Resistivity Index

Key Takeaways

• The Archie equation combined with the resistivity index concept provides the mathematical framework for calculating water saturation from the deep resistivity log: Archie's equation in its standard form is Sw^n = Rw / (phi^m x Rt), where Sw is water saturation (the fraction of pore volume occupied by water), Rw is the formation water resistivity, phi is porosity, m is the cementation exponent, n is the saturation exponent, and Rt is the true formation resistivity measured by the deep induction or laterolog tool; the resistivity index RI = Rt/Ro = Rt/(Rw/(phi^m)) = (phi^m x Rt)/Rw = 1/Sw^n relates the measured deep resistivity (corrected for borehole, invasion, and environmental effects) to the water saturation through the saturation exponent n; determination of Sw from the wireline log therefore requires knowledge of four parameters: Rw (from produced water analysis or the SP log), phi (from the density, neutron, or acoustic log), m (from laboratory measurements on core samples), and n (also from laboratory measurements); errors in any of these four parameters translate directly into errors in the calculated water saturation, and water saturation errors propagate into reserves calculation (because OOIP = GRV x phi x NTG x (1-Sw) for an oil reservoir, and every 5% error in Sw at 80% average porosity-weighted Sw translates into approximately 25% error in hydrocarbon pore volume), making the resistivity index measurement and the saturation exponent determination the most commercially significant laboratory petrophysical measurements for a hydrocarbon reservoir.
• Laboratory measurement of the resistivity index as a function of water saturation uses core plugs desaturated by porous plate or centrifuge drainage (for drainage curves) or resaturated by imbibition (for imbibition curves) to establish different water saturation levels, with the resistivity of the core plug measured at each saturation step by two-electrode or four-electrode methods on brine-saturated samples: the porous plate method (applying gas pressure to the top of the core plug to displace brine from the pore space against the capillary entry pressure of the porous plate, with the plate acting as a semi-permeable membrane that retains the brine at the bottom while gas displaces it at the top) achieves very uniform water saturation distribution across the core plug but is time-consuming (days to weeks per saturation step for tight formations); the centrifuge method (spinning the core plug at increasing rotational speeds to apply capillary pressure and drain brine from the pore space) is faster but less uniform and does not allow electrical measurements at intermediate saturation steps without stopping the centrifuge; the resistivity measured at each saturation step is recorded, and the RI versus Sw data is plotted on log-log paper to determine n from the slope of the best-fit line (n = -log(RI)/log(Sw) for each data pair); the standard deviation of n from repeated measurements on sister plugs from the same formation provides the uncertainty in n that propagates into the water saturation uncertainty and ultimately into the reserves uncertainty.
• The saturation exponent n is strongly affected by wettability, and this sensitivity is the primary reason why resistivity-based water saturation calculations fail in oil-wet or mixed-wettability reservoirs unless the n value is measured under representative wettability conditions: in a water-wet rock, water forms a continuous connected phase along grain surfaces even at low water saturations, maintaining electrical conduction through the interconnected water films and yielding a saturation exponent close to 2.0 (the value predicted by Archie's purely geometric model); in an oil-wet rock, water is confined to isolated pore centers rather than coating grain surfaces, the electrical conduction path through the water phase becomes disconnected at lower water saturations than in water-wet rock, and the resistivity increases more steeply with decreasing saturation (n greater than 2, sometimes 5-10 in strongly oil-wet systems); when the Archie equation with n = 2.0 (the water-wet assumption) is applied to an oil-wet reservoir, the calculated water saturation is overestimated (the reservoir appears more water-wet than it is), which underestimates the hydrocarbon saturation and the reserves; wettability restoration of core plugs before n measurement (using techniques such as aging the core in crude oil at reservoir temperature and pressure for 4-8 weeks) provides n values representative of the in-situ reservoir wettability, which are significantly more accurate inputs to the water saturation calculation than n measured on cleaned, solvent-washed core plugs that have been inadvertently rendered water-wet by the cleaning process.
• Conductive minerals in the reservoir rock — particularly clay minerals (kaolinite, illite, smectite) and pyrite — contribute to the bulk electrical conductivity of the rock independently of the water saturation, causing the Archie equation (which assumes that only the pore fluid conducts electricity) to underestimate water saturation in clay-bearing or pyrite-bearing formations: clay minerals have a surface conductivity (cation exchange capacity, CEC) that allows electrical conduction along the clay surface through exchangeable cations (Na+, K+, Ca2+) in the electrical double layer, even when the bulk pore fluid is not the conduction pathway; the effective conductivity of a shaly sandstone is therefore higher than the Archie conductivity for the same porosity and water saturation, and the deep resistivity log reads lower than it would for a clean sandstone of the same Sw, causing the Archie equation to calculate a higher apparent water saturation (closer to 1.0) than the actual hydrocarbon saturation; the resistivity index concept is modified in shaly sand models (Waxman-Smits, dual-water, Simandoux) to include an additional conductivity term proportional to the CEC and the cation exchange capacity per unit pore volume (Qv), correcting the resistivity for clay contribution before applying the saturation exponent to determine Sw; measurement of CEC on core samples (by the calcium chloride exchange method, ammonium acetate, or methylene blue absorption) provides the calibration data for the clay conductivity correction in these shaly sand water saturation models.
• The resistivity index and saturation exponent are used beyond water saturation calculation in petrophysical studies that relate the electrical properties of rock to its pore geometry: the relationship between RI and Sw on a log-log plot can be non-linear (showing a curve rather than a straight line) when the pore geometry includes pores of very different size and connectivity (bimodal pore systems in carbonates, or dual-porosity systems with matrix and fracture porosity), when conductive minerals other than pore water are present, or when the wettability changes systematically with water saturation (mixed-wettability systems where the contact angle at the pore wall varies with local oil saturation); non-linear RI-Sw relationships require more complex saturation models (the modified Archie equation with variable n, the Swanson model, or the geometric mean model) that provide better fit to the measured data and more accurate Sw predictions than the simple power law; recognition of non-linear RI behavior from laboratory data is a critical quality control step in reservoir petrophysical characterization, because applying a simple Archie n to a non-linear RI-Sw system produces systematic Sw errors that are largest in the hydrocarbon-bearing interval where the RI is highest and the non-linearity is most pronounced.