An improved cuckoo search (ICS) algorithm is developed to identify temperature dependent thermal conductivity for transient heat conduction problems. Kirchhoff transformation is adopted to transform nonlinear transient heat conduction problems into linear problems. The direct problems are solved by boundary element method. Inversion of thermal conductivity is transformed to estimate unknown coefficients, which is solved by ICS algorithm. ICS algorithm is less sensitive to iterative initialization than conjugate gradient method and ICS algorithm has high efficient convergence compared with cuckoo search (CS) algorithm. For ICS, numerical examples indicate that increase of measured point number causes increase of iteration numbers, whereas increase of nest number decreases iteration numbers. The less the measured noise is, the higher the precision of results is. Iteration numbers decrease at the same time. It shows that ICS algorithm is an accurate and efficient method for identification of thermal conductivity.

A double medium mathematical model for coalbed methane displacement with gas injection is established. Multi-physics coupling process containing Darcy flow,adsorption/desorption and diffusion of multiple component gas and variation of porosity and permeability is involved. The model is solved numerically with finite difference method and validity of the model is verified. In example simulation calculations,improved recovery,evolution of produced gas composition and variation of coal seam properties under injection of CO₂、N₂and 70% N₂+ 30% CO₂ are contrastively analyzed. It indicates that injections of CO₂、N₂and their mixed gas are able to improve coalbed methane recovery significantly by a degree over 28 %. N₂ breaks through rapidly after injected,while CO₂ occurs in production well later. Shrinkage /swell effect plays a dominant role in variation of porosity and permeability after gas injection.Adsorption of CO₂ reduces porosity and permeability,while adsorption of N₂ leads their increase.

A local convergence condition of Newton-Laphson's method in solving diseretization nonlinear equation8 of coupled problems is shown and proved.It gives out relation among time-step and space.step and quasi.compres8ion factor. And it provides theoretically an assurance for convergence of Newton.Laphson's method within numerical analysis. Numerical example shows that the time-step in actual calculating can be greater than theoretical value 5lightly.