Water Injection into a Low-Permeability Rock - 1 Hydrofracture Growth

In this paper, we model water injection through a growing vertical hydrofracture penetrating a low-permeability reservoir. The results are useful in oilfield waterflood applications and in liquid waste disposal through reinjection. Using Duhamel's principle, we extend the Gordeyev and Entov (1997) self-similar 2D solution of pressure diffusion from a growing fracture to the case of variable injection pressure. The flow of water injected into a low-permeability rock is almost perpendicular to the fracture for a time sufficiently long to be of practical interest. We revisit Carter's model of 1D fluid injection (Howard and Fast, 1957) and extend it to the case of variable injection pressure. We express the cumulative injection through the injection pressure and effective fracture area. Maintaining fluid injection above a reasonable minimal value leads inevitably to fracture growth regardless of the injector design and the injection policy. The average rate of fracture growth can be predicted from early injection. A smart injection controller that can prevent rapid fracture growth is needed.     

基于扩展有限元的页岩水平井多裂缝模拟研究

页岩储层水平井分段多簇压裂簇间距优选是压裂技术的关键,建立了水力压裂流固耦合数学模型,基于扩展有限单元法模拟多条裂缝的扩展过程,研究多条裂缝同时扩展的转向规律,以及应力干扰、水平主应力差、裂缝间距等因素与裂缝转向角度的关系.结果表明:应力干扰作用对裂缝宽度具有限制作用,单条裂缝张开宽度比两条裂缝的大;裂缝转角随应力差的减小而增大,随压裂时间的增加而增大.簇间距越小,应力干扰越强,转角越大,综合主缝均匀扩展、支撑剂填充以及复杂裂缝网络形成等条件,确定最优簇间距为30~40 m.多条裂缝同时扩展时,中间裂缝会受到两边裂缝的限制作用,簇间距越小,限制作用越强,裂缝发育时间越长,扩展速度越慢.     

Water Injection into a Low-Permeability Rock - 2: Control Model

In Part 1, we have demonstrated the inevitable growth of the fluid injection hydrofractures in low-permeability rocks. Thus, a smart controller that manages fluid injection in the presence of hydrofracture extension is highly desirable. Such a controller will be an essential part of automated waterflood project surveillance and control. Here we design an optimal injection controller using methods of optimal control theory. The controller inputs are the history of the injection pressure and the cumulative injection, along with the fracture size. The output parameter is the injection pressure and the control objective is the injection rate. We demonstrate that the optimal injection pressure depends not only on the instantaneous measurements, but it is determined by the whole history of the injection and of the fracture area growth. We show the controller robustness when the inputs are delayed and noisy and when the fracture undergoes abrupt extensions. Finally, we propose a procedure that allows estimation of the hydrofracture size at no additional cost.