“Rigid-elastic chimera” pore skeleton model and overpressure porosity measurement method for shale: A case study of the deep overpressure siliceous shale of Silurian Longmaxi Formation in southern Sichuan Basin, SW China

Based on analysis of pore features and pore skeleton composition of shale,a“rigid elastic chimeric”pore skeleton model of shale gas reservoir was built.Pore deformation mechanisms leading to increase of shale porosity due to the pore skeleton deformation under overpressure were sorted out through analysis of stress on the shale pore and skeleton.After reviewing the difficulties and defects of existent porosity measurement methods,a dynamic deformed porosity measurement method was worked out and used to measure the porosity of overpressure Silurian Longmaxi Formation shale under real formation conditions in southern Sichuan Basin.The results show:(1)The shale reservoir is a mixture of inorganic rock particles and organic matter,which contains inorganic pores supported by rigid skeleton particles and organic pores supported by elastic-plastic particles,and thus has a special“rigid elastic chimeric”pore structure.(2)Under the action of formation overpressure,the inorganic pores have tiny changes that can be assumed that they don’t change in porosity,while the organic pores may have large deformation due to skeleton compression,leading to the increase of radius,connectivity and ultimately porosity of these pores.(3)The“dynamic”deformation porosity measurement method combining high injection pressure helium porosity measurement and kerosene porosity measurement method under ultra-high variable pressure can accurately measure porosity of unconnected micro-pores under normal pressure conditions,and also the porosity increment caused by plastic skeleton compression deformation.(4)The pore deformation mechanism of shale may result in the"abnormal"phenomenon that the shale under formation conditions has higher porosity than that under normal pressure,so the overpressure shale reservoir is not necessarily“ultra-low in porosity”,and can have porosity over 10%.Application of this method in Well L210 in southern Sichuan has confirmed its practicality and reliability.

Application of Lagrange＇s equation to rigid-elastic coupling dynamics

A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum mechanics.This paper uses the concept of a variational derivative and its laws of operation to investigate the derivation of Lagrange's equation,which is then applied to nonlinear elasto-dynamics.In accordance with the work-energy principle and the energy conservation law,kinetic and potential energies are proposed for rigid-elastic coupling dynamics,whose governing equation is established by manipulating Lagrange's equation.In addition,case studies are used to demonstrate the application of the proposed method to spacecraft dynamics.

Stability of a Class of Coupled Rigid-elastic Systems With Symmetry-breaking

In this paper, the Poisson structures and Casimir functions, which play an important role in stability analysis of stationary motions, are given for a class of coupled rigid-elastic systems with symmetry-breaking. As a practical example, the specific Casimir function is given for a rigid-elastic coupled body with a fixed point subjected to gravitational force. At last, a set of sufficient conditions for stability of stationary motions of a rigid-elastic body in a circular orbit are given by the energy-Casimir method.

HAMILTONIAN STRUCTURE FOR RIGID BODY WITH FLEXIBLE ATTACHMENTS IN A CIRCULAR ORBIT

Hamiltonian structure of a rigid body in a circular orbit is established in this paper. With the reduction technique, the Hamiltonian structure of a rigid body in a circular orbit is derived from Lie-Poisson structure of semidirect product, and Hamiltonian is derived from Jacobi's integral. The above method can be generalized to establish the Hamiltonian structure of a rigid body with a flexible attachment in a circular or- bit. At last, an example of stability analysis is given.

Planar motion and stability for a rigid body with a beam in a field of central gravitational force

Planar motion for a rigid body with an elastic beam in a field of central gravitational force wasinvestigated, and both of the orbital motion and attitude motion were under consideration. The equations ofmotion of the system were derived by the variational principle, and on view point of generalized Hamiltoniandynamics, the sufficient conditions for the stability of one class of relative equilibria were given by the energy-momentum method.