We investigate the influence of finite-length fluid-filled fracture on a tube wave propagation in a borehole using approximate low-frequency formalism. Previous approach provides description of reflection/transmission on an infinite fracture. Here we propose elegant way to treat the effect of the fracture tips and present combined approach that handles interaction of tube wave with fracture of an arbitrary finite length. New formalism is verified by comparison with a finite difference computations.

At low frequencies tube or Stoneley waves represent a dominant arrival propagating along boreholes. They can be excited by the source in a well or by external source due to conversion from other wave types. Tube wave experiences reflection at the bed boundaries, borehole diameter changes and fractures or permeable zones. It was proven in previous studies that 1D effective wavenumber approach provides simple and accurate low-frequency description of tubewave propagation in open boreholes surrounded by radially homogeneous formation. Tube waves become even more dominant in cased boreholes, but casing further modifies wave propagation and reflection/transmission phenomena. In this study we apply 1D effective wavenumber approach to radially inhomogeneous media and demonstrate that it still provides excellent description of low-frequency tubewave propagation. In particular, we focus on three models representative of cased boreholes: reflection from geological interfaces behind casing, reflection from corroded casing section and reflection from idealized diskshaped perforation in cased hole. In all three cases frequency-dependent reflection coefficient obtained by 1D effective method and by finite-difference computations show excellent agreement.

Рассмотрена методика синтеза комплексных дискретных режекторных и селективных фильтров на основе дифференциальных уравнений непрерывных фильтров-аналогов с использованием разностных уравнений. Для получения разностных уравнений, описывающих работу синтезируемых комплексных дискретных фильтров, производные комплексных дифференциальных уравнений заменяются аналогами в виде комплексных разностных уравнений. При правильном выборе периода дискретности частотные свойства синтезированных фильтров практически совпадают с частотными свойствами соответствующих непрерывных фильтров. Приведены примеры проектирования комплексных дискретных режекторных и селективных фильтров методом инвариантных дифференциальных уравнений.

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The post COVID-19 era will undoubtedly present paradigm shifts in operational planning and execution and advanced automation will become an important factor. However, drilling automation without directional drilling (Cayeux 2020) capability will exclude the use of automation in a vast number of fields where precise placement of the wellbore has shifted from a luxury to a necessity. This is important in unconventional plays where automation can make a step change in operational outcomes (Chmela 2020). However, most efforts in automating directional drilling are using bespoke rigs (Slagmulder 2016) and bespoke bottom hole assembly (BHA) that limit operational options. The goal is in designing systems that enable directional drilling automation (Chatar 2018) with existing BHAs. This paper will look at three challenges that were identified and overcome to deploy a vendor agnostic system for automating the directional drilling (DD) process. The three challenges identified here are as follows:Using any mud motor including low-cost motors in a closed loopIntegration with an existing measurement and logging while drilling (MLWD) systemAbility to roll out automation systems on any operations with existing rigs The system is a modification of an operator’s autonomous drilling system (Rassenfoss 2011), designed to use existing rigs, BHAs and have minimum footprint on the rigs for operational use. The system will have a dedicated connection to the rig’s programmable logic controller (PLC) via common industrial protocols including Modbus, EthernetIP or Profinet, a physical connection the MLWD receiver and a brain box with a cloud connection to aggregate, process data and send commands to the rig PLC to execute directional commands. A vendor agnostic system will increase adoption of automated technologies and further drive improvements in operational and business performance.