Perpendicular Resistivity: Electrical Anisotropy, Rv Versus Rh, and Laminated-Sand Pay

Perpendicular resistivity is the resistivity of a formation measured by current flowing perpendicular to the bedding planes, conventionally written Rv (vertical resistivity) because in a flat-lying bed the direction normal to bedding is vertical. It is paired with parallel resistivity, Rh (horizontal resistivity), the resistivity to current flowing along the bedding planes. In an isotropic formation the two are equal, but in many real reservoirs they are not, and the formation is said to be electrically anisotropic. The physical cause is layering at a scale finer than a logging tool can resolve. A package of thin, alternating conductive and resistive laminae, sand and shale, or water-wet and hydrocarbon-bearing streaks, behaves like a stack of parallel resistors when current runs along the layers and like a series of resistors when current runs across them. Current flowing parallel to bedding takes the path of least resistance through the most conductive laminae, so Rh is low and dominated by the conductive shale or wet sand. Current forced perpendicular to bedding must cross every resistive layer in turn, so Rv is high and reflects the resistive, often hydrocarbon-bearing, streaks. The result is that Rv is greater than Rh, frequently by a factor expressed as the anisotropy ratio Rv/Rh, which can reach 5 or more in finely laminated shaly sands at low resistivity and approaches unity as resistivity rises. This distinction is not academic in the Western Canadian Sedimentary Basin: thin-bedded, laminated sequences such as the Belly River, the Viking, parts of the Cardium, and the Mannville carry productive sand laminae too thin to resolve individually, and a conventional induction tool, which induces current loops circulating in the horizontal plane, reads only Rh. Reading only Rh in a laminated sand systematically underestimates the true resistivity of the hydrocarbon-bearing laminae because the parallel conductive shale shorts the measurement, which in turn drives the calculated water saturation too high and can cause a genuine pay zone to be dismissed as wet. Recovering Rv requires a tool sensitive to the perpendicular direction, historically achieved with triaxial or multi-component induction arrays that excite and measure magnetic dipoles in three orthogonal orientations, allowing both Rv and Rh to be inverted along with the formation dip. With both components in hand, a laminated-sand analysis based on the parallel and series resistor model can split the bulk resistivity into sand and shale fractions and compute a saturation for the sand laminae alone, often turning apparent wet rock into booked pay.

The Laminated-Sand Pay Trap

Consider a 3 m interval of alternating 2 cm sand and 2 cm shale laminae, half net sand, where the sand is gas charged and the shale is conductive. A conventional induction tool reads a bulk Rh perhaps near 4 ohm-m, low enough that an Archie calculation returns a water saturation around 70 percent and the zone is flagged non-commercial. The true sand-lamina resistivity, recovered from Rv via a tensor resistivity model, may be 20 ohm-m or higher, corresponding to a sand water saturation near 35 percent and clearly productive. The entire economic difference rides on whether the perpendicular component was measured, which is why low-resistivity-pay programs in the WCSB increasingly specify triaxial induction.

Measuring Rv: Triaxial and Multi-Component Induction

A triaxial induction tool carries transmitter and receiver coils oriented along the x, y, and z axes, capturing the full resistivity tensor rather than a single horizontal value. Inversion software solves simultaneously for Rh, Rv, formation dip, and dip azimuth, separating true anisotropy from apparent anisotropy caused by relative dip between the borehole and the beds. The same physics underlies geosteering resistivity in horizontal Montney and Duvernay wells, where the directional response to Rv and Rh contrast is used to keep the wellbore inside the target lamina. Proper Rv recovery demands borehole correction and a dip solution, because an uncorrected deviated well mimics anisotropy.

Related Terms

Perpendicular resistivity is one axis of formation anisotropy and is meaningful only against its companion horizontal resistivity, the parallel-to-bedding value a conventional tool reads. Both are obtained from induction log measurements, and both feed the water saturation calculation, where using Rh alone in a laminated sand drives saturation too high and hides pay.

Real-World WCSB Scenario: Reviving a Belly River Sand near Lochend

An operator re-evaluating a Belly River interval near Lochend in central Alberta had logged a 4 m laminated sand at a bulk Rh of about 5 ohm-m on a legacy induction run, computed a water saturation near 65 percent, and perforated nothing, calling the zone wet. A re-log with a triaxial induction tool returned Rv near 22 ohm-m against the same Rh, an anisotropy ratio above 4, and a laminated-sand model gave a sand water saturation near 38 percent. The interval was recompleted and flowed gas at commercial rate.

The triaxial logging run added roughly CAD 90,000 to the intervention, against an incremental recompletion that booked several hundred thousand dollars of reserves and produced from a sand the original Rh-only interpretation had written off. The case became an internal template for screening older laminated WCSB sands for bypassed low-resistivity pay.