Abstract: A casing string is augmented with one or more variable flow resistance devices or “vibrating tools” to facilitate advancement of the casing and distribution of the cement in the annulus once the casing is properly positioned. The method includes vibrating the casing string while advancing the casing down the wellbore or while the cement is pumped into the annulus, or both. After the cementing operation is completed, the devices may be drilled out to open the casing string for further operations. The casing string assembly may include a vibrating tool at the end in place of a conventional float shoe or float collar. Multiple vibrating tools can be employed in the casing string, and they may be combined with conventional float shoes and collars. Additionally, vibrating tools in the form of plugs can be pumped down and landed inside the casing string.

Abstract: Tools and methods for abrasively cutting downhole pipes and casing. The tools and methods are ideally suited for situations where the pipe to be cut or perforated is positioned partly or wholly inside another pipe and damage to the outer pipe must be avoided. The jet nozzles are positioned at a non-normal angle to the target surface to reduce the jets' effective cutting distance. While pumping the abrasive fluid, the jets are supported at a selected radial distance from the target surface so that within a predetermined operating time the jets will cut or perforate the inner pipe but leave the outer pipe substantially intact. The tool may be rotated with a motor to perform cutoff operations or held in a fixed position for perforating.