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

Abstract

AbstractThe authors solve the task set in Part I of the paper, namely they find experimentally the calibration coefficients for the operator Ω(…) of analytical connection between the Langmuir and Oparin equations in high-stress and multiphase coal-bearing rock masses and in hydrocarbon reservoirs (oil, gas, shale, etc.). To this effect, the authors implemented the X-ray micro-/nanodiffraction analysis and in situ mass spectrometry of different-grade coals. Part II of this paper presents the geomechanical invariant \({\mu }_{\Delta }\left(\delta \right)\) and its analog for supramolecular coal structures—\({\mu }^{*}\) meant for the description of nonlinear elastic pendulum wave-caused modulation of the piston mechanism of physicochemical mass transfer and gas exchange processes in high-stress and multiphase coal-bearing rock masses in thermodynamic disequilibrium induced by mineral mining. The canonical-type estimates are given for the influence exerted by temperature and porosity on evolution of supramolecular structure in different-rank coal. As a result, the analytical expression is proposed for the physicochemical parameter \({\mu }_{\Delta }^{*}\) which governs dynamics and kinematics of pendulum waves in coal-bearing rock masses.KeywordsAnalytical connection operator \({\Omega }\)(…)Langmuir and Oparin equationsNonlinear geomechanical and physicochemical processesPendulum wavesCoal-bearing rock massesMultiphase compositionSupramolecular structureMass transfer and gas exchange processesStress stateMass spectrometryX-ray micro-/nanodiffraction analysisCoal ranksGeomechanical invariant \(\mu_\Delta \left( \delta \right)\) and its physicochemical analog \(\mu_\Delta^*\) for supramolecular structures of coal substance