Permeability Correlation And Pressure Transient Analysis Of Shale Reservoirs

With the development of new techniques and equipments, the shale gas, an unconventional energy which is considered as unprofitable in the past, are receiving world wide concern in recent years. Shale gas reservoirs are different from traditional reservoirs in many aspects, including the rock property, the gas storage mechanism, the transport behavior and so on. Because of this, applying traditional models and well test methods to shale reservoir may cause unexpected errors. New models and methods which can fully describe the shale reservoir is urgently needed. In this paper we carried out rigorous research on shale gas reservoir as well as well test model, so that we can better understand the flow behavior underground, the production and development strategy. On the other hand, with accurate bottom-hole pressure prediction, we can fulfill guidance and improvement toward production.Knowing that the shale matrix is highly compacted and the pore in which are usually with very small size, molecular dynamics simulation is introduced to study the microscopic transport behavior in shale. Results show that gas molecules are not uniformly distributed across the pore in the nanoscale and great amount of molecules accumulate near the pore wall. Thus, the assumption of uniform distribution fails and the apparent permeability correlation based on this assumption may cause fatal erros. To deal with this, basing on the second-order slip boundary condition of Hongwu Zhang, a new second-order apparent permeability correlation is derived for the shale matrix. Comparison with former models are provided and it is found that the impact of molecule accumulation can not be ignored. Parametric analysis show that the apparent permeability is mostly decided by the TMAC(Tangential Momentum Accomodation Coefficient) and slightly influenced by the ratio of slip distance to mean free path.In this paper, full analysis of storage and tranport characteristics of shale is carried out. Real gas state equation is applied to describe the gas in shale reservoir and calculation methods of the gas property are provided. The natural fracture network is included in the modeling with the dual-porosity assumption. Langmuir adsorption theory is applied to describe the sorption/desorption behavior of shale, and the Palmer-Mansoori model is introduced to approximate the stress-dependent behavior of porosity and permeability. Basing on above assumptions and models, governing equations describing the gas flow behavior in shale is derived and then linearized basing on the pseudo-pressure concept. Finally, a partial differential equation describing the shale gas seepage behavior is given with similar forms to the single-phase case.Considering that shale reservoirs are typically developed applying the Multiple Hydraulically Fractured Horizontal Well technique, the inner boundary condition is proposed discretizing the hydraulic fractures into small source pieces with the assumption of infinite conductivity. The solution to the seepage equation is given in the Laplace domain with the superposition principle. Finding this solution is computationally complicated and unreusable for other different types of boundaries, we derive a Green function solution by defining an auxiliary equation, which can be solved with the Newmann product principle. This solution can be easily applied to different boundary types only by changing the corresponding Green function. Considering wellbore storage and skin effect, the expression for bottom hole pressure with wellbore storage and skin in Laplace domain is provided.With the well test model proposed in this paper, the underground flow characteristics during early time and late time production is analyzed. The bottomhole pressure and derivative is plotted against time and six flow regime can be detected with different behavior on the plot. Parametric investigation is then carried out to find out the influence of adsorption index, inter-porosity flow coefficient, wellbore storage and skin effect on the bottomhole pressure. Validation of this model with in-situ data shows that the calculated results fit well with the field-test data, which means our model is precise and applicable for shale gas reservoirs. Then basing on the flow characteristics, further simplification assumption is proposed for the case of uniform fracture spacing and half-length.