Shock-induced borehole waves in fractured formations

Abstract

Natural or hydraulic fractures are of major importance for the productivity of hydrocarbon reservoirs. Besides fracture detection, also the aperture and extension of the fractures are essential for a correct reservoir productivity estimate. There are many ways to detect and measure fractures, such as borehole televiewers and electrical borehole scans. A practical approach to investigate fracture properties is by means of acoustic logging. In this thesis, borehole waves along fractured media are investigated theoretically and experimentally. Theoretically, the effect of a fracture intersecting a vertical borehole can be described by the introduction of a frequency-dependent (dynamic) borehole fluid compressibility which is measured in the laboratory. The dynamic fluid bulk modulus comprises the intrinsic fluid stiffness, the borehole wall distensibility, and the radial fluid seepage into the adjacent (horizontal) permeable zones. The latter two effects tend to diminish the intrinsic fluid’s stiffness, giving rise to a lower effective bulk modulus amplitude and thus to a lower wave speed in the borehole. The radial oscillatory fluid seepage causes viscous friction in the adjacent zones and results in a phase lag between the pressure increase and the compression of the borehole fluid, leading to attenuation of the borehole waves. This seepage effect is expressed in terms of a so-called borehole dynamic wall impedance specifying the radial fluid velocity at the borehole wall as a function of the borehole pressure variations. If a borehole wave travels down from an undamaged zone into a fracture zone, it will encounter an impedance contrast causing the wave to partially reflect and partially transmit, thus revealing the presence of permeable fracture zone adjacent to the borehole. Stoneley wave propagation in porous and fractured formations is studied experimentally by means of a vertical shock tube facility. In this set-up, shock waves in air are generated that travel downwards into a water-saturated cylindrical rock sample that has a borehole drilled along the center axis. In this way, high-energy borehole waves can be generated with excellent repeatability. A logging probe is installed in the borehole to measure the pressure profiles. Reflection from the water-sample interface and from the free water interface can be recorded by means of a fixed pressure transducer mounted in the wall of the shock tube above the sample in the water layer. The fractures in the formation are represented by small horizontal slits in composite cylinders whose upper and lower parts are separated by small spacer poles. In this way, a variable horizontal fracture (slit) aperture can be obtained. Obviously these fractures form an open connection between the borehole fluid and the fluid outside the cylinder. Also mandrel samples are used for horizontal slits that are not open to the fluid outside the cylinder, thus representing fractures with finite radial extension. Wave experiments show that varying fracture widths significantly alter the recorded Stoneley wave pressure signal at fixed depth. The reflection and transmission of borehole tube waves over 1 and 5 mm fractures are correctly predicted by theory. Other wave experiments show that attenuation in boreholes adjacent to porous zones without fractures can be predicted by theory. This technique even allows a direct measurement of the permeability, although the acoustically measured permeability and the permeability measured by falling-head technique still show a significant discrepancy. This technique is directly applicable to fractured porous reservoir core samples.