室内实验规模的出砂数学模拟

为了研究疏松砂岩的出砂特征,根据连续性孔隙介质渗流、微粒释放和微粒运移理论,建立了室内实验规模的出砂数学模型,并采用有限差分法对该模型进行了求解。结果表明,实验条件下数学模拟与物理实验模拟的结果吻合较好。用理论出砂模型模拟了胶体力、水动力导致的出砂和砂粒运移过程中滞留引起的渗透率变化。模拟结果表明,渗流速度高于临界流速才引起冲刷出砂;胶体力和冲刷力是出砂的诱发因素,砂微粒在运移过程中在孔隙表面再沉积和孔喉处被捕集将降低出砂程度;渗透率比值与注水孔隙体积倍数或渗流速度的关系曲线均呈"S"形;在运移过程中,砂微粒滞留导致渗透率比值随岩心长度的变化呈线性降低趋势。

Mathematical simulation of sand production in laboratory

In order to study the sanding behaviors of unconsolidated sandstone, a laboratory-scale mathematical model for sand production was developed on the basis of flow theories for the continuous porous media and sand particle release and migration principles. The model was solved with finite-difference method. The results of mathematical simulation under experimental conditions agreed well with the experimental results. Sanding induced by colloidal and hydrodynamic forces and the change of permeability caused by particles retention during migration of particles were simulated with the theoretical sanding model. The simulation shows that sanding will occur when the seepage velocity of medium is over the critical velocity of fluid. The colloidal and hydrodynamic forces are the stimulate factors for sanding. Deposition of sand particles on the porous surfaces and sand capture at throat of pore during migration of particles will lead to reduction in sanding. The relative curves of the ratio of transient permeability to initial permeability with the injected fluid volumes or seepage velocity are like a character "S". The retention of sand particles during migration results in the linear reduction in the ratio of transient permeability to initial permeability from the inlet to outlet of sandstone core.