Geological constraint using probability functions in stochastic mineralogy modeling
Methods and devices for estimating at least one property of a volume of interest of an earth formation from a radiation based measurement. Methods include using an optimization procedure to determine an optimal mineralogical model in dependence upon a secondary dependence relation between tool measurements, the mineralogical model including a mineralogical composition of the volume. The secondary dependence relation may include a relation between a plurality of estimated elemental concentrations for the volume. The mineralogical composition may include a concentration of each mineral of a plurality of minerals of the volume. The relation may include a ratio of a first elemental concentration of the plurality of estimated elemental concentrations and a second elemental concentration of the plurality of estimated elemental concentrations. Methods may include using at least one cost function to determine the optimal mineralogical model, wherein the at least one cost function is determined using the relation.
1. A method for estimating at least one property of a volume of interest of an earth formation from a radiation based measurement, the volume of interest surrounding a borehole intersecting the earth formation, the method comprising:
obtaining tool measurements from the borehole including a response indicative of radiation detected in the borehole;
estimating a plurality of estimated elemental concentrations for the volume using the response;
solving for an optimal mineralogical model comprising apportioning downhole measurement phenomena to candidate minerals by using an optimization procedure to determine the optimal mineralogical model in dependence upon the plurality of estimated elemental concentrations and a secondary dependence relation between the tool measurements, the mineralogical model including a mineralogical composition of the volume, wherein the mineralogical composition comprises a concentration of each mineral of a plurality of minerals of the volume and wherein the secondary dependence relation is indicative of a relative probability between two or more minerals of the candidate minerals, comprising:
constraining the candidate minerals for a solution in dependence upon the secondary dependence relation; and
conducting further operations in the formation in dependence upon the optimal mineralogical model.
2. The method of claim 1 , wherein the secondary dependence relation comprises a relation between two or more of the plurality of estimated elemental concentrations for the volume.
3. The method of claim 1 , wherein the relation comprises a ratio of a first elemental concentration of the plurality of estimated elemental concentrations and a second elemental concentration of the plurality of estimated elemental concentrations.
4. The method of claim 3 , wherein the ratio of the first elemental concentration and the second elemental concentration is used to constrain a mineral which lacks both the element of the first elemental concentration and the element of the second elemental concentration.
5. The method of claim 1 , comprising selecting the optimal mineralogical model from a plurality of candidate models.
6. The method of claim 1 , comprising using at least one cost function to determine the optimal mineralogical model, wherein the at least one cost function is determined using the secondary dependence relation.
7. The method of claim 6 , wherein the at least one cost function is determined in dependence upon a probability function.
8. The method of claim 7 , wherein the relation comprises a ratio between a first concentration of the plurality of estimated elemental concentrations and a second concentration of the plurality of estimated elemental concentrations.
9. The method of claim 1 , comprising deconvolving a response spectrum obtained from the response to estimate the plurality of estimated elemental concentrations for the volume.
10. The method of claim 1 , wherein obtaining tool measurements comprises making a gamma ray measurement using a gamma ray tool.
11. The method of claim 1 , wherein the further operations comprise at least one of: i) geosteering; ii) drilling at least one borehole in the formation; iii) performing measurements on the formation; iv) estimating at least one parameter of interest of the formation; v) installing equipment in a borehole in the formation; vi) evaluating the formation; vii) optimizing development in the formation; viii) optimizing development in a formation related to the formation; ix) optimizing exploration in the formation; x) optimizing exploration in a formation related to the formation; xi) producing at least one hydrocarbon from the formation.
12. The method of claim 1 , comprising displaying the optimal mineralogical model on a display.
13. The method of claim 1 , wherein the relative probability is representative of a geological inconsistency of at least one of the two or more minerals of the candidate minerals with the optimal mineralogical model.
14. The method of claim 1 , wherein constraining the candidate minerals for the solution comprises constraining the candidate minerals to favor at least one of the two or more minerals of the candidate minerals for the solution and disfavor at least one other of the two or more minerals of the candidate minerals for the solution.