Research On Productivity Of Fractured Horizontal Wells In Shale Gas Reservoir Based On Multi-scale Nonlinear Flow

The recoverable resource of shale gas is abundant in China,which is regarded as an alternative energy of great development potential.Shale is very tight,multi-stage fracturing of horizontal wells(MFHW)is the main effective means to develop shale gas reservoir.As a special kind of reservoir,Shale reservoir has multi-scale pore space.Obviously,the multi-scale pore space may lead to the multi-mechanisms gas flow in shale,such as seepage,ad-desorption,diffusion and slippage.Therefore,the gas linear flow models of conventional reservoirs are not suitable for describing shale gas multi-scale flow.Therefore,this dissertation carried out an in-depth study on the multi-scale flow mechanisms of multi-stage fractured horizontal wells in shale gas reservoir and the following studies were carried out:1)The shale gas storage and transport pore space is mainly comprised of nanopore and micronpore.Through calculating the Knudsen numbers at different pressure and pore scale conditions,It is concluded that the flow type of micro-nanopores in shale mainly includes continuous flow,slip flow and transition flow,in which nanoscale pore is dominated by slippage flow and transition flow,micron pore and fracture are dominated by continuous flow.2)Shale gas is mainly composed of free gas and adsorbed gas.In consideration of vicious flow,Knudsen diffusion and slippage for free gas,ad-desorption and surface diffusion for adsorbed gas,the unified apparent permeability model is established by combining the mechanics of continuous media and molecular kinematics method.This new model is able to calculate the apparent permeability in different flow types.Based on the apparent permeability model,the relevant parameters are comprehensively analyzed,including the temperature,pressure,reservoirs characteristics and gas characteristics.3)Based on the apparent permeability model and point source function of reservoir with infinite boundary,the point source function of box-shaped reservoir with sealed boundary is obtained by mathematical methods such as Poisson summation,Superposition principle and Newman integral principle.According to the presented apparent permeability modle,the reservoir seepage model is established by discreting the fracture into point resource.And the fracture seepage model with consideration of non-uniform distribution along the fracture surface is established.The productivity model of multi-stage fractured horizontal well could be solved by Gauss elimination method.By the in-depth study of this dissertation,the conclusions were obtained as follows:1)It is concluded that the apparent permeability of shale is not affected only by the characteristic of the solid matrix,but also gas characteristic and operating conditions such as temperature and pressure.The apparent permeability is higher at smaller pores and lower pressures.Temperature and gas molar mass have minimal effects on the apparent permeability.Multiple migration mechanisms show different effects in different pore size.The surface diffusion is dominated in the small size pore.Surface diffusion contribution is lower in medium size pores.The vicous flow is dominated in the macro size pore,then is the seepage,knudsen diffusion and surface diffusion.2)When the parameters of the homogeneous closed box-shaped reservoir fracture network are consistent,the production rate distribution of the fracture network in the middle of the production is evenly distributed,but the production rate is distributed uniformly in the early time and late time,and the distribution of the production rate shows a low "U"symmetrical distribution on both sides.For a single fracture network,the flow rate distribution f every discret fracture is a "W" shape symmetrical distribution in the early time,and become a "U" shape symmetrical distribution in the late time.3)The simulation results of productivity model show that the predicted production rate would be smaller than the real production rate when ignoring the multi-scale effect,and the difference increased when the pore size is bigger.Multi-scale effect is higher at smaller pores and lower bottom hole pressures;production rate increases in higher Langmuir volume and Langmuir pressure.The fracture network parameters mainly affect the early production,the production increases when the number of fracture network,permeability of facture network or fracture length increased.The presented multi-scale nonlinear flow models can provide theoretical basis for evaluating and predicting the productivity of shale gas well,and is of great theoretical and practical significance for shale gas reservoir fracture parameter optimization.