The BP Network Study of the Time Series Overrolling Model for Forecasting the Oilfield Output

Liang Hui-zhen, Xie Jun, Yu Jiang-tao Meng Ning-ning Shandong University of Science and Technology, Qingdao 266510 China

Xiejun0532@163.com Abstract Based on analyzing fundamental principle of Back Propagation Network Model, in view of the limitations of BP algorism, this paper proposed the homologous improved-algorism from the two aspects of quickening the BP learning speed and raising the degree of convergence. In the course of the complex water flood development, the paper, considering the adaptability feature of the different random factors affecting the wells yield, built the BP time series overrolling model for forecasting the oilfield output, and predicted the wells output using the model, the result indicate that the model have better predicted-accuracy, and fitting to predict the oil production rate and water production rate for different development phase. Keywords: Neural Network, Back Propagation Network,

Oilfield Output, Time Series, Forecast Model

I. Introduction Oilfield development faced by the target is a

complex geological conditions, among the information which have collected, most of them are unstructured and non-deterministic, using traditional mathematical methods for processing and analysis them encountered great difficulties, sometimes it is impossible, so the artificial intelligence methods is of significance in the development of oil field. At present, artificial neural network is a new, more intelligent way and it has begun to apply for oil exploration, such as the extraction of seismic primary waves, the identify of the potential field characteristics and the earthquake pattern, and the analysis of the oil reservoir damage, Etc[1][2][3]. Here, it is trying to apply this new method to the oil field development and to provide an important basis for formulating the oil field development and adjustment arrangement.

II. The basic principles of BP algorithm In neural network, each neuron is a non-linear

element of calculation; it receives information from the large numbers of other neurons, generated an output, and provides input for the other number of neurons[4].

Neurons own their local memory, they storage the connecting right values from the net learning.

BP algorithm is through the back-propagation of artificial neural network (ANN) calculation error to gradually correct the connection weight between neurons, to achieve the purpose of study. For a given input X0, ANN calculated its corresponding network output Y0, then based on dissimilarity of Y0 and ideals of the output T0, amending the link intensity between neurons of output layer and its most recent hidden layer, and then use the factors what are give rise to the intensity changes of the couple of neurons to amend the link intensity between the hidden layers neurons, so it, until complete the link intensity amendment between the neurons of input layer and the first hidden layer. Repeat this process, until the difference between Y0 and T0 meet the require precision. Then operate the next sample in the same way.

III. The limitations and improve of BP algorithm 3.1 The limitation of BP algorithm

BP algorithm generally has two major limitations [5]: (1) Convergence slow

As BP network requires adequate study sample, the output error may be small when a sample of the network training, but the output error may be very big when the other number of samples of the network training, at this time, the connection weights must be largely adjusted, and the training samples set are also repeated and circulate to input to learn many times, the process is enough to consume time.

(2) Local minimum BP algorithm inherited the thinking of the error

back-propagation learning algorithm LMS (Least- Mean- Square) that error gradient to the minimum. In the multilayer-network model, there are many minimum, this problem not only make the expression

2009 IITA International Conference on Services Science, Management and Engineering

978-0-7695-3729-0/09 $25.00 © 2009 IEEE

DOI 10.1109/SSME.2009.102

307

2009 IITA International Conference on Services Science, Management and Engineering

978-0-7695-3729-0/09 $25.00 © 2009 IEEE

DOI 10.1109/SSME.2009.102

307

2009 IITA International Conference on Services Science, Management and Engineering

978-0-7695-3729-0/09 $25.00 © 2009 IEEE

DOI 10.1109/SSME.2009.102

307

of error space to become difficult but also that it can't gain the global optimal solution because the solution usually remain in the local minimum . 3.2 Improved BP algorithm

The one of main shortcomings of BP network is training and learning too slow, a little training samples set, often need to go through many iterations, can be adjusted to the degree of accuracy, it is the main improve orientation for BP network how to accelerate the pace of the weighting coefficient. Another main shortcoming of BP network is easy to involve to a local minimum, the optimal solution of the overall situation can not be obtained. For the two shortcomings, the BP algorithm can improve as follows:

(1) Change the error function in BP algorithm Output function will add a factor , so that the output

xey −+

=1

1 becomes β

x

e

y−

+

=

1

1

in it >1. This will enable y gradient from zero, escape the

flat area Figure 1 express the neuron output function curve of x coordinate change before and after. After leaving the local minimum, resume to 1, this method is very valid to avoid the local minimum, it can avoid most of the local minimum so as to the convergence rate of algorithm go faster.

Fig1 The curve of output of nerve cells before and after x

compress (2) Add a momentum

In order to accelerate the convergence and to prevent shocks, this paper call in a momentum factor , then cycle and iterative expression turn into:

( ) ( ) ( ) ( )( )11 −−⋅+⋅⋅+=+ twtwxtwtw ijijjjijij αδη

In it: wij—the weights between two nodes; t—time

interval variable; —gain; j—error; xj—the input element value of No. j; —momentum factor

0< <1 . During the study , the weight should be

proportionally amended according to the error’s derivative, the gain of the above formula reflect the rate of this kind of amendment. If is too small, then the efficiency of study will be too slow; on the contrary, if is too big, then it may cause oscillation. So the momentum item is introduced. That is, the changes of weight no only have something with , but also with wij (t)-wij(t-1), this will filter High-frequency deviation of error curve in the weight space(that is, the high curvature tremendous changes in the error curve), and increase the effective weight interval(that is, reduce the number of study ).

IV. The network time series prediction model and its applications

4.1 The network time series prediction model It has two steps to predict the oil well production

and water production by the nerve networks. First, the past real average well production and water production are used as the network’s training samples, let the network do training study, by continuously adjust the weight between the nodes to distribute the non-linear relationship between the time series and production of well and water to all the right connections, until to meet the expected requirements, that is, network has been trained so far, this achieved by the back-propagation algorithm. This is the learning process of training. Second, input the month which is predictable to the trained network, the output value after network is the corresponding month’s average well production and water production, this is the pre-determination procedure of the network.

(1)The Learning Process Take the single well’s average well production Qo

and water production Qw past a certain period of time as the network’s inputs. Such as: from the first month’s to the m month’s Qo1 Qw1 Qo2 Qw2 Qom

Qwm .take the next period’s (such as the month of NO. m+1) average well production Qo(m+1) and water

x

yBefore X compress

After X compress

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production Qw(m+1) as the expectations output value of network, let the network to learn. Adjust the link weight between the layers, and then learn new samples, that is, remove the first set of data(such as the first month’s average well production Qo and water production Qw), add a new set of data(such as the No.m+1 month’s average well production Qo(m+1) and water production Qw(m+1)),then ,we got a new samples Qo2,Qw2 Qo3 Qw3 Qom QwmQo(m+1) Qw(m+1) take this as the network s inputs , take the next period’s (such as the month of No. m+2) average well production Qo(m+2) and water production Qw(m+2) as the expectations output value of network, make the network to train and learn once again. So reciprocating, until trained all the samples, make the total error minimized after learning network, that is, the network training success. At this time, the network has comprehensively learned all the characteristics of the production information in the past, the effect of learning mainly express in the value of link weights between all the neural network connecting layers.

Its training learning process is as follows: A: Normalize all the valves of the input nodes

(average well production and water production) Qo1 Qw1 Qo2 Qw2 ... Qom

Qwm between 0 and 1, and normalize all the output valves between 0 and 1;

B: Assignment the random value to the various layers of the network;

C: Calculate the output value yp of the No.p sample D: Calculate the difference value between the value

of node and the expected value of output E: Amendment the weight according to the margin

to reduce the network error: F: Transfer to the C step to repeat the above steps,

to train the No. p +1 sample; G: Calculate the global error when all the samples

have been trained ; H: end.

(2)The Forecast Process When the network trained, the values of the link

weight between all the layers of the neural network have been fixed. At this time, take the 1 to m+1 months’ average well production and water production as the network’s inputs, after the network calculating, the corresponding output is this month’s normalized average well production and water production, then make a normalized inverse transform for the normalized value, the corresponding average well production and water production can be predicted.

Its working process goes as follows: A. Enter the value of samples, converse each node

into the normalization between 0 and 1; B. Read trained weight value and threshold value

with various levels C. Obtain the production and capacity for water after

the normalization of network; D. Reverse the water production and capacity for the

normalization of value so as to change in output forecast of a certain period of production and capacity

E. Repeat the above steps, predicate average oil production in different periods

F. over 4.2 Practical Sample

According to the theory, the common computer software is compiled and the production of GD Oilfield 16 wells is calculated by using the above software. Examples show that the outcome forecasted by the Software closely with the actual value of the oil well. For example: GD8 well, using the output of wells from January 2005 to December 2007 as a study sample, when the adjustment factor =1.8, Learning efficiency factor =0.116, momentum factor =0.31, cumulative error for the overall situation E=0.005, the system convergence after 26,533 iteration, the end of training. Use the model to predict the produce of the fuel and water Of GD8 wells in 2008(Table 1), The results show that production of the single well oil predicted by the BP network model of rolling time series closely with actual output well (Figure 2).

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Tab1 The correlation table of actual output and forecast production by the BP time series overrolling model in GD8 well

Production time

Daily oil productiont/d

Daily water production t/d Production

time

Daily oil production t/d

Daily water production t/d

Reality value

Predictive value

Reality value

Predictive value

Reality value

Predictive value

Reality value

Predictive value

2006.1 19.58 167.34 2007.7 9.90 212.68 2006.2 18.39 178.61 2007.8 8.41 207.04 2006.3 13.87 172.18 2007.9 8.61 182.19 2006.4 12.04 151.87 2007.10 8.58 207.95 2006.5 13.12 146.84 2007.11 8.24 132.02 2006.6 14.69 164.23 2007.12 9.00 178.72 2006.7 16.77 182.93 2008.1 8.08 8.33 189.36 180.08 2006.8 13.96 181.77 2008.2 8.31 7.65 210.31 193.38 2006.9 11.09 152.81 2008.3 7.85 7.07 209.99 199.91 2006.10 10.37 168.89 2008.4 7.16 6.33 210.19 204.22 2006.11 13.64 201.90 2008.5 5.39 6.13 198.88 205.18 2006.12 13.89 191.33 2008.6 5.11 5.39 214.04 206.67 2007.1 9.76 193.90 2008.7 6.98 5.55 218.3 210.09 2007.2 9.02 193.44 2008.8 4.59 4.83 220.1 212.13 2007.3 8.66 184.55 2008.9 4.11 4.77 233.03 222.55 2007.4 8.58 166.61 2008.10 3.68 4.01 225.32 228.83 2007.5 8.65 179.66 2008.11 3.16 3.88 231.01 233.38 2007.6 9.82 211.63 2008.12 2.77 2.98 234.22 238.36

0

5

10

15

20

25

30

2005

.1

2005

.7

2006

.1

2006

.7

2007

.1

2007

.7

2008

.1

2008

.7

2009

.1

Production time

Dai

ly w

ater

pro

duct

ion

t/d

Study samplePredictive valueReality value

A. Monthly average daily oil production B. Monthly average daily water production Fig2 The comparison diagram of actual output and forecast production by the BP time series overrolling model in GD8 well

V. Conclusions The proposed BP network time series overrolling

model for the oilfield output sufficiently used the nonlinear mapping rule of artificial neural network, through the adjustment and match of connecting weight in network to describe the complex relationship between reservoir input and output, it has strong auto-adapted capability, it overcomes the effect in well yield change both the trend change of the time and the random disturbance factors. Through apply the actual data of the 16 wells, it acquires well pre-determination effects, so nerve network is a more successful oilfield output forecasting method.

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