Operator of Connection Between the Langmuir Equation and Oparin’s Kinematic Equation for Pendulum-Type Waves. Part I

Abstract

AbstractFor the analytical description of interaction between nonlinear deformation waves and physicochemical mass transfer and gas exchange processes in high-stress different rank coal-bearing rock masses in thermodynamic disequilibrium induced by mining operations, the authors introduce the operator-based connection between the Langmuir equation and Oparin’s kinematic equation of pendulum-type waves. The found phenomenological relations are based on the in-situ X-ray micro/nano diffraction analysis and mass spectrometry data, as well as on the correlation of real-time data on geomechanical properties of coal-bearing rock masses in Kuzbass. The obtained results are applicable in quantification and prediction of similar processes in any hydrocarbon reservoir (shale, oil, gas, etc.) subject to introduction (if necessary) of relevant corrections in the calibration coefficients of Oparin’s connection operator using the procedure described in this part of the paper. The authors review the current advances in the study into the interaction between nonlinear geomechanical and physicochemical mass transfer and gas exchange processes in high-stress and multiphase structural hierarchies of blocks composing rock masses and geomaterials—from supramolecular to macro scale of internal clustering. These scientific advances underlie the operator-type representation of analytical connection between the Langmuir equation and Oparin’s equation for pendulum waves. The further research objective is to find the calibration coefficients for the analytical connection operator. The experimental and theoretical solution of this task is presented in Part II of this paper.KeywordsAnalytical connection operatorNonlinear mass transfer and gas exchange processesStructureLangmuir and Oparin equationsCalibration coefficientsHydrocarbon reservoirsThermodynamic disequilibriumMicro/nano diffraction analysisCoal-bearing strata in KuzbassCoal ranks