Estimating mineralogy and reconstructing elements of reservoir rock from spectroscopy data
Methods and systems are provided to learn and apply a mapping function from data representing concentrations of atomic elements in a geological formation (or other data corresponding thereto) to mineral component concentrations in the geological formation (and/or from mineral component concentrations to reconstructed elemental concentrations in the geological formation). The mapping function can be derived from a trained neural network (such as an autoencoder). The output of the mapping function can be used to determine estimates of one or more formation properties, such as formation matrix density, formation porosity, matrix Sigma, formation saturation, other formation property, or combinations thereof.
1. A method for characterizing a geological formation comprising:
a) generating or obtaining data pertaining to concentrations of a set of atomic elements in a part or sample of the geological formation based on at least one measurement of the part or sample of the geological formation;
b) using the data of a) as input to a mapping function that derives at least one of i) concentrations of a set of mineral components in the part or sample of the geological formation or ii) reconstructed concentrations of the set of atomic elements in the part or sample of the geological formation, wherein the mapping function is based on training a neural network; and
c) determining at least one parameter characterizing the part or sample of the geological formation based on the concentrations of the set of mineral components in the part or sample of the geological formation or the reconstructed concentrations of the set of atomic elements in the part or sample of the geological formation,
wherein the mapping function of b) is derived from minimization of a cost function given a set of data comprising: input data, latent space data, output data, uncertainties in the input data, uncertainties in the latent space data, missing data, and data of different fidelities as captured by their uncertainties.
2. A method according to claim 1 , wherein:
the data of a) represents the concentrations of the set of atomic elements in the part or sample of the geological formation or otherwise corresponds to the concentrations of the set of atomic elements in the part or sample of the geological formation.
3. A method according to claim 1 , wherein:
the mapping function derives a vector of data representing at least one of mineral component concentrations in the part or sample of the geological formation and reconstructed elemental concentrations in the part or sample of the geological formation.
4. A method according to claim 1 , wherein:
the mapping function derives a matrix of data representing at least one of mineral component concentrations in a plurality of parts or samples of the geological formation and reconstructed elemental concentrations in the plurality of parts or samples of the geological formation.
5. A method according to claim 1 , wherein:
the part or sample of the geological formation comprises a portion of the geological formation surrounding a borehole, rock core, rock chips, rock drill cuttings, or rock outcrop.
6. A method according to claim 1 , wherein:
the at least one measurement of a) measures photon counts attributable to the part or sample of the geological formation.
7. A method according to claim 6 , wherein:
the photon counts are selected from the group consisting of X-rays and gamma rays.
8. A method according to claim 1 , wherein:
the at least one measurement of a) comprises a nuclear logging measurement.
9. A method according to claim 8 , further comprising:
performing the nuclear logging measurement using a nuclear logging device within a borehole that traverses the geological formation.
10. A method according to claim 1 , wherein:
the at least one measurement of a) is selected from the group consisting of X-ray fluorescence spectroscopy, atomic absorption spectroscopy, mass spectrometry, neutron activation, other measurement(s), or combinations thereof.
11. A method according to claim 1 , wherein:
the at least one parameter characterizing the part or sample of the geological formation is selected from the group consisting of formation matrix density, formation porosity, matrix Sigma, formation saturation, other formation parameter(s), or combinations thereof.
12. A method according to claim 1 , wherein:
the cost function is selected from the group consisting of a mean square error function, a least squares error function, a maximum likelihood error function, a mean absolute error function, and a cross-entropy function.
13. A method according to claim 1 , wherein:
the cost function optimizes or otherwise accounts for both model (aleatoric) uncertainty and data (epistemic) uncertainty.
14. A method according to claim 1 , wherein:
the cost function includes a regularization function to optimize accuracy and robustness.
15. A method according to claim 1 , wherein:
the mapping function of b) includes at least one function that determines at least one of i) uncertainties for the concentrations of the set of mineral components in the part or sample of the geological formation, or ii) uncertainties for the reconstructed concentrations of the set of atomic elements in the part or sample of the geological formation.
16. A system for characterizing a geological formation comprising:
a processor configured to
a) generate or obtain from memory data pertaining to concentrations of a set of atomic elements in a part or sample of the geological formation based on at least one measurement of the part or sample of the geological formation;
b) use of the data of a) as input to a mapping function that derives at least one of i) concentrations of a set of mineral components in the part or sample of the geological formation or ii) reconstructed concentrations of the set of atomic elements in the part or sample of the geological formation, wherein the mapping function is based on training a neural network, and
c) determine at least one parameter characterizing the part or sample of the geological formation based on the concentrations of the set of mineral components in the part or sample of the geological formation or the reconstructed concentrations of the set of atomic elements in the part or sample of the geological formation,
wherein the mapping function of b) is derived from minimization of a cost function given a set of data comprising: input data, latent space data, output data, uncertainties in the input data, uncertainties in the latent space data, missing data, and data of different fidelities as captured by their uncertainties.
17. A system according to claim 16 , wherein:
the data of a) represents the concentrations of the set of atomic elements in the part or sample of the geological formation or otherwise corresponds to the concentrations of the set of atomic elements in the part or sample of the geological formation.
18. A system according to claim 16 , wherein:
the at least one measurement of a) measures photon counts attributable to the part or sample of the geological formation.
19. A system according to claim 18 , wherein:
the photon counts are selected from the group consisting of X-rays and gamma rays.
20. The system according to claim 16 , wherein:
the cost function is selected from the group consisting of a mean square error function, a least squares error function, a maximum likelihood error function, a mean absolute error function, and a cross-entropy function.