Determine a formation's textural parameters using advancing logging data
Examples described herein provide a computer-implemented method for deriving textural properties of a reservoir formation. The method includes acquiring multi-frequency dielectric data (ε meas ). The method further includes applying a dielectric mixing model between different fluid phases to generate an effective fluid permittivity (ε fluid ) by mixing the permittivity of water and hydrocarbon fluids. The method further includes applying the dielectric mixing model between the effective fluid permittivity (ε fluid ) and a matrix permittivity (ε m ). The method further includes minimizing a difference between a measured dielectric response and the dielectric mixing model by optimizing model parameters. The method further includes computing a cementation exponent (m) and a saturation exponent (n) from the multi-frequency dielectric data (ε meas ). The method further includes estimating a formation property based at least in part on the cementation exponent (m) and the saturation exponent (n). A wellbore operation is controlled based at least in part on the formation property.
1. A method for deriving textural properties of a reservoir formation, the method comprising:
acquiring multi-frequency dielectric data (ε meas );
applying a dielectric mixing model between different fluid phases to generate an effective fluid permittivity (ε fluid ) by mixing the permittivity of water and hydrocarbon fluids;
applying the dielectric mixing model between the effective fluid permittivity (ε fluid ) and a matrix permittivity (ε m ) to generate an effective permittivity (ε eff );
minimizing a difference between a measured dielectric response and the effective permittivity by optimizing model parameters, wherein minimizing the difference between the measured dielectric response and the effective permittivity comprises optimizing a water saturation, a textural parameter for water/oil interfaces, and a textural parameter for fluids/matrix interfaces;
computing a cementation exponent (m) and a saturation exponent (n) from the multi-frequency dielectric data (ε meas );
estimating a textural property of the resorvoir formation based at least in part on the cementation exponent (m) and the saturation exponent (n); and
controlling a wellbore operation based at least in part on the textural property of the reservoir formatiom.
2. The method of claim 1 , wherein the effective permittivity (ε eff ) for a porous media, partially filled with water and hydrocarbon fluids, is expressed as:
ε eff =ψ(Ø, S w ,ε w ,ε m ,ε HC ,λ w ,λ HC ,λ m )
where ψ represents the dielectric mixing model, ε eff is the effective, ε w is a permittivity of water, ε HC is a permittivity of hydrocarbon, ε m is the matrix permittivity, Ø is a porosity of a medium, S w is a water saturation, λ w is a textural parameter related to water phase, λ HC is a textural parameter related to hydrocarbon phase, and λ m is a textural parameter related to a matrix.
3. The method of claim 1 , wherein the multi-frequency dielectric data (ε meas ) is measured from the reservoir formation.
4. The method of claim 1 , further comprising computing the matrix permittivity (ε m ) from different minerals.
5. The method of claim 4 , further comprising measuring a measured cementation exponent (m) and a measured saturation exponent (n) from a plurality of core plugs with a formation type similar to a type of the reservoir formation.
6. The method of claim 5 , further comprising:
correlating between the measured cementation exponent (m) and the textural parameter for fluids/matrix interfaces; and
correlating between the measured saturation exponent (n) and the textural parameter for water/oil interfaces.
7. The method of claim 1 , wherein the dielectric mixing model accounts for a polarization between different fluid phases to extract a textural parameter related to the saturation exponent (n), and a polarization between a matrix and the different fluid phases to extract a textural parameter related to the cementation exponent (m).
8. The method of claim 1 , wherein controlling the wellbore operation based at least in part on the textural property of the reservoir formation comprises causing, by an autonomous drilling system, a drilling rig to be autonomously controlled based at least in part on the textural property of the reservoir formation.
9. A method for evaluating petrophysical textural parameters based on acoustic velocity measurements and multi-frequency dielectric measurements, the method comprising:
acquiring the multi-frequency dielectric measurements at a plurality of frequencies using a plurality of transmitters, the multi-frequency dielectric measurements performed at a partially saturated formation at a first depth;
acquiring the acoustic velocity measurements by transmitting and receiving elastic compressional or shear waves inside the partially saturated formation at the first depth;
integrating the acoustic velocity measurements into a dielectric mixing model, the dielectric mixing model generated by mixing a permittivity of multiple fluids in a fluid mixture, to provide an effective permittivity of the multiple fluids and a matrix permittivity;
estimating a textural parameter (λ fluid ) of the fluid mixture or a saturation exponent (n) related to the textural parameter, wherein the estimating includes substituting a matrix textural parameter (λ m ) or a related cementation exponent (m) with a function that includes at least one of a compressional wave velocity (V p ), a shear wave velocity (V s ), and a ratio of the compressional wave velocity (V p ) to the shear wave velocity (V s ); and
controlling a wellbore operation based at least in part on the textural parameter (λ fluid ) of the fluid mixture.
10. The method of claim 9 , further comprising comparing a measured multi-frequency dielectric constant of the partially saturated formation and a dielectric constant calculated from the dielectric mixing model.
11. The method of claim 10 , wherein the comparing is performed using the following equation:
ε eff =ψ(Ø, S w ,ε w ,ε m ,ε HC ,λ w ,λ HC ,αV p )
wherein ψ is the dielectric mixing model, ε eff is the effective permittivity of the multiple fluids, Ø is a porosity of a medium, S w is a water saturation, ε w is a permittivity of water, ε m is the matrix permittivity, ε HC is a permittivity of a hydrocarbon, λ w is a textural parameter related to a water phase, λ HC is a textural parameter related to a hydrocarbon phase, and α is a proportionality constant to relate the compressional wave velocity (V p ) with the cementation exponent (m) from standard core analysis.
12. The method of claim 11 , wherein the compressional wave velocity (V p ) is substituted by another acoustic measurement.
13. The method of claim 10 , wherein the wellbore operation is one of a wireline logging operation or a logging while drilling operation.
14. The method of claim 9 , wherein controlling the wellbore operation based at least in part on the textural parameter of the fluid mixture comprises causing, by an autonomous drilling system, a drilling rig to be autonomously controlled based at least in part on the textural parameter of the fluid mixture.
15. The method of claim 12 , wherein the another acoustic measurement includes at least one of the shear wave velocity (V s ) and the ratio of the compressional wave velocity (V p ) to the shear wave velocity (V s ).
16. The method of claim 12 , further comprising obtaining the function by comparing the compressional wave velocity (V p ), the shear wave velocity (V s ), or the ratio of the compressional wave velocity (V p ) to the shear wave velocity (V s ) to the matrix textural parameter or a cementation exponent for a formation region having a formation type that is similar to the partially saturated formation at the first depth.