Prediction of Steam Distillation Efficiency during Steam Injection Process using a Riable Method

In: Handbook on Oil Production Research ISBN: 978-1-63321-856-7

Editor: Jacquelyn Ambrosio © 2014 Nova Science Publishers, Inc.

Chapter 6

PREDICTION OF STEAM DISTILLATION

EFFICIENCY DURING STEAM INJECTION

PROCESS USING A RIGOROUS METHOD

Sh. Mohammadi,1 M. Nikookar,*2

M. R. Ehsani,1

L. Sahranavard2 and A. H. Mohammadi†

3,4

1 Department of Chemical Engineering,

Isfahan University of Technology, Isfahan, Iran 2 Department of Chemical Engineering,

Tarbiat Modares University, Tehran, Iran 3 Institut de Recherche en Génie Chimique et Pétrolier (IRGCP),

Paris Cedex, France 4 Thermodynamics Research Unit, School of Chemical Engineering,

University of KwaZulu-Natal, Howard College Campus,

Durban, South Africa

ABSTRACT

Steam distillation mechanism is one of the important and effective

mechanisms during steam injection process in fractured heavy oil

reservoirs. Due to its important effect in oil recovery, several attempts

have been made to simulate this process experimentally and theoretically.

* Corresponding Author: M. Nikookar: E-mail: [email protected]. † Corresponding Author: A. H. Mohammadi, E-mail: [email protected].

Complimentary Contributor Copy

Sh. Mohammadi, M. Nikookar, M. R. Ehsani et al. 198

Because of limitations in implementing experiments, various models have

been studied to predict the distillation effect with minimum entry

parameters. So, in this study, a Multi-Layer Perceptron (MLP) neural

network is used as an effective method to simulate the distillate recovery,

so that some parameters such as API, viscosity, characterization factor

and steam distillation factor are the input parameters and distillate yield is

the model‘s output. After gathering our data from some references, 77

data of 128 input data were used for training, 33 data for testing, and 18

data for cross validation. Then, the results of one-layer and two-layer

networks with various neurons were compared with the experimental data

and some other models.

Keywords: Heavy Oil, Steam Injection, Distillation, Neural Network, Multi

Layer Perceptron

INTRODUCTION

Naturally fractured reservoirs contain about 30% of the world oil supply.

Oil recovery from such reservoirs can be modelled as a two-step process:

mechanisms causing oil to be expelled from the matrix and mechanisms

expelling the oil through the fracture network to a production well [1].

An important phenomenon during steam injection is steam distillation of

light components of the crude oil, so that if pressure is lower than sum of the

partial pressures of water and oil, the liquid mixture will boil and give off a

vapor phase composed of steam and organic compounds. Steam and vaporized

hydrocarbons will be condensed as they reach to the cooler regions and mixed

with the crude oil and decrease its viscosity and increase the oil recovery.

Since steam is injected continuously in this process, condensation and

vaporization mechanisms are repeated during the process. [1]

Enhanced oil recovery processes based on steam injection are of the most

popular and effective methods used widely in the oil recovery industries. Oil

displacement in these processes involves simultaneous heat, mass, and fluid

transport. Several investigations have been performed to evaluate the

contribution of different mechanisms to oil recovery in these methods.

According to above studies, steam distillation mechanism highly affects

on enhanced oil recovery as same as viscosity reduction [2]. The earliest

simple mathematical models have been presented by Bailey, Holland and

Welch, and Winkle [3,4,5]. Wu and Elder [6] proposed correlations to estimate

steam distillation yields. Then, Dureksen and Hsueh [7] developed correlations


Prediction of Steam Distillation Efficiency … 199

for prediction of steam distillation yield with different crude characteristics

and operating conditions. They also found that steam distillation yield can be

well correlated with API gravity and wax content. Langhoff and Wu [8], based

on the simple and practical method of Holland and Welch, presented one

equation for prediction of steam distillation yield. They assumed that steam

injection rate is constant and the solubility of hydrocarbon and water are

negligible [4]. Van Winkle predicts the amount of steam required for

distillation of a specific amount of a volatile material based on the Raoult and

Dalton laws [5]. Northrop and Venkatesan [9] presented an analytical model to

predict steam distillation yield by using the modified Van Winkle approach.

Their model predicts an increased distillation yield by an increased

temperature.

Some researchers calculcated steam distillation yield by using a cubic

equation of state [10]. Most of the presented models depended on efficiency

factors that are obtained from experimental data. So, they could not be used

for new crude oil samples. Therefore, using a general model that can predict

steam distillation yield with less entry parameters is necessary. Recently,

neural network has been used for thermodynamic calculation of vapor - liquid

equilibrium. Considering the above issue and also, nonlinearity of steam

distillation mechanism, using artificial neural network (ANN) for simulation

of steam distillation yield seems to be suitable. [11,12,13,14,15]

In this study, steam distillation yield during steam injection has been

modeled by the Multi Layer Preceptron (MLP). Input parameters include API,

viscosity, and steam distillation factor and output parameter is steam

distillation yield. Finally, the results of one-layer and two-layer ANN with

various neurons were compared with the experimental data and other available

models.

ARTIFICIAL NEURAL NETWORK

Components of Neural Network

Generally, one neural network includes 1) inputs and outputs: numbers as

one or more variables make inputs. After training, the input parameters are

converted to one or more output variables. The inputs are independent, but the

outputs are dependent variables. 2) neurons: the most important components of

an artificial neural network are neurons. They are placed on three types of

layer: input, output and hidden layers. The neurons of input layer receive input



data and the hidden layers process them. In this layer, algebraic calculation is

done on the input data and its output is sent to the other units to the next layer.

Number of neurons in the input and output layers depends on the number of

variables. 3) weights: input variables of the network have different value.

These values are defined by weights. Weights are used in calculation before

hidden and output layers. They are obtained by training and testing the

network. 4) transfer functions: these functions are used in the output and

hidden layers. By using weights of each input variable, the outputs are

calculated. There are different types of transfer function that can be selected

by the user, based on the problem. Most common functions are as follows:

(a) Linear

(1)

b) Sigmoid

(2)

(c) Hyperbolic tangent

(3)

(d) Radial basis function

f(z) = exp(−z2) (4)

One artificial neural network consists of some neurons placed in input,

hidden and output layers. In general, several hidden layers could exist between

the input and output layers. One neural network uses input variables in the first

layer. The outputs are usually the solution of one problem. For calculating the

outputs, the network uses weights. They show contact between two neurons

numerically, and present importance of each input variable. Each training

process includes calculation of outputs and correction of the weights. This

zf(z)

ze1

1f(z)

zeze

zezef(z)



process continues until the correct weight values are found. For some certain

input parameters, the error is defined as the difference between experimental

data and output of the network [25]. There are three criteria for stopping the

training: maximum number of epochs, training time, and target mean square

error (MSE)1. However, in many cases, the mean absolute error (MAE)

2 and

the Pearson Product Moment Correlation Coefficient (R-value)3 are considered

as network selection process, too: Figure 1a shows a flowchart for choosing

architecture. The experimental data are split into three subsets: training,

validation and testing data. The training data are used to find the optimal

model (Figure 1b). The second subset is used for validation of generalization

capacity of the model. The testing data are used to check how well the model

is trained. [16]

(a) (b)

Figure 1. (a) Flow chart for choosing architecture. (b) A training process flowchart

[16].

1 ∑ ((

)

(

) )

2 ∑ (

(

)

(

)

(

)

)

3 *

∑ ((

)

)

+



Types of Artificial Neural Network

How to connect neurons in a neural network makes the type of network.

There are different types of neural network. The two general types are static

and dynamic. In static models, the path of data training is from input data to

hidden layer without any reverse. Whereas, in dynamic models, there are some

reverse paths from hidden layers to input layer. Static networks are named as

feedforward and dynamic models as feedback. Multi-layer perceptron and

Hopfield networks are the most popular feedforward and feedback networks,

respectively.

The feedforward networks are commonly used. These networks consist of

several layers, so that each neuron in each layer connects to the neurons of the

previous layer. These networks have one output layer and some hidden layers.

The outputs of the first layer are used as the inputs of the second layer, and the

outputs of the second layer are the inputs of the third layer. Finally, the outputs

of the last layer are the results of the network. Each layer can have different

number of neurons and different types of transfer function.

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

of inputs and outputs variables, respectively. The disadvantage of FNNs is

determination of the ideal number of neurons in the hidden layer(s); 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. One simple type of

feedforward network commonly used is perceptron neural network. [17]

PROBABILISTIC NEURAL NETWORKS

The ANNs can be used for different purposes; approximation of functions

and classification are examples of such applications. The most common types

of ANNs used for classification are the feed forward (that explained) neural

networks (FNNs) and the radial basis function (RBF) networks.

Probabilistic neural networks (PNNs) are a kind of RBFs that use a

Bayesian decision strategy [18]. In PNNs, each input has its distance from the

input vector calculated in the first layer. This process results in a vector whose

elements indicate how close the input is in relation of the training input. The

second layer produces a vector of probabilities that will be used in

determination of the input class.



Design of PNNs is faster than that of their feedforward counterparts, and

their generalization capabilities are very good. However, for PNNs, the

number of neurons depends on the size of the input set. Therefore, the PNNs

are bigger than the FNNs, but no optimization of the number of neurons is

necessary. [19]

The Multi-Layer Perceptron (MLP) Network

This type of network is composed of an input layer, an output layer and

one or more hidden layers (Figure 2). Bias term in each layer is analogous to

the constant term of any polynomial.

Figure 2. Multilayer perceptron with one hidden layer [20].

The number of neurons in the input and output layer depends on the

respective number of input and output parameters taken into consideration.

However, the hidden layer may contain zero or more neurons. All the layers

are interconnected as shown in the figure and the strength of these

interconnections is determined by the weights associated with them. The



output from a neuron in the hidden layer is the transformation of the weighted

sum of output from the input layers and is given as:

∑ (5)

The output from the neuron in the output layer is the transformation of the

weighted sum of output from the hidden layer and is given as:

∑ (6)

where, pi is the ith output from the input layer, zj is the jth output from the

hidden layer, wij is the weight in the first layer connecting neuron i in the input

layer to the neuron j in the hidden layer, is the weight in the second layer

connecting the neuron j in the hidden layer to the neuron k in the output layer

and g and are the transformation functions. The transformation function is

usually a sigmoid function with the most common being,

(7)

The other commonly used function is,

(8)

One of the reasons for using these transformation functions is the ease of

evaluating the derivatives required for minimization of the error function. [20]

Training

ANN is an adaptive network that changes its structure based on external or

internal information flowing through the network during the learning (training)

phase. Estimation of optimum weights and biases of network needs an

algorithm called propagation method. Several kinds of propagation methods

are available and back propagation (BP) is the easiest and simplest one with

enough reliability. BP and other usual propagation methods are explained

completely in the mathematical literatures [21,22].



Rules of Training

Training is implemented by change of weights in transfer function.

Generally, there are two types of training; supervised and unsupervised

trainings. In supervised training, the inputs and hidden layer variables are

defined to the model as dependent variables. But, in unsupervised training, just

the input variables are defined to the model.

Modeling Procedure: Back Propagation

For calibration of the network, firstly the data points are used to train the

network and then, some other data points (which are completely new) will be

used to test the calibrated network. As mentioned in the previous section,

training of a network requires a propagation method and BP is a simple

propagation method for training of the ANN. The algorithm of back

propagation error was chosen for our modeling. This section provides a

summary of BP.

First, data points must be divided into two parts: the first part for training

and the second part for testing. Usually about 30% of the data points are

selected randomly for the testing phase. Some random values must be chosen

as the initial guess for weights and biases, and then training phase begins.

Inputs are entered to the network and produce the output, and the output is

checked by the real data.

As explained in the previous sections: Each layer is made of some neurons

connected to the other neurons in the previous and next layers. A neuron has

an input, an output and a transfer function. The tangent hyperbolic transfer

function is one of the performed functions, expressed as the following

equation:

( )

(9)

where, is the output of the jth neuron and Sj is the input of the jth neuron,

produced by outputs of the previous layer. Sj is given 10.

∑ ( ) (10)



The deviation, , defined as the difference between the appropriate output

( and the calculated output for the data point ( ) can be presented as:

(11)

where, presents the last layer. Summation of squared deviations ( ) is a

better choice for further operations, described as the following equation:

∑

(12)

Eq. (15) is used to renew weights and biases as described below:

(13)

(14)

where, α is the propagation rate and usually is chosen from 0.1 to 0.9. The last

terms of the above equations (∂F/∂wij and ∂F/∂bi) are complicated and after

straightforward algebra can be presented in the following form:

(15)

Where,

(16)

(17

(18)

The general form of Eq. (10) is given by

(19)



where, is the transfer function. Thus,

(20)

By replacing the equations derived above in the Eq. (13), below equation

is resulted:

(21)

In the same way, Eq. (14) can be represented as:

(22)

Eqs. (21) and (22) are used for the last layer ( , but in hidden layers, it is

required to introduce a new parameter for corrective calculations in the

following form:

(23)

where, l presents the layer number and . Thus, the last terms of Eqs. (13)

and (14) (∂F/∂wij and ∂F/∂bi) must be rewritten as:

(24)

(25)

In mathematical literatures [23, 24], there are suitable methods for

calculating left sides of Eqs. (24) and (25). in the following form:

(

)∑

(26)

Eq. (26) shows that δs of the layer (l) are calculated by δs of the next layer

( +1). ∂F can be represented as:



∑

(27)

where,

(28)

(29)

(30)

The above equations are used for calculating and renewing the weights

and biases of ANN method. The selected training data points are used to

obtain the network parameters in a cycling process, e.g. cycling equal to 100

means that all training data points are used 100 times for improving the

parameters of the network. Then, the reliability of the trained network may be

checked using some new data points (testing). Small error of testing phase

confirms that the propagation method avoids over fitting [21, 22, 23, and 24].

Modeling Steps

1) Collecting the experimental data including API, viscosity, steam

injection rate, characterization factor as our inputs and steam

distillation yield as our output.

2) Editing these data in a suitable format that can be used in our

program.

3) Dividing the input file to 3 main parts such as testing, training, and

cross validation data.

4) Choosing the best transfer function (hyperbolic tangent).

5) Making different neural networks with one and two hidden layers and

different number of neurons.

6) Training these different neural networks.

7) Calculating the ARE%, MSE%, MAE%.

8) Finding the best neural network with the high accuracy.

9) Comparing our results with the previous models.



RESULTS AND DISCUSSION

In this study, for prediction of steam distillation yield, a multi-layer

perceptron neural network was used. Tanh-axon was selected as the transfer

function, and Levenberg–Marquardt back propagation was used in all training

steps. Input layer had four neurons consisting of API, viscosity of the crude

oil, steam distillation factor and steam characterization factor, which are

defined as follows:

(31)

(32)

Hidden layer and its number of neurons will be discussed in the next

section. Finally, the last layer has one neuron that is steam distillation yield.

Figure 3 shows this neural network used in this study.

Figure 3. Schematic of the MLP network used in this study.

Experimental data obtained from the literature were used as training and

testing [26,27,28]. 77 data of 128 input data were used for training, 33 data for

testing, and 18 data for cross validation. The difference between experimental

and obtained results of steam distillation yield were minimized by

optimization of the weights.

gravity specefic

point boiling averagemean factorzation characteri



The obtained results indicate that the best network was the net with one

hidden layer, whose number of neurons were found by trial and error. The

obtained results show that (Table 3) the net with four neurons has minimum

error. So, this net is used for prediction of steam distillation yield. The

accuracy of this model is determined by comparing the experimental data and

the obtained results in training and testing steps. For this model, R2

=0.99 and

ARE%=2.105. These parameters show the accuracy of this model (Figure 4,

Table 3).

Figure 4. Comparison of the results of one-hidden layer neural network with 4 neurons

and experimental data at different injection rates.

The values of weights for the output and hidden layers for the best one-

hidden layer are reported in Table 4.

Then, a network with two hidden layers were studied that the optimum

neuron number was obtained 5 neurons, like one-layer nets (Table 5). For this

network, values of R2 and ARE% are 0.995 and 7.443, respectively. They are

reported in Figure 5 and Table 5. The values of weights for the output and

hidden layers for the best two hidden layer are reported in Tables (6,7,8). In

this network, first hidden layer consists of 3 neurons and second hidden layer

has 5 neruons. The number of nerurons of input and output layers depends on

the number of input and output variables. In this work, the number of neurons

for input and output layers is 4 and 1, repectively. The average relative errors

for the best networks are calculated and reported in Table 9.



Table 1. Exprimental properties of different crude oil fields [26,27,28]

Crude Oil API

Viscosity at

100°f-CSt-m2/s

Characteriza

tion Factor

1 South Belridge 12.4 0.4085 9.7

2 Winkleman Dome 14.9 0.0488 9.6

3 White Castle 16 0.0308 9.7

4 Edison 16.1 0.0397 9.7

5 Red Bank 17.1 0.03 9.9

6 Slocum 18.9 0.0395 10

7 Hidden Dome 20.7 0.0086 10.1

8 Toborg 22.2 0.0036 10.1

9 Brea 23.5 0.0039 10

10 Shanrion 24.5 0.0032 10.2

11 Robinson 26 0.0029 10.3

12 El Dorado 32.5 0.0005 10.1

13 ShiellsCanyOn 33 0.0006 10.2

14 Teapot .Dome 34.5 0.0006 10.4

15 Rock Creek 38.2 0.0005 10.4

16 Plum Bush 39.9 0.0006 10.5

Table 2. Experimental results of steam distillation yield (Vo/Voi) in

different steam injection rate [26,27,28]

crude oil (

) 1 2 3 4 5 10 15 20

1 South Belridge 0.031 0.046 0.06 0.069 0.075 0.1 0.119 0.13

2

Winkleman

Dome 0.089 0.111 0.125 0.136 0.142 0.17 0.182 0.195

3 White Castle 0.07 0.095 0.11 0.122 0.137 0.185 0.21 0.23

4 Edison 0.092 0.12 0.14 0.151 0.164 0.19 0.198 0.209

5 Red Bank 0.128 0.162 0.18 0.195 0.205 0.231 0.241 0.25

6 Slocum 0.032 0.08 0.097 0.11 0.122 0.172 0.195 0.2

7 Hidden Dome 0.119 0.148 0.169 0.19 0.205 0.25 0.28 0.295

8 Toborg 0.196 0.196 0.267 0.285 0.3 0.339 0.349 0.36

9 Brea 0.21 0.24 0.265 0.283 0.296 0.33 0.34 0.354

10 Shanrion 0.14 0.192 0.22 0.24 0.26 0.307 0.328 0.331

11 Robinson 0.128 0.176 0.208 0.228 0.245 0.295 0.312 0.32

12 El Dorado 0.345 0.4 0.43 0.441 0.45 0.47 0.475 0.48

13 ShiellsCanyOn 0.378 0.438 0.47 0.49 0.508 0.541 0.558 0.57

14 Teapot .Dome 0.24 0.32 0.36 0.396 0.425 0.503 0.534 0.57

15 Rock Creek 0.295 0.36 0.4 0.412 0.42 0.447 0.465 0.48

16 Plum Bush 0.28 0.338 0.36 0.38 0.4 0.46 0.489 0.53



Table 3. One-hidden layer neural network with different neuron number

Number of neurons Training data Test data

MSE MAE MSE MAE

3 0.0085 0.0769 0.0118 0.0865

4 0.0012 0.0273 0.0021 0.0347

5 0.0007 0.0213 0.0022 0.0364

6 0.0003 0.0149 0.0267 0.1386

Table 4. Values of weights for the output and hidden layer

output layer

hidden layer j=1 2.000 3.000 4.000 k=1

i=1 -0.175 -0.341 0.026 -2.214 -4.434

2.000 0.383 -1.820 -2.415 0.907 -12.959

3.000 0.148 0.439 -0.351 -0.137 10.900

4.000 -2.252 0.107 0.116 0.301 1.674

i= the neuron number of input layer.

j= the neuron number of hidden layer.

k= the neuron number of output layer.

Table 5. Two-hidden layer neural network with different neurons

Number of neurons Training data Test data

MSE MAE MSE MAE

3 0.0015 0.0316 0.0083 0.0802

4 0.0042 0.0466 0.0075 0.0725

5 0.0024 0.0427 0.0013 0.0295

6 0.0006 0.0201 0.0043 0.0527

Table 6. The values of weights for first hidden layer

First hidden layer j=1 2.000 3.000

i=1 0.697 -2.628 -1.214

2 0.076 1.657 0.536

3 0.158 -0.195 2.960

4 -0.898 -0.001 -0.042

The obtained results indicate that the accuracy of one-hidden layer

networks is more than two-hidden layer nets. Finally, the results of this model



were compared with some available models. High accuracy of this model

compared to the other models is one of the most important advantage (Table

10).

Table 7. The values of weights for the output for second hidden layer

Second hidden layer k=1 2 3 4 5

j=1 0.390 0.098 0.524 -1.979 0.378

2 0.696 0.438 2.149 0.180 -1.688

3 -0.117 0.021 1.043 -2.221 -0.357

Table 8. The values of weights for output

Out put layer m=1

k=1 0.937

2 0.572

3 -1.563

4 1.265

5 1.292

i= the neuron number of input layer.

j= the neuron number of first hidden layer.

k= the neuron number of second hidden layer.

m= the neuron number of output layer.

Figure 5. Comparison of the results of two-hidden layer neural network with 5 neurons

with experimental data at different injection rate.


Table 9. Comparison of experimental and simulated results by testing one-hidden layer and two hidden layer in

ARE%, two-hidden layer with 5 neurons ARE%, one hidden-layer with 4 neurons

0.0228 0.077 0.1 0.0254 0.102 0.1

0.0578 0.179 0.17 0.0108 0.168 0.17

0.0044 0.185 0.185 0.0117 0.187 0.185

0.0364 0.183 0.19 0.0428 0.181 0.19

0.0657 0.215 0.231 0.0067 0.229 0.231

0.1086 0.153 0.172 0.0297 0.1666 0.172

0.1695 0.207 0.25 0.0021 0.249 0.25

0.1315 0.294 0.339 0.0017 0.344 0.339

0.0694 0.307 0.33 0.0292 0.339 0.33

0.0934 0.278 0.307 0.0201 0.3131 0.307

0.0191 0.300 0.295 0.0035 0.293 0.295

0.0930 0.426 0.47 0.0122 0.464 0.47

0.0541 0.511 0.541 0.0282 0.525 0.541

0.0318 0.486 0.503 0.0493 0.478 0.503

0.0235 0.457 0.447 0.0441 0.446 0.447

0.0038 0.461 0.46 0.0027 0.458 0.46

7.44309244 2.105483337 overall1

1

10oVwV

expoiVoV

simoiVoVexpoiVoV simoiVoV expoiVoV

expoiVoV

simoiVoVexpoiVoV simoiVoV expoiVoV

16

16

1 expoiVoV/simoiVoV

expoiVoV

overall



Table 10. Comparison of the results with the other models

Method ARE%

Modified Holland and Welch methods. 14.3

EOS 18.48

Neural network- Vafayi 5.78

our neural network-one layer 2.1055

our neural network- two layer 7.44309244

CONCLUSION

The MLP neural network was developed to predict steam distillation

yield. Two kinds of network were compared (one-hidden layer and two-

hidden layer). In each step, the number of neurons changed to find optimum

neuron number. The one-hidden layer with four neurons had more accuracy

compared to the two-hidden layer. This model has been compared with

Holland and Welch, Van Winkle, EOS, and Vafayi models. The results show a

high accuracy for our model.

ACKNOWLEDGMENT

The authors would like to thank Dr. Shahab Ayatollahi for his help during

our study. Support of IOR Research Institute and NIOC R&T is gratefully

acknowledged.

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Prediction of Steam Distillation Efficiency during Steam Injection Process using a Riable Method