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Volume 19 Issue 1
Feb.  2008
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Effect of Multipoint Heterogeneity on Nonlinear Transformations for Geological Modeling: Porosity-Permeability Relations Revisited

  • Received Date: 2018-07-15
  • Ananalysisofstatisticalexpectedvaluesfortransformationsisperformedinthisstudytoquantifytheeffectofheterogeneityonspatialgeologicalmodelingandevaluations.Algebraictransformationsarefrequentlyappliedtodatafromloggingtoallowforthemodelingofgeologicalproperties.Transformationsmaybepowers,products,andexponentialoperationswhicharecommonlyusedinwell-knownrelations(e.g.,porosity-permeabilitytransforms).Theresultsofthisstudyshowthatcorrectcomputationsmustaccountforresidualtransformationtermswhichariseduetolackofindependenceamongheterogeneousgeologicalproperties.Inthecaseofanexponentialporosity-permeabilitytransform,thevaluesmaybepositive.Thisprovesthatasimpleexponentialmodelback-transformedfromlinearregressionunderestimatespermeability.Inthecaseoftransformationsinvolvingtwoormoreproperties,residualtermsmayrepresentthecontributionofheterogeneouscomponentswhichoccurwhenpropertiesvarytogether,regardlessofapair-wiselinearindependence.Aconsequenceofpower-andproduct-transformmodelsisthatregressionequationswithinthosetransformationsneedcorrectionsviaresidualcumulants.Ageneralizationofthisresultisthattransformationsofmultivariatespatialattributesrequiremultiple-pointrandomvariablerelations.Thisanalysisprovidespracticalsolutionsleadingtoamethodologyfornonlinearmodelingusingcorrectbacktransformationsingeology.
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通讯作者: 陈斌, bchen63@163.com
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    沈阳化工大学材料科学与工程学院 沈阳 110142

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Effect of Multipoint Heterogeneity on Nonlinear Transformations for Geological Modeling: Porosity-Permeability Relations Revisited

  • 1. Saudi Aramco, Dhahran, 31311, KS

Abstract: Ananalysisofstatisticalexpectedvaluesfortransformationsisperformedinthisstudytoquantifytheeffectofheterogeneityonspatialgeologicalmodelingandevaluations.Algebraictransformationsarefrequentlyappliedtodatafromloggingtoallowforthemodelingofgeologicalproperties.Transformationsmaybepowers,products,andexponentialoperationswhicharecommonlyusedinwell-knownrelations(e.g.,porosity-permeabilitytransforms).Theresultsofthisstudyshowthatcorrectcomputationsmustaccountforresidualtransformationtermswhichariseduetolackofindependenceamongheterogeneousgeologicalproperties.Inthecaseofanexponentialporosity-permeabilitytransform,thevaluesmaybepositive.Thisprovesthatasimpleexponentialmodelback-transformedfromlinearregressionunderestimatespermeability.Inthecaseoftransformationsinvolvingtwoormoreproperties,residualtermsmayrepresentthecontributionofheterogeneouscomponentswhichoccurwhenpropertiesvarytogether,regardlessofapair-wiselinearindependence.Aconsequenceofpower-andproduct-transformmodelsisthatregressionequationswithinthosetransformationsneedcorrectionsviaresidualcumulants.Ageneralizationofthisresultisthattransformationsofmultivariatespatialattributesrequiremultiple-pointrandomvariablerelations.Thisanalysisprovidespracticalsolutionsleadingtoamethodologyfornonlinearmodelingusingcorrectbacktransformationsingeology.

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