多层合采阶梯井产能计算模型的建立与求解

Development and Solution to the Coupling Model of the Productivity of Interbeded Reserviors in Stepped Horizontal Wells

在阶梯井多个生产段同时对多个油层合采时产能预测难度较大。针对该问题,依据渗流力学、工程流体力学、油藏工程和数值分析有关理论,考虑油藏各向异性、渗流干扰、井筒管流压降和钻完井污染等因素,利用离散化处理方法,建立了阶梯井与薄互层油藏耦合的多层合采阶梯井产能计算模型,分析了该模型具有唯一解的充要条件,给出了求解方法。利用某三层薄互层油藏数据进行了实例计算,分析了井筒径向流率、井筒流量和井筒流压的分布规律,发现阶梯井生产过程中,井筒径向流率分布规律满足高阶偶次多项式,流量分布规律满足三次多项式,流压沿井筒呈抛物线状分布且越靠近跟端下降越快,并认为管流摩阻造成的压降和产量损失不可避免;将利用该模型计算的全井产量与Joshi公式的计算结果进行了对比,发现二者仅相差1.79%。研究表明,建立的多层合采阶梯井产能计算模型的计算结果合理,为相关产能预测提供了新方法。

It is difficult to forecast the production capacities of stepped horizontal wells when producing multiple reservoirs at multiple sections.On the basis of the relevant theories such as seepage mechanics,engineering fluid mechanics,reservoir engineering and numerical analysis,a new detailed coupled model of stepped wells and thin interbedded reservoirs was established by utilizing discretization processing and considering factors such as anisotropy,filtering interference,pipe flow pressure drop and contamination caused by drilling and/or completion.This productivity calculation model of multilayer commingled production of stepped wells has a unique solution.Taking a three thin interbedded reservoir as an example,we analyzed with this model the wellbore radial flow rate,wellbore flow and wellbore flow pressure distribution rules of stepped horizontal wells.Numerical simulation results showed that flow friction in the wells should not be overlooked,and the stepped horizontal well flow rate distribution presented the shape of a high-order polynomial,the flow rate distribution adhered to cubic polynomial law,flow pressure distribution stayed within parabolic limits,and pressure dropped faster at the heel section.The entire well production calculated by this model is just 1.79%less than Joshi＇s.It demonstrated that the calculation results for production were reasonable and provided a new method for productivity prediction of stepped horizontal wells.