Patent EA-000940-B1 (EA)
Title: Determining a parameter in a physical system
Inventor: KOELMAN JOHANNES MARIA VIANNEY
IPC: G01N33/24
Filed: 1996-03-19
Abstract: 1. A method of determining a parameter of a physical model representing the electrical behavior of an earth formation the method comprising: interpreting logging measurements of a plurality of the electrical properties of the earth formation, including a first electrical property and a plurality of physical variables of the earth formation; defining said model by a relationship between at least one electrical property of the earth formation, a plurality of physical variables of the earth formation and said parameter; selecting an incoherence function defining a difference between the measured electrical properties and the electrical properties as calculated from said relationship, said incoherence function being such that measurements determining a weighting factor reflective of the accuracy of the measurements; determining said parameter by minimization of said incoherence function; characterized in that  measuring a second electrical property of the core sample, typical for the earth formation, for various magnitudes of at least one of said physical variables, wherein the incoherence function includes the first and the second electrical property of the earth formation and the core sample, typical for the earth formation. 2. The method of claim 1 wherein the step of determining said parameter by minimization of said incoherence function includes an iterative process. 3. The method of claim 1 or 2, wherein a plurality of said parameters are determined simultaneously by minimizing the incoherence function, each parameter being represented in said relationship. 4. The method of any claims 1 to 3, wherein said incoherence function is selected such that independent measurements of substantially equal accuracy are substantially equally represented therein. 5. The method of any claims 1 to 4, wherein the electrical properties of the earth formation as defined in said relationship and the measured electrical property of the sample are selected from the conductivity, the resistivity and the membrane potential. 6. The method of any claims 1 to 5, wherein the measured electrical property of the composition is selected from the conductivity and the resistivity. 7. The method of any claims 1 to 6, wherein said composition includes a fluid and the model forms a saturation model for the fluid in the composition. 8. The method of claim 7, wherein said composition comprises an earth formation, and the model forms a saturation model for a selected one of brine and hydrocarbon fluid contained in the formation. 9. The method of any claims 1 to 8, wherein said relationship is selected to include the conductivity of the composition and a plurality of composition parameters including, for each component in the composition, physical parameters representing the conductivity and the volume fraction of the component, said relationship being such that the components are substantially equally represented in said relationship by means of said physical parameters. 10. The method of claim 9, wherein the relationship is selected as:   wherein σ0 represents an auxiliary parameter in the form of a conductivity tensor, k=1... N, where N being the number components in the composition, σeff represents the conductivity tensor of the sample, σk represents the conductivity tensor of component k, φk represents the volume fraction of component k, L represents a depolarization tensor. 11. The method of any claims 1 to 8, wherein said model is selected from the group consisting of Waxman-Smits model, the Archie model, the Poupon-Leveaux model, the Simandoux model, the Dual-Water model of Clavier-Coates-Dumanoir, and the effective medium model of Spalburg. 12. The method of any claims 1 to 11, wherein the step of determining said parameter by minimization of said incoherence function is carried out in a minimization algorithm. 13. The method of any claims 1 to 12, wherein said incoherence function is monotonically increasing with the deviation between the measured electrical properties and the calculated electrical properties. 14. The method of any claims 1 to 13, wherein said incoherence function is of the form:   wherein i=1 . . . N, where N being the number of physical measurements, Xi represents the measured electrical property, Yi represents the calculated electrical property, G and H represent functions of the electrical property (H(Xi)>0), F represents a function with  any X  [not equal] 0[F(X)>F(0)], wi represents the weight attributed to the physical measurement (w1 >=0). 15. The method of claim 14, wherein  F(X) = |X|<a>, a  [belongs to]  R, a > 0 G(X) = X<β>, β  [belongs to]  R, β  [not equal]  0 H(X) =1 or H(X) = G(X). 16. The method of any claims 1 to 13, wherein said incoherence function is of the form:   wherein i=1 . . . N, N being the number of physical measurements, Xi represents the measured electrical property, Yi represents the calculated electrical property, wi represents the weight attributed to the physical measurement (wi>=0). 17. The method of any claims 1, wherein said incoherence function is of the form:   wherein i=1 . . . N, N being the number of physical measurements, Xi represents the measured electrical property, Yi represents the calculated electrical property, wi represents the weight attributed to the physical measurement (wi>=0).