Mathematical Models Of Crushed Fragmentation At Broken Area Of Well Casing

At present, after water injection exploitation for a long time at many domestic and foreign oilfield, casing failure well's number increased year by year, while casing broken is one of the main types of casing failure. After casing broken, rock would be damaged at broken area, rock fragments would enter the well through broken area under formation fluid's influence and plug the borehole, seriously, rock block would be carried out of the wellhead, the normal production of oilfield is affected, however workover construction technology existing could not settle the rock block stacking problem appropriate. In the paper, on the basis of damage mechanics model of rock mass at broken area and acoustic propagation features of damaged rock, mathematical model of damaged rock fragmentation is established, which could describe the distribution discipline of rock block exactly, provide technology indorsation for casing broken well's repairing and enrich the research methods of rock mechanics.Firstly, rock deformation feature around fracture in casing broken well is analyzed, injury mechanics theory is applied, rock injury phenomenon near broken area is researched, rock injury mechanism around the fracture is analyzed. Secondly, according to the rock's damage formula, considering the effect of high pressure fluid on the stability of sidewall rock under seepage and different degree injury rock's mechanical parameters's difference, sidewall rock around fracture is divided into three areas, including of broken zone, damage zone and elastic zone, injury mechanical model of sidewall rock around fracture is established, radial stress and tangential stress distribution of different damage region is obtained, broken zone radius equation is derived, prediction of rock injury range is completed, affecting factor of broken zone radius is analyzed, destabilizing situation of sidewall around casing break part under hi-pressure fluid′s action is depicted really. At last, in view of damaging bock acoustic characteristic and probability theory, fragmentation calculation model is established using fractal theory, rock fragmentation size and volume which enter borehole could be judged according to casing break part′s size, which could provide reference foundation for workover program's drafting.