Porosity for resource in place calculations

The accurate calculation of porosity at the wellbore is essential for an accurate calculation of original oil in place (OOIP) or original gas in place (OGIP) throughout the reservoir.

Importance of porosity calculation

The porosity and its distribution also need to be calculated as accurately as possible because they are almost always directly used in the water saturation (S_w) and permeability calculations and, possibly, in the net pay calculations. In most OOIP and OGIP studies, only the gross-rock-volume uncertainties have a greater influence on the result than porosity does. Occasionally, where porosity estimates are difficult, porosity is the leading uncertainty. Fractured and clay-mineral-rich reservoirs remain a challenge.

For this discussion, it is assumed that the core data have been properly adjusted to reservoir conditions, that the data from various logs have been reviewed and validated as needed, and that all of the required depth-alignment work has been completed. The petrophysical data sources and databases page discusses the specifics of these topics. This article discusses the use of:

• Core porosity data
• Total and effective porosity
• Core-log calculation approaches
• Consistency of calculations
• Uncertainty.

Use of core porosity data

There are a few preliminary steps in the use of routine core porosity data over the reservoir interval. First, this data set needs to be restricted to those porosity measurements made in pay intervals; the nonpay porosity measurements should be excluded from the porosity calculations. Second, if more than one type of porosity measurements are made, then a hierarchy of these measurements needs to be developed for use in subsequent log/core porosity calculations. For example, it is possible that whole-core Boyles-law porosity measurements, core-plug Boyles-law porosity measurements, and sum-of-fluids porosity measurements are made with several of these measurements made on the same feet of core. Also, if enough of two data types are taken for the same footage of cores, then these data need to be crossplotted to determine if there are any systematic differences between the various types of core porosity data. If more than one porosity measurement are available for a given depth, then only the highest priority in the hierarchy should be included in the log/core porosity calculations; otherwise, there will be unequal weighting in the statistical calculations.

The core porosity measured in shaly sands may include some volume that is associated with the dehydration of certain types of clay minerals (see clay-mineral properties). When smectite (montmorillonite) clay mineral is present as a significant fraction [e.g., a V_cl (not V_sh) of 40% BV], the core porosity may be increased, by approximately 12% BV, solely because of the smectite present. However, when other species of clay are present that have much less clay-mineral physically bound water (e.g., chlorite, illite, kaolinite), the clay water will add little to the core porosity. The effects of the presence of shale and clay minerals must be understood to yield the correct evaluation of the hydrocarbon and water content of a reservoir’s pore network.

Total and effective porosity

The estimation of porosity and water saturation in shaly formations is, where possible, based on various types of laboratory core data. Where core measurements are not available, estimates based wholly on log measurements and selected interpretation models are widely used. Rock models are based on "total" or "effective" porosity and "total" or "effective" S_w definitions. Both definitions account for the usual grain volume and hydrocarbon and capillary-water volumes seen in the porosity of nonshaly sands, and both models include volumes for the clay-mineral physically adsorbed water (sometimes known as clay-bound water) and the volume of dry clay minerals. Fig. 1 is a schematic of a shaly-sand-reservoir model. It indicates the various solid and fluid volumes and pore networks to which core measurements, density, and neutron logs correspond.

• 

  Fig. 1 – Total, effective, and core porosities and their associated water saturations in shaly sands (after Woodhouse and Warner).

Core analysis

This discussion is restricted to siliciclastic rocks; carbonate rocks are not discussed. The porosity measured on core plugs containing clay minerals is dependent on the methods used to clean and dry the sample before it is measured. Cleaning removes oil from the pores. It is widely, if not universally, accepted that drying the core in a vacuum oven at temperatures just above the boiling point of water (110°C) will remove most, or all, of the clay-mineral adsorbed water and the capillary water, but not the chemically bonded hydroxyl groups within the clay minerals. The standard reported core porosity, ϕ_c, is, therefore, a total porosity including the effective porosity, ϕ_e, and the clay-mineral adsorbed water volume, V_clϕ_cl or V_shϕ_sh.

....................(1)

OBM-core S_w determined using Dean-Stark water-volume extraction is also accomplished with boiling toluene at approximately 110°C. Subsequent preparation of the OBM-core sample to measure porosity uses the same maximum temperature.

The core total porosity, ϕ_c, and core water saturation, S_wc, are, therefore, fully compatible with each other. They are used together to accurately quantify hydrocarbon pore volume (V_HCP) [the "core" V_HCP = ϕ_c×(1-S_wc) ]. When smectite clays are present, the core total porosity will be higher than the effective porosity, ϕ_e, as defined in the previous paragraph. However, for the same sample, the core water saturation, S_wt (capillary water plus clay-mineral adsorbed water volumes as a fraction of ϕ_t), will also be greater than S_we (capillary water volume as a fraction of the effective porosity) and will fully compensate the V_HCP for the increased porosity.

V_HCP is used instead of F_HCP in the following discussion because the equalities apply at all scales.

....................(2)

For porosity,

....................(3)

For water saturation,

....................(4)

"Humidity-dried" cores, extracted at temperatures lower than boiling water and partially dried, retain some, or all, of the clay-mineral physically bound water and, therefore, approximate the effective porosity. There is, however, no generally accepted way to measure accurately the values of effective porosity on shaly-formation cores. In smectite-rich shaly sands, humidity-dried porosity is incompatible with the Dean-Stark S_w, and, if combined, the result will understate V_HCP.

Cores extracted at much higher temperatures may give compatible porosity and S_w results, but other problems can sometimes occur. The mineral gypsum dehydrates between 110 and 120°C and must be corrected for in the retort method of water-volume measurements. At 110°C, the structural, chemically bound hydroxyl groups that are part of the clay-mineral lattice are not liberated. However, at very high temperature (500°C or more), these hydroxyl groups react to form water and condense as water in the collecting tubes of a high-temperature retort apparatus. This "structural water" is not captured during standard core analysis but is the hydrogen component of clay minerals that is detected by the neutron porosity log even though it is a part of the solid mineral (Fig. 1).

Log analysis

Log-interpretation methods for porosity and S_w all seek the same end result in terms of porosity and hydrocarbon volume. They are divided into methods that model the effective porosity and the clay-mineral adsorbed water separately and methods that model the total porosity containing both clay-mineral adsorbed water and capillary water. The total porosity is often calculated from the density log and the core grain density, as Fig. 1 shows. Estimates of interconnected porosity (effective porosity) at reservoir conditions come from combinations of many different logs, but all of them attempt to quantify the clay-water volume fraction and subtract it from the total porosity.

Core/log calculation approaches

In calculating porosity values from the core and log data, the first step is to create depth plots and crossplots of the core data against the various log data, like those in Figs. 2 and 3, respectively. These crossplots visually show which of the logs has the strongest correlation with the core porosity measurements. For example, the density log readings vs. core porosity data may have a less-scattered data cloud than the sonic log vs. core porosity data, or, if there are heavy-mineral complications, the opposite may be the case. These crossplots show, and the correlation coefficient, r , of each correlation indicates which of the log/core combinations should be used for the log/core calibration step discussed next. Where possible, it is best to use a single-log porosity estimator because multiple-log estimators will have problems at bed boundaries because of imperfect depth matching. The volumes sampled by different logs also vary, with the neutron log "seeing" a larger volume than the density log.

• 

  Fig. 2 – Well-log and core data from gas-bearing sandstone with predicted porosity and permeability(South Morecambe gas field, offshore UK) After Woodhouse.

• 

  Fig. 3 – Core-plug porosity vs. well-log bulk density with y-on-x and RMA line fits (South Morecambe gas field, offshore UK) After Woodhouse.

The variance of core-plug data is always larger than the equivalent variance of a log because of the small plug volume compared with the larger volume seen by the running-average log reading. One way to reduce the core-plug variance is to create a modified core property curve that is the running average of the core data (a 1-2-1 filter may be appropriate). Core data modified in this way are considered by some to be a superior calibration standard.

Calibration line-fitting

The generally recommended method for obtaining a line-fit for porosity prediction is the "y-on-x" ordinary least-squares regression method. The recommendation presumes that the calibration data set has accurate depth adjustments and is fully representative in all respects of the environment of the equation’s future use. The dependent-variable calibration data, y, the values wanted in the future (e.g., core porosity), are regressed against the selected independent x-variable data [the values available to make the future prediction (e.g., the density log values)]. The same x-variable must be used when the calibration line is applied in the uncored wells. Multiple regression uses more than one independent variable (e.g., the density and GR logs).

For y-on-x regression lines, removal of x-y data outliers, far from the general trend, must be considered. The y-on-x method assumes that the y and x measurements apply to the same rock sample, so data pairs that are not likely to represent similar rocks must be edited from the data set.

Although straight (linear) regression lines are often created with the data in their original form, the regression method applies equally to curved relationships. These are achieved by transforming one or more of the variables. For example, it is common to transform permeability to a logarithm, thereby creating a log 10 (permeability) and linear porosity relationship. This transform preserves the geometric averages of the permeability. As an alternative, a permeability and exponential porosity relationship should be considered because this will preserve the arithmetic averages of permeability, instead of the geometric averages.

To some observers, the y-on-x line-fit initially is awkward and less central than some other line-fits. The reduced-major-axis (RMA) line-fit, for example, follows the intuitive middle ground along the major axis of the data cloud (see Fig. 3). The "structural" line-fits estimate the relationship that would be observed if both the y and x variables were error-free. The RMA line provides this relationship for the particular case when y and x have equal fractional errors. These structural line-fits are not generally used in practice because, for their future use, they apply to error-free x-input data, not the real measured data. The RMA slope is defined by the ratio of the standard deviations (SDs) of y and x together with the sign of r. The y-on-x slope is equal to the RMA slope multiplied by the correlation coefficient r.

The initial impression of y-on-x does not weaken its status as the method with the lowest overall residual error in the required y estimates. When viewed from any position on the x-axis, the y-on-x line is central within the y-data values near that x-position (see Fig. 4). Providing average y-estimates from measured x-data is the main feature of y-on-x lines; however, the y-variance of the calibration data is not preserved by y-on-x predictions and the extremes of the y-range are averaged. The RMA line-fit does honor the y-variance; but if y and x are only moderately correlated, high porosity values are overestimated and low porosity values are underestimated (see Fig. 5). The depths of the RMA-predicted high and low y-values will not be at the same depths as the core high and low values.

• 

  Fig. 4 – Residual plot for y-on-x predicted porosity vs. well-log bulk density. Residuals are evenly distributed around zero (South Morecambe gas field, offshore UK) After Woodhouse.

• 

  Fig. 5 – Residuals plot for RMA-predicted porosity. Residuals trend from negative at high densities to positive at low-density values (South Morecambe gas field, offshore UK) After Woodhouse.

Cores are not always regularly sampled (e.g., at one per foot) and are typically sampled at a lower frequency in the shale intervals. In these cases, the plotted data can sometimes have no trend, for example, in a high-porosity reservoir. External information, not in the standard log/core variables, can be used to provide a useful line-fit. The zero-porosity end of the line might be derived from the core grain-density data. Calibration lines may be calculated by joining this grain density to the means (arithmetic averages) of the x-y data, or a fixed-point regression might be used.

There are circumstances when line-fits such as RMA should be considered. Some reservoirs (e.g., carbonates and finely laminated sandstones) are so heterogeneous that it is difficult, if not impossible, to make accurate core-to-log depth adjustments. In these cases, where the data pairs do not reliably sample similar rocks, core porosity vs. log plots have a poor correlation, and the y-on-x line-fit has a low slope. Here, the RMA line can be a better practical approximation of the underlying core/log relationship. If the core/log correlation is very poor, deterministic or simultaneous-equations log analysis —without using the core—remain useful options.

Calibration lines should be determined for a single population, not a mixture of two or more populations. For example, when density logs are used to predict porosity, if two zones in a well have significantly different lithologies or grain densities, they should, where possible, be separated into different population groups. Likewise, significant grain-density trends across the reservoir area should be honored; however, this process must not be taken to an extreme. Calibration lines with excellent apparent correlations can be achieved with very fine subdivisions of the calibration sample data. Unfortunately, when they are applied in prediction mode to the uncored wells, these "overfitted" calibrations will not yield robust and accurate porosity estimates.

Density log

The density log is often the best log for making porosity estimates. In their simplest form, the density-log readings are considered to be a linear relationship between the zero-porosity limit where the density log reads the rock-matrix density and the 100% BV porosity limit where the density log reads the fluid density.

....................(5)

where ϕ = porosity, ρ_ma = matrix density, ρ_b = formation bulk density, and ρ_fl = fluid density.

This physical relationship assumes constant matrix density and insignificant variation in the fluid saturation and fluid density within the pore system. These are not necessarily the case in real reservoirs. Where core measurements and regression analysis are used to quantify the relationship, the regression coefficients (slope and intercept) do not represent true matrix and fluid-density properties. The regression coefficients are "catch-all" fitted parameters without a physical meaning.

When using the density log for porosity calculations, it should be expected that a different log/core relationship will be found for the aquifer, the oil column, and the gas column because of the different fluid densities in these various fluid environments. Also, there may be curvature of the relationship if the near-wellbore gas saturations increase as porosity increases. This curvature does not always occur, and gas saturations "seen" by the density tool (up to 4 in. into the borehole wall) may be fairly constant. Differences in the core/log relationship are also expected for water-based mud (WBM) vs. oil-based mud (OBM) wells.

In a density-log vs. core-porosity crossplot, the low-porosity portion of the data cloud needs to be handled carefully. Typically, these rocks have lower porosity because of either a much higher clay-mineral content or various cements filling some of the pore system, either of which is likely to alter the average matrix density. Also, the lower-porosity rocks within the hydrocarbon column will have significantly higher S_w. Hence, either of these effects can cause curvature of this crossplot that will need to be accounted for in the correlation of log and core data.

For reservoirs that are buried sufficiently deep and in which no smectite clay mineral is present, the sandstone and shale core grain densities are often similar, and the core porosity of the shale is low, less than approximately 5% BV. In these particular conditions, there are very small volumes of adsorbed water in the clay molecules, ϕ_cl and ϕ_sh in Eq. 3H.2 are low, and it is possible to use the density log alone to estimate effective porosity. Neutron logs usually do not indicate such low apparent shale porosities because of chemically bound hydroxyl groups in clay-mineral structures and neutron-adsorbing elements. Sonic logs in shales usually read higher than quartz travel-time. The sonic and neutron are, therefore, not satisfactory single-log effective-porosity predictors in shaly sands.

Other approaches

Evaluations based on the sonic log follow a logic similar to that of the density-log methods described previously. The sonic-derived porosities are particularly useful when conditions are adverse for the density log, such as in caved holes or when heavy minerals are present. See the acoustic logging page for more information.

Two-log combination solutions, such as density/neutron or density/GR, are useful in carbonate and siliciclastic reservoirs, including shaly sands. Gas-bearing sands may require multiple-log methods. Multiple-log and multivariate regression methods can be used but are often difficult to apply in practice. All multilog methods will have problems where one of the input logs reads incorrectly, for example:

• Hole washouts
• Tool sticking
• Cycle skipping
• GR statistical variations
• Poor depth alignment

Some prefer to use core data for nonquantitative, visual comparison with log-analysis porosity developed from a variety of methods. When the volume of core data is low, making simple qualitative presentations of the measured core may be satisfactory. When there is sufficient core data to provide a representative sample of the formations in one or more wells, quantitative use will lead to more accurate OOIP and OGIP. It is not possible to provide strong guidance on the amount of core required, because the geological and engineering issues of each reservoir differ greatly. However, as a starting point, one might consider coring one well in approximately every 10 if this fits sensibly with the unique parameters of the reservoir under study.

Consistency of calculations and uncertainty

Calculations of porosity and S_w must be compatible with each other. They must both be evaluated within the "total ϕ/S_w system," or both be evaluated within the "effective ϕ/S_w system" (see the discussion on the water saturation page). When preserved OBM ("native") core measurements of both porosity and water saturation are available, the core sample F_HCP [ = ϕ × (1 – S_w)] is, after a few small standard adjustments, usually the best estimate of the V_HCP at each cored depth. This core-based V_HCP can be used to validate, or calibrate, the V_HCP given by either the "effective" or the "total" ϕ/S_w evaluation systems, as calculated from the log data (see Eq. 2).

The uncertainty of porosity evaluations varies from case to case. The porosity of a single cleaned core plug can be repeated to within approximately ± 0.2% BV, where this uncertainty refers to one SD. This very small instrument-repeatability uncertainty does not, however, include the many other noninstrumental variables that affect the systematic uncertainty and overall accuracy. Before the measurement is made, there may be core-plug cleaning problems from native salt in the pore space and incomplete oil removal. The drying time of water-adsorbing clay minerals adds further uncertainty. Surface roughness causes the plug volume to be uncertain especially when there are large grains and vugs. The uncertainty of the average core porosity will be improved when many plugs are selected at approximately one per foot without regard for the rock quality (i.e., randomly). However, because of commercial pressures and common sense, plug samples are not always selected at random, so care must be exercised, especially concerning the porosity values predicted at depths where core is not available. It must also be remembered that 1-in. core-plug samples, taken from each foot of whole core, sample only approximately 2% of the whole core volume.

Log readings are also uncertain, and, for example, the bulk-density-log random uncertainty may be approximately ± 0.015 g/cm³ or approximately ± 1% BV. Systematic errors, such as poor density-tool pad contact with the borehole wall, increase the uncertainty in some wells. Further uncertainty in the final calculated porosity arises from the grain- and fluid-density values (or the related regression coefficients) and from mixed-mineral and shaly-sand effects.

The evaluations of zone-average porosity in the net-pay intervals in a single well that has relevant core control might have an accuracy of approximately ± 1.0% bulk volume (BV). This is largely the result of systematic uncertainty because the random uncertainties will be very small for zone-average values. In other words, an average porosity of 20% BV has an uncertainty range of 19 to 21% BV. This is a one SD estimate. In 32% of cases, zone-average uncertainties of greater than ± 1.0% BV are considered likely. Where core control is not available, these accuracy estimates should probably be doubled. Effective-porosity accuracy in very shaly sands is also more uncertain because of the associated V_sh estimates.

For fractured reservoirs, imaging tools now provide better visualizations of the borehole wall, but quantification of the open-fracture porosity, which may be approximately 0.1 to 1.0% BV, is highly uncertain. Production testing and test analysis are recommended to determine the nature and extent of any fracture system within the reservoir interval.

Nomenclature

Sw	=	water saturation, %PV
Swc	=	connate water saturation, %PV
Swc	=	core water saturation, %PV
Swe	=	water saturation of the effective porosity, %PV
Swt	=	water saturation of the total porosity, %PV
VHCP	=	hydrocarbon pore volume, L3, ft3 [m3]
Vsh	=	shale content, %BV
ρb	=	formation bulk density, m/L3, g/cm3
ρfl	=	fluid density, m/L3, g/cm3
ρma	=	matrix or grain density, m/L3, g/cm3
ϕ	=	porosity, %BV
ϕc	=	core porosity, %BV
ϕcl	=	clay porosity, %BV
ϕe	=	effective porosity, %BV
ϕsh	=	shale porosity, %BV
ϕt	=	total porosity, %BV

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See also

Porosity determination

Petrophysics

PEH:Petrophysical_Applications