Formation Evaluation

Wireline logging principles

A wireline log is recorded by lowering a logging tool on a cable into the borehole and plotting the formation response against depth. Each tool responds to one physical property, so the key to any question is to match the measurement principle with the tool. The main principles are:

• Induction log — measures formation electrical conductivity. A transmitter coil induces eddy currents in the formation, and a receiver reads the resulting secondary field. Because it does not need a current path through the borehole fluid, it works in non-conductive oil-based mud.
• Dual laterolog — measures resistivity by focusing current into the formation, so it requires a conductive mud to carry the current.
• Gamma-ray log — records natural radioactivity emitted by potassium, thorium and uranium in the formation.
• Sonic log — measures the interval transit time of compressional elastic waves.
• Neutron log — responds mainly to hydrogen concentration, that is, the hydrogen index of the formation.
• Density log — measures bulk density, from which the electron density of the formation is derived.
• NMR log — polarises hydrogen protons and measures their induced magnetic moment through the relaxation signal.
• MSFL — the microspherically focused log measures the resistivity of the flushed zone close to the borehole wall.
• FMS — the Formation MicroScanner is a micro-resistivity imaging tool, with button electrodes pressed against the wall, so its response is electrical in origin.

Tools also differ in depth of investigation. Neutron, density and sonic tools read only a limited zone near the wall, whereas deep resistivity measurements investigate the formation over a much larger radial distance.

Porosity well logs

Porosity logs estimate the fraction of pore volume from different physical responses, and the readings differ when the pore fluid or the rock fabric is not simple.

• Density porosity — \phi_D = (\rho_{ma} - \rho_b)/(\rho_{ma} - \rho_f). Example: with \rho_{ma} = 2.65, \rho_b = 2.30 and \rho_f = 1.0 g/cc, \phi_D = 0.35/1.65 = 0.212.
• Sonic porosity — the Wyllie time-average relation \phi_S = (\Delta t - \Delta t_{ma})/(\Delta t_{f} - \Delta t_{ma}). Example: with \Delta t = 80, \Delta t_{ma} = 55 and \Delta t_f = 189 µs/ft, \phi_S = 25/134 = 0.187.
• Neutron porosity — reads total hydrogen-bearing porosity, so it is the reference for total porosity in combination with other logs.
• Secondary porosity — the sonic log responds mainly to interparticle (primary) pores, while density and neutron logs respond to total porosity. The excess of the density or neutron porosity over the sonic porosity indicates vuggy or fracture porosity.

Fluid and tool effects matter for interpretation. Gas has a low hydrogen index, so the neutron log reads low, and gas also lowers bulk density, so the density log reads high. Gas increases the acoustic transit time, so the sonic porosity is overestimated.

• NMR in gas — with a short wait time, the long-relaxing gas signal is not fully polarised, so the NMR porosity is underestimated.

Hydrocarbon initial in place requires porosity, water saturation and net pay. Porosity comes from a neutron or density log, water saturation from a resistivity log through Archie's relation, and net pay from a gamma-ray log.

Log-based lithology and fluid identification

Lithology and fluid type are read from the combined response of several logs.

• Gamma-ray response — clays and organic-rich shales are rich in potassium, thorium and uranium, so they give high readings. Clean sands read low, and clean carbonates and evaporites read lowest. Oil shale gives the highest reading among common rocks because of its clay and organic content.
• Gamma-ray index — the linear index is I_{GR} = (GR - GR_{min})/(GR_{max} - GR_{min}). Example: with GR_{min} = 20 and GR_{max} = 120 API, a reading of 60 API gives I_{GR} = 0.40. Under a linear assumption the shale volume equals this index.
• Neutron-density overlay — in clean sand, a gas zone shows density porosity above neutron porosity, which is the crossover signature. A light oil zone shows a mild separation with neutron porosity slightly above density porosity. A water zone shows the two porosities close together. Shale increases the neutron reading and pushes the points toward the shale response.
• Limit of the crossplot — the neutron-density crossplot identifies gas and shale distribution, but oil and water give similar hydrogen responses, so a resistivity log is needed to separate them.

In a sand-shale sequence, the gamma-ray response, the neutron-density separation and the resistivity together give the lithology and fluid type of each zone.

Sonic log velocity and elastic moduli

The sonic log measures the transit time \Delta t of a compressional wave, and the velocity is the reciprocal of this time. A convenient conversion is V_p (m/s) = 304800/\Delta t (µs/ft). For example, \Delta t = 100 µs/ft gives about 3048 m/s.

The elastic moduli link the velocities to the density:

• Compressional velocity — V_p = \sqrt{M/\rho_b}, where M = K + \tfrac{4}{3}\mu is the P-wave modulus, K the bulk modulus and \mu the shear modulus.
• Shear velocity — V_s = \sqrt{\mu/\rho_b}.
• Ratio of velocities — if K = 2\mu, then M = \tfrac{10}{3}\mu and V_p = V_s\sqrt{10/3} \approx 1.83\,V_s. Example: with V_s = 2000 m/s, V_p \approx 3651 m/s.
• Bulk density from velocity — if V_p and M are known, then \rho_b = M/V_p^2.
• Porosity-based density — the bulk density is \rho_b = (1-\phi)\rho_{ma} + \phi\rho_f, which is used to compute V_p from the moduli when porosity is given.

Fluid velocity depends on the bulk modulus and density, v = \sqrt{K_f/\rho_f}. Dissolved gas in live oil lowers the bulk modulus, so dead oil is faster than live oil. Rising temperature lowers the velocity of oil, so a cold, dead-oil mud has the highest velocity among these cases.

Archie's law water saturation

Archie's law relates the true resistivity of a water-bearing rock to its porosity and water saturation: R_t = aR_w/(\phi^m S_w^n). The parameters are the tortuosity factor a, the cementation exponent m and the saturation exponent n, which is usually taken as 2.

• Formation factor — F = a/\phi^m = R_o/R_w, where R_o is the resistivity of a brine-saturated rock. It is measured on a core plug as the ratio of the saturated-plug resistivity to the brine resistivity.
• Water saturation — S_w = (FR_w/R_t)^{1/n}.
• Flushed zone — the invaded zone is filled with mud filtrate, so S_{xo} = (FR_{mf}/R_{xo})^{1/n}, and the residual hydrocarbon saturation is S_{hr} = 1 - S_{xo}.
• Porosity from the flushed zone — when the invaded zone is taken as fully water-filled, F = R_{xo}/R_{mf}, which gives porosity through a correlation such as F = 0.9/\phi^2 used for water-bearing carbonates.
• Generalised Humble relation — F = a/\phi^m, with the sandstone form F = 0.62/\phi^{2.15}.
• Temperature correction of brine — brine resistivity falls as temperature rises, and the correction can use R_w(T_2) = R_w(T_1)(T_1+6.77)/(T_2+6.77) with temperatures in °F.
• Core resistance to resistivity — R = rA/L, where r is the measured resistance, A the cross-sectional area and L the length of the sample.

Timur permeability chart

The Timur relation estimates absolute permeability from porosity and irreducible water saturation, in the form k \propto \phi^{4.4}/S_{wirr}^{2}. Permeability rises steeply with porosity and falls with the square of irreducible water saturation.

The Timur chart is therefore a plot of porosity on one axis against irreducible water saturation on the other, with curves of constant permeability drawn across it. A point read from porosity and irreducible water saturation gives the permeability directly. Water saturation and true resistivity are not the axes of this chart, because the relation requires the irreducible value.