Method for evaluation of permeability anisotropy using NMR diffusion measurements for oil and gas wells
A method for predicting formation permeability by measuring diffusional tortuosity in several directions by pulse gradient NMR. The method comprises evaluating an anisotropic diffusion coefficient by pulsed gradient NMR, determining diffusional tortuosity from the restricted diffusion data, supplementing the NMR results with resistivity and sonic logging data, measuring anisotropic tortuosity and porosity by resistivity and sonic data and combining all components in a single fitting model. The 11-coefficient model is trained to recognize the true values of permeability by comparing the real oil permeabilities measured in a library of oil-carrying rock cores with the NMR, resistivity and sonic correlates. The fitting coefficients are extracted by minimizing the discrepancy between the laboratory measured permeabilities and the predicted values combining all rapid logging information components with the agreement-maximizing weights.
1. A method of determining permeability anisotropy of a hydrocarbon-containing geological formation, comprising:
a) determining a first 1 H self-diffusion coefficient (D b ) of bulk water in a portion of the hydrocarbon-containing geological formation where the water is present outside of the pores, by exposing the out of the pore portion of the hydrocarbon-containing geological formation to an NMR pulse gradient along an axis Z of the portion of the hydrocarbon-containing geological formation; wherein the out-the pore portion comprises brine flooding the borehole, wherein the brine is measured by NMR prior to flooding, post-flooding samples of the brine extracted from the borehole;
b) determining a second 1 H self-diffusion coefficient (D R ) of water in a portion of the hydrocarbon-containing geological formation in a restricted porous environment by an NMR sequence with the magnetic pulse gradient along the axis Z;
c) selecting the timescale of performing the NMR sequence in (a) and (b) such that the timescale corresponds to the asymptotic minimal values of the restricted diffusion coefficients for the entire pore size distribution;
d) calculating a diffusion tortuosity value τ z as τ z =D b /D R ;
e) repeating steps (a)-(d) with the magnetic pulse gradient along any directions in a plane XY perpendicularly to the axis Z of the hydrocarbon-containing geological formation and computing a diffusion tortuosity metric τ xy ;
f) determining the permeability of the hydrocarbon-containing geological formation based on a ratio of a plurality of diffusional tortuosity values measured in different directions.
2. The method of claim 1 , wherein the NMR-measured diffusional tortuosity is the only parameter used to predict permeability by relating each tortuosity index τ z and τ xy to directional permeability by:
K z =C 1 *(τ z ) C2 +C 3 ;K xy =C 4 *(τ xy ) C5 +C 6 ;
wherein C 1 -C 6 are empirical coefficients; K z , K xy are directional permeability values [m 2 ], τ z , τ xy are directional diffusional tortuosity values.
3. The method of claim 1 , wherein the NMR pulse gradient is an APGASTE 13 sequence of formula:
S
S
0
=
exp
{
-
D
R
γ
2
[
δ
2
(
4
Δ
+
6
λ
-
2
δ
3
)
g
a
2
+
2
λ
δ
(
δ
1
-
δ
2
)
g
a
g
0
+
4
3
λ
3
g
0
2
]
}
wherein
S 0 is the NMR signal in the absence of applied magnetic field gradients (μV),
D R is the restricted self-diffusion coefficient of the fluid (m 2 /s),
Δ is the duration between two applied magnetic field ‘Diffusion Time’ (msec),
δ is the duration of the applied magnetic field gradient (msec),
γ is the gyromagnetic ratio of the nucleus being studied (=2.68×10 8 Hz/T for 1 H nucleus),
g a is the strength of the applied magnetic field gradient (T/m),
g o is the strength of the internal magnetic field gradient (T/m),
λ is the time between the first two (π/2) RF pulses (msec), and
δ 1 and δ 2 =pre- and post-pulse time respectively (msec).
4. The method of claim 3 , further comprising:
deconvoluting the self-diffusion coefficient of water from hydrocarbon contributions in the NMR measurement with DOSY.
5. The method of claim 1 , wherein one or more of the determining steps is carried out in a bore hole with a downhole sensor assembly comprising an NMR apparatus.
6. The method of claim 5 , wherein the downhole sensor assembly further measures resistivity and acoustic logs.
7. The method of claim 6 , further comprising:
integrating pulse NMR, resistivity and acoustic data into a single expression:
PERM= A 1 ×[τ NMR B1 ]×[τ RES B2 ]×[Φ NMR B3 ]×[Φ RES B4 ]×[Φ SONIC B5 ]×[(τ NMRZ ) B6 /(τ NMRXY ) B6 ]×[(τ RESZ ) B7 /(τ RESXY ) B7 ]×[(Φ SONICZ ) B8 /(Φ SONICXY ) B8 ]× S w B9 ×S wir B10
wherein:
PERM—is the permeability of formation;
A 1 —is the empirical proportionality factor;
[τ NMR B1 ]—is the diffusional tortuosity determined by NMR;
[τ RES B2 ]—is the tortuosity determined by resistivity;
[Φ NMR B3 ]—is the overall porosity determined by NMR;
[Φ RES B4 ]—is the overall porosity determined by resistivity logging;
[Φ SONIC B5 ]—is the overall porosity determined by acoustic probing;
[(τ NMRZ ) B6 /(τ NMRXY ) B6 ]—is the ratio of diffusional tortuosity in the direction Z to one measured in the plane XY;
[(τ RESZ ) B7 /(τ RESXY ) B7 ]—is the ratio of resistivity tortuosity (formation factors) measured in the direction Z to one measured in the plane XY;
[(Φ SONICZ ) B8 /(Φ SONICXY ) B8 ]—is the ratio of porosity determined by acoustic probing in the direction Z to the porosity determined by the acoustic probing in the plane XY;
S w B9 —is the water saturation fraction;
S wir B10 —is the irreducible water content;
R B11 —is the resistance at the given extent of water saturation.
8. The method of claim 7 , further comprising:
calculating a permeability according to
v =( K /μ)×Δ P/ΔL , wherein:
K—is permeability [m 2 ],
V—is flow velocity [m/sec],
ΔP/ΔL—is pressure gradient [kg/sec 2 ×m 2 ], and
μ—is the dynamic viscosity [kg×m×s −1 ].
9. The method of claim 1 , wherein the one or more of the following NMR sequences is applied during the determining:
a Hahn stimulated echo STE;
a longitudinal encode decode pulse sequence;
a bipolar gradient longitudinal encode-decode pulse sequence;
a gradient compensated stimulated spin-echo pulse sequences; and
a double stimulated echo sequence.
10. The method of claim 7 , wherein the coefficients A1, B1-B10 are determined by:
a) collecting a library of oil-carrying cores;
b) measuring any of: true permeability, wettability, porosity or fracturing gradient of the cores in controlled laboratory conditions;
c) repeating (b) in different directions and including water in the tested system to enable water saturation of oil phase and at least irreducible water presence on the pore walls;
d) measuring tortuosity and porosity by NMR, resistivity and acoustic data in different directions;
e) repeating the measurements (d) for different oil models and water contents;
f) repeating (a)-(e) for all sample cores in the library.
11. The method of claim 1 , further comprising:
calculating an anisotropic pore size distribution based on a dependent of an effective diffusional tortuosity on the timescale of pulsed gradient NMR sequences.