Summation of Fluids Method

The summation of fluids method is a petrophysical technique for calculating the total porosity of a formation from wireline well logs by algebraically summing the measured apparent porosities from two or more independent log responses, based on the principle that each log measurement responds to the volumetric fractions of the rock's constituent phases (matrix, porosity filled with different fluids) in a characteristic and predictable way; the method is most commonly applied using the neutron log and the density log in combination, where the apparent neutron porosity (phi_N) and the apparent density porosity (phi_D) are averaged (or summed according to a specific weighting formula) to compute the total porosity that cancels the systematic over-reading and under-reading errors that each log exhibits individually in the presence of gas in the pore space; the density log underreads porosity in gas-bearing formations because gas is less dense than the water or oil that fills the pores at surface conditions, making the bulk density appear higher than it would if the same pore space were filled with liquid, and hence the apparent density porosity is less than the true porosity; the neutron log over-reads porosity in gas formations because hydrogen is concentrated in water and oil molecules but sparse in gas molecules, and gas replaces some of the hydrogen-rich liquid that the neutron log is calibrated to, making the formation appear to have lower hydrogen content and therefore higher apparent porosity than if it were liquid-filled; the simultaneous over-reading of the neutron and under-reading of the density in the presence of gas creates the characteristic crossover pattern (where the neutron porosity reading falls below the density porosity reading, a reversal of their normal order in liquid-filled formations) that is the primary qualitative indicator of gas on the neutron-density log pair.

Key Takeaways

The neutron-density crossplot is the graphical implementation of the summation of fluids method for lithology and porosity determination, plotting the apparent neutron porosity on the x-axis against the apparent density porosity on the y-axis for each depth sample, with pure mineral end-points (the neutron and density porosities for quartz sandstone, limestone, dolomite, and anhydrite matrices) defining reference lines that allow identification of the mineralogy from the data point's proximity to each mineral trend: a formation whose neutron-density crossplot point falls on the sandstone trend (typically close to the sandstone line where neutron porosity equals density porosity for zero porosity at quartz bulk density of 2.65 g/cc) is identified as a quartz sandstone, and its porosity is read from the crossplot as the distance of the point from the sandstone line toward the higher-porosity region; a point falling between the sandstone and limestone lines indicates a mixed lithology of quartz and calcite, and the proportion of each mineral is estimated by interpolation between the mineral end-points; in gas-bearing formations, the crossplot point falls above and to the left of the water-filled trend (neutron porosity lower than density porosity for the same total porosity), creating the characteristic "gas effect" triangle on the crossplot that identifies gas-bearing intervals even before formation fluid analysis; the summation of fluids method uses the crossplot geometry to compute the total porosity as approximately (phi_N + phi_D) / 2 for liquid-filled formations or sqrt((phi_N^2 + phi_D^2) / 2) for gas-bearing formations, with the quadratic average (root mean square) formula more accurately compensating for the gas effect on both tools than the arithmetic average.
Shale correction of the neutron-density log pair before applying the summation of fluids method is required in shaly formations because the clay minerals in shale have a large effect on both log readings: shale has a high apparent neutron porosity (due to the hydrogen bound in clay hydroxyl groups and absorbed water in the clay interlayer space, which the neutron log reads as high apparent porosity even though this water is not producible) and a lower apparent density porosity (due to the bulk density of clay being intermediate between clean quartz and formation water); the shale effect shifts the neutron-density crossplot point toward the high-neutron, low-density quadrant for the same true porosity, mimicking the signature of gas and potentially masking a gas response or creating a false gas indication in shaly water-saturated sands; the shale correction subtracts the volumetric shale fraction (Vsh, estimated from the gamma ray log using the linear gamma ray index or other shale indicators) multiplied by the shale neutron and density end-point values from the measured neutron and density readings, correcting them to a shale-free basis before applying the summation of fluids formula; the corrected neutron and density porosity values represent what the logs would read if the shale were replaced by additional clean reservoir rock, and the summation of the corrected values gives the true effective porosity (the porosity in the non-shale portion of the formation that is potentially connected and producible).
Fluid substitution using the summation of fluids method is applied in quantitative log interpretation to estimate how the neutron and density log responses would change if the original pore fluid (gas) were replaced by liquid (oil or water), allowing the petrophysicist to compute the expected log response in a liquid-filled version of the same reservoir and to calibrate the gas effect correction: the Gassmann fluid substitution equations relate the bulk modulus of the saturated rock to the bulk moduli of the dry rock frame, the mineral grains, and the pore fluid, allowing calculation of the density and acoustic impedance that would be measured if the gas were replaced by liquid; for the neutron log, the fluid substitution is simpler — the apparent neutron porosity in a gas-bearing formation is approximately phi_N_gas = phi_N_liquid - delta_phi_gas, where delta_phi_gas is the gas correction factor that depends on the gas saturation, gas density, and hydrogen index of the gas; the summation of fluids method provides the practical approximation of this fluid substitution by computing the total porosity from the neutron-density combination in a way that is less sensitive to the pore fluid than either individual measurement, so that the computed total porosity better approximates the true porosity regardless of whether the reservoir is gas-filled or liquid-filled; the total porosity from the summation is then used to compute the water saturation from the resistivity log (using the Archie equation or a shale-corrected model), and the hydrocarbon saturation is calculated as (1 - Sw), allowing the reserve calculation to proceed from the log-derived porosities without requiring knowledge of the exact gas saturation for the porosity calculation.
Matrix density effects on the density porosity component of the summation of fluids method require correct selection of the matrix density value used to convert bulk density to density porosity: the density porosity formula is phi_D = (rho_matrix - rho_bulk) / (rho_matrix - rho_fluid), where rho_matrix is the assumed grain density of the mineral framework and rho_fluid is the assumed density of the pore fluid; for quartz sandstone, rho_matrix = 2.65 g/cc; for limestone, 2.71 g/cc; for dolomite, 2.87 g/cc; for anhydrite, 2.98 g/cc; if the matrix density assumed in the density porosity calculation does not match the actual mineralogy of the formation (for example, using the limestone matrix density for a dolomite formation), the computed phi_D will be systematically offset from the true porosity, and the summation of fluids result will carry this systematic error; in mixed-mineralogy formations (dolomitic sandstone, calcitic shale, or formations with heavy minerals like pyrite or siderite), the effective matrix density must be estimated from the mineralogy determined by other log measurements (photoelectric factor PE from the density log, neutron-density lithology crossplot, or spectroscopy log) before the density porosity component of the summation can be computed correctly; the spectral gamma ray log (measuring potassium, thorium, and uranium concentrations in addition to total natural gamma ray) and the spectroscopy tool (measuring elemental concentrations of silicon, calcium, iron, magnesium, and other elements from neutron-induced gamma ray spectrometry) provide the mineral composition data needed to compute the correct matrix density for the summation of fluids calculation in complex lithologies.
Total porosity versus effective porosity distinction in the summation of fluids method requires distinguishing between the pore space that contributes to fluid storage and flow (effective porosity) and the pore space occupied by bound water in clay minerals (clay-bound water porosity): the neutron-density summation gives the total porosity that includes all hydrogen-bearing fluids in the pore space, including the clay-bound water that is electrochemically bound to clay surfaces and cannot be produced; the effective porosity (the porosity relevant for hydrocarbon storage and conventional flow) is computed by subtracting the clay-bound water porosity from the total porosity; the clay-bound water volume is estimated as the product of the clay volume (Vclay from log analysis) and the clay-bound water content per unit volume of clay (determined from core measurements of clay mineralogy and cation exchange capacity); in clean sandstones with negligible clay content (Vclay < 5%), the effective porosity is essentially equal to the total porosity from the summation of fluids calculation; in shaly sands with Vclay of 10-30%, the clay-bound water can reduce the effective porosity by 3-10 porosity units below the total porosity, significantly affecting the calculation of movable hydrocarbon volume (hydrocarbon pore volume = phi_effective * (1 - Sw)) and therefore affecting the reserve estimate; the choice between total and effective porosity models in petrophysical interpretation is a significant decision that must be made consistently across the entire formation evaluation to avoid double-counting or omitting the clay-bound water contribution to the total porosity.

Fast Facts

The neutron-density log combination that underlies the summation of fluids method was developed in the 1960s as wireline logging technology advanced to provide independent measurements of the formation's hydrogen content (neutron log) and bulk density (gamma-gamma density log), with the combination offering the redundancy needed to detect gas in the pore space and to separate lithology effects from porosity effects. The crossover of the neutron below the density log (the gas crossover) as a gas indicator was recognized as a practical log interpretation rule in the 1960s and formalized by log analysis charts published by Schlumberger, Halliburton, and Western Atlas in their log interpretation chartbooks that became the standard references for petrophysical log analysts from the 1970s onward.

What Is the Summation of Fluids Method?

The summation of fluids method is a way of combining two different well log measurements — most commonly the neutron porosity and density porosity logs — to get a single, more accurate estimate of the formation's true porosity than either log provides alone. The reason for combining them is that each log has a different and opposite bias in the presence of gas: the neutron log over-reads porosity in gas zones (because gas has less hydrogen than liquid, making the tool think there is more pore space than there really is), while the density log under-reads porosity in gas zones (because gas is lighter than liquid, making the tool think the rock is denser than it really is). These two biases partially cancel each other when the two readings are averaged, giving a combined porosity estimate that is closer to the true total porosity than either reading alone. The crossover pattern on the log display — where the neutron porosity reading dips below the density porosity reading, reversing their normal order — is the qualitative indicator of gas in the pore space that petroleum geologists and log analysts look for when evaluating a potential gas-bearing formation from the wireline logs. The summation of fluids calculation makes that qualitative observation quantitative, providing a corrected total porosity value that can be used in reserve calculations.