Estimation of Oil Saturation Using Neural Network

1. 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

2. 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

4. Fitting Functions • Benson-Anli fitting function S = exp{ (1-J)/a} for J >= 1, where a is unknown parameter • Brooks-Corey fitting function • Thoneer fitting function • O’Meara Unimodel • O’Meara Bimodel

5. 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( ) = Σ ( Sm – S )^2

6. 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(ak+1)< 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

7. 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.

8. 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 • ΔW = - μ əE / əW, where μ is learning rate

9. 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

10. 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

11. 50 patterns training

12. Thank you!