Method of estimating permeability using NMR diffusion measurements
This invention is useful for determining the permeability of a geological formation using 1 H NMR diffusion measurements acquired in the laboratory and using downhole 1 H NMR well logging. The current technology for obtaining formation permeability downhole using NMR is not adequate for low-permeability, unconventional source rock formations with high organic content. This new method uses laboratory 1 H NMR diffusion measurements for creating continuous downhole well logs of the mobile-hydrocarbon permeability of the hydrocarbon-filled pore space of downhole geological formations.
1. A method of mapping, in at least a vertical direction, subsurface permeability as a function of downhole-location, the method comprising:
a. acquiring a set CORE_SET of N core samples {CS 1 , CS 2 . . . CS N } where CS i is the i th core sample, and N is a positive integer, and 1≤i≤N, wherein each core-sample CS i is extracted from a respective downhole extraction-location EXTRACTION-LOC(CS i ) within the subsurface;
b. for each core sample CS i of CORE_SET, respectively performing the following set of measurements:
(i) a respective lab-NMR measurement of a respective porosity ϕ M (CS i ) describing the porosity of movable hydrocarbons;
(ii) a respective lab-NMR measurement of one or more pore-dimension properties; and
(iii) a respective lab measurement of the permeability k(CS i ) of the core sample CS i ;
c. for each core sample CS i of CORE_SET, estimating a respective downhole hydraulic tortuosity τ hy (EXTRACTION-LOC(CS i )) representing the downhole tortuosity at the extraction-location from which core sample CS i was extracted;
d. computing, from the results of steps (b) and (c), an at least 1-D BTR-map of subsurface BTR (body throat ratio) as a function of subsurface location;
e. for a plurality of downhole locations, downhole-NMR-logging the following parameters: (i) subsurface porosity; and (ii) a subsurface pore-size parameter;
f. computing an at least 1-D map of subsurface permeability as a function of downhole-location from all of the following: (i) the at least 1-D BTR-map; (ii) the results of the downhole-NMR-logging; and (iii) the results of step (c).
2. The method of claim 1 wherein the lab-NMR-measured pore-dimension property of step b(ii) is a surface-to-volume ratio.
3. The method of claim 1 wherein the lab-NMR-measured pore-dimension property of step b(ii) is a pore diameter.
4. The method of claim 1 wherein step (d) comprises computing, from the results of steps (b) and (c), a respective laboratory BTR(CS i ) value for each core sample CS i .
5. The method of claim 4 wherein the respective laboratory BTR(CS i ) value is computed using a modified Carman-Kozeny relationship.
6. The method of claim 1 , further comprising drilling one or more horizontal or vertical wells in location(s) determined by the content of the at least 1-D map of subsurface permeability.
7. The method of claim 1 further performing at least one of the following in location(s) determined by the content of the at least 1-D map of subsurface permeability: (i) casing and perforating; and (ii) deploying a pump in the well.
8. The method of claim 1 wherein the core samples of CORE_SET are obtained from a selection of depths covering different lithologies (i.e. rock types).
9. The method of claim 1 wherein step (b)(i) comprises saturating, in the laboratory, each core sample with decane and step b(ii) comprises saturating, in the laboratory, each core sample with methane.
10. The method of claim 1 wherein step (b)(i) comprises measuring, in the laboratory, D-T 2 , on core samples of CORE_SET to determine a respective movable hydrocarbon fluid porosity ϕ M (CS i ) i.e. porosity above T 2 >T 2cutoff .
11. The method of claim 1 wherein step (b)(ii) comprises measuring, in the laboratory,
restricted diffusion (D/D 0 ), where D 0 is bulk diffusion versus diffusion length
(
L
D
=
D
0
t
Δ
,
where t Δ is the diffusion encoding time.
12. The method of claim 11 wherein step b(ii) comprises fitting D/D 0 versus
L D using Padé fit to determine pore body size (d), heterogeneity length scale (L M ), and tortuosity (τ) for each core.
13. The method of claim 1 wherein step b(iii) is performed by setting each core sample CS i in a Hassler sleeve and applying confining stress on the sample CS i and then flowing fluid (either gas or liquid) through each sample CS i to produce a pressure drop across the sample CS i and measuring the fluid flow rate.
14. The method of claim 1 wherein step (c) comprises subjecting each core sample CS i to laboratory NMR.
15. The method of claim 1 wherein step (c) is performed by at least one of (i) downhole NMR and (iii) downhole electrical resistivity measurements, for example, at EXTRACTION-LOC(CS i ).
16. The method of claim 1 wherein step (f) comprises employing at least one of the modified Carman-Kozeny equations.
17. A method comprising performing NMR restricted diffusion measurements on a core with connate water present by:
a) pressure-saturating the core with two hydrocarbons (sequentially high-pressure methane and decane, or high-pressure methane and high-pressure butane),
b) measuring NMR restricted diffusion of the two hydrocarbons under pressure in the core to obtain their restricted diffusivity in the hydrocarbon-bearing porosity of the core,
c) estimating the tortuosity and surface-to-volume ratio of the hydrocarbon-filled pore space of the core, and
d) using the tortuosity, surface-to-volume ratio, and porosity occupied by the hydrocarbon fluids, and estimating the pore body-to-pore-throat ratio for the lithology, determining the permeability of the mobile hydrocarbons in the core.
18. The method of claim 17 wherein the tortuosity and pore size are determined by applying a Padé fit to restricted diffusivity NMR measurements of the two hydrocarbons.
19. The method of claim 17 wherein the two hydrocarbons comprise methane and at least one other hydrocarbon such as decane or butane.
20. The method of claim 17 wherein the equation for the permeability of the mobile hydrocarbons in the core is given by the equation
k
=
ϕ
d
2
32
τ
BTR
2
.
21. A method comprising obtaining a downhole wireline permeability log by measuring NMR diffusion-T 2 (D-T 2 ), and permeability on a selection of cores of different lithologies (i.e. rock types), then using the core-calibrated parameters with D-T 2 well logs to obtain a permeability well log, the method comprising the following steps:
a. obtaining cores from a selection of depths covering different lithologies,
b. measuring D-T 2 on cores to determine movable fluid porosity (ϕ M ), i.e. porosity above T 2 >T 2cutoff , and restricted diffusion (D/D 0 ), where D 0 is bulk diffusion versus diffusion length
(
L
D
=
D
0
t
Δ
,
where t Δ is the diffusion encoding time) using a light hydrocarbon and a heavier hydrocarbon to cover a range of L D ,
c. fitting D/D 0 versus L D using Padé fit to determine pore body size (d), heterogeneity length scale (L M ), and tortuosity (τ) for each core,
d. determining the cementation exponent (m) for each lithology using
τ
=
ϕ
M
1
-
m
,
e. determining the heterogeneity length-scale (L M ) for each lithology,
f. measuring core permeability (k) and determining the body-throat ratio BTR for each lithology from the Carman-Kozeny equation
k
=
ϕ
M
d
2
3
2
τ
B
T
R
2
,
g. measuring D-T 2 log to determine movable fluid porosity (ϕ M, log ), i.e. porosity above T 2 >T 2cutoff , and D log /D 0 versus T 2 ,
h. determining tortuosity log (τ log ) using
τ
l
o
g
=
ϕ
M
,
log
1
-
m
,
where m is known for each lithology from step (d),
i. fitting D log /D 0 versus T 2 using Padé fit to determine pore-body size (d log ), with τ log known from step (h), and L M fixed for each lithology from step (e), and
j. determining downhole permeability (k log ) from
k
l
o
g
=
ϕ
M
,
log
d
log
2
3
2
τ
log
B
T
R
2
,
with BTR known for each lithology from step (f).