a data-driven smart proxy model for a comprehensive
TRANSCRIPT
A Data-Driven Smart Proxy Model for AComprehensive Reservoir Simulation
Faisal AleneziDepartment of Petroleum and Natural Gas Engineering
West Virginia University
Email: [email protected]
Shahab MohagheghDepartment of Petroleum and Natural Gas Engineering
West Virginia University
Email: [email protected]
Abstract— One of the most important tools for studying fluidflow behavior in oil and gas reservoirs is reservoir simulation. Itis constructed based on a comprehensive geological information.A comprehensive numerical reservoir model has tens of millionsof grid blocks. Therefore, it becomes computationally expensiveand time consuming to run the model for different reservoirsimulation scenarios. There are many efforts have been madeto reduce the computational size using the proxy models. Proxymodels are the substitute to the complex numerical simulationby producing a meaningful representation of the complex systemin a very short time. The conventional proxy models are eitherstatistical or mathematical approaches. These conventionalapproaches are still limited to the complexity of the reservoirand the number of the numerical simulation runs needed tobuild the proxy model. In this study, a smart proxy model thatis based on artificial intelligence and data mining is presented.A grid based smart proxy model is developed to reproduce thedynamic reservoir properties of a full- field numerical simulationin few seconds. A comprehensive spatio-temporal database isbuilt using the conducted numerical simulation run. The datafrom the database is trained, calibrated, and verified throughoutthe development of the smart proxy model. Smart proxy modelis able to produce pressure and saturation at each reservoirgrid block accurately and with a significantly less computationaltime compared to the numerical reservoir simulation model.
Keywords—Artificial Intelligence, Data Mining, Proxy Model-ing, Reservoir Simulation.
I. INTRODUCTION
Petroleum industry strives to find oil and gas reserves,
developing these resources, meet the world energy demand,
and maximize profits. One of the most important tools in oil
and gas reservoirs development and management is reservoir
simulation. It is a necessary tool for reservoir engineering
strategy plans. The key goal of reservoir simulation is to
predict future performance of the reservoir and find ways and
means of optimizing the recovery of some of the hydrocarbons
under different operating conditions. Accurate reservoir simu-
lation involves a comprehensive description of the reservoir
properties. To date, the computational science, addressing
numerical solution to complex multi-physic, non-linear, and
partial differential equations, are at the lead of engineering
problem solving and optimization [1].
Due to the complexity of a reservoir, sometimes it is com-
putationally extravagant to develop and run numerical simu-
lation models. Therefore, the petroleum industry investment
in reservoir simulation tools is expensive. The rate of return
on these investments should be calculated to maximize the
benefits from the reservoir simulation. Reservoir simulation
proxy models are one way to increase the return on investment
in reservoir simulation. Proxy-modeling (also known as surro-
gate modeling) is a computationally inexpensive alternative
to full numerical simulation in assisted history matching,
production optimization, and forecasting. A proxy model is
defined as a mathematically, statistically, or data driven model
defined function that replicates the simulation model output
for selected input parameters [2]. The proxy model’s results
are not to mimic the numerical simulation results with 100%
accuracy, but the outputs generated with the amount of time to
run these models, give a reasonable range of error. Reducing
the computational time to few seconds, make these models sig-
nificantly competent and attractive to the reservoir engineers
[3].
There are several approaches for generating the proxy models.
Response surface methodology (RSM), reduced order models
(ROD), reduced physics models (RPM) are the first techniques
introduced in this field. The most widely used approach is the
response surface methodology. Response surface methodology
(RSM) consists of a group of mathematical and statistical
techniques used in the development of a sufficient functional
relationship between a response of interest and a number of
associated input variables [4].
In recent years, a newly developed technique for generating
proxy modeling has introduced to the reservoir simulation. It
is neither statistical nor mathematical; it is a smart approach
that is based on data mining and artificial intelligence.
II. DATA MINING AND ARTIFICIAL INTTLEGENCE
TECHNIQUE
The amount of data in the world is increasing dramatically.
Data mining is about solving problems by analyzing and
discovering the patterns already present in databases [5].
Artificial Intelligence is a powerful technique that teaches the
machines how to process data. Data mining and Artificial
Intelligent have been applied in petroleum engineering field.
In his series of articles in Society of petroleum engineers
journal, Shahab D. Mohaghegh presented three types of the
virtual intelligence (neural networks, genetic algorithm, and
fuzzy logic) and their applications in the oil and gas industry
978-1-4673-8956-3/16/$31.00 ©2016 IEEE
[6][7][8]. The conclusions from these articles show the ability
and the potential of the Artificial Intelligence to solve complex
problems in reservoir engineering.
In reservoir simulation, Artificial Intelligence is used before
to generate a proxy model that is able to reproduce the
numerical simulation outputs. In 2006, Mohaghegh developed
the first SRM (surrogate reservoir model) based on data mining
and artificial intelligence (which is later called smart proxy
model). The proxy model built was able to solve the time
consuming challenge to run uncertainty analysis in one of the
giant oil fields [9]. Since then, the smart reservoir model has
applied to several studies to replicate the numerical reservoir
simulation outputs. Alireza Shahkarami verified the ability
of the smart proxy model in performing reservoir simulation
history matching [10]. S. Amini developed a smart proxy
model that is capable of mimicking a numerical reservoir
simulation results in a complex reservoir [11].
The main part of developing the smart proxy model is to
build a spatio-temporal database from a number of numerical
simulation runs in order to train, validate, and test the data for
successful predication. In this paper, the author investigates
the ability of the smart proxy model to mimic the numerical
simulation results using one numerical simulation run of a
complex reservoir. The main advantages of using the smart
proxy model against other proxy models in reservoir simula-
tion are; 1. There is no limitation in reservoir complexity; 2.
There is no simplification in the reservoir physics; 3. The time
to run the smart proxy model is very short.
III. FIELD OF STUDY AND GEOL-CELLULAR MODEL
The SACROC unit (Scurry Area Canyon Reef) is part of
the Kelly-Snyder Field located northeastern of the Permian
Basin in West Texas. The field discovered in 1948 with
approximately 2.73 billion barrels oil in place. In 1954, a
pressure maintenance program has established in the reser-
voir by water injection. A geo-cellular model is developed
for the SACROC unit with 221 layers and 149X287 cells
spatially. The high number of grid blocks (9,450,632) with
more than 2000 wells, make conducting study in the field time
consuming. Therefore, to serve the objective of this study, the
geo-cellular is upscale to 100X142 spatially and to 16 layers.
Also, a northern area of up-scaled geo-cellular is picked with
dimensions of 39X51 spatially. The final total number of grid
blocks for the study is 31,200. It is important to mention that
the porosity-permeability heterogeneity is preserved with the
up-scaled geo-cellular model. Figure 1 and Figure 2 show
the porosity-permeability histograms before and after the up-
scaling process.
Figure 3 shows the porosity 3D model of the study area. Using
the scale on the right side of the figure, this figure provides
strong evidence of the field heterogeneity.
There are 27 production wells and 12 water injection wells in
this part of the field.
Fig. 1. Porosity-Permeability Histogram of the High Resolution Geo-cellularModel
Fig. 2. Porosity-Permeability Histogram of the Up-scaled Geo-cellular Model
Fig. 3. Porosity Geo-cellular Model of the Study Area
IV. SMART PROXY DEVELOPMENT
As aforementioned, the smart proxy model is a data mining
and artificial intelligence approach. The development proce-
dure fall in four main stages; Design full field reservoir simu-
lation, extract the output data from the reservoir simulation to
generate the database, develop the smart proxy model by train
and validate data for a targeted output, and verify the smart
proxy model performance using blind sets of data (Figure
4). The following sections are discussing these steps in more
details.
A. Numerical Simulation Design
The purpose of designing and running the numerical sim-
ulation is using its outputs as inputs to the neural network
for training. The key of designing the simulation model is
to take into consideration the objective of the smart proxy
model. The aim of this study is to replicate and predict the
reservoir dynamic properties at grid block level under different
water injection flow rates. With this in mind, the simulation
run is designed to calculate the well production data at each
formation layer (grid block). Certainly, having the production
data at every grid block of the wells is generating the required
Fig. 4. Smart Proxy Model Work Flow
data heterogeneity for the neural network training (Figure 5).
In sum, it is only one simulation run designed to develop the
smart proxy model.
Fig. 5. Production Data Histogram at Grid Block
B. Database Generation
The majority of time in developing the smart proxy model
is consumed in database generation. The smart proxy model
is constructed to represent the principles pf the reservoir
physics. Therefore, reservoir engineer knowledge and inputs
are essential to achieve the goal of developing the smart proxy
model. The data input in the database are coming from two
sources; the geo-cellular model (static data) and from the
fluid flow model (dynamic data) at each grid block. Also, the
static and dynamic data from the neighboring grid blocks are
collected to monitor the pressure and saturation movement.
The static data include reservoir structure and grid blocks
information. The dynamic data are the properties that change
with time, such as well production/injection values and the grid
Data TypeStatic Data Dynamic DataGrid Location Grid Injection RateGrid Top Grid Injection CumulativeGrid Thickness Grid Production RateGrid Porosity Grid Production CumulativeGrid Permeability Grid PressureDistance to Injection and Bound-aries
Grid Saturation
TABLE IDATA SELECTED TO DEVELOP SMART PROXY MODEL
block pressure/saturation values. Data selected to construct the
smart proxy are shown in table 1.
C. Data Sampling
Mining data from 31200 grid blocks is generating a huge
data set of 1.5 million records. The tools used in this study
are not able to handle such an amount of data. Therefore, data
sampling is utilized for developing the smart proxy model.
Two sampling methods were verified. First, random sampling
is used with acceptable training and prediction results. Then, a
smart sampling technique designed. In this sampling approach,
the histogram of the targeted output is plotted. Then the
output distribution is divided based on the values of the
targeted output. In this data sampling process, the output
value represented by a high number of data will take a lower
percentage of data sampling. On the other hand, the values
with less number of data will take a higher proportion of the
data sampled. This sampling process will give the proxy model
the required data heterogeneity for a better training. Figure 6
explains the smart sampling procedure.
Fig. 6. Smart Sampling Technique for Pressure Data
D. Neural Networks Development and Training
A neural network is designed for each of the three reservoir
properties investigated in this paper (pressure, oil saturation,
and water saturation). The algorithm used to construct the
neural networks is Back Propagation. In this algorithm, the
error for each output is back-propagate to the input in order to
adjust the weights in each layer of the neural network [12]. The
network typically consists of three layers; input layer, hidden
layer, and the output layer. Each neural networks developed
in this work has 64 inputs (table 1), 90 hidden layers, and
1 output. The selection of the inputs is followed by data
partitioning. The objective of data partitioning is to divide the
input data during the training process into training data-set,
validation data-set, and testing data-set. Random partitioning
is used in this study (80% of the input data is assigned to
training set, 10% is assigned to validation set, and 10% is
assigned to testing set).
Once the network is constructed, the training process starts
and the network performance can be monitored using several
visualization plots in the software used [13].
V. RESULTS
A. Training Results
The static and dynamic input data (table 1) have been
gathered for 10 years (from 1953 to 1963). The gathered inputs
are used to train the neural networks for the targeted reservoir
properties (pressure, oil saturation, and water saturation). For
each property, neural network training is performed. For the
pressure property, the coefficient of determination (R-squared)
for the three data-sets, training, validation, and testing, is 0.99
(figure 7). The same R-squared values are achieved for the
training models for oil saturation and water saturation from
neural networks (figures 8 and 9).
Fig. 7. Training cross plots for the Pressure
B. Validation and Prediction Results
In addition to the objective of replicating the numerical
simulation results, the smart proxy model is verified by testing
its ability to predict the dynamic reservoir properties for the
forthcoming time steps under the same operational constraint.
The smart proxy model is verified by comparing the smart
proxy model prediction results to the numerical reservoir
model. The error is then measured between the two models.
In this study, the smart proxy model (trained neural networks
model) is applied to predict pressure, oil saturation, and water
saturation for the years from 1964 to 1968 (which are not
included in the training process). The results show that the
average error of the three reservoir properties is less than 4%.
Fig. 8. Training cross plots for the Oil Saturation
Fig. 9. Training cross plots for the Water Saturation
.
Figure 10 shows the distribution maps of pressure values of
layer 2 in 1964. The top part of the figure shows the pressure
map of the numerical simulator. The middle section of the
figure shows the pressure map of the smart proxy model. Next
to these maps is the pressure scale. At the bottom of the
figure is the error map, which measured between the upper
and middle pressure maps with the error scale next to it.
The same explanation can be written for the figures from 11
to 14 with different reservoir properties, different layers, and
different years.
VI. CONCLUSION
This paper presented an alternative tool for reservoir simu-
lation. The smart proxy model uses data mining and artificial
intelligence techniques, and the development procedure of this
model is discussed. It is shown that the smart proxy model is
able to replicate the complex numerical simulation results at
grid block level in a very short time (seconds).
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Fig. 10. Distribution map of Layer 2 pressure in 1964 (Numerical SimulatorOutput, Smart proxy Output, and Error)
Fig. 11. Distribution map of Layer 13 pressure in 1965 (Numerical SimulatorOutput, Smart proxy Output, and Error)
Fig. 12. Distribution map of Layer 5 pressure in 1968 (Numerical SimulatorOutput, Smart proxy Output, and Error)
Fig. 13. Distribution map of Layer 3 Oil Saturation in 1964 (NumericalSimulator Output, Smart proxy Output, and Error)
Fig. 14. Distribution map of Layer 10 Oil Saturation in 1965 (NumericalSimulator Output, Smart proxy Output, and Error)
Fig. 15. Distribution map of Layer 12 Oil Saturation in 1968 (NumericalSimulator Output, Smart proxy Output, and Error)