Although several researches have been conducted for CO 2 injection in shale gas reservoirs, there is definite lack of study that concentrates on the multi-component transport and geomechanical effect. This paper presents shale gas model for CO 2 injection considering dissolution, molecular diffusion and stress-dependent permeability as well as multi-component adsorption. Based on information of Barnett shale reservoir, a simulation model is constructed for CO 2 flooding. Extended Langmuir isotherm is used to simulate the competitive sorption among the molecules involved. Gas solubility is represented by Henry's law. Co-and counter-diffusive transportsare depicted by Sigmund correlation. Stress-dependent permeability in shale reservoir is considered by exponential correlation with the linear-elastic constitutive model. In the proposed model, the mechanisms and parameters which could influence on CO 2 injection are studied. A series of reservoir simulations based on these effects are performed to study effective injection of CO 2 .Mechanisms of CO 2 injection in shale gas reservoir contribute to both enhanced CH 4 recovery and storage of CO 2 . Desorption of CH 4 in the model with the multi-component adsorption is activated by competitive sorption with the CO 2 which is preferentially adsorbed over CH 4 with a ratio up to 5:1. Molecular diffusion enables CO 2 to displace CH 4 in ultra-low matrix permeability condition. The model with molecular diffusion presents wide spread CO 2 in the reservoir compared with the model not considering molecular diffusion. Because of ultra-low permeability of shale reservoir, effect of diffusion is higher than conventional reservoirs so that it should be considered in the CO 2 injection model of shale reservoir. CO 2 injection supports the reservoir pressure so that effect of stress-dependent permeability is mitigated compared with primary recovery model. In this model, CO 2 injection improves shale gas recovery about 12%. The CO 2 injected in the reservoir exists as a super-critical phase, adsorption trapping, and dissolution trapping of 45.8, 46.5, and 3.6%, respectively. According to reservoir and fracture parameters, amount of each state would be changed. The sensitivity analysis for either enhanced CH 4 recovery or CO 2 storage is conducted to investigate the critical parameters that control these CO 2 -EGR process and CO 2 storage, respectively.This work presents study for mechanisms of CO 2 injection in shale gas reservoir taking account of multi-component adsorption, dissolution, molecular diffusion, and geomechanical effect and sensitivity analysis for uncertain parameters of the shale reservoir. The investigation is important for better understanding and design of CO 2 injection in order to enhance CH 4 recovery and CO 2 storage.
We have reviewed 25 cases of vascularised osteocutaneous fibular transfers carried out between 1982 and 1988. The patients all had chronic osteomyelitis of the tibia, with extensive bone loss and associated soft tissue defects, following severely comminuted fractures. Union of the grafted bone could be seen in radiographs taken 3 to 4 months after operation. The results were generally satisfactory, but there were some complications.
In this study, a mathematical analysis by considering the effect of an actual index of expansion clearly shows a persistent of the existence of subsonic flow after the throat to a down stream in the region of divergent part to produce a supersonic velocity at the exit of a convergent-divergent nozzle. The length of the divergent part where subsonic velocity found is dependent upon the magnitude of the nozzle efficiency and the actual index of expansion. The change in velocity from subsonic, sonic and supersonic occurs only in the divergent part while the corresponding frictionless behavior has the classical features (subsonic in the convergent, sonic at the throat, and supersonic in the divergent). This is mainly due to thermodynamic processes which result a change in enthalpy due to friction and a gain in entropy. The reference conditions are newly derived for an actual frictional flow condition. This design aspect differs in a physical manner corresponding to that from an isentropic flow. An actual nozzle shape for convergent-divergent nozzles is also investigated under a nonisentropic flow condition.
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