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# ESTIMATION OF OIL SATURATION - PowerPoint PPT Presentation

ESTIMATION OF OIL SATURATION. Hong Li Computer System Technology NY City College of Technology – CUNY Ali Setoodehnia Kamal Shahrabi Technology Department Kean University. introduction. Estimation of oil saturation has been an important issue for petroleum engineer

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Presentation Transcript

Hong Li

Computer System Technology

NY City College of Technology – CUNY

Ali Setoodehnia Kamal Shahrabi

Technology Department

Kean University

• Estimation of oil saturation has been an important issue for petroleum engineer

• Collectable data includes pressure, rock type, depth and etc.

• Permeability and saturation are not easy to measure during their study of the oil fields

• Engineers attempt to determine parameters that produce the best match with observation.

J value

Fitting

function

saturation

pressure

Leverett J

function

Fitting fuctions has become the problem of parameter estimation by applying different fitting functions

• Benson-Anli

• Brooks-Coery

• Thomeer

• O'Meara Unimodel

• O’Meara Bimodel

Assumptions has become the problem of parameter estimation by applying different fitting functions

• Suppose that saturation S is function of Leverett J function with unknown parameters a = ( a1, a2, …, an), i.e. S = S(J, a), where J function value is determined by capillary pressure.

• (Ji, Smi ) is a set of measured data, J function value and saturation

Problem statement has become the problem of parameter estimation by applying different fitting functions

• Determine parameters (ak) in fitting functions that produce the best match with observation, in the sense that minimizes an objective function depended on parameters (ak).

• objective function is defined as

Numerical method has become the problem of parameter estimation by applying different fitting functions

• A numerical method of optimization generally consists of three steps:

• Choose a starting point, i.e. given initial value of parameters.

• Designate a way to generate a search sequence, A1,… An, such that

E(Ak) < E(Ak-1)

3. Stipulate a convergence criterion

Search algorithm has become the problem of parameter estimation by applying different fitting functions

• The search sequence has the following general form: Ak = Ak +λk Dk

• Search method: it only utilizes values of objective function

Dk = -E(Ak)

Newton Method has become the problem of parameter estimation by applying different fitting functions

• Newton Method: It utilizes the gradient of objection function and Hessian matrix (second order derivatives of objection function with respect to parameters), denoted by G and set the search direction

Dk = -G-1E(Ak)

Advantage and disadvantage has become the problem of parameter estimation by applying different fitting functions

• rapidly converge and be more robust when number of parameters is small

• When is not close to the minimum, is not necessarily positive definite

• Given initial guess of parameters, has become the problem of parameter estimation by applying different fitting functions, suppose that the first derivative of E() with respect to parameters is denoted by E() and the second derivative of E() with respect to parameters is called Hessian matrix, denoted by

• G= 2 E() / i j

Modified Newton Method has become the problem of parameter estimation by applying different fitting functions

• A descent algorithm using the Newton (or near Newton) direction.

• E() = E(0) +(-  0 )E(-  0 )

• + (-  0 )G (-  0 )

• so, E() = E(0) +G (-  0 )

• Set E()=0 to determined the next iteration point

•  =  0 +G-1 E(0)

Summary have that the Hessian matrix G be positive definite

• The modified Newton method

• applied the second order derivatives of the objective function with respect to the parameters

• promised convergence in computer simulation.

• Numerical analysis was driven to prove the problem solvability and the convergence.

• Computer simulation with collected data from oil field has shown improvement in convergence speed and estimation accuracy.

Future Research have that the Hessian matrix G be positive definite

• Neural Network has been widely applied in different fields to solve problem with parameter estimation

• Preliminary research was done to estimate the oils saturation in simplified situation.

• Prospect of neural network applied in saturation estimation