Porosity From the Neutron Log
The response equation for the neutron porosity log also follows the classical form:

      1: PHIN = PHIe * Sxo * PHINw                                            (water term)
                  + PHIe * (1 - Sxo) * PHINh                                       (hydrocarbon term)
                   + Vsh * PHINsh                                                       (shale term)
                   + (1 - Vsh - PHIe) * Sum (Vi * PHINi)                        (matrix term)

WHERE:
  PHINh = log reading in 100% hydrocarbon
  PHINi = log reading in 100% of the ith component of matrix rock
  PHIN = log reading
  PHINsh = log reading in 100% shale
  PHINw = log reading in 100% water
  PHIe = effective porosity (fractional)
  Sxo = water saturation in invaded zone (fractional)
  Vi = volume of ith component of matrix rock
  Vsh = volume of shale (fractional)

To solve for porosity from the neutron log, we assume PHINh, PHINi, PHINsh, PHINw, and Vsh are known. We also assume PHINw = PHINh and Sxo = 1.0 when no gas is present. If gas is indicated, we make assumptions about PHINh and Sxo, usually in the form of a correction factor to the gas free case, as described later.

We usually assume PHINw = PHINh = 1.0, and that PHINsh and Vsh are known.
  Apply lithology and shale corrections:
        2: PHINm = (PHIN = PHINMA) / (PHINW - PHINMA)
        3: PHInc = PHINm - Vsh * PHINSH

Mineral and fluid parameters are shown HERE. Shale properties are selected from the log in an obvious shale zone.

Compute neutron log gas correction.
      4: IF NEUTRONGASSWITCH$ = "ON"
      5: THEN PHIN = KN * PHIN

WHERE:
  KN = neutron gas correction factor (fractional)
  PHIN = porosity from neutron log corrected for lithology or gas (fractional)
  PHInc = porosity from neutron log corrected for shale (fractional)
  PHINSH = apparent neutron log porosity of 100% shale (fractional)
  Vsh = volume of shale (fractional)

COMMENTS:
A chart to solve this equation, along with the lithology shifts can be found below.


Chart for Estimating Shale Corrected Neutron Porosity

KN is in the range of 1.0 to 3.0 depending on depth of invasion, gas density and logging tool type. Use local experience. Apply this correction only if gas is known to be present and log reading is still too low after lithology corrections.

The neutron log corrected for shale is one of the least accurate methods and should only be used if no other porosity data is available. This is common for wells drilled prior to 1957 or for wells logged through casing or drill pipe.

NOTE: If neutron log is on a scale (sandstone, limestone) that does not match the rock mineral, lithology corrections are required.

NUMERICAL EXAMPLE:
1. Assume data from Sand "D" in Classic Example 1
    PHIN = 0.28
    PHINSH = 0.30
    Vsh = 0.33
    Neutron log type = CNL
    CNL / FDC units = Sandstone
Rescaling is not required, as log is in correct units.
No gas correction is required.

PHInc = 0.28 - 0.33 * 0.30 = 0.18
 

Porosity from ANCIENT Neutron Logs
Old style gamma ray neutron (GRN) logs are un-scaled neutron logs recorded in counts per second or API units. They are common in ancient wells. The log carries a gamma ray curve (GR) in the left hand track and a neutron curve (NEUT) in the right hand track. No borehole or casing corrections have been applied to these logs. Neutron log deflections to the left (lower count rate) represent higher porosity.

A large number of charts for specific tools, spacings, borehole conditions and rock types were available from service companies, such as the one shown below. These may no longer be easily found today, and the semi-logarithmic approach described below works well except in very low porosity .


GNT-F or G neutron porosity interpretation chart. Hundreds of such charts exist for dozens of tools for a large range of hole sizes, mud weights, and casing sizes. most are not contained in conventional chart books. Some are available on the Denver Well Log Society CD set sold by SPWLA.

There were three source types used (RaBe, PuBe, and AmBe) and several source - detector spacings (15.5 and 18.5 inches were common), combined with hole size, mud weight, and casing variations, leading to a plethora of transforms. Some service companies didn't have a lot of faith in their charts - one used the term "Strata Index" instead of "Porosity" on the Y-axis.

If no appropriate chart exists, or if you don't believe in them, it is expedient to use the "High porosity- Low porosity" method. A logarithmic scale can be applied algebraically with the following formulae using the high porosity/low porosity method.

Calculate slope and intercept of semi-logarithmic relationship between neutron count rate and porosity:
      1: SLOPE = (log (PHIHI / PHILO)) / (CPSHI - CPSLO)
      2: INTCPT = PHIHI / 10 ^ (CPSHI * SLOPE)

Calculate total porosity:
      3: PHIn = INTCPT * 10 ^ (SLOPE * NCPS)
      4: PHIe = PHIn - (Vsh * PHINSH)

WHERE:
  CPSHI = GRN counts at high porosity point (cps)
  CPSLO = GRN counts at low porosity point (cps)
  NCPS = neutron log reading in CPS or arbitrary units (cps)
  PHIHI = high porosity point (fractional)
  PHILO = low porosity point (fractional)
  PHIn = apparent neutron log porosity, uncorrected for shale (fractional)

COMMENTS:
The graphical solution to this formula is given below. Complete gas, shale and matrix corrections will still be required and are detailed in the following sections.


Chart for Estimating Porosity from Neutron Counts per Second - no shale correction.
A graph like this must be made for each well to be analyzed since the original logs were
seldom calibrated to any fixed standard.

A large number of charts for specific tools, spacings, borehole conditions and rock types are available from service companies.

RECOMMENDED PARAMETERS:
PHIHI should be in the range 0.20 to 0.35.
PHILO should be in the range 0.01 to 0.05, and cannot be zero.

NUMERICAL EXAMPLE:
1. Assume an old GRN log where:
    PHIHI = 0.30
    PHILO = 0.01
    NCPS = 2500 cps
    CPSHI = 1500
    CPSLO = 4500
   
    SLOPE = (log (0.30 / 0.01)) / (1500 - 4500) = - 0.000492 (rounded to - 0.0005)
    INTCPT = 0.30 / 10 ^ (1500 * (-0.0005)) = 1.6432
    PHIn = 1.6432 * 10 ^ (-.0005 * 2500) = 0.096


  NEUTRON ENVIRONMENTAL CORRECTIONS
Environmental corrections are based on the following equations, taken from “Experimental Determination Of Environmental Corrections For A Dual-Spaced Neutron Porosity Log”, by Dan M. Arnold and Harry D. Smith, Jr., SPWLA June 1981, updated January, 1982. These are for the Welex-Halliburton tool. Equations for other tools will vary somewhat due to differences in tool design and experimental error.

In open hole, borehole size corrections are normally made automatically  during logging based on the caliper log, For cased hole, borehole size, casing thickness, and cement thickness corrections are made automatically, based on input parameters. The equations for the remaining corrections are often used in computer post-processing of the log. All porosity values and corrections are in fractional porosity units.

Basic Porosity Equation
      1: IF NRAT <= 200
      2: THEN PHIN = - 2.552 * 10^-2 + 2.513 * 10^-3 * NRAT - 0.930 * 10^-6 * NRAT^2
      3: ELSE PHIN =  2.2754 - 1.980 * 10^-2 * NRAT + 5.311 * 10*-5 * NRAT^2

Where:
  NRAT = ratio of short spaced to long spaced detector count rates
  PHIN = raw neutron porosity before corrections (fractional)

Borehole Size Correction
      4: Kbh1 = (CAL - 8) * (-0.0025 - 0.1063 PHIN + 0.5419 PHIN^2 - 0.6946 * PHIN^2.8)
                   
+ (0.001445 * (CAL - 8)^2) * PHIN
      5: Kbh = MAX (Kbh1, - 0.16)
      6: PHINbh = PHIN + Kbh

Where:
  CAL =  diameter of the borehole (inches)
  Kbh = borehole size correction  (fractional porosity)
  PHINbh = raw neutron porosity corrected for borehole size

This correction has usually been applied at time of logging - do not apply it again.

Equivalent Open Hole Conversion
     7: PHINoh = - 0.0174 + 0.3702 * PHINbh + 2.958 * PHINbh^2 - 4.070 * PHINbh^3 + 3.00 * PHINbh^6

This is the equivalent of limestone porosity (PHIN_LS) before any other corrections are made and is what we read from a compensated neutron log. Further corrections and lithology conversion are shown below..

Mud Cake Correction
      8: Hmc = MAX (0, CAL – BITZ)
Automatic caliper compensated
      9A: Kmc = (- 0.0120 - 0.061 * PHIN + 0.271 * PHIN^2) * Hmc
                     + (- 0.0129 + 0.088 * PHIN - 0.154 * PHIN^2) * Hmc^2
No caliper compensation
     
9B: Kmc = (- 0.0048 - 0.039 * PHIN + 0.353 * PHIN^2) * Hmc
                     + (- 0.0221 + 0.107 * PHIN - 0.195 * PHIN^2) * Hmc^2

Where:
  Hmc = mud cake thickness (inches)
  Kmc = mud cake correction (fractional porosity)

Formation Salinity Correction
    10: Kfs = PHIN * ( - 3.5 * 10^-4 * WS/1000 + 6.0 * 10^-7 * (WS/1000)^2))

Where:
  WS = water salinity (ppm NaCl)
  Kfs = formation salinity correction (fractional porosity)

Borehole Salinity Correction
      11: Kbs.= PHIN * ( - 2.0 * 10^-4 * MS/1000 + 1.9 * 10^-6 * (MS/1000)^2))

Where:
  MS = mud salinity (ppm NaCl)
  Kbs = borehole salinity correction (fractional porosity)

The reference paper uses the same salinity for both formation and borehole (MS = WS) – this only true if invasion is fairly deep.

Mud Weight Correction
For normal mud
      12A: Kmw = PHIN * (1.04 * 10^-2 * (WM - 8) + 3.47 * 10^-4 * (WN - 8)^2)
For barite mud
      12B: Kmw = PHIN * (5.21 * 10^-3 * (WM - 8) + 8.68 * 10^-5 * (WN - 8)^2)

Where:
  WM = mud weight  (pounds per gallon)
  Kmw = mud weight correction (fractional porosity)

Standoff Correction
For standoff X <=
0.5
      13A: A2 = 14 * X
      14A: B2 = 1.6 * X
      15A: C2 = 0.05 * X
For standoff X > 0.5
      13B: A2 = - 6.5 + 25 * X
      14B: B2 = 1.5 - 4.6 * X
      15B: C2 = - 0.08 + 0.21 * X
      16: A1 = A2 + B2 * CAL + C2 * CAL^2

      17: B1 = - 0.0254 + 0.06834 * PHIN - 0.08814 * PHIN^2
      18: C1 = 0.0025 - 0.0081 * PHIN - 0. 00994 * PHIN^2
      19: Kst = B1* A1 + C1 * A1^2

Where:
  CAL = borehole diameter (inches)
  X = standoff (inches)
  Kst = standoff correction (fractional porosity)

Temperature Corrections
      20: Ktc
= (0.008 + 0.062 * PHIN + 0.092 * PHIN^2) * (FT – 75) / 225)

Where:
  FT = borehole temperature (deg F)
  Ktc = temperature correction (fractional porosity)

CASED HOLE CORRECTIONS
Casing Thickness Correction
      21: He = 0.5 * (Dcsg - (Dcsg^2 - 0.3667 * WTcsg)^0.5)
      22: Kcs = 0.171 * (0.3 - He)

Where:
  He = casing thickness (inches)
  Dcsg = outside diameter of casing (inches)
  WTcsg = casing weight (lb/ft)
  Kcsg = casing correction (fractional porosity)

Cement Thickness Correction
      23: Hcmt = 0.5 * (CAL - Dcsg)

      24: Kcmt
= (1.5 - Hcmt) * (0.020 - 0.0667 * PHIN^2) 

Where:
  Hcmt = cement thickness (inches)
  Kcmt = temperature correction (fractional porosity) 

Limestone Porosity
Open Hole - assuming Kbs has been applied at logging time
      25A: PHIN_LS = PHINoh + Kmc + Kfs + Kbs + Kmw + Kst + Ktc

Cased Hole - assuming Kbs has been applied at logging time
      25B: PHIN_LS = PHINoh + Kfs + Kbs + Kmw + Ktc + Kcsg + Kcmt

Borehole size, casing, and cement corrections are normally made automatically during logging, DO NOT APPLY THEM AGAIN. Salinity and temperature corrections may or may NOT have been applied while logging. Some commercial software packages apply ALL corrections with no options to apply only those that are needed. When in doubt, apply NO corrections.

See next section to apply Lithology corrections.


Matrix Offset for Neutron Logs
It is often necessary to rescale a neutron log, which is already in porosity units, for lithology.

PHINm - Neutron Log Porosity Corrected for Lithology
Mud cake thickness correction (SNP only).
     1: PHINmc = PHIN - 0.01 * (max (0, CAL - BITZ) / KX1)

Where:
  BITZ = bit size (inches or mm)
  CAL = caliper (inches or mm)
  KX1 = 1.0 for English Units (inches)
  KX1 = 25.4 for Metric Units (millimeters)

QUICKLOOK METHODS
Sandstone porosity units to limestone units.
    CASE 2a: PHIN_LS = PHIN_SS - 0.03   SNP Log
    CASE 2b: PHIN_LS = PHIN_SS - 0.04    CNL Log

Limestone porosity units to sandstone units.
    CASE 3a: PHIN_SS = PHIN_LS + 0.03   SNP Log
    CASE 3b: PHIN_SS = PHIN_LS + 0.04    CNL Log

MORE RIGOROUS METHODS
If the log is recorded in limestone units and a more accurate lithology correction is desired, use the following formulae. CAUTION: There are ,many tool variations with specific charts for each. The equations below are two published versions and are not guaranteed to be correct or appropriate for your case - check the specific chart for your tool to be sure.

If lithology is quartz and tool type is SNP.
    CASE 4a: PHIN_SS = 0.222 * PHIN_LS^2 + 1.021 * PHIN_LS + 0.024       Schlumberger SNP
    CASE 4b: PHIN_SS = - 0.14 * PHIN_LS^2 + 1.047 * PHIN_LS + 0.0482      Dresser Atlas SNP

If lithology is dolomite and tool type is SNP.
    CASE 5a: PHIN_DL = 0.60 * PHIN_LS^2 + 0.7490 * PHIN_LS - 0.00434     Schlumberger SNP
    CASE 5b: PHIN_DL = 0.34 * PHIN_LS^2 + 0.8278 * PHIN_LS - 0.01249     Dresser Atlas SNP

If lithology is quartz and tool type is CNL.
    CASE 6a: PHIN_SS = 0.222 * PHIN_LS^2 + 1.021 * PHIN_LS + 0.039          Schlumberger CNL
    CASE 6b: PHIN_SS = PHIN_LS + 0.04                                                        Dresser Atlas CNL
    CASE 6c: PHIN_SS =  - 0.4778 * PHIN_LS^2 + 1.220 * PHIN_LS + 0.0311     Welex/Halliburton CNL

If lithology is dolomite and tool type is CNL.
    CASE 7a: PHIN_DL = 1.40 * PHIN_LS^2 + 0.389 * PHIN_LS - 0.01259                                          Schlumberger CNL
    CASE 7b: IF PHIN_DL < 0.10 THEN PHIN_DL = 3.11 * PHIN_LS^2 + 0.102 * PHIN_LS - 0.00133    Dresser Atlas CNL
                    ELSE PHIN_DL = - 0.06
    CASE 7c: PHIN_DL = 1.397 * PHIN_LS^2 + 0.345 * PHIN_LS - 0.0152                                  Welex/Halliburton CNL

If no lithology correction is needed.
    CASE 8: PHINm = PHIN_LS

Finally:
    PHINm = SELECT CASE

WHERE:
  PHIN_LS = original neutron log reading in Limestone units
  PHINm = apparent neutron log porosity corrected for lithology (fractional)


SNP neutron chart for lithology and scale conversions, including salinity corrections (red lines)


CNL neutron chart for lithology and scale conversions, including salinity corrections (red lines)

The charts and math shown above are for older CNL and SNP type neutron logs (NPHI curve). More modern CNL tools have additional porosity transforms (eg TNPH). Refer to the appropriate service company correction chart for newer tools. In particular, epithermal CNL logs have considerably less lithology correction.

NEUTRON LOG PARAMETERS


 

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