Theis井流注水导致的含水层水平位移与应变

Horizontal displacement and strain of aquifer caused by injecting water into Theis confined system

注水问题的含水层位移模型求解的难点在于边界条件的恰当处理。根据Theis定流量抽水与注水水流模型的反对称特性,假定注水位移模型的无限远通量边界与抽水位移模型的无限远通量边界也具有反对称性,从而得到Theis定流量注水的含水层位移模型解答,发现定流量注水与抽水的含水层骨架颗粒位移速度、累计位移量、径向应变及切向应变的解答均互为反号值。注水过程中含水层在径向有两种形变区,依次为膨胀区和挤压区。在膨胀区和挤压区的界限处,径向位移取得最大值。如果假定含水层顶底板不动,注水导致的地层相对位移足以产生水井或油井套管变形和折断破坏。注水时含水层在切向处于恒拉张状态,这可能导致井壁围岩产生径向放射状张裂缝。

The model of aquifer＇s horizontal elastic displacement caused by water injection is difficult to solve because adequate description of its boundary conditions is unavailable. According to the anti-symmetric characteristics of constant-rate pumping and injection flow in Theis confined systems, it is assumed that their infinite boundaries of bulk flux should be also anti-symmetric and then the solution of aquifer＇s horizontal elastic displacement with constant-rate water injection is derived. The results show that the skeletal solids movement velocity and its accumulated displacement, radial strain and tangential strain are expressed in constant-rate injection process as negative ones as they are expressed in constant-rate pumping process. In the injection process, there are two types of radial deformation areas： extension one is near to the well and compressive one is far from the well. The maximum displacement exists along the line dividing the two areas. If the confining beds of the aquifer are relatively stable, the relative displacement of the aquifer caused by water injection is enough to make well casings of water and oil wells deformed or even damaged. The aquifer keeps extension in tangential direction and the maximum tangential strain locates in the borehole wall, which can lead to radial tensile fractures of well adjacent rock.