List of Tables

Table 4.1-1: Reservoir, well and fluid properties for hypothetical gas field……………47

Table 4.1-2: Performance predictions for hypothetical natural gas field………..…..…..57

Table 4.3: Economic parameters for hypothetical natural gas field……….………..…..64

Table 5.2-1: ANN input ranges……………………………………………………..…...74

Table 5.2-2: Possible input values for ANN implementation………………………..….75


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Nomenclature

A = Area

Bgi = Initial gas formation volume factor

Cwell = Per-well Performance Coefficient

Cw = Cost of well

Cw_ft = Cost of well per foot

G p_yr = Annual gas field production

G p = Cumulative gas produced

G p|tp = Cumulative gas produced at end of production plateau

h = Thickness of reservoir

ID = Inner diameter of well tubing

n = Pressure drawdown exponent

n* = neuron

Nw = Number of wells

Nw_opt = Optimum number of wells

Pi = Initial reservoir pressure

P pc = Critical pressure of gas

P pr = Reduced reservoir pressure

Pr = Reservoir pressure

Pr |tp = Reservoir pressure at end of production plateau

Pwh = Wellhead pressure


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Pwh|i = Initial wellhead pressure

Pwh_min = Minimum wellhead pressure

Pwf = Well flowing bottom-hole pressure

Pwf |tp = Well flowing bottom-hole pressure at end of production plateau

Qa = Abandonment field production rate

Qfield = Field production rate

Qfield_ave = Average field production rate

Qfieldpl = Field production during production plateauQwell = Well production (flow) rate

Qwellpl = Flowrate of each well during production plateau

r = Deferment rate

RFa = Recovery factor at field abandonment

RF pl = Recovery factor at end of production plateau

RV = Annual revenue from gas production

RV| PV = Present value of revenue from gas production

RV| t = Revenue from gas production in year ‘t’

Sgi = Initial gas saturation

Swi = Initial water saturation

t = Time

ta = Final year of production

t p = Time period till end of production plateau

Tr = Reservoir temperature


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T pc = Critical temperature of gas

T pr = Reduced temperature of gas

Twh = Wellhead temperature

Twf = Well flowing bottom-hole temperature

u = Cash generated per thousand cubic feet of gas sold

w = Weight associated with a neuron

x = Perceptron input

Z = Compressibility factor of gasZi = Compressibility factor of gas at P i

Z|tp = Compressibility factor of gas at P r |tp

Greek

ϕ = Porosity

γg = Specific gravity of gas

Abbreviation

ANN = Artificial Neural Network

Bscf = Billion standard cubic feet

DF = Deferment factor

Mmscfd = Million standard cubic feet per day

NPV = Net Present Value

OGIP = Original gas in place


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Acknowledgements

I would like to express my sincere gratitude and appreciation to Dr. Luis Ayala

for his continued guidance and supervision during the period of writing my thesis and my

graduate program in general. His patience, motivation and technical contributions helped

me tremendously through the process of writing this thesis.

I would also like to thank Dr. Larry Grayson and Dr. Thaddeus Ityokumbul for

accepting to be on my thesis committee.

My thanks also go to my fellow PME students whose friendship helped me

through the graduate program at Penn State and beyond.

Last but not least, I am forever indebted to my parents for their moral and

financial support throughout my graduate study and educational pursuits in general.


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location of the gas needs to be established, after which the actual amount of gas in place

and how much gas the well will actually produce will be determined. To address these

fundamental questions, an integrated reservoir evaluation approach needs to be adopted.

One of the most important tasks of the petroleum engineer is predicting the

amount of oil and gas that will be recovered from a reservoir. Choosing the methodology

is critical for accurate forecasts which of course are vital for sound managerial planning.

Predicting reservoir performance using conventional deterministic models can be tasking,

especially for very complicated reservoir systems. In this study, a model that usesArtificial Neural Network (ANN) to determine the optimum production of hydrocarbons

from natural gas reservoirs that can be produced per dollar spent would be developed.

The model will provide a basic and general tool for natural gas field development which

can be used as a framework for future implementation. The model that will be presented

will be one that employs realistic ranges of reservoir, fluid and well properties for natural

gas fields in North America. While this range will not cover all the possible combinations

of parameters in these fields, it will attempt to capture a wide enough sample collection

for both the lower and upper boundaries of possible scenarios such that it can be

applicable to a vast number of natural gas fields. The ranges of field parameters used in

this study and assumptions made will be shown in later chapters.


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Chapter 2

Background

Predicting reservoir performance using conventional deterministic models can be

tasking, especially for very complex reservoir systems. The literature is replete with

studies that have been conducted on reservoir performance prediction and natural gas

field development. A review of the literature gives us an understanding of how findings

from these studies have impacted the industry. This literature review will essentially

focus on reservoir performance prediction as it pertains to natural gas field development

and how ANN can, and has been incorporated and used as a tool in petroleum

engineering projects.

2.1 Gas Field Development from Initial Discovery to Abandonment

When a field is first discovered where there is scope for gas exploration, the gas-

in-place is estimated, usually by applying volumetrics. For this, some knowledge of the

areal extent and the petrophysical and gas properties of the reservoir are required. As an

alternative, the material balance method or production decline can be applied where some

pressure-production history of that place is required to make an assessment of the gas-in-

place (Ikoku, 1984).

The next step in the process is the assessment for reservoir performance for the

development plan by preparing a production schedule. Included in this schedule are the


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contractual obligations such as the maximum field rate (Q field ) required, the duration of

the production, and the time to abandonment. The investment required to maintain the

desired rate of production must also be determined at this point. For this, the producer

must specify the number of wells he requires to be drilled, when they should be drilled,

and the desired deliverability per well and field.

Once the initial well is drilled, additional appraisal wells (if needed) are drilled

and tested to delineate the size and performance of the reservoir. This is the information

which is required for the producer to negotiate contracts with his/her buyers. Once thecontracts are signed, the producer gives the go-ahead for the field development and gas

production to commence and pipelines are made available to transport the gas to market.

Figure 2.1 shows a typical life cycle of a natural gas field from the time of its exploration

and field development to the end of its reservoir life.

Figure 2.1: Life cycle of a typical natural gas field (After Rojey et al., 1997)


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As seen in Figure 2.1, the initial stage of gas field development is rapid and

production rate increases as new wells are drilled and surface facilities are installed to

meet the contracted field rate (Q field ). After the initial development phase, production

goes through a protracted period of consistency or production plateau. During this period

the reservoir capability is greater than the maximum, contractual rate, and therefore

maintenance of the rate is of primary importance. At some point in the life of the field,

the reservoir would have drawn a sizable amount of its storage that the volume of

production would have come down against its contractual obligation, at which point the production rate starts to decline.

Alternatively, the production plateau may be prolonged or extended by making

further investment such as recompression or drilling additional wells to maintain the

contracted production rate. The choice to implement this additional investment in

extending the production plateau beyond the initial decline point is based primarily on

economics. When production can no longer be sustained at the contracted rate due to

additional investment costs exceeding production revenue, reservoir production begins to

decline until it reaches a point when it is no longer economic to continue production. This

point is usually considered the end of the life of the field and the field is typically

abandoned unless external factors such as new technology, secondary or tertiary recovery

methods, or expected hike in price of natural gas increase the potential of future

economic production. In running a reservoir, the risks involved, especially in terms of the

finance must be kept in mind, considering the fluctuations which take place due to the

decreases or increases in demand and price for gas (Ikoku, 1984).


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Field experience has shown that, an aspect which is of prime importance in the

continuous optimization of production in a gas field is in the prediction of the relationship

between the flowrate and the pressure drop in a reservoir. This is where an inflow

performance relationship (IPR) is typically used. An IPR model allows one to better plan

various operating processes such as determining the optimum production scheme,

designing production equipment and artificial lift systems. Maravi (2003) stated that an

IPR model (inflow) combined with tubing performance analysis (outflow) using a ‘nodal

analysis’ technique allows one to monitor well productivity and to choose a properremedial treatment option such as acidizing, fracturing, workovers, and so on, to restore

optimum well performance.

As was mentioned earlier, natural gas field development is a highly capital

intensive venture. Thus the economic analysis of the project viability is a very important

first-step that must be made before production operations can commence. van Dam

(1968) stated that there is a great difference between gas and oil production, not only

because of their different characteristics and structure, but also because of the cost

involved. van Dam (1968) also stated that, while production from an oil field can be

based mainly on the optimum capacity of the reservoir to produce, this is not the case for

natural gas fields. He went further to say that there is a very close interrelationship

between the production and marketing of natural gas because gas fields are directly

connected through pipelines to consumers. Therefore the capacity of the market to accept

the gas has to be considered when planning the development of a gas field. van Dam

(1968) further stated that another major difference is that in oil fields, the production of


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oil starts at an early stage of field development and subsequently, the information

obtained at this stage is used to design the optimum development plan of the field. On the

other hand, gas production usually cannot commence until a gas sales contract has been

signed, hence the information required in developing an optimum field development plan

must be known before production can begin. This creates a wider degree of uncertainty

during gas field development since the information required usually cannot be accurately

obtained until the field has started to produce.

Since the objective for any natural gas field development is to maximize profitfrom the production of gas, the knowledge of the optimum number of wells, and

optimum deliverability per well and for the field is very important to the producer.

However, for any gas field development optimization technique to be efficient, a reliable

method of predicting reservoir performance over the life of the field is required. This

method can then be applied to a variety of scenarios based on the field properties to

determine the number of wells and deliverability per well that maximizes profit.

Predicting the amount of oil and gas that will be recovered from a reservoir

remains one of the most important tasks of the petroleum engineer. Emanuel et al (1989)

stated that the procedure for calculating reservoir performance is by:

• Establishing the porosity/permeability characteristics of the reservoir from well

logs and pores, and determine its statistical structure using random fractals.

• Using a random fractal-interpolation scheme based on the fractal characteristics

determined from the well logs to project well data to the inter-well region.


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• Establishing fluid-flow and displacement parameters from PVT, relative

permeability, and if possible, coreflood data.

• Assembling geologic and fluid data into a highly detailed finite-difference cross-

sectional model representing reservoir flow between a typical injector/producer

pair.

• Running the finite-difference model for projected flood conditions and developing

a dimensionless characteristic solution that relates phase fractional flow at the

producer to PV of injected fluid.• Developing a streamtube model of the reservoir to represent area conformance,

where the formation of the streamtube will incorporate variable mobility ratios,

permeability trends, and no-flow boundaries.

• Coupling the streamtube model with the characteristic solution to estimate field-

wide project performance.

The determination of volume of gas reserves is another important aspect in

reservoir engineering (Mattar and McNeil, 1998). This information is crucial in the

development of a production strategy, design of facilities, contracts and valuation.

Depending on data availability and judgment on the reliability of the data, an estimator

will select from the several methods to make a proved reserves estimate. Methods based

on production performance data are commonly preferred over those inferred from

geological and engineering data for their accuracy. Two prominent ways to estimate the

gas reserves in reservoirs are:


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• The volumetric method, and

• Material balance method

There are also other reservoir types and production mechanisms available, such as the

production decline method; but again, it is the reliability of the data which determines

which of these methods is more appropriate for a given reservoir. The volumetric and

material balance methods are usually employed in determining the original gas-in-place,

while the production decline method estimates recoverable gas.

Volumetric Method

The volumetric method computes the total volume or cumulative three

dimensional space a fluid occupies at any point in time based on the existing conditions.

The volumetric method can be very valuable in making a determination of the original

gas reserves in place (OGIP) and also, the remaining reserves during the life cycle of a

field. The volumetric computation of the OGIP is based on the initial pressure and

temperature of the reservoir and uses information from sources such as contour maps,

well logs and core analysis to determine the volume of the gas bearing portion of the

reservoir. The drawback to this method is that the factors inherent in its calculations may

sometimes be difficult to accurately determine. The volume of gas originally in place is

simply the product of area (A), thickness (h), porosity ( φ ) and initial gas saturation of the

formation (S gi = 1 – S wi), where S wi = initial water saturation. The value from this

computation represents the volume of gas at reservoir conditions, and has to be converted


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to the volume at standard conditions using the initial gas formation volume factor, B gi.

The OGIP can be calculated using the volumetric method shown in Equation 2.2-1.

OGIP = gi

wi

BS 1 Ah56043 )(, −φ

Equation 2.2-1

The initial gas formation volume factor, B gi being a ratio of the volume of gas at

reservoir conditions to the volume of gas at standard conditions (14.7 psia and 60 oF) can

be calculated as shown in Equation 2.2-2 below:

B gi =i

ir

P Z T 02827 0.

Equation 2.2-2

where ‘T r ’ is the reservoir temperature, ‘P i’ is the initial reservoir pressure, and ‘Z i’ is the

compressibility factor at P i.

In the readings of volumetrically determined reserves, it can be erratic because of

the method it employs in determining reservoir characteristics that are often unknown as

in the case of the areal extent of a pool (Mattar and McNeil, 1998). However, material balance method is considered more accurate.

Material Balance Method

The material balance method uses actual reservoir performance data to make an

assessment of the gas reserves in a reservoir. It is based on the concept of conservation of

mass by analysis of the quantity of what enters, builds up in, and leaves the reservoir.

Because of this, the material balance method is used more widely to estimate remaining

reserves. Once the estimate of the original gas-in-place, OGIP is determined, it can be

used reliably to forecast the recoverable gas reserves under various operating conditions.


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The material balance equation presents an inversely linear relationship between

the amount of gas produced (G p) and P r /Z where ‘P r ’ is the reservoir pressure and ‘Z’ is

the compressibility factor at P r . The material balance equation for a natural gas reservoir

is shown in Equation 2.2-3 and a corresponding plot in Figure 2.2-1. It should be noted

that the intercept of the material balance curve on the x-axis (G p) in Figure 2.2-1 is OGIP.

Z P r =

i

i

Z P

–

OGIP

G

Z P p

i

i Equation 2.2-3

Figure 2.2-1: Natural gas reservoir material balance plot


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Inflow Performance Relationship

In order to maximize the value of a gas field, it is necessary to understand the

performance of the system by integrating its components in an integrated well or field

production system model. The inflow performance relationship (IPR), which is the ability

of the reservoir to produce to the wellbore is usually the first component necessary to

build a system model, and the selection of the right curve is critical in predicting the

inflow performance under varying conditions of pressure drawdown, fluid and gas ratios,

reservoir depletion, vertical effective stress, relative permeability, and wellbore skin. Thisrelationship is usually affected by reservoir rock and fluid properties, including near-

wellbore effects and heterogeneities in the well drainage area, average reservoir pressure

and field development activities (Lee and Wattenbarger, 1996). The IPR is basically a

relationship between the well flowrate (Q well) and the well bottom-hole flowing pressure

(Pwf ) and can be formulated as an equation:

Qwell = C well (P r 2 – P wf 2 )n Equation 2.2-4

where ‘C well’ is the per-well performance coefficient, and ‘n’ the pressure drawdown

exponent.

The per-well performance coefficient, C well can be obtained from reservoir

deliverability tests and is a representation of the flow performance from the reservoir to

the wellbore. The IPR equation mentioned above can be described as a more general

form of the pseudo-steady state equation for radial flow of real gases in terms of showing

the relationship between flowrate and pressure drawdown squared. The pseudo-steady

state equation for radial flow of real gases incorporates more individual reservoir


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parameters such as viscosity, z-factor, skin factor, etc in its computation but the IPR

equation incorporates the relationship into just C well and n. In this study, the IPR equation

will be used to express this relationship as opposed to the pseudo-steady state equation

because the former utilizes less individual parameters which will make the neural

network implementation more efficient and less cumbersome. Back pressure testing and

isochronal testing are two commonly used methods to estimate the inflow performance

parameters (C well , n) of a reservoir.

The IPR relationship is shown graphically in Figure 2.2-2 for decreasing values ofreservoir pressure. As can be seen from the graph, the IPR curve shifts downward and

becomes smaller for lower P r , accounting for the effects of reservoir depletion.

Figure 2.2-2: IPR curves for decreasing values of reservoir pressure, P r


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range of gas-well pressures and temperature” since it “makes no simplifying assumptions

for the variation of either temperature or Z-factor”. However, this method assumes

steady-state flow, a single-phase gas stream and that the change in kinetic energy is

negligible (Ikoku, 1984). The Cullender and Smith method provides a functional

relationship between the well flowing bottom-hole pressure (P wf ) and the wellhead

pressure (P wh) as shown in Equation 2.2-5.

P wf = ƒ(P wh , Q well , T wf , T wh , depth, ID, γ g , P pc , T pc ) Equation 2.2-5

where ‘Q well’ is the well flowrate, ‘T wf ’ the well bottom-hole temperature, ‘T wh’ the

wellhead temperature, ‘depth’ the depth of the producing formation from surface, ‘ID’

the inner diameter of the tubing, ‘ γg’ the specific gravity of the gas, ‘P pc’ the critical

pressure of the gas, and ‘T pc’ the critical temperature of the gas. Figure 2.2-3 shows the

typical behavior of the tubing performance equation based on the Cullender and Smith

correlation. This is shown for two different wellhead pressures, P wh1 and P wh2, Pwh1 being

the higher wellhead pressure of the two.


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Figure 2.2-3: Typical TPR curves for two wellhead pressures based on the

Cullender & Smith Correlation

Typically, the minimum wellhead pressure for a gas well is specified by the

pressure of the pipeline through which it is transported because gas pipelines usually

require delivery of the gas at a specific minimum pressure. At the constant rate stage of

gas production when the reservoir is capable of producing at a rate higher than the

specified rate, the specified rate is maintained at each wellhead by adjusting a well

control device called the choke. Once the reservoir is no longer able to deliver gas at the

specified pipeline pressure, compressors can be installed and the wellhead pressure

lowered.


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Well Deliverability

A combination of an inflow performance curve (IPR) and a tubing performance

curve (TPR), generally identifies the flowrate and corresponding flowing bottom-hole

pressure at a particular reservoir pressure and tubing parameters such as tubing size and

wellhead pressure. The deliverability or instantaneous flowrate of a flowing natural gas

well can then be said to be this combination of the reservoir performance (inflow) and the

tubing performance (outflow). This is so because the rate of flow to the surface can be

restricted by the ability of the reservoir to deliver the gas as well as the capacity of thewell tubing to allow flow to the surface. A graphical representation of the well

deliverability is shown in Figure 2.2-4. Typically, a well will flow or deliver gas at a rate

that is defined by the more restrictive of the inflow performance and tubing performance.

In Figure 2.2-4, this is shown by the points identified as “Operating points” where the

intersections of both the inflow performance curve and the tubing performance curve

correspond to the flowrate of the well for the respective reservoir pressure and wellhead

pressure. Based on this relationship between the inflow performance and tubing

performance, if the reservoir pressure, P r is unknown and the flowrate, Q well (‘operating

point’) is known beforehand, the flowing bottom-hole pressure, P wf can be obtained from

the tubing performance method (Cullender & Smith) described above. Then the

corresponding reservoir pressure at that flowrate can be computed from the IPR equation

shown in Equation 2.2-4.

A point worthy of note is that as the reservoir pressure of gas field declines due to

depletion, the IPR curve reduces and shifts downward, resulting in a decline in well


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deliverability. The well deliverability can also change due to a shift in the TPR curve

resulting from a change in wellhead pressure. This behavior can also be observed in

Figure 2.2-4 where the intersections of both the multiple inflow performance curves and

the tubing (outflow) performance curves identify the production (flow) rates for declining

reservoir pressures at a given tubing size and two tubing head pressures.

Figure 2.2-4 : IPR curves showing reservoir depletion effects over time

The importance of predicting the performance of a natural gas field in terms of its

production over time cannot be overemphasized. Just as it is essential for natural gas

producing companies to estimate the value of their proven reserves to determine its

worth, it is equally vital to reliably predict reservoir performance to be able to forecast


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future production. This also helps the producing company to project cash flows and make

reliable economic decisions.

For a good prediction of reservoir performance to be made, one needs to have the

necessary and relevant information including reservoir properties, tubing properties and

fluid properties. Other parameters that need to be known beforehand include the

abandonment pressure or flowrate and the maximum flowrate allowed which may be

restricted by the surface network and/or stipulated by the contract terms. The maximum

flowrate should be one that effectively maximizes the profit for the developer whilesatisfying the constraints imposed by the surface facilities and equipments such as

flowlines, compressors, pipelines, etc.

Typically, before production from a gas field can commence, there should be a

commercial market ready to accept the gas. This can be done in form of a gas sales

contract. Thus, the basic factors required to determine the optimum development plan of

the field will have to be known from the outset. This creates significant improbabilities

since these factors cannot be accurately ascertained before the field is actually developed

and the field is put on production. Such uncertainties produce a risk which is put into

consideration when an analysis of the plan is done. The use of artificial neural network is

increasingly becoming a means of mitigating some of the risks and uncertainties involved

in the analyses of field development projects.


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2.3 Optimization of the Field Development

The objective of any gas field developer is to maximize profit. This can usually be

achieved by efficiently managing the development of the field such that its production is

optimized and costs are minimized. In order to optimize production, wells will have to be

drilled, however there comes a time where the production that will be obtained from

drilling an additional well does not justify such drilling in terms of the cost of drilling the

well. Gas field development costs can be capital expenses or operating expenses. The

majority of capital expenses are incurred at the beginning of the project and may includethe cost of wells, flowlines, surface equipment and pipelines. Operating expenses include

expenses incurred throughout the life of the field. These include preventive and

maintenance costs, monitoring costs and labor. This distinction is particularly important

during the optimization of any gas field development because of the time value of money.

Where possible, it may be more cost-efficient to defer expenses to the future as the

monetary value decreases. This is more easily done with operating expenses.

There are two main limitations in the eventual deliverability of a gas field. Firstly,

the gas delivery should be done in such amount that there is sufficient market for the gas

so it is fully utilized. This is because the gas is usually transferred directly to the market

by means of pipelines; hence the market must be ready to receive the gas as it is produced

from the field. This situation usually limits the amount of gas that can be produced from

the field. Secondly, the operating conditions on ground such as the ability to drill wells

and construct field and transport facilities may also be a limiting factor in the amount of

gas that can eventually be delivered to the market. This may impose a limitation on the


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production rate at which the buildup stage of the field development can occur. Finally,

limitations may also exist due to purely economic and financial reasons. Irrespective of

the initial two limiting factors described above, it is very important to incorporate

economics in deciding the optimum rate at which to produce the field since the objective

of gas field development is to generate maximum profit. This economic optimum

production is what this study seeks to identify and this will be the basis of the artificial

neural network implementation.

To realize a strategy that optimizes delivery based on the economic constraint butthat ignores the market limitations, van Dam (1968) states that an economic scheme

needs to be implemented and this can be done by first employing a random production

model that can be built upon to yield a more efficient and optimized delivery strategy.

van Dam (1968) further states that that random model should be made up of three

different stages of production that include a buildup of production, a time of constant

production, and the final stage which is one of a steady reduction in production. The

production model and optimization process presented in this study will focus mainly with

the second and third stages of production.

The first stage of van Dam’s proposed model will be a period of drilling new

wells which will lead to an increase in production accordingly. The second stage involves

a stoppage of drilling activities so that the production is maintained at a constant rate.

This continues until the production starts to decline which leads to the third stage. A point

worthy of note is that the second stage may be extended by drilling additional wells to

maintain the total output of the reservoir without lowering the minimum tubing head


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pressure (P wh_min ) of the well. At some point afterwards, when the drilling of additional

wells becomes uneconomical and impractical, the minimum tubing head pressure may

have to be reduced and eventually compressors installed (van Dam, 1968). In some

instances though, it may be more desirable or efficient to drill additional wells, after first

reducing the minimum tubing head pressure and installing compressors; and before the

third stage when the reduction in production starts to take effect (van Dam, 1968). This

part of the process involving the reduction of minimum tubing head pressure and

installation of compressors will not be covered in the study however.The purpose for the optimization procedure that this study seeks to implement is

to identify the number of wells for the field that maximizes profitability. Initially, as more

wells are drilled, the field production or deliverability increases thereby increasing the

revenue and consequently, profit generated from gas production. This continues to a point

where the additional revenue generated from the incremental field production is less than

the cost associated with drilling a new well and hence, cannot justify doing so. At this

point, the net present value (NPV) of the field has been maximized. van Dam (1968)

corroborated this by stating that “this optimum production rate of a gas field will be

reached if any further increase in the production rate by increasing the number of wells

will no longer contribute to an increase in present value profit.”


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2.4 Artificial Neural Networks

An artificial neural network (ANN) is a mathematical model or computational

model that tries to simulate the structure and/or functional aspects of biological neural

networks. It consists of an interconnected group of artificial neurons and it processes

information using a connectionist approach to computation. In most cases, an ANN is an

adaptive system that changes its structure based on external or internal information that

flows through the network during the learning phase. In more practical terms neural

networks are non-linear statistical data modeling tools. They can be used to modelcomplex relationships between inputs and outputs or to find patterns in data.

ANN can also be viewed as a machine that is designed to model the way in which

the brain performs a particular task or function of interest. There have been several

definitions of ANN (Haykin, 1994). However, a widely accepted term is that adopted by

Alexander and Morton (1990) who defines a neural network as “a massively parallel

distributed processor that has a natural propensity for storing experiential knowledge and

making it available for use”.

Neural networks, in general terms, are input-output mapping models that can be

used to attack complex or non-straightforward problems. Neural networks are particularly

useful in cases where mathematical or statistical methods, such as linear, nonlinear

regression, curve fitting, etc., cannot provide a satisfactory solution. Neural networks use

a model that imitates the human brain, both structurally and computationally. They

consist of interconnected neurons that might have several layers of input, and hidden

output working sequentially and in parallel. When an input pattern is introduced to the

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neural network, the synaptic weights between the neurons are stimulated and these

signals propagate through layers and an output pattern is formed. Depending on how

close the formed output pattern is to the expected output pattern, the weights between the

layers and the neurons are modified in such a way that the next time the same input

pattern is introduced; the neural network will provide an output pattern that will be closer

to the expected response. In that sense, the neural network is a system that will learn from

examples or from its own mistakes, just like how a human is expected to behave.

There are several types of artificial neural networks. However, the mostcommonly used ones are the feed-forward neural networks FNNs, (Scalabrin, Marchi,

Bettio, and Richon, 2006) which are designed with one input layer, one output layer and

hidden layers. The number of neurons in the input and output layers equals to the number

of inputs and outputs physical quantities, respectively. The principal disadvantage of

FNN s is the difficulty in determining the ideal number of neurons in the hidden layer(s).

Also few neurons produce a network with low precision and a higher number leads to

over-fitting and bad quality of interpolation and extrapolation. The use of techniques such

as Bayesian regularization, together with a Levenberg-Marquardt algorithm, can help

overcome this problem (Marquardt, 1963).

Features of Artificial Neural Network

Neural networks have the following important features (Marquardt, 1963):

1. They respond with high speed to input signals.

2. They have generalized mapping capabilities.


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3. They filter noise from data.

4. They can perform classification as well as function modeling.

5. They can encode information by regression or iterative supervised learning.

In spite of these important features, they also have some drawbacks; some of which are:

1. They are data intensive.

2. Training is computationally intensive and may require significant elapsed time.

3. Predictions are unreliable if extrapolated beyond the boundaries of the training

data.4. They have a tendency to over-train if the network topology is not optimized,

resulting in their mapping training data extremely well but becoming unreliable in

dealing with new data.

Structure of Artificial Neural Network

The basic building block of all biological brains is a nerve cell, or a neuron, with

each neuron acting as a simplified numerical processing unit. The brain is a formation of

billions of such biological processing units, all heavily interconnected and operating in

parallel. In the brain, each neuron takes several input values from other neurons, applies a

transfer function and sends its output on to the next layer of these neurons. These neurons

in turn send their output to the other layers of neurons in a cascading fashion. Similarly,

ANNs are usually formed from many hundreds or thousands of simple processing units,

connected in parallel and feeding forward in several layers. Using neural network

terminology, the strength of an interconnection is known as its weight (Mehta, Mehta,


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Manjunath, and Ardil, 2006). Figure 2.4-1 shows the basic components of a neuron

including the nucleus, the synapse, the axon, the dendrites and the cell body.

Figure 2.4-1: Basic Components of a Neuron (From Mehta et al, 2006)

With the advent of cheaper computing systems, the interest in ANNs has

blossomed. The basic idea of the development of the neural network was to make

computers do things which a human being couldn’t do easily. Therefore, ANN was

developed with the concept to simulate the human brain, and hence, its architecture can

be compared with that of the human brain.

The various sub structures of neural networks are presented hereunder:

Perceptron

The perceptron, is a basic neuron that was invented by Rosenblatt in 1962. It is a

single layer neuron that contains the adjustable weight and some threshold values. The

inputs are x0 , x1 , x2 , x3 ,....x N and their corresponding weights are w0 , w1 , w2 , w3 ,....w N as


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shown in the Figure 2.4-2. The processor itself consists of weights, the summation

processor, and the adjustable threshold. This weight can be viewed of as the “propensity

of the perceptron to fire, irrespective of its inputs” (Mehta et al, 2006). This weight is

known as the bias terms (Simpson, 1992).

Figure 2.4-2: Basic Components of a Perceptron (From Mehta et al, 2006)

Neuron

A neuron (or cell or a unit) is an autonomous processing element. A neuron is

more like a computer. It receives information from other neurons, performs a relatively

simple processing of the combined information, and sends the results back to one or more

neurons. In most pictorial representations, neurons are generally shown in circles or


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squares. Sometimes they are denoted by 1 2....N , where N is the total number of neurons

in the networks.

There has been a concerted effort made in the past century to create a model of a

neuron, with remarkable success. Neural connections are significantly fewer and similar

to the connections in the brains. The basic model of ANN is shown in Figure 2.4-3. It is a

combination of perceptrons which form the Artificial Neural Network.

Figure 2.4-3: Basic Model of ANN (From Mehta et al, 2006)

A layer is a collection of neurons that can be thought of as performing some

common functions. They are numbered by placing the numbers or letters beside each

neuron and it is believed that no two neurons are connected to another in the same layer.

All neuron nets have an input layer and an output to interface with the external


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environment. Each input layer and each output layer has at least one neuron. Any neuron

that is not in an input layer or in an output layer is said to be in a hidden layer. Sometimes

the neurons in a hidden layer are called feature detectors because they respond to

particular features in the previous layer.

Synapses (arcs/links)

An arc or a synapse can be a one- or two-way communication link between two

cells as shown in Figure 2.4-1. A feed-forward network is one in which the informationflows from the input cells through hidden layers to the output neurons without any paths

whereby a neuron in a lower-numbered layer receives input from the neurons in a high-

numbered layer. A recurrent network, by contrast, also permits communication in the

backward direction (Guo, Hill, and Wang, 2001).

Weights

A weight (generally denoted as wij) is a real number that indicates the influence

that a neuron n* i has on another neuron n* j. If positive weights indicate reinforcement,

and negative weights indicate inhibition, then a zero weight will indicate no direct

influence or connection exists. The weights are often combined into a matrix w. These

weights may be initialized and given as predefined values, or initialized as random

numbers, but they can also be altered by experience. It is in this way that the system

learns. Weights may be used to modify the input from any neuron. However, the neurons


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in the input layer have no weights, and therefore, their external inputs are not modified

before the input layer.

Back Propagation

The field of neural networks can be said to be related to artificial intelligence,

machine learning, parallel processing, statistics, and other fields. They are best suited to

solving problems that are the most difficult to solve by traditional computational

methods. Figure 2.4-4 shows the structure of a neuron, where inputs from one or more previous neurons are individually weighted, then summed.

Figure 2.4-4: Structure of a Neuron, where inputs from one or more previous

neurons are individually weighted, then summed (McCollum, 1998)

Since intelligence of the network exists in the values of the weights between

neurons, a method to adjust weights to solve a particular problem is thus required. It is in

such networks that the common learning algorithm called Back Propagation (BP)

becomes important. A BP network learns by example, therefore, it must be provided with


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a set of input values and also fed known correct output values. These input-output

examples, models the network to act in a way in which it is expected to compute, and this

is where BP algorithm becomes important (McCollum, 1998).

Propagation Rule

A propagation rule is a network rule that applies to all the neurons and specifies

how outputs from cells are combined into an overall net input to neuron n* . The term

‘net’, indicates this combination. The most common rule is the weighed sum rulewherein, adding the products of the inputs and their corresponding weights forms the

sum:

net i = b i + Σ wij * n* ij

where ‘j’ takes on the appropriate indices corresponding to the numbers of the neurons

that sends information to the neurons ni. The term in j represents the inputs to neuron n* i,

from neuron n* j. If the weights are both positive and negative, then this sum can be

computed in two parts - Excitory and Inhibitory. The term bi represents a bias associated

with neuron n* i. Adding one or more special neuron(s) having a constant input of unity

often simulates these neuron biases (Mehta et al, 2006).

Training ANN as an Optimization Tool

Training a neural network is, in most cases, an exercise in numerical optimization

of a usually nonlinear function. Methods of nonlinear optimization have been studied and

there is huge literature on the subject in fields such as numerical analysis, operations


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research, and statistical computing. There is no single best method for nonlinear

optimization. One needs to choose a method based on the characteristics of the problem

to be solved.

For functions with continuous second derivatives, three general types of

algorithms have been found to be effective for most practical purposes (Mohaghegh,

2000a):

1. For a small number of weights, stabilized Newton and Gauss-Newton algorithms,

including various Levenberg-Marquardt and trust-region algorithms are efficient.2. For a moderate number of weights, various quasi-Newton algorithms are efficient.

3. For a large number of weights, various conjugate-gradient algorithms are

efficient.

All of the above methods find local optima (Mohaghegh, 2000b). For global

optimization, there are a variety of approaches. One can simply run any of the local

optimization methods from numerous random starting points, or one can try more

complicated methods designed for global optimization such as simulated annealing or

genetic algorithms.

A fully trained ANN is effectively a nonlinear map between specified variables

that is capable of filtering noise in the input data and has a predictive capacity; i.e., it is

capable of making predictions for situations not previously encountered. The procedures

for optimizing ANN use “goodness-of-fit” criteria based on minimum residual prediction

errors for test data (Mohaghegh, 2000b). It should be noted that one of the greatest


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advantages of neural networks is that they do not break down once they face new

environments. They degrade gracefully (Mohaghegh, 2000a).

Perhaps the greatest advantage of ANNs is their ability to be used as an arbitrary

function approximation mechanism which 'learns' from observed data. However, using

them is not so straightforward and a relatively good understanding of the underlying

theory is essential. When correctly implemented, ANNs can be used naturally in large

dataset applications. Their simple implementation and the existence of mostly local

dependencies exhibited in the structure allows for fast, parallel execution. The utility ofartificial neural network models lies in the fact that they can be used to infer a function

from observations. This is particularly useful in applications where the complexity of the

data or task makes the design of such a function by hand impractical. Optimizing the

development of a natural gas field is one of such tasks and the fifth chapter of this work

will show how ANN can be used to carry out this task with a view to determining the

optimum production scenario. ANN will be used to plan and design an optimum

development scenario for natural gas fields that will not only provide an efficient

production pattern but will also satisfy economic considerations. The goal is to determine

the optimum number of wells for the gas field that will produce the maximum net present

value profit.

2.5 Artificial Neural Networks in Petroleum Engineering

The recent development and success of applying artificial neural networks (ANN)

to solve complex engineering problems has drawn attention to its potential applications in

the petroleum industry. The use of artificial intelligence in petroleum industry can be


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The curves were developed by iteration with an earlier developed model of the surface

piping network from wellhead to gathering center/flowstation for Prudhoe Bay (Litvak,

Hutchins, Skinner, Wood, Darlow, and Kuest, 2002). It was identified that in order to

achieve this objective, the first step was to build a representative model of the entire gas

transit pipeline system. The neural network model had two main characteristics:

i. The model accurately represented the complex dynamic system

ii. The model provided fast results (close to real-time) once the required information

was presented.The trained model was extensively tested and verified using 30% of the data that

was not used during the training process. The results showed good accuracy in

reproducing the actual rates and pressures at the separation facilities and at the gas

compression plant. The correlation coefficient for rate and pressure were 0.997 and 0.998

respectively.

Studies have been conducted for determination of flow parameters for two-phase

flow through horizontal circular pipes using ANN. Ternyik et al. (1995) explored

application of neural networks in predicting the flow pattern and liquid holdup on the

basis of experimental data collected by Mukherjee (1979). Osman (2004) conducted a

study on identification of flow regimes and liquid holdup for horizontal two-phase flow

using ANN. He used the experimental data obtained by Minami and Brill (1987) and

Abdul-Majeed (1996). He applied a three-layer back-propagation technique and obtained

promising results. Finally, Shippen and Scott (2004) conducted a study on liquid holdup

prediction using artificial neural networks. They also used back-propagation technique


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for training the network. Their network estimated the liquid holdup with a reasonable

accuracy.

In their work, Ayala and Ertekin (2005) analyzed gas cycling performance in gas

condensate reservoirs, using neuro-simulation. The research, which was aimed at

demonstrating the applicability of ANN to the study of pressure maintenance operations

in gas condensate reservoirs, developed a gas-cycling performance predictor for

production operations in gas/condensate reservoirs using a back-propagation algorithm.

Ayala and Ertekin (2005) advocated that the proposed tool can be used to establishguidelines to optimize a gas cycling strategy at a much more reasonable computational

cost. Analysis of the performance of the model showed an excellent agreement with the

prediction of compositional simulators, based on results of all cross-plots and absolute

error analysis. Case studies from their work also indicate that neuro-simulation has the

potential to improve the capabilities of reservoir engineers to design optimum production

schemes to be used in the exploitation of gas/condensate fields.

Additional works implementing artificial neural networks for optimization

purposes at The Pennsylvania State University were performed by Al-Farhan and Ayala

(2006), and Mann and Ayala (2009). The former used ANN to predict the optimum

middle stage separation for a collection of hydrocarbon mixtures while the latter applied

ANN in optimizing the design of natural gas storage facilities.

A very obvious deduction that can be made from the literature is that any credible

optimization process may have to examine hundreds and sometimes thousands of

realizations in order to achieve the global optimum values it is searching for. Therefore,


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both the accuracy and speed of providing the results are very important in the success of

any ANN development. Neural network models have the capability of providing almost

instantaneous results upon representation of the input data. Therefore, no matter how

complex the problem is, once, and if, an accurate model is built, calibrated and verified, it

can serve as the ideal objective function for any optimization routine (Mohaghegh et al.,

2008).


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Chapter 3

Problem Statement

Global demand for natural gas is growing faster than it is for any other fossil fuel

and several factors will continue to affect long-term natural gas demand. According to

recent Energy Information Agency statistics (EIA, 2009), the world has approximately

6,254 trillion cubic feet (Tcf) of proven gas reserves. At 2009 production rates, this

represents approximately a 50-year supply. But while the volumes are huge, many new

reserves are situated further from major consumer markets. To ensure that supplies to

major markets go on uninterrupted requires new developments in production and

infrastructure. This therefore necessitates the requirement to come up with modern means

of ensuring that both new and existing natural gas field development and production can

be carried out in a technically sound and cost-effective way. These new methods must

have the capability to minimize risk, maximize reservoir deliverability, reduce cycle

time/costs and deliver technical innovations that extend field development and increase

the recovery from natural gas resources. The use of Artificial Neural Networks as a tool

in tackling some of these challenges is increasingly gaining plausibility in the oil and gas

industry.

In the light of the foregoing, the objective of this study is to demonstrate how

Artificial Neural Networks can be utilized to optimally design and develop a natural gas

field based on reliable predictions of natural gas reservoir performance. The ultimate


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This parameter has to be defined for the gas field in consideration and it represents the

cumulative gas produced at the end of the production plateau, G p|tp as shown in Equation

4.1-1.

G p| tp = RF pl * OGIP Equation 4.1-1

The desirable RF pl is usually dictated by market considerations; once this is established,

the amount of gas to be produced by the end of the production plateau can be computed

and the field production rate of the plateau (Q fieldpl ) subsequently determined. The rate for

each well during the plateau, Q wellpl can then be obtained by dividing Q fieldpl by thenumber of wells (N w) in the field. This study assumes that all wells in the field are

identical, produce at the same rate, and do not interfere with each other.

The performance prediction process is used to determine the relationship between

flowrate over time from the beginning of the production plateau until abandonment is

reached. In addition, it can show the relationship between cumulative gas production over

time; and also, the change in reservoir pressure and bottom hole flowing pressure over

time which may be helpful in further analysis of the field. Flow rate vs. time and

cumulative gas production vs. time curves can be generated from the performance

prediction. The recovery factor, being the amount of cumulative gas produced as a

fraction of the OGIP can also be predicted by the performance prediction process for any

time in the future productive life of the field. Figures 4.1-1a and 4.1-1b show the typical

behavior of field production rate, Q field and cumulative gas production, G p as functions of

time respectively.


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Figure 4.1-1a: Production rate, Q field as a function of time

Typically, at the start of the production plateau, the reservoir has the capability to

deliver the gas to each well at a rate higher than the well production rate Q wellpl that is

specified by the desired RF pl. The constant rate is maintained at the surface by the choke

which controls the wellhead pressure (P wh) on each well. The field is produced at this

constant rate until such a time (t p) that the reservoir is depleted and the reservoir pressure

has declined to a point where it cannot sustain this rate. This point is identified as RF pl in

Figure 4.1-1a. After this point, if no compressors are installed or additional wells drilled,

the field production rate declines continuously until abandonment point is reached.


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4.1-1b: Cumulative production, G p as a function of time

Figure 4.1-1b shows the typical plot for the cumulative gas produced for a natural

gas field and corresponds to the production rate plot shown in Figure 4.1-1a. This plot

shows a linear relationship between G p and time t, from the start to the end of the

production plateau at t p; this linearity occurs due to the rate of production being constant

during the plateau. As the flow rate decreases over time after the plateau, the increase in

G p (ΔG p) reduces over time and this is reflected in the curved shape of the plot after t p.

The G p vs. t plots allows for the recovery factor of the field to be calculated at any time

during production since this can be obtained by simply dividing the G p at that time by the

OGIP of the field. Recovery factor computations provide gas field developers with a tool


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for field analysis and also provide a means to compare performance of fields with

different OGIPs.

4.1-1c: Pressure drawdown as a function of time, t.

The typical natural gas field pressure-drawdown plot in Figure 4.1-1c shows the

relationship between the reservoir pressure, P r and the wellhead pressure, P wh as the

reservoir is depleted from the onset of the production plateau to field abandonment. As

mentioned earlier, during the plateau, production at each well is maintained at a constant

rate (Q wellpl ) by controlling the wellhead pressure with a device called the choke. This

constant rate of production during the plateau occurs at a result of the constant pressure

drawdown between the reservoir pressure and the wellhead pressure. As reservoir


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this information is given, the proposed protocol can be easily modified to account for this

without any reduction in the generality or applicability of the procedure.

Table 4.1-1: Reservoir, well and fluid properties for hypothetical gas field

Number of wells (N w) 2

Original Gas In Place (OGIP) 100 Bscf

Initial Reservoir Pressure (P i) 3000 psia

Reservoir Temperature (T r ) 630o

R (170o

F)

Well performance coefficient (C well) 0.412 mscfd/psi n

Back pressure exponent (n) 0.633

Minimum wellhead pressure (P wh_min ) 400 psia

Tubing inner diameter (ID) 2.5 inches

Well depth 5000 ft

End-of-plateau recovery factor (RF pl) 50%

Wellhead temperature (T wh) 530 oR (70 oF)

Gas Specific Gravity (γ g) 0.60

Abandonment field rate (Q a) 400 mscfd

The information given shows that two wells are desired to be produced in the field

for a constant rate until a total of 50% of the original gas in place has been recovered

(RF pl = 50%), at which point the production rate will start to decline. The objective is to


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predict the performance of the reservoir until it reaches abandonment conditions

estimated to occur when the field production rate drops to 400 mscfd.

The properties required for the determination of the inflow performance such as

the well performance coefficient C well , and the back pressure exponent n, are given for the

hypothetical gas field. Hence, an inflow performance curve can be generated using the

inflow performance equation shown in Equation 2.2-4. Likewise, the fluid and well

tubing properties such as the specific gravity of gas, tubing inner diameter, well depth,

and wellhead temperature required for the determination of the tubing (outflow) performance are also given. The tubing performance curve for the hypothetical gas field

has been generated using the Cullender and Smith method by implementing the

procedure in a MATLAB subroutine, CullSmith (Appendix A.3). The resulting IPR curve

at initial reservoir pressure (P i = 3000 psia), and the TPR curve at minimum wellhead

pressure (P wh_min = 400 psia) are displayed in Figure 4.1-2 and Figure 4.1-3 respectively.


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Figure 4.1-2: IPR curve at initial reservoir pressure, P i for hypothetical gas field

0 2 4 6 8 10 120

500

1000

1500

2000

2500

3000

Well flow rate, Qwell

(mmscfd)

W

e l l f l o

w i n

g b o t t o m

h o l e

p r e s s u r e , P w

f ( p

s i a )

Well f lowing pressure, Pwf

vs. Well flow rate, Qwell

IPR @ Pi = 3000 psia


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Figure 4.1-3: TPR curve at minimum wellhead pressure, P wh_min for hypothetical

gas field

For the performance prediction process, compressibility (Z) factor calculations are

needed. Several methods exist to determine the compressibility factor of fluids, but for

natural gases, the Standing-Katz Chart (1942) has a wide applicability. Several semi-

empirical methods have been proposed to correlate the Standing-Katz Chart into

computer programmable equations. These methods include Sarem’s method (1961), Hall-

Yarborough’s method (1974), Brill and Begg’s method (1974), Dranchuk–Abou–

Kassem’s method (1975) and Gopal’s method (1977). Standing compared most of these

0 2 4 6 8 10 12400

500

600

700

800

900

1000

1100

Well flow rate, Q w ell (mmscfd)

W e l

l f l o w

i n g

b o t t o m

h o l e p r e s s u r e ,

P w

f ( p s i a )

Well flowing pressure, P w f vs. Well flow rate, Q w ell

TPR @ Pwh

= 400 psia


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methods and showed that the Dranchuk–Abou–Kassem method had shown the smallest

absolute error among them; hence this will be the method of choice in Z-factor

calculations for this study (Appendix A.8). The Z-factor calculation requires the value of

the pseudo-critical pressure, P pr and the pseudo-critical temperature, T pr of the fluid.

Equations for computing these parameters are given by Lee and Wattenbarger (1996) and

are shown below:

P pr = 756.8 – 131*γ g – 3.6*γ g 2 Equation 4.1-2

T pr = 169.2 + 349.5*γ g – 74*γ g 2

Equation 4.1-3where ‘ γ g ’ is the specific gravity of the gas.

There are several steps involved in the prediction of reservoir performance. These

are highlighted hereunder.

The first step is to determine pressure at the end of the production plateau, P r |tp.

This is done using the material balance equation described in Chapter 2 which can be

rearranged to yield the following equation that defines P r |tp:

tp

tpr

| Z

| P = ( ) pl

i

i RF 1 Z P −

Equation 4.1-4

where ‘Z| tp’ is the compressibility factor of the gas at P r |tp, and ‘Z i’ is the compressibility

factor at P i. The subroutine, Zfactor (Appendix A.8) has been implemented to compute

the compressibility factor at P i for this hypothetical gas field as Z i = 0.8988. From

equation 4.1-4, the value of the left hand side of the equation, ‘P r |tp / Z| tp’ is equal to 1669

psia. Since Z| tp is itself dependent on P r |tp and cannot be computed independently, the


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determination of P r |tp requires an iterative procedure. A MATLAB subroutine

Bisection_Pz , shown in Appendix A.2 that utilizes the bisection method as the iterative

procedure has been implemented to compute the value of P r |tp. This value is determined

to be P r |tp = 1511 psia.

Having computed the pressure at the end of the production plateau, the flow rate

of each well during the production plateau, Q wellpl will have to be determined. This flow

rate corresponds to the intersection point of the inflow performance curve at P r |tp = 1511

psia and the outflow performance curve at P wh_min = 400 psia, or the operating point of both curves as described in Chapter 2. The bisection method has been programmed into a

MATLAB subroutine called Bisection (Appendix A.1), and has been implemented to

numerically solve for Q wellpl . This subroutine takes the relevant reservoir, tubing and fluid

properties as input parameters, solves for the flow rate (Q wellpl ) and bottom-hole pressure

at time t p (Pwf |tp) and outputs the same. The solution gives values of rate Q wellpl = 3.99

mmscfd and bottom-hole pressure P wf |tp = 550 psia. This bottom-hole pressure

corresponds to the minimum pressure that is required at the bottom of the well to

overcome flow inhibiting forces to produce the flowrate of Q wellpl = 3.99 mmscfd to a

wellhead that has a minimum pressure of P wh_min = 400 psia.

The graphical representation of the inflow and tubing performance curves is

displayed in Figure 4.1-4 below, which shows the TPR curve at minimum wellhead

pressure P wh = 400 psia, and IPR curves at initial reservoir pressure P i = 3000 psia, and

end-of-plateau reservoir pressure P r |tp = 1511 psia. The bottom-hole pressure at the end of

the production plateau, P wf |tp as observed, is below the bottom-hole pressure at initial


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reservoir pressure when there is maximum flowrate capability from the reservoir. The

reservoir has the capability to produce each well at a rate of Q well = 9.78 mmscfd at its

initial pressure, P i and this corresponds to a bottom-hole pressure of P wf = 913 psia. The

difference in P wf at P i and at P r |tp occurs as a result of the drop in reservoir pressure as the

reservoir is depleted from initial conditions to the end of production plateau.

Figure 4.1-4: IPR curves at P i = 3000 psia and P r |tp = 1511 psia

0 2 4 6 8 10 120

500

1000

1500

2000

2500

3000

Well flow rate, Qwell

(mmscfd)

W e l

l f l o w

i n g b o t t o m - h o l e p r e s s u r e , P w f

( p s i a )

Well flowing bottom-hole pressure, Pwf

vs. Well flow rate, Qwell

IPR @ Pr|tp

= 1511 psia

IPR @ Pi = 3000 psia

TPR @ Pwh

= 400 psia


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The next step is to compute the duration of the constant rate production, t p. This is

basically the cumulative production to date divided by the field production rate and is

calculated using Equation 4.1-4.

t p =wwellpl

tp p

N *Q

|G Equation 4.1-4

G p|tp is computed from equation 4.1-1 as G p|tp = RF pl * OGIP = 50 Bscf.

Substituting G p|tp = 50 Bscf, Q wellpl = 3.99 mmscfd and N w = 2 into Equation 4.1-4 gives a

time period of t p = 6267.2 days or t p = 17.2 years. This means that each of the wells will

produce the gas at a constant rate of 3.99 mmscfd for a period of 17.2 years, after which

the reservoir pressure will drop to a point where it is unable to sustain this rate.

Production rate will decline after this point. The computations for the declining rate

periods are presented next.

The procedure for the declining rate period is done in discrete intervals to make

the process more efficient and is initiated by applying values from the previous constant

rate analysis. The values to be applied are P r |tp = 1511 psia, G p|tp = 50 Bscf and Q fieldpl =

3.99 mmscfd/well * 2 wells = 7.98 mmscfd. There could be a variation in the approach to

the declining rate computations depending on whether the field abandonment condition is

defined by the field production rate or reservoir pressure. In this study, it is defined by the

field rate i.e. Q a = 400 mscfd.

Each interval is treated as a time step to determine the flowrate at the end of each

interval, its incremental gas produced and the time period of each interval. The lower the


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value of Δ Pr , the more the detail the prediction gives. In this case, an initial default value

of Δ Pr = 100 psia has been selected. At the new decreased reservoir pressure P r = 1411

psia, the compressibility factor Z at this new reservoir pressure is determined and the

quotient P r /Z is computed. The Z-factor at P r = 1411 psia is Z = 0.909, and its

corresponding P r /Z value is P r /Z = 1552 psia. The next step is to update the cumulative

gas produced (G p) for the new reservoir pressure using the material balance method

shown in Equation 2.2-3. This gives a cumulative gas produced of G p = 53.51 Bscf and

an incremental gas produced of ΔG p = 53.51 – 50 = 3.51 Bscf.After computing the incremental gas produced during the interval, the intersection

point between the inflow performance at the updated reservoir pressure and the outflow

performance will have to be identified. This will be the gas rate at which both the inflow

and outflow produce at the same bottom-hole flowing pressure or the ‘operating point’ as

described in Chapter Two. This gas rate corresponds to the well deliverability at the

given minimum wellhead pressure of P wh_min = 400 psia. This can be done manually by

constructing both the inflow and outflow performance curves to find the intersection but

as stated earlier, a MATLAB subroutine, Bisection has been developed (Appendix A.1)

to automate this process to give the gas rate required. This gas rate is found to be Q well =

3.63 mmscfd. Since there are 2 wells in the field, the field rate Q field = 3.63 * 2 = 7.26

mmscfd. The average reservoir flowrate over the time period, Q field_ave then has to be

calculated. This is calculated here using the geometric average of the flow rates and is

given as log Q field_ave = (log Q fieldn-1 + log Q field n)/2, where n-1 is the previous time step

and n is the current time step. This gives a computation of log Q field_ave = (log 7.98 + log


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7.26)/2, and a value of Q field_ave = 7.61 mmscfd. The time period for the interval ( Δt) is

then calculated as the incremental gas produced (ΔG p) divided by the average flow rate

for the field (Q field_ave ) and is calculated as Δt = 3.51 Bscf / 7.61 mmscfd. This gives a

value for the time period Δt = 461.24 days or Δt = 1.26 years. This is the end of

computations for this time step.

The process is repeated for the next time step by reducing the reservoir pressure

by Δ Pr = 100 and computing corresponding new values for the flow rates Q well , Q field and

Qfield_ave , incremental gas produced ΔG p, and time period, Δt. The value of the Q field_ave atthe end of a time step is used as the initial value of Q field for computations in the next time

step. As the computations for the declining reservoir pressures are done when

approaching the abandonment condition (Q a = 0.40 mmscfd), the ΔP r value may need to

be reduced. The iterations continue for subsequent time steps until abandonment

condition is reached. In this instance, the iteration is terminated when the computed field

production has declined to a value of 0.41 mmscfd, since further reducing the reservoir

pressure by 1 psia will yield a field rate lower than 0.40 mmscfd which was given as the

abandonment field rate for the problem. The results for the performance prediction of this

hypothetical

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Olatunji Adewale