Estimation of Oil Saturation Using Neural Network

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Estimation of Oil Saturation Using Neural Network

• Hong Li
• Computer System Technology
• NYC College of Technology CUNY
• Ali Setoodehnia, Kamal Shahrabi
• Department of Technology
• Kean University
• Zahra Shahrabi
• Englehard Corporation

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Introduction

• Estimate oil saturation has been an important
  issue for petroleum engineers
• Engineers attempt to determine parameters that
  produce the best match with observation
• Fitting functions
• Artificial neural network

3
Numerical Method

• Authors previous work modified Newton Method in
  parameter estimation using Leverett J function
• J function value is determined by capillary
  pressure
• Suppose that saturation S is function of Leverett
  J value
• Determine parameters in fitting function
  describing relation between saturation and J value

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Fitting Functions

• Benson-Anli fitting function
  S exp (1-J)/a for J gt 1, where a is unknown
  parameter
• Brooks-Corey fitting function
• Thoneer fitting function
• OMeara Unimodel
• OMeara Bimodel

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Minimization problem

• The determination of parameters is a nonlinear
  least square minimization problem
• Attempt to determine (An) in fitting function
  that produce the best match with observation in
  the sense that minimizes an objective function
• E( ) S ( Sm S )2

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Modified Newton Method

• A numerical method generally consists of three
  steps
• Choose a starting point
• Designate a way to generate a search sequence,
  a0, a1, a2, so that E(ak1)lt E(ak)
• Stipulate a convergence criterion
• Modified Newton method is a decent algorithm that
  ensure the objective function always decrease at
  each step.
• Local minimum might occur

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Artificial Neural Network

• Artificial neural network has been applied in
  different fields for modeling dynamic system
• Feedforward multilayer perceptron with
  backpropagation learning rule has been
  successfully used to model nonlinear static
  systems, where the behavior of the system is not
  function of time.

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Backpropagation Algorithm

• In FMP, input patterns are fed into multilayer
  and propagated forward to the output layer. The
  output is compared with a measured output
• BPA is a generalized least square algorithm that
  minimizes the mean Square Error
• ?W - µ ?E / ?W, where µ is learning rate

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Problem formulation

• Output Saturation
• Inputs underground pressure, permeability,
  location indicator, and rock type indicator are
  major inputs that affect saturation value.
• Nodes in hidden layers try and error between 1
  10

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Simulation

• Data including permeability, pressure, elevation,
  and type indicator and saturation are collected
  from field.
• 50 patterns of actual saturation and estimated
  saturation.
• With the learning rate of 0.1, slop of 0.2 and
  momentum of 0.2, the neural network was selected
  with two hidden layers and each layer has five
  and three nodes respectively

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50 patterns training
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Thank you!