低渗透油藏非线性渗流模式应用

采用分段函数模型描述低渗透油藏非线性渗流特征,推导了低渗透油藏稳定渗流的非线性渗流压力分布关系式及产量与生产压差的关系式,并进行了实例计算。结果表明,采用分段模型计算出的压力分布与拟线性的不同,并且在相同的产量下,采用分段模型计算出的生产压差要比拟线性渗流大。因此,对低渗透油藏,可适当加密井网,缩小井距,以减小非线性渗流区域,改善开发效果。

动态渗透率三维油水两相低渗透油藏数值模拟

考虑流体在低渗透油藏流动过程中的非线性渗流特征和启动压力梯度的影响,基于动态渗透率的概念,建立了综合考虑非线性渗流和拟线性渗流的三维油水两相油藏数值模拟数学模型,通过全隐式差分格式建立了低渗透油藏数值模拟数值模型,并采用预处理共轭梯度法进行了求解。通过对均质油藏五点法井网和大庆油田某区块的计算结果表明,启动压力梯度对低渗透油藏的压力场有着显著的影响,在定产条件下,启动压力梯度越大则压力变化越剧烈,压降的影响范围越大,注采井间的压力梯度越高。由于非线性渗流规律较好地表达了流体在低压力梯度下的流动规律和最小启动压力梯度的影响,因此采用非线性渗流规律计算的压力变化要比拟线性情况平缓,更加符合低渗透油藏的开发实际。

低渗透砂岩油藏平面径向渗流流态分布

为了研究低渗透储集层中流体非达西渗流规律,在室内非达西渗流实验的基础上,将低渗透储集层中流体的渗流分为非流动、非线性渗流和拟线性渗流3种渗流状态并给出了各渗流状态的渗流方程,以此为依据,推导出了单相平面径向渗流流态分布规律公式,可用以定量地确定油井周围3种流态的分布范围。两相平面径向渗流流场中各点的饱和度不断变化,拟线性渗流区、非线性渗流区的范围也不断变化,因此在确定流态分布范围时,应在单相最小驱替压力梯度和临界驱替压力梯度公式中乘以两相驱替系数。根据流态分布,提出了确定低渗透油藏合理井距的方法和理论公式。应用该研究成果对国内5个典型加密试验区进行了井距计算,取得了较好的效果。

油层内非线性渗流分布区域确定方法

针对非线性渗流对应的压力梯度范围以及油层内的分布区域进行了研究。依据实验确定最小启动压力梯度,结合最小启动压力梯度、最大启动压力梯度与喉道半径的关系,提出了先计算极限剪切应力,然后再计算最大启动压力梯度的方法。通过回归分析得到非线性渗流对应的压力梯度范围,该压力梯度范围与注采井间压力梯度剖面相耦合,即可得到油层中非线性渗流分布区域,两个井组的实例分析表明,非线性渗流分布区域与油井动态吻合,从而证明该方法可行。根据注采井间压力梯度分布计算公式,提出了新的极限注采井距确定方法,对开发方案中注采井距的确定具有重要意义。

Nonlinear flow numerical simulation of low-permeability reservoir

A nonlinear flow reservoir mathematical model was established based on the flow characteristic of low-permeability reservoir.The well-grid equations were deduced and the dimensionless permeability coefficient was introduced to describe the permeability variation of nonlinear flow.The nonlinear flow numerical simulation program was compiled based on black-oil model.A quarter of five-spot well unit was simulated to study the effect of nonlinear flow on the exploitation of low-permeability reservoir.The comprehensive comparison and analysis of the simulation results of Darcy flow,quasi-linear flow and nonlinear flow were provided.The dimensionless permeability coefficient distribution was gained to describe the nonlinear flow degree.The result shows that compared with the results of Darcy flow,when considering nonlinear flow,the oil production is low,and production decline is rapid.The fluid flow in reservoir consumes more driving energy,which reduces the water flooding efficiency.Darcy flow model overstates the reservoir flow capability,and quasi-linear flow model overstates the reservoir flow resistance.The flow ability of the formation near the well and artificial fracture is strong while the flow ability of the formation far away from the main streamline is weak.The nonlinear flow area is much larger than that of quasi-linear flow during the fluid flow in low-permeability reservoir.The water propelling speed of nonlinear flow is greatly slower than that of Darcy flow in the vertical direction of artificial fracture,and the nonlinear flow should be taken into account in the well pattern arrangement of low-permeability reservoir.

Blow-up Estimates for a Non-Newtonian Filtration Equation

In this paper, blow-up estimates for a class of quasiliuear reaction-diffusion equations(non-Newtonian filtration equations) in term of the nouexistence result for quasilinear ordinary differential equations are established to extends the result for semi-linear reaction-diffusion equations(Newtonian filtration equations).