Summary The EWR-Phase 4 sensor is the first measurement-while-drilling (MWD) electromagnetic resistivity tool to offer multiple depths of investigation by use of measurements made from signals originating at different distances from the receivers. As a propagating-wave resistivity device, it measures four phase shifts and four attenuations. This yields eight different apparent depths of investigation, allowing more meaningful information about the invasion profile.
With the phase-shift measurements alone, the traditional three-parameter step invasion model can be used to obtain the virgin formation resistivity, Rt; the flushed zone resistivity, RXO; and the diameter of invasion, Di. These same four measurements can also be interpreted with a ramp invasion model, a sloped-transition invasion model, and a continuous-monotonic invasion model. For more complex invasion profiles, such as an annular invasion profile, all eight measurements can be used to describe the invasion profile accurately.
Invasion profiling starts with an examination of the trends among measurements. These trends are used to select one or more invasion model(s) to use in the interpretation (step, ramp, sloped transition, continuous monotonic, or annulus). Once the form of a model has been selected, the model parameters are computed by use of a modified Levenberg-Marquardt algorithm, which minimizes the sum of the squares of the differences between the measured and reconstructed resistivities. Examples are presented that compare the results of interpreting invasion following one of the previously stated invasion profiles with one of the others as a reference model. Guidelines on the use of these models are given. Finally, some field examples are analyzed and presented.
Introduction Steady advances have been made in propagating-electromagnetic-wave resistivity sensors since their inception in 1983. The first sensors were capable of accurately measuring the phase shift across a pair of receivers from a single transmitter located 24 in. from the nearest receiver. Attenuation measurements available at that time were not sufficiently accurate to allow resistivity to be determined from attenuation. Multiple-depth-of-investigation capability by means of measurement of phase shift and attenuation was introduced in 1988.
Multiple depths of investigation were achieved by exploiting the fact that phase shift- and attenuation-based resistivity measurements respond differently in the presence of a radial inhomogeneity when they are interpreted vs. a homogeneous model. In most cases where invasion is the only perturbing influence, attenuation-based measurements will provide a reading closer to Rt than phase-shift-based measurements. However, because these are measurements of different properties of the waves, their interpretation is not without ambiguity. For example, it is possible for the phase-shift - and attenuation-based resistivity measurements to provide an indication of invasion when none is present. In addition, attenuation-based measurements are far more sensitive to dielectric effects than phase-shift-based measurements. When dealing with measurements made at a single spacing from a transmitter, these factors can cloud the interpretation. The possibility of making interpretation simultaneously with phase shift and attenuation with a step invasion model as the reference model is discussed in Ref. 7. This approach, known as the combined phase and attenuation (CPA) technique tends to provide a more accurate estimate of Rt than earlier techniques based on phase shift or attenuation alone. However, it suffers from limitations similar to those of interpretations based on attenuation alone, such as not being applicable at high resistivities.
A sensor was introduced in 1991 that provides measurements of phase shift and attenuation at four different transmitter/receiver spacings. One purpose for developing such designs is to provide an indication of invasion and a set of measurements from which one can interpret Rt and RXO. Because Rt and RXO are still not determined directly with these sensors, any interpretation of data from these sensors must still be tied to a reference model. In our analyses, we will examine the effects of assuming step, ramp, sloped-transition, and continuous-monotonic invasion models when the actual invasion profile corresponds to the assumed model and when it does not. We also examine the response of the EWR-Phase 4 tool when the invasion profile includes an annulus.
In all cases, the tool's radial response was forward modeled by use of a modified eigenmode expansion that accounts for the details of the antenna design. In all cases, the invaded zone was divided into a number of small steps and the number of steps was increased until the solutions for the fields at the receivers were constant. All inversions of synthetic and field data were carried out with a modified Levenberg-Marquardt method.
Monotonic Invasion Monotonic Invasion Models.
We have a monotonic invasion profile (Fig. 1) when resistivity varies monotonically with radial distance into the formation from the borehole. Figs. 1b, 1c, and 1d show three different monotonic invasion profiles. Fig. 1b describes a ramp invasion in which the resistivity varies monotonically from RXO at the borehole wall until a fixed radius is reached, after which the resistivity is constant at Rt. In the sloped-transition invasion profile, the invading fluid has flushed the formation out to a fixed radius, producing a constant resistivity to this radius, and there is a monotonic transition from RXO to Rt between this radius and a second radius at which the resistivity is Rt (see Fig. 1c). Step profile invasion is the limiting case of sloped-transition invasion with an infinite slope [i.e., sloped-transition invasion in which the two radii defining the transition are identical (see Fig. 1a)]. The invasion profile of Fig. 1d, introduced by Howard, describes a continuous-monotonic invasion model.
Monotonic Invasion Models. We have a monotonic invasion profile (Fig. 1) when resistivity varies monotonically with radial distance into the formation from the borehole. Figs. 1b, 1c, and 1d show three different monotonic invasion profiles. Fig. 1b describes a ramp invasion in which the resistivity varies monotonically from RXO at the borehole wall until a fixed radius is reached, after which the resistivity is constant at Rt. In the sloped-transition invasion profile, the invading fluid has flushed the formation out to a fixed radius, producing a constant resistivity to this radius, and there is a monotonic transition from RXO to Rt between this radius and a second radius at which the resistivity is Rt (see Fig. 1c). Step profile invasion is the limiting case of sloped-transition invasion with an infinite slope [i.e., sloped-transition invasion in which the two radii defining the transition are identical (see Fig. 1a)]. The invasion profile of Fig. 1d, introduced by Howard, describes a continuous-monotonic invasion model.