literature reviews

OTC 24981

ANN Powered Virtual Well Testing A. Aggarwal, S. Agarwal, Indian School of Mines

Copyright 2014, Offshore Technology Conference This paper was prepared for presentation at the Offshore Technology Conference Asia held in Kuala Lumpur, Malaysia, 25–28 March 2014. This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

Abstract

Due to the drying up of old oil fields throughout the

globe, the age of easy oil is over and the newly discovered

fields have reservoirs with complex heterogeneous media.

The reservoir parameters are identified indirectly by

correctly interpreting well test model which is recognized

by the feature of pressure derivative curves. Well testing

involves creation of disturbance in fluid flow by injecting

liquids and simultaneously recording the pressure

transient data. Lost production, equipment and personnel

costs turn well testing as highly cost intensive job making

it difficult to cover all the important wells in a particular

field. But with the advent of artificial neural networks

(ANN) it is now possible to generate synthetic pressure

transient data. This technique provides a basis to leach out

detailed information from the available pressure transient

data and it doesn’t eradicate the need for actual well tests.

This technique can also prove to be very vital in cases

where equipment breakdown may have taken place and

full set of data couldn’t be availed. This simulated well

testing involves training of a neural network from

pressure transient data obtained from designated wells in

the field, which has the potential to generate pressure

transient responses at other well sites where no well test

has been conducted.

In this paper a 3 layer multi-layer perceptron (MLP) Time

Delay Neural Network - NARX model has been designed

working on resilient backpopagation algorithm for

training. Cubic Spline Interpolation has been used from

enriching the data before feeding it to NARX model. A

simulated example which highlights the efficiency of

NARX model in attaining accurate synthetic pressure

transient data has been discussed. The neural network is

successful in predicting well test interpretation model.

The ANN thus produces expeditious and reliable synthetic

data which has the potential to revamp the industry.

Introduction

Due to the complex structures and heterogeneous media,

of oil and gas reservoirs, characterizing reservoirs

precisely is a herculean task. Petroleum Engineers solve

this challenge by acquiring and analyzing in depth

reservoir information, which is crucial for the study of the

reservoir performance (Vaferi et al., 2011). Well Testing

or Pressure Transient Testing has proved to be a powerful

reservoir characterization tool to study such complex

media (Muskat, 1937). Pressure testing is conducted by

recording the well bore bottom hole pressure responses

which are created as result of induced flow disturbances.

The most general test methods are 1) By creating a

pressure drawdown in the wellbore by producing the well

at a constant rate, after keeping it in shut-in condition for

a set period (Figure 1); 2) By developing a pressure

build-up in the wellbore by shutting-in at the bottom hole,

due to which formation fluids cannot flow into the

wellbore. Thus, measured flow rates and pressures during

these tests can provide sufficient information for the

characterization of the tested well (Matthews et al., 1967;

Earlougher et al., 1977).

Well testing enables accurate determination of cash flow

of the well by obtaining comprehensive reservoir

description. The core purpose of well testing lies in the

determination of the fluid production capability of a

formation and incurring the inherent reason for

productivity of well. A meticulously designed and

performed well test operation can provide accurate facts

and figures about formation permeability, average

conductivities, extent of wellbore damage or stimulation,

reservoir pressure, and extended testing may deliver

information regarding underlying geological barriers

(faults, pinch-outs, etc.), reservoir boundaries and

heterogeneities (Matthews et al., 1967; Earlougher et al.,

1977). On the same note Da Prat et al. in 1992 have

classified well test objectives into short term and long

term objectives. Obtaining the reservoir description in the

vicinity of the well bore, from analysis of gathered data,

are categorized as short term objective. While, long term

objectives of well test are to analyze gathered data for

obtaining complete description of the whole reservoir.

However, huge production time losses, manpower and

equipment costs turn it into a cost intensive affair

(Dakshindas, 1999). Since its introduction to the

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petroleum engineering industry around 1937 by ground

water hydrology scientists (Gringarten, 2008), plethora of

novel technologies have been introduced both for data

acquisition and analysis. The introduction of electronic

pressure gauges was a great step ahead in enhancing

obtaining of reservoir description, and continuously

upgraded versions of these are being developed to meet

current challenges. Moreover, for expeditious data

acquisition and interpretation, and in depth rigorous

insight into the reservoir, industry anticipates close

integration of advanced microprocessors and innovative

computational techniques.

Theory

This paper features a unique approach for synthetic

pressure transient data generation by application of Cubic

Spline Interpolation technique and Artificial Neural

Networks (ANN). The main objective of the work

presented is to formulate an artificial neural network

which has the ability to forecast transient pressure

responses without any need for an actual well test. The

data thus generated can be analyzed using traditional well

test analysis methods for reservoir characterization. In a

nutshell, this is made possible by training the neural

network using pressure transient data available from

proximate wells, flow parameters values and reservoir

characteristics, and then the error is reduced significantly

by retraining the network and testing the network

efficiency by comparing the network results to the data

available from actually conducted well tests.

Cubic Spline Interpolation

Data points are interpolated by using cubic spline curve

fitting (CSCF) technique. This can be realized by

arranging the available data into a table [pi,qi], i ϵ [0,n],

thus providing with n intervals for n+1 control points. The

cubic spline curve is a continuous piecewise third order

polynomial, satisfying all the input values (Figure 2).

Each polynomial’s second derivative is usually set to zero

at the endpoints, as this offers a boundary condition which

makes the system of n-1 equations complete. Also this is

not the only possible option, as other boundary conditions

can also be used. Thus a "natural" cubic spline is

produced that results to an elementary tridiagonal system,

which is computed to deliver coefficients of the

polynomials.

The main purpose of using CSCF technique is to increase

data points between minimum and maximum, as with

higher amount of input data points better results through

ANN can be obtained. Moreover its high accuracy of

estimation and capacity to produce seamless curves makes

it a popular interpolation technique.

Neural Networks

Neural Networks are a form of massive parallel

distribution of biologically inspired processing units

comprising of smaller units termed as neuron, as these

seek to imitate the brain microstructure (Noriega, 2005).

The multilayer perceptron, a widely applied example of

artificial neural networks, is a programming epitome that

was developed around half a century back by W.S.

McCulloch and W. Pitts in 1943. The neural network is an

intensely parallel, distributive, adaptive, non-arithmetic

and non-digital system, which can solve problems ranging

from pattern recognition, to innovative symbolic

manipulation

Biological Basis

The neural network attempts to model functioning of

biological nervous system or human brain. The brain is

made up of huge parallel interconnected processing units.

These processing units or neurons are electrically

excitable, which through electrical and chemical signals

transmits and process information. Majorly dendrites,

soma and axon form the neuron body. A neuron receives

the input information from other neurons in the network

connected to it at synapses through dendrites. The

received information is then processed at the soma, which

integrates it over time and space, the generated output is

activated depending on the input. The synapses located at

the end of axon transmit the output signal to connected

dendrites. This forms an intensely complex parallel

computer.

Similarly, an artificial neural network is a composite

architecture of soft computing based neurons integrated

into numerous parallel layers which are connected to all

the neurons of preceding and succeeding layers by the

means of weights. A variety of developed neurons and

network specifications can be programmed to interpret,

recognize and retrieve patterns to solve optimization

problems and clear noise from input data (Kumar, 2012).

Network Mechanics

The neural network has two types of learning processes,

supervised and un-supervised. Supervised learning or

training process is the crux of ANN mechanics, initially

random weight values (between -1 to 1) are assigned to

network connections, furthermore the network analyses

input data to estimate weights of the connections between

successive neuron layers (Figure 3). The data is input to

the first layer in which each neuron multiplies the data

with the associated weight and is summed with a bias.

The result is then fed to an activation function, or transfer

function, of the neuron which determines if the result is

above the threshold or not, to instruct the neuron for

transmitting data. This output to activation function is

calculated by

The output values and the input values are compared for

error and then accordingly weights are updated for

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minimising error. This process is repeated a number of

times (epochs) to achieve precise weight values. Now, the

network output is tested against the input data sets for

measuring the prediction quality, which if acceptable can

be applied to generate data, for environments whose

outputs are unknown.

Background

These are being applied to counter a large variety of

challenges from simple pattern-recognition task, to

advance symbolic manipulation (Noriega, 2005). Neural

networks have gained ground in geophysical application

and well test interpretation in last couple of decades.

Their effective application is to provide remarkably

precise solution to solve a range of problems like well-log

analysis (Huang et al., 1991), seismic deconvolution

(Wang et al., 1992; Calder´on–Mac´ias et al., 1997),

waveform recognition and first-break picking (Murat et

al., 1992; McCormack et al., 1993); for electromagnetic

(Poulton et al., 1992), magnetotelluric (Zhang et al.,

1997), and seismic inversion purposes (R¨oth et al., 1994;

Langer et al., 1996; Calder´on–Mac´ias et al., 1998);

event classification (Dowla et al. 1990; Romeo, 1994),

zone identification (White et al., 1995), trace editing

(McCormack et al., 1993) and for shear-wave splitting

(Dai et al., 1994), in geophysics domain (Van der Bann et

al., 2000), while making significant contribution to the

well test interpretation domain by enabling permeability

prediction (Singh et al., 2005), reservoir model

identification (Vaferi et al., 2011), well test model

recognition (Sung et al., 1996) and many more.

However, not much application of this Artificial

Intelligence (AI) technology has been observed in the

generation of synthetic well test Pressure Transient Data

(PTD) and rigorous utilization of advanced neural

network functions, training algorithms and advanced

computational techniques in this specific field have not

been witnessed.

Time Delay Neural Networks (TDNN)

The designing of neural networks can be understood by

classifying them into two categories dynamic and static.

Static networks are comparatively simple with neither

feedback elements nor delays. On the other hand, in case

of dynamic networks, the output generated is governed by

current inputs, previous inputs, outputs and network

states. However, dynamic networks can be trained by the

same algorithms used by static networks but due to

complex nature of error surfaces computing gradients is

more intensive. Moreover in this study NARX model has

been implemented which is a type of dynamic network or

more specifically Time Delay Neural Network (TDNN)

(Figure 4).

NARX Neural Network Model

Instead of conventional dynamic networks that are either

feedforward networks or focused networks, with only

input layer dynamics. In this, fully connected feedback

connections are enclosed in numerous layers of a

recurrent dynamic network which is Nonlinear

Autoregressive with eXogenous inputs (NARX recurrent

models). Contrary to other recurrent networks, feedback

comes only from output neuron instead from hidden

states, it is modeled with a tapped delay line (embedded

memory) which is clubbed to a delayed feeding line from

the output, second tapped delay line. This type of limited

viewed on part of the input series is referred to as time

window (Diaconescu, 2008). A NARX model is

formulated by the following equation

y(t) = f(y(t-1), y(t-2),….., y(t-ny), u(t-1), u(t-2),….., u(t-nu))

where, y(t) and u(t) denotes input and output signal of the

network at time t, ny and nu signifies input and output

order, while f represent the mapping performed by

Multilayer Perceptron (Siegelmann et al., 1997). The

value of dependent output y(t) is reverted to earlier output

values and values of eXogenous input (Figure 5). This

real-time feeding of output to the network is called as

parallel architecture, which results in more accurate

training and due its purely feedforward architecture, static

backpropagation can be used.

Application Methodology

The steps incurred in throughout this process are

explained below:

1. Candidate Identification: A set of wells are chosen,

which are producing from a particular formation

(zone). Segregate the wells where prediction is to be

done.

2. Information Gathering: Pressure Testing is

performed on the selected zone at all picked well

locations and PTD is recorded. Other vital

information about the test and reservoir is also

acquired.

3. Data Enrichment: NARX works best when highly

dense data sets are fed to it. Thus according to the

type of cures produced by the specific pressure

testing procedure followed, data interpolation

technique is chosen and applied.

4. Normalization: The input data for the NARX is

scaled down to the range of 0 to 1.

5. Network Training: The network is configured with

appropriate parameters and then input data is fed to

the network for training it.

6. Network Testing: Performance of the network is

validated against known data sets, if the results are

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unsatisfactory then the network parameters are

tweaked and the NARX is retrained.

7. Prediction: Utilize the trained NARX for simulating

data for unknown outputs.

To minimize error and produce the best pressure transient

predictions, the whole process was tested numerous times

with varied network models and interpolation techniques.

Due to the monotonically increasing nature of pressure

curve generated using PTD the best suited technologies

are identified was Cubic Spline Curve Fitting (CSCF) and

NARX neural model (Figure 6).

Case Study

This case deals with simulator generated pressure build-

up test data considering of five active producing wells for

an infinitely large homogenous field (Figure 7). The data

was generated using analytical simulator, which is based

on principle of superposition and infinite acting line

source solution. All the five wells considered had

identical shut-in and production time, and different flow

rates. The wells are shut-in at 215 hours and the data is

recorded for 67 hours.

The ANN is trained from pressure responses of four wells

and the data for well 5 is predicted. Complete data set for

each well is prepared for training the NARX network.

Each well’s pressure transient data, (tp+∆t)/∆t, modified

inter-well distances, and flow rates along with their

functional links are used as inputs for the network

(Figure). The output from the network is pressure which

is generated by also taking into account the interference

effects from the proximate wells. Modified distance is

formulated to be:

Distmod = QW1 * Dist(W1 – W2)/QW2

After taking into account modified distance and functional

links better prediction results were observed but with

increased CPU usage and network training time.

Similarly, initially 60 data values were available, which

by using Cubic Spline Interpolation were increased to 89.

Resilient backpropagation algorithm was used to update

bias values and connection weights during training

because it enables optimizing the magnitude of weight

change by reducing it in case weights are oscillating and

increasing it when for several iterations weight changes

continuously in the same direction. Sigmoid or

‘squashing’ functions were used as transfer functions for

all the neurons at every layer, as the derivative of sigmoid

function can be swiftly calculated which is needed to be

backpropagated to calculate error. It is defined by:

F(i) = (1+e -i )

-1

Where, F(i) is the function output and ‘i’ is the input. The

performance of the network was judged on the basis of

mean square error (MSE). The input set was divided using

interleaved indices. The applied NARX model is a three

layer network with 18 input layer neurons, 25 neurons in

hidden layer and 1 output layer neuron. The time delay

configured for this particular problem is 1:2, thus

producing 87 outputs for 89 inputs.

A good match is observed is observed between the

network and the simulator output (Figure 8-11),

confirming that NARX has the potential to predict well

test pressure responses accurately. The prediction

performed by the network for well 5 is also remarkable

considering the complexity of the problem (Figure 12).

With increased available data from more number of wells

the network will deliver more precise predictions but the

wells must be chosen meticulously to ensure inclusion of

interference effects, flow rate effects, shut-in and

production effects, boundaries and heterogeneity effects.

But the risk that network might get over-trained also

escalates with increased number of training wells.

Conclusions

In this paper a unique synthetic pressure transient data

generation has been introduced. The discussed simulated

field case study has justified the approach and delivered

recommendations on how to increase the accuracy of the

prediction. The precision of the network remarkably

improves when neural network is exposed to variety of

data from more number of strategically selected wells.

Incorporation of more data functional links, multiple

inputs from the field after rigorous iterative testing can

increase reliability of the network.

The NARX model has been able to analyze and interpret

the response almost perfectly which is proved by the

fashion in which the output curve closely traces the

simulator curve. Moreover, for cases where due to some

downhole equipment failure test couldn’t be completed or

some data is lost, by using this we can complete the data.

This doesn’t eradicate the need for actual well tests, but it

remarkably curbs the frequency of actual tests when

clubbed with tactical well test pattern planning. Using

NARX technology more informed well tests can be

designed by extracting more information from the

available data, thus reflecting enormous potential to

revamp the petroleum industry by delivering expeditious

and reliable solutions.

Acknowledgements

The authors are indebted to officials from Schlumberger,

ONGC, Reservoil and Dept. of Petroleum Engineering,

Indian School of Mines Dhanbad for their constant

support during this research. The authors are also obliged

to Mr. Mohit Punjabi, Mr. Swapnil Gupta, Mr. Ajay

Singh, Mr. Paras Goel and Mr. Praveen Pushkar, all from

Indian School of Mines Dhanbad, for always stimulating

and rejuvenating us.

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Figure 1: A Schematic diagram of drawdown test of a homogeneous reservoir with infinite acting boundary (Vaferi et al. 2011)

(a) (b)

Figure 2: (a) Three polynomials making up a cubic spline; (b) Input curve for cubic spline interpolation

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Figure 3: Mathematical neuron (Baan et al., 2000)

Figure 4: A fully connected recurrent Time Delay neural network (Siegelmann et al., 1997)

Figure 5: A NARX neural network with ny = 2, nu = 3 and H= 4 (Lin et al., 1998)

Figure 6: Overall flowchart for synthetic pressure transient data generation system

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Figure 7: Case evaluating infinitely large field with 5 wells

Figure 8: Comparison of simulator and ANN data for Training Well 1

Figure 9: Comparison of simulator and ANN data for Training Well 2

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Figure 10: Comparison of simulator and ANN data for Training Well 3

Figure 11: Comparison of simulator and ANN data for Training Well 4

Figure 12: NARX model prediction result for Well 5

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