Method and apparatus for producing a porosity log of a subsurface formation corrected for detector standoff

A method for converting signals representing the die-away of nuclear radiation in a subsurface formation surrounding a borehole into a log representing porosity versus depth within said subsurface formation corrected for the effect of detector standoff from the borehole wall, comprising the steps of:

• a) lowering a logging tool having a source of fast neutrons and a spaced-apart neutron detector into a borehole traversing a subsurface formation whose porosity is to be determined,
• b) irradiating said subsurface formation at an initial depth position within said borehole with fast neutrons from said neutron source,
• c) recording intensity signals representing the die-away of nuclear radiation with said spaced-apart neutron detector after said fast neutrons from said neutron source have passed through and been moderated by said subsurface formation,
• d) generating a model of the die-away of nuclear radiation in a subsurface formation having amplitudes and decay constants varying exponentially in response to borehole, formation and background effects on said intensity signals,
• e) producing weighted moments of said model and of said intensity signals,
• f) producing a ratio of the borehole amplitude to formation amplitude components of said intensity signals derived from said weighted moments,
• g) producing an initial formation decay constant signal from at least formation and thermal neutron background terms of said model and said intensity signals,
• h) producing an epithermal neutron lifetime signal of said formation,
• i) producing an epithermal neutron lifetime correction signal and apparent standoff value S from said epithermal neutron lifetime signal and borehole-to-formation amplitude ratio R using a trained neural network,
• j) producing a standoff corrected epithermal neutron lifetime signal in accordance with a function of said epithermal neutron lifetime signal and said epithermal neutron lifetime correction derived from die-away signals recorded in borehole models at known porosities and conditions of detector standoff from the borehole wall,
• k) traversing said logging tool along said borehole from said initial depth position,
• l) repeating steps b) to j) as said logging tool traverses along said borehole, and
• m) generating a log of porosity versus depth within said subsurface formation corrected for detector standoff from the borehole wall as a function of said standoff corrected epithermal neutron lifetime signal derived from calibrated measurements in borehole models at known porosities and conditions of detector standoff from the borehole wall.

A method for converting signals representing the die-away of nuclear radiation in a subsurface formation surrounding a borehole into a log representing porosity versus depth within said subsurface formation corrected for the effect of detector standoff from the borehole wall, comprising the steps of:

• a) lowering a logging tool having a source of fast neutrons and a spaced-apart neutron detector into a borehole traversing a subsurface formation whose porosity is to be determined,
• b) irradiating said subsurface formation at an initial depth position within said borehole with fast neutrons from said neutron source,
• c) recording intensity signals representing the die-away of nuclear radiation with said spaced-apart neutron detector after said fast neutrons from said neutron source have passed through and been moderated by said subsurface formation.
• d) generating a model of the die-away of nuclear radiation in said subsurface formation having three exponential terms varying in response to borehole, formation and thermal neutron background effects on said intensity signals as follows:
• ##EQU11## where .mu..sub. = borehole decay constant,
• .mu..sub.2 =formation decay constant,
• .mu..sub.3 =thermal neutron background decay constant
• A.sub.1 =borehole amplitude,
• A.sub.2 =formation amplitude,
• A.sub.3 =thermal neutron background amplitude,
• t=time,
• e) determining the expected value of weighted model moments with exponential weighting in accordance with the three-exponential model of step d) as follows:
• ##EQU12## where z.sub.j =weighting function decay constant
• t.sub.a =starting time,
• t.sub.b =ending time,
• f) determining weighted moments of said intensity signals with exponential weighting in accordance with the three-exponential model of step c) as follows:
• ##EQU13## where y(t)=intensity
• g) equating said weighted model moments with said weighted intensity moments;
• E[t.sub.j (t.sub.a,t.sub.b)]=t.sub.j (t.sub.a,t.sub.b)
• h) utilizing said equated weighted model and intensity signal moments from step g) to determine a ratio signal R of the borehole amplitude A.sub.1 to the formation amplitude A.sub.2 components of said intensity signal:
• R=A.sub.1 /A.sub.2,
• i) determining an initial formation decay constant .mu..sub.2 utilizing at least two-exponential terms of said equated weighted model and intensity signal moments from step g) attributable to the formation and thermal neutron background effects,
• j) determining an epithermal neutron lifetime .tau.:
• .tau.=1/.mu..sub.2,
• k) determining an epithermal neutron lifetime correction .DELTA..tau..sub.2 and apparent standoff S from said epithermal neutron lifetime .tau..sub.2 and amplitude ratio R using a trained neural network,
• l) determining a standoff corrected epithermal neutron lifetime .tau..sub.2 * for detector standoff from the borehole wall in accordance with a function f(.tau..sub.2,.DELTA..tau..sub.2), derived from calibration measurements taken in borehole models at known porosities and conditions of detector standoff from the formation:
• .tau..sub.2 *=f(.tau..sub.2, .DELTA..tau..sub.2),
• and
• m) traversing said logging tool along said borehole from said initial depth position,
• n) repeating steps b) to l) as said logging tool traverses along said borehole, and
• o) producing a porosity versus depth log of said subsurface formation corrected for detector standoff from the borehole wall as a function of said standoff corrected epithermal neutron lifetime .tau..sub.2 * derived from calibrated measurements in said borehole models at said known porosities and conditions of detector standoff from the borehole wall.

A method for converting signals representing the die-away of nuclear radiation in a subsurface formation surrounding a borehole into a log representing porosity versus depth within said subsurface formation corrected for the effect of detector standoff from the borehole wall, comprising the steps of:

• a) lowering a logging tool having a source of fast neutrons and a spaced-apart neutron detector into a borehole traversing a subsurface formation whose porosity is to be determined,
• b) irradiating said subsurface formation at an initial depth position within said borehole with fast neutrons,
• c) recording intensity signals representing the die-away of nuclear radiation with said spaced-apart neutron detector after said fast neutrons from said neutron source have passed through and been moderated by said subsurface formation,
• d) generating a model of the die-away of nuclear radiation in said subsurface formation having three exponential terms varying in response to borehole, formation and thermal neutron background effects on said intensity signals as follows:
• ##EQU14## where .mu..sub. = borehole decay constant,
• .mu..sub.2 =formation decay constant,
• .mu..sub.3 =thermal neutron background decay constant
• A.sub.1 =borehole amplitude,
• A.sub.2 =formation amplitude,
• A.sub.3 =thermal neutron background amplitude, and
• n=1, 2, , . . . , N (discrete intervals of time)
• e) determining the expected value of weighted model moments with exponential weighting in accordance with the three-exponential model of step d) as follows:
• ##EQU15## where z.sub.j =weighting function decay constant
• n.sub.a =discrete interval starting time,
• n.sub.b =discrete interval ending time,
• f) determining weighted moments of said intensity signals with exponential weighting in accordance with the three-exponential model of step c) as follows:
• ##EQU16## where Y(n) represents discrete data, g) equating said weighted model moments with said weighted intensity moments:
• E[n.sub.j (n.sub.a,n.sub.b)]=n.sub.j (n.sub.a,n.sub.b),
• h) utilizing said equated weighted model and intensity moments from step g) to determine a ratio signal R of the borehole amplitude A.sub.1 to the formation amplitude A.sub.2 components of said intensity signal:
• R=A.sub.1 /A.sub.2,
• i) determining an initial formation decay constant .mu..sub.2 utilizing at least two-exponential terms of said equated weighted model and intensity signal moments from step g) attributable to the formation and thermal neutron background effects, and
• j) determining an epithermal neutron lifetime .tau.:
• .tau.=1/.mu..sub.2,
• k)determining an epithermal neutron lifetime correction .DELTA..tau..sub.2, and apparent standoff S from said epithermal neutron lifetime .tau..sub.2 and borehole-to-formation amplitude ratio R using a neural network,
• l) determining a standoff corrected epithermal neutron lifetime .tau..sub.2 * for detector standoff from the borehole wall in accordance with a function f(.tau..sub.2,.DELTA..tau..sub.2), derived from calibration measurements taken in borehole models at known porosities and conditions of detector standoff from the formation:
• .tau..sub.2 *=f.sub.1 (.tau..sub.2,.DELTA..tau..sub.2),
• and
• m) traversing said logging tool along said borehole from said initial depth position,
• n) repeating steps b) to l) as said logging tool traverses along said borehole, and
• o) producing a porosity versus depth log of said subsurface formation corrected for detector standoff from the borehole wall as a function of said standoff corrected epithermal neutron lifetime .tau..sub.2 * derived from calibrated measurements in said borehole models at said known porosities and conditions of detector standoff from the borehole wall.