Medical, Pharma, Engineering, Science, Technology and Business

University of Calgary, Calgary, Alberta, Canada

- *Corresponding Author:
- Ehsan Amirian

Professor, University of Calgary

Calgary, Alberta, Canada

**Tel:**5877078489

**Fax:**5877078489

**E-mail:**[email protected]

**Received Date:** Feb 13, 2017 **Accepted Date:** Mar 09, 2017 **Published Date:** Mar 16, 2017

**Citation: **Amirian E, Chen ZXJ (2017) Cognitive Data-Driven Proxy Modeling for Performance Forecasting of Water-flooding Process. Global J
Technol Optim 8: 207. doi:10.4172/2229-8711.1000207

**Copyright:** © 2017 Amirian E, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Global Journal of Technology and Optimization

Assessment of diverse operational constraints and risk appraisal associated with reservoir heterogeneities are essential foundation of production optimization and oil field development scenarios. Water-flooding performance evaluation that comprises comprehensive numerical simulations is typically cumbersome in terms of time and money, which is not reasonably appropriate for practical decision making and future performance forecasting. Cognitive data-driven proxy modeling practices, which incorporate data-mining techniques and machine learning concepts, offer a fascinating substitute for explicit models of the underlying process that can be instantaneously reassessed, especially for extremely nonlinear system forecasts. In this paper, an exploratory data analysis is applied to create a comprehensive data set from Water-flooding actual field data, which entails different characteristics labeling reservoir heterogeneities and other pertinent operational constraints. Artificial neural network (ANN) is applied as a cognitive data-driven proxy modeling effort to predict Water-flooding production in heterogeneous reservoirs. This study presents the great potential of cognitive data-driven proxy modeling techniques for practical applications and as a feasible add on for investigating a huge quantity of real field data efficiently. In addition, the suggested methodology can be incorporated directly into most present reservoir development decision making routines.

Data-driven; Cognitive; Artificial neural network; Waterflooding

**Symbols**

f(Y): Activation function; k: Permeability, mdk_{avg}: Average
permeability; mdS_{ro}: Residual oil saturation; S_{rw}: Residual water
saturation; V_{DP}: Dykstra-Parson coefficient; x_{i}: Signal from input node;
iY_{j}: Weighted sum of input signals; w_{0}: bias; w_{ij}: Weight associated with
the connection between nodes i and j.

**Greek letters**

φ=Porosity, (%); φ_{avg}=Average porosity, (%).

**Acronyms**

ANN=Artificial Neural Network; BPNN=Back-Propagation Neural Network; MLP=Multilayer Perceptron; NN=Neural Network; SAGD=Steam Assisted Gravity Drainage; SL= Single Layer; RF= Recovery Factor (%).

Water flooding or water injection is one of the most vital techniques for enhancing oil recovery. Injected water into a reservoir aims to provide pressure support to the reservoir which is called voidage replacement, and to displace or drive oil from the reservoir to production wells. Water flooding performance assessment has been widely investigated in both experimental [1-5] and detailed numerical simulation [6-10] frameworks. Numerical modeling of water flooding recovery performance can be carried out with traditional simulators. The current flow simulators require a huge number of input parameters such as initial saturation and pressure distributions, porosity, permeability, multi-phase flow functions, and well parameters. Inference of these input parameters is time-consuming, while accurate measurements are often not readily available. Furthermore, many assumptions associated with the process physics are often invoked for a numerical solution. Given the extremely nonlinear relationships between input variables and output objective functions (e.g., an oil production profile), the computational time is also extremely high. Therefore, there has been an increased drive and interest to integrate data-driven proxy approaches for modeling the recovery response of Enhanced Oil Recovery (EOR) processes. A datadriven proxy modeling approach provides a practical alternative for assessment of diverse operational constraints and risk appraisal associated with reservoir heterogeneities, which are essential foundation of production optimization and oil field development plans. High-dimensional data including enormous geological and operational parameters can be processed for efficient and fast decisionmaking.

Cognitive data-driven proxy modeling employs machine-learning techniques to construct induced models that explain the behavior of the underlying physical process. Detailed data analysis characterizing the desired process is the foundation of this data-driven modeling approach. Common techniques utilized in cognitive data-driven proxy modeling include data-mining and statistical methods, artificial and computational intelligence tools, and fuzzy logic concepts. Currently, these approaches have progressed outstandingly beyond the ones applied in traditional empirical regression. These techniques are employed for big data classification, predictive modeling, recreating extremely nonlinear relationships, and constructing rule-based expert systems.

The common themes of data-driven modeling have been developed
with integration and contribution from various interdisciplinary
specializations involving artificial and computational intelligence,
machine learning and pattern recognition, data-mining alongside with
the statistical data analysis, knowledge discovery in databases, and soft
computing. A data-driven modeling layout is based on the assumption
that a primary process has generated a database of observed cases,
expert experience and knowledge. As demonstrated in **Figure 1**, the
ultimate goal of cognitive data-driven proxy modeling is to fuse these
multiple information sources to present a representative model for the
primary process. If the presented model approximation is acceptable
for that process, it can be employed to address the other questions
regarding the properties of the underlying process [11].

In this study, an artificial intelligence (AI) technique, called artificial
neural network (ANN), is used to identify or approximate a complex
nonlinear relationship connecting pertinent input variables to the
desired target objective functions. Artificial neural network (ANN)
employs a series of processing units (neurons, nodes) in the hidden
layers where the weighted summation of input variables is subjected to
a nonlinear transfer function. A data set consisting of both input
(pertinent predicting) variables and desired target objective functions
is employed to train the network. The network unknown parameters,
classically the connecting weights and biases (thresholds) that link
between all the nodes, are assessed using the procedure of inverse
problem theory in which the objective is to minimize the existing
mismatch between the artificial neural network predicted output and
the known actual values of the desired objective functions variables. In
**Figure 2**, a typical flow chart for artificial neural network training is
illustrated. Since various parameters can be both continuous and
discrete (categorical), the most universal uses of ANN include
cognitive proxy modeling for function estimation and pattern
classification. Brief history and advancements for the artificial neural
network technique including ANN learning rules, architecture
configuration, hybrid practices and convergence situations are
described in [12-14].

ANN is developed by training a network to represent the intrinsic relationships existing within the data. The idea of neural network alludes back to 1943 when neurophysiologist Warren McCulloch and mathematician Walter Pitts published their research work on how neurons might perform [15]. Any neural network is trained using a learning algorithm and training data set. In general, there are two types of neural network learning algorithms classification: unsupervised learning and supervised learning. The unsupervised learning is used to find hidden structure in unlabeled data. The objective is to categorize or discover features or regularities in the training data. A cluster analysis is the most common use of unsupervised learning. In contrast, the supervised learning method requires that target values be provided. A training dataset is needed as the input vector and will generate the rules according to the desired output by adjusting the weights. The weights are then used for processing the inputs of a test data set. After providing the desired output to the net, the weights will be adjusted to match the model to the desired goal. The learning process iteration will be continued until the desired goal is reached.

In petroleum engineering an extensive variety of neural network
applications can be found [16-19], particularly in the areas of: reservoir
characterization or property prediction [20-23], classification [19],
proxy for recovery performance prediction [24,25], history matching
[26], and design or optimization of production operations and well
trajectory [27-33]. In particular, neural networks have been utilized in
recent years as a proxy model to predict heavy oil recoveries [34-39], to
perform EOR (enhanced oil recovery) screening [40-42]to characterize
reservoir properties in unconventional plays [43], and to evaluate
performance of a CO_{2} sequestration process [44]. As a data-driven
proxy modeling workflow numerical reservoir simulation models are
subjected to the commercial simulator to build the comprehensive
training data set. This representative data set consist of pertinent input
variables labelling reservoir uncertainty due to the geological
heterogeneities and crucial injection/production constraints with the
corresponding desired objective function output values including
cumulative oil production profile and ultimate recovery factor for the
underlying recovery process. Artificial neural network models are
trained employing the representative training data set and eventually
applied as a data-driven proxy modeling alternate to forecast the
desired objective function target values including cumulative oil
production profile and ultimate recovery factor during the SAGD
process [38,39].

The principal objective of this research is to develop a data-driven proxy model using artificial neural network as a substitute to smartly forecast Water-flooding recovery performance in heterogeneous reservoirs. This research aims to assess the key demonstrative predicting (input) variables related to Water-flooding performance forecasting with practical application to the heterogeneous reservoirs.

Artificial neurons that are linked together according to specific
network architecture create an artificial neural network. The two most
common categories of network architectures are Single Layer
Perceptron (SLP) and Multilayer Perceptron (MLP) which consists of
single input and output layer with any number of hidden layers. Since
the complexity, heterogeneity and nonlinearity are the main challenges
when facing a comprehensive real field data set, multilayer perceptron
stands as the most common neural network architecture. A general
schematic of MLP neural network is shown in **Figure 3**. Selection of
the number of hidden layers and the number of hidden processing
units (neurons, nodes) within the hidden layers are of great
importance during an artificial neural network architecture design.
There is a transaction between accuracy and overfitting of data: A
difference between artificial neural network forecasts and desired
target values of output objective functions could not be minimized
with an insufficient number of neurons, whereas too many neurons
can result in an overfitting of network parameters (i.e., weights and
bias connections).

Researchers have established some rules of thumb to opt the number of neurons in a neural network. The number of independent (input) variables is generally much larger than the number of dependent (target) variables. Ferreira [45] proposed that the number of neurons should lie between the number of input parameters and the number of output parameters; in particular, the number of neurons should be two thirds of the number of input parameters, plus the number of output parameters, but no more than twice the number of input parameters. Haykin [46] explained that the number of free parameters (i.e., the number of weights and bias connections) in the hidden layer should be a function of the input vector dimension and the total training data set size. In this paper, a sensitivity analysis on the network configuration is implemented; the optimal architecture is selected by comparing the error/mismatch in network prediction between different configurations.

In a feed-forward neural network, a signal is passed from an input
layer of neurons (nodes) through a series of hidden layers to an output
layer of neurons. The input nodes represent the independent variables
that are nonlinearly related to a set of dependent or target variables,
characterized by a series of neurons at the output layer. Free
parameters including weights and biases specified for each connection
are determined using a training data set via a supervised learning
process in which a gradient-based minimization technique is utilized
to minimize the mismatch between artificial neural network
predictions and actual values of the desired target objective function
values [47]. **Figure 4** illustrates exactly how the signal flows forward
(feed-forward) from the input to the output layer and also who the
error is back-propagated from the output to the input layer.

The sum of the multiplication of the input values is added to the biases of each processing unit to get the value of Y as in Equation 1.

(1)

where Yj is a weighted sum of input signals at node j; w0 is a bias value; wij is the weight linked with the connection between node j and the input node i; xi is the value of input node i; n is the number of input nodes. As shown in Equation 2, a sigmoid activation function is applied to the weighted Yj.

(2)

The value calculated from Equation 2 is the output signal from node j, which can be considered as the input signal to the next layer.

In this paper, a Feedforward Backpropagation Neural Network or
Backpropagation Neural Network (BPNN) model as the most common
algorithm for estimating the unknown network parameters (weights
and biases) is employed. As a gradient-based minimization technique
that utilizes a supervised learning process with feed-forward network
architecture, BPNN propagates an error backwards from the output
nodes to the input nodes which is shown in **Figure 4**. The algorithm
evaluates the gradient of the error associated with the network's
unknown parameters. A gradient-descent algorithm is then applied to
estimate parameters that minimize the error [48].

**Data assembly**

Core data is frequently quoted as the "ground-truth" in petrophysical assessment of reservoir rock [49]. Cores can be physically studied and measurements made can be interpreted in terms of representative lithological characteristics. It should be noted that the cores themselves must be representative of the evaluated reservoir section. A core analysis is employed to define not only the porosity and permeability of the reservoir rock, but also to exhume the fluid saturation and grain density. All of these measurements help geologists and engineers better understand the conditions of a well and its potential productivity.

Core data based on core analyses for 700 cored wells are collected from a public domain in an oilfield located in the Alberta province, where Water-flooding has been performed during years. Given that these data contain noises and considering the missing data attributes in some locations, 61 cored wells are used as the representative data set for this data-driven modeling. A number of input/output attributes describing the reservoir properties and production characteristics including permeability, porosity, residual oil and water saturations and cumulative oil production have been analyzed for this data set. Although other information such as a log analysis and seismic data might be available for a portion of the data set, we are interested in building records that have the reliable measurements from core data.

**Case study**

Heterogeneity in hydrocarbon reservoirs creates a great amount of risk during recovery processes. In this case study, ANN is employed to forecast Water-flooding oil recovery performance for a series of producing wells with varying porosity and permeability values.

An ANN model is constructed involving one output/target variable
cumulative oil production after five years for each well and a total of
five input variables that include the mean of porosity values in each
well: ϕ_{avg}, the mean of permeability values in each well: kavg, the
Dykstra-Parsons coefficient: V_{DP}, residual oil saturation: S_{ro} and
residual water saturation: S_{rw}. The Dykstra-Parsons coefficient [50] has
been employed in much research to characterize heterogeneous
permeability distribution in layered reservoirs.

According to the immense discrepancy in scales of different databases, normalization is frequently implemented [47]. As an essential preliminary processing (pre-processing) stage for data driven proxy modeling, normalization is applied to transform all data values to shift and lie in a certain positive range, for instance (0, 1), shown in Equation 3. This step boosts the equality of the training stage by retaining inputs with large values from replacing out other inputs that are equally important with smaller values [51].

(3)

All 61 well records are subjected to a pre-processing stage and afterwards the ANN training and testing phases. In this study, 75 percent of the recorded data points are used as the training data set and the rest 25 percent are utilized as the testing data set. A sensitivity analysis of the network configuration is performed where the mismatch between network predictions and actual values of target variables after a fixed number of epochs is compared among different configurations.

The ANN model configuration is set to have one hidden layer with
six hidden nodes. The predicted results for this configuration are
illustrated in **Figure 5**. As one can see, the training stage performance
after a constant number of epochs is unsatisfactory and the ANN
predicted results for cumulative oil production are different from the
ones from real field data (**Figure 5a**). This insufficiency is revealed in
the testing stage where the trained network parameters are employed
to predict the cumulative oil production for the testing data set after
five years of production, as shown in **Figure 5b**.

The error evolution in the training stages is plotted per number of
epochs for this ANN model configuration (**Figure 6**). The error has
been stabilized after epoch no. 4,000 and there is no decrease in the
mismatch between ANN prediction and real field target values.
Increasing the number of hidden nodes made no improvements in the
model predictability. This fact lead us to increase the number of hidden
layers to capture the nonlinearity existing among the data-driven
proxy model input variables and desired output parameters.

Next, two hidden layers, each including six nodes, are employed to
train the proxy model and estimate the network unknown parameters.
Cross-plots of the real field cumulative oil production values against
proxy forecasts for training and testing data segments are
demonstrated in **Figure 7**. A decent match between the objective
function desired actual values and data-driven proxy model
predictions can be observed, as most points lie very close to the 45°line. **Figure 8** presents a decline of the error/mismatch as a function
of the number of epochs for this network configuration; a significant
error reduction is achieved as the training progresses. The decrease in
error evolution after reaching the end of an epoch limit is comparable
to the one from one hidden layer ANN model. The results suggest that
the chosen network configuration can be used successfully to predict
recovery performance.

Performance of a three hidden layer ANN model is also investigated
for this case study with the same six nodes in each hidden layer. ANN
performance during the training stage is fundamentally flawless as
excellent matches between targets and predicted output values
demonstrated in **Figure 9a**. The error evolution plot also certifies a
good training stage where the error has been significantly decreased as
shown in **Figure 10**. Nevertheless, once the trained data-driven proxy model is applied to the testing data set, evaluation of proxy model
forecasts with the desired target objective function actual values
revealed to be awfully ill-conditioned. As seen in **Figure 9b**, the crossplot
between ANN predicted values and real field data for cumulative
oil production after five years are way far from the 45° line which
indicates a drop in network predictability.

The other issue rather than over-fitting due to the network configuration can be the existence of hidden structures within the data set. In this case, a cluster analysis and principal components analysis can be applied in upcoming research works to detect the internal hidden patterns within the input attributes of the underlying process and make recommendations for dimensionality reduction to have independent input parameters for cognitive data-driven proxy modeling [39].

Comparison between all three network configurations implies that too many hidden layers will increase the chance of an over-fitting issue, whereas the forecasting performance of a cognitive data-driven proxy model is conceded with inadequate number of hidden processing nodes. In this study the optimum network configuration has been shown to be a two hidden layer ANN model where the network prediction is in a good match with the target values from real field data.

A core data analysis is employed to identify numerous parameters describing characteristics associated with reservoir heterogeneities. A comprehensive Water-flooding real field data set from a public domain is compiled. The constructed data set involves one output/target variable cumulative oil production after five years for each well and a total of five input variables that include the mean of porosity and permeability, the Dykstra-Parsons coefficient, residual oil saturation and residual water saturation.

Data-driven modeling processes such as artificial neural networks are still considered recent advancements and have not been widely adopted in most sectors of the oil sands industry. In this research, ANN is successfully applied to predict recovery performance of the Water-flooding process.

Performance of different ANN model configurations is evaluated and the optimal network architecture is tested successfully to forecast the Water-flooding performance for the testing data set.

The proposed research has great potential to be integrated directly into most existing reservoir management and decision-making routines and applied in SAGD and other solvent-additive steam injection projects.

Future studies will incorporate data from other producing fields and integrate other data mining techniques, such as clustering to recognize internal hidden structures among a data set and a principal component analysis as a treatment to the curse of dimensionality to reduce the number of independent input parameters.

This research is supported by the NSERC/AIEES/Foundation CMG and AITF (iCORE) Chairs.

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