1. The Development and Application of a New Semi-Analytical Model
10 March 2016 Texas A&M University | College Station, TX
The Development and Application of
a New Semi-Analytical Model
to Estimate Permeability
from Mercury Injection Capillary Pressure
Department of Petroleum Engineering
Texas A&M University
College Station, TX (USA)
Sarin Apisaksirikul
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

2. Executive Summary Historical Perspectives: Accomplishments:
Huet (2005) proposed a semi-analytical model for permeability using 89 sets of mercury pc data.
Swanson (1981) proposed an empirical model for permeability using 319 sets of mercury pc data. Swanson model is based on the work of Thomeer (1960).
Accomplishments:
We propose a new correlation for permeability based on Huet’s relation using 323 sets of mercury pc data.
We show that our optimized permeability relation (Huet’s model) outperforms the Swanson model fitted to the same data.
We derive a direct relationship between the (Huet) semi- analytical correlation model and the Swanson model.
We propose an alternative method to determine the Brooks- Corey capillary pressure model parameters using our derived relationship between the Huet and Swanson models.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

3. Outline Executive Summary Introduction
Development/Application of a Semi-Analytical Model
Data collection and analysis
Regression analysis — semi-analytical model
Regression analysis – Swanson model
Models comparison
Analytical Relationship between k-pc Models
Relationship between Swanson and Brooks-Corey parameters
Relationship between Swanson and Huet k-models
Alternate determination of the Brooks-Corey parameters
Conclusion
Recommendations for Future Work
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

4. Introduction: Capillary Pressure Concepts
Washburn (1921):
Wu, T Permeability Prediction and Drainage Capillary Pressure Simulation in Sandstone Reservoirs. Doctoral dissertation, Texas A&M University, College Station, Texas (December 2004).
Keelan, D.K. and Marschall, D.M.: The Fundamentals of Core Analysis, Core Laboratories, Inc., Dallas (1972, 79, 89).
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

5. Introduction: Capillary Pressure Measurement
Porous-Plate Method
Very accurate.
Uses reservoir fluids.
Pressure limited by displacement pressure of the porous-plate.
Long equilibrium time for each pressure step ( days).
Centrifuge Method
Shorter time to reach equilibrium.
Pressure is limited by the rotational speed.
Indirect method: pc is calculated from saturation and speed.
Mercury Injection Method (used in this study)
Fast (short equilibration time).
Can apply high pressure (>60,000 psia).
Does NOT use reservoir fluids.
May not replicate the reservoir displacement process.
Loss of samples due to the contamination.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

6. Introduction: Capillary Pressure-Saturation Model
Leverett (1940):
Thomeer (1960):
Brooks-Corey (1964):
Wu (2004):
Plot of mercury injection capillary pressure versus wetting phase saturation
Xu and Torres-Verdín (2013): Bimodal Gaussian Distribution Model
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

7. Introduction: k-pc Relations
Analytical Models:
Purcell-Burdine (1949)
Wyllie-Spangler (1952)
Wyllie-Gardner (1958)
Katz-Thompson (1986)
Ruth et al. (2013)
Semi-Analytical Model:
Huet (2005)
Empirical Models:
Kwon-Pickett (1975)
Winland (1980)
Swanson (1981)
Thomeer (1983)
Guo et al. (2004)
Gates, J. l. and Templaar-Lietz, W.: "Relative Permeabilities of California Cores by the Capillary Pressure Method," API Drilling and Production Practices (1950)
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

8. Introduction: k-pc Relation Swanson (1981)
Air permeability
Brine permeability
Swanson apex = [Sb/pc]A = [Sb/pc] at Thomeer’s apex = maximum value of [Sb/pc]
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

9. Introduction: k-pc Relation Huet (2005)
Wyllie-Gardner (1958), Nakornthap-Evans (1986):
Brooks-Corey (1964):
Ali (1995):
Power-law relationship:
(Simple) Regression Relation:
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

10. Introduction: k-pc Relation Huet (2005)
Semi-Analytical Model:
89 MICP data sets
Petrophysical Characteristics:
< k < md
< f < (fraction)
< Swi < (fraction)
< pd < psia
Huet, C. C Semi-Analytical Estimates of Permeability Obtained from Capillary Pressure. MS thesis, Texas A&M University, College Station, Texas (December 2005).
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

11. New Semi-Analytical Model: After Huet (2005)
Objectives:
To verify the power-law relationship between permeability and capillary pressure proposed by Huet (2005).
To develop a new semi-analytical model to predict absolute permeability from mercury injection capillary pressure data.
To compare the semi-analytical model to the Swanson model.
Outline:
Data collection and analysis
Regression analysis – Semi-analytical model
Regression analysis – Swanson model
Models comparison
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

12. Data Collection and Analysis: Data Orientation
Mercury injection capillary pressure (MICP)
Number of samples studied:
Total database = 573 samples, selected 323 samples
Petrophysical Characteristics:
4.5 x < k < 8.3 x 103 md
< f < (fraction)
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

13. Data Collection and Analysis: pd, l, Swi
Discussion:
Data deviates from Brooks-Corey model at low Sw.
Subjective match, but consistent process.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

14. Regression: Semi-Analytical Model
Semi-analytical correlation model
Semi-analytical correlation model: (log form)
Perform regression using R statistical software (2015)
R: A Language and Environment for Statistical Computing, version Vienna, Austria: R Foundation for Statistical Computing.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

15. Regression: Semi-Analytical Model
Regression Results
95% of data within a factor of 9.1.
58% of data within a factor of 2.
Correlation best for k>1 md.
Scatter centered on perfect-trend.
Low Sw does not affect results.
Statistical Variable
Value
Sum of Squared Residuals
367 ln(md)2
Mean Squared Error
ln(md)2
Residual Standard Error
ln(md)
R-Squared
0.9467
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

16. Regression: Semi-Analytical Model
Model Prediction Ability:
95% prediction interval
k ≥ 1 md: factor of 3.97
(95% chance that the measured permeability is within a factor of of the predicted permeability)
k < 1 md: factor of 12.70
(95% chance that the measured permeability is within a factor of of the predicted permeability)
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

17. Regression: Swanson Model
Swanson model: (log form)
Perform regression using R statistical software (2015)
R: A Language and Environment for Statistical Computing, version Vienna, Austria: R Foundation for Statistical Computing.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

18. Regression: Swanson Model
Regression Results
95% of data within a factor of 10.4.
56% of data within a factor of 2.
Correlation best for k>1 md.
Scatter centered on perfect trend.
Statistical Variable
Value
Sum of Squared Residuals
392 ln(md)2
Mean Squared Error
ln(md)2
Residual Standard Error
ln(md)
R-Squared
0.9431
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

19. Comparison of Huet and Swanson Models
Statistical Variable
Semi-Analytical Model
Swanson Model
Sum of Squared Residuals
367 ln(md)2
392 ln(md)2
Mean Squared Error
ln(md)2
ln(md)2
Residual Standard Error
ln(md)
ln(md)
R-Squared
0.9467
0.9431
95% of the data are within
A factor of 9.1
A factor of 10.4
Within a factor of 2
58%
56%
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

20. Regression: Semi-Analytical Model (forced)
(All exponents = 2)
Regression Results
95% of data within a factor of 10.1.
56% of data within a factor of 2.
Correlation best for k>1 md.
Scatter centered on perfect-trend.
Low Sw does not affect results.
Statistical Variable
Value
Sum of Squared Residuals
397 ln(md)2
Mean Squared Error
ln(md)2
Residual Standard Error
ln(md)
R-Squared
0.9423
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016 Texas A&M University | College Station, TX The Development and Application of a New Semi-Analytical Model to Estimate Permeability from Mercury Injection Capillary Pressure

21. Regression: Swanson Model (forced)
(Swanson exponent = 2)
Regression Results
95% of data within a factor of 10.2.
57% of data within a factor of 2.
Correlation best for k>1 md.
Scatter centered on perfect trend.
Statistical Variable
Value
Sum of Squared Residuals
393 ln(md)2
Mean Squared Error
ln(md)2
Residual Standard Error
ln(md)
R-Squared
0.9429
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016 Texas A&M University | College Station, TX The Development and Application of a New Semi-Analytical Model to Estimate Permeability from Mercury Injection Capillary Pressure

22. Comparison of Huet and Swanson Models (forced)
Optimized Huet model
with exponents = 2
Optimized Swanson model with exponent = 2
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

23. Comparison of Huet and Swanson Models
Swanson model correlated with Huet model
Discussion:
Used Huet and Swanson models with exponents forced = 2.
Correlation model reverse-calculated to yield l (as a consistency check).
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

24. Analytical Relationship: k-pc Models
Objectives:
To derive an analytical relationship between the semi-analytical (Huet) correlation model and the Swanson correlation model.
To propose an alternative method to determine the Brooks- Corey capillary pressure model parameters from MICP data.
Outline:
Relationship between the Swanson correlating parameter and the Brooks-Corey pc model parameters.
Relationship between the semi-analytical correlation model and the Swanson model.
Alternative approach to determine the Brooks-Corey pc model parameters.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

25. Relationship Between: [Sb/pc]A and pd, l, Swi
Brooks-Corey Model
Thomeer-Swanson Model
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

26. Correlation of Huet and Swanson Models
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

27. Relationship Between: [Sb/pc]A and pd, l, Swi
From analytical derivation:
Obtained relationship from data
From regression (forced exponents):
Assumed relationship validated with data.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

28. Correlation of Huet and Swanson Models
Generalized Swanson relation in terms of l
Swanson model
correlated with
Brooks-Corey model.
x-axis = l-term from Huet model.
y-axis = l-term from Swanson model.
Swanson model with independent parameters is the same as semi- analytical (Huet) model.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

29. Alternative Approach: Determination of l and Swi
Swanson model
correlated with
Brooks-Corey model.
Coefficient
Optimized Value n1 d1 n2 d2 n3 d3 n4 d4 n5 d5
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

30. Alternative Approach: Determination of l and Swipd
Estimate pd using a semi-log plot of pc vs. Sw by extrapolation of the pc plateau trend to Sw = 1.
Calculate for [Sb/pc] for the data set.
Plot [Sb/pc] versus Sb on a Cartesian plot.
Estimate (Sb)A from the Cartesian plot in Step 3 where the [Sb/pc] trend has a maximum (i.e., [Sb/pc]A).
Calculate for (pc)A from [Sb/pc]A obtained in step 4 using the point (Sb)A.
Solve for l from (pc)A obtained in Step 5 and pd obtained in Step 1.
Solve for Swi from l obtained in Step 6.
(Sb/pc)A
(Sb)A
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

31. Alternative Approach: Determination of l and Swi
Method Validation – Sample #71
High quality MICP data set.
pd and the Swanson Apex [Sb/pc]A can easily be identified.
The calculated pc matched the MICP data.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

32. Alternative Approach: Determination of l and Swi
The Swanson apex parameter, [Sb/pc]A, is a strong cor- relating variable and appears to uniquely represent the pc trend.
From the analytical derivation:
1 ≤ (pc)A/pd ≤ (i.e., Exp(1))
0 ≤ l ≤ infinity (assumed pd ≤ (pc)A)
-infinity ≤ Swi ≤ 1 (requires attention, Swi can be < 0)
We observed that l < 10, is typically < 5.
We found cases where Swi is negative –— requires additional effort and attention.
This is not to replace the regression approach:
Use information from a single point (not the whole pc curve).
MICP data should have a clear pd and Thomas-Swanson apex .
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

33. Conclusion
Permeability correlation valid for 1x10-7 < k < 1x104 md.
Statistics:
k ≥ 1 md: factor of 3.97
(95% chance that the measured permeability is within a factor of of the predicted permeability)
k < 1 md: factor of 12.70
(95% chance that the measured permeability is within a factor of of the predicted permeability)
The proposed (semi-analytical) permeability correlation model (originally given by Huet) is more robust than the Swanson model (statistically and analytically).
[Sb/pc]A = f(pd,l,Swi) correlation provides an interrelation between the Brooks-Corey and Swanson pc models.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

34. Recommendations for Future Work
Include more data samples with k < md.
Include data from shale samples.
Extend to other capillary pressure data (not just MICP).
Develop methods that avoid negative values of Swi.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

35. What I Learned in This Research
Concept of capillary pressure in porous media
k-pc models
Data collection
Statistical analyses
Technical writing
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

36. The Development and Application of a New Semi-Analytical Model to Estimate Permeability from Mercury Injection Capillary Pressure
End of Presentation
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

37. Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

38. The Development and Application of a New Semi-Analytical Model to Estimate Permeability from Mercury Injection Capillary Pressure
Back-Up Slides
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

39. Introduction – Capillary Pressure-Saturation Model
Thomeer (1960): Fg
= Pore geometrical factor pc
= Capillary pressure pd
= Displacement pressure Sb
= Percent bulk volume occupied by
mercury at a given capillary pressure
Sb∞
mercury at infinite capillary pressure
Schematic diagram of the Thomeer hyperbolic pc model
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

40. Introduction – Capillary Pressure-Saturation Model
Brooks-Corey (1964): a. b.
l = Pore-size distribution index
Sw* = Effective saturation function
Sw = Wetting phase saturation
Swi = Irreducible wetting phase saturation
pc = Capillary pressure
pd = Displacement pressure
Plot of logarithm of capillary pressure versus wetting phase saturation
Plot of logarithm of capillary pressure versus logarithm of effective wetting phase saturation
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

41. Introduction – k-pc Relation: Purcell (1949)
Model: Bundle of capillary tubes
Key parameters:
Fp = lithology factor
Information from pc curve:
Modification:
Ma et al. (1991): Using a different lithology factor (Fp) for samples with different Leverett J-function.
Related J-function to tortuosity as:
Blasingame, T.A.: “Petrophysics Lecture 5 — Relative Permeability, ” Petroleum Engineering 620 Course Notes, Texas A&M University (2014).
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

42. Introduction – k-pc Relation: Wyllie-Spangler (1952)
Model: Bundle of tortuous-non-circular tubes
Key parameters:
k0 = shape factor (2.0 – 3.0), approximately constant (2.5)
F = Archie formation factor, to measure the tortuosity
Information from pc curve:
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

43. Introduction – k-pc Relation: Wyllie-Gardner (1958)
Model: Cut-and-rejoin bundle of capillary tubes
Key parameters:
b = pore throat impedance factor
n = number of entrances/exits in a
pore
Swi = irreducible wetting phase
saturation
Sw* = effective wetting phase
Information from pc curve:
Nakornthap, K., Evans, R. D Temperature-Dependent Relative Permeability and Its Effect on Oil Displacement by Thermal Methods. SPE Reservoir Engineering 1 (03): SPE PA.
(a) n = 1, (b) n > 1
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

44. Introduction – k-pc Relation: Katz-Thompson (1986)
Katz, A., Thompson, A Quantitative Prediction of Permeability in Porous Rock. Physical review B 34 (11): 8179.
length scales determination from mercury injection capillary pressure data: a. length scale of le, b. length scale of lh
Model: Percolation and conductance
Key parameters:
lc = characteristic length, represent largest pore size
le = electrical conductance
lh = hydraulic conductance
Information from pc curve:
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

45. Introduction – k-pc Relation: Ruth et al. (2013)
Model: Representative elemental
volume (REV)
Key parameters:
F = Archie formation factor, to measure tortuosity
Information from pc curve:
Modification:
Salimifard et al. (2014): approximation of F gave an acceptable prediction.
Ruth, D., Lindsay, C., Allen, M Combining Electrical Measurements and Mercury Porosimetry to Predict Permeability. Petrophysics 54 (06):
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

46. Introduction – k-pc Relation: Empirical model
Kwon-Pickett (1975):
Winland (1980):
Reference
Correlation Model
Representative
pore-throat radius
Winland
(Kolodzie Jr 1980)
r35 = pore-throat radius at mercury saturation of 35%
Pittman (1992)
r25 = pore-throat radius at mercury saturation of 25%
Jaya et al. (2005)
r15 = pore-throat radius at mercury saturation of 15%
Rezaee et al. (2006)
Carbonate
r50 = pore-throat radius at mercury saturation of 50%
Dastidar et al. (2007)
rwgm = weighted geometric mean of the pore-throat radii over the whole range of mercury saturation
Rezaee et al. (2012)
Tight gas sand
r10 = pore-throat radius at mercury saturation of 10%
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

47. Introduction – k-pc Relation: Empirical model
Thomeer (1983):
Guo et al. (2004):
Xiao, L., Liu, X.-P., Zou, C.-C. et al Comparative Study of Models for Predicting Permeability from Nuclear Magnetic Resonance (Nmr) Logs in Two Chinese Tight Sandstone Reservoirs. Acta Geophysica 62 (1):
Capillary Parachor = [Sb/pc2]max
MICP curves and the corresponding Swanson apex and capillary parachor for three representative core samples
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

48. Data Collection and Analysis – Data Orientation
Data sets for each sample:
Mercury injection capillary pressure data
Measured permeability
Measured porosity
Data Sources:
Huet (2005)
Byrnes et al. (2009): Mesaverde tight gas sandstones
Xu (2013): Hugoton carbonate gas field
Number of samples studied:
Total collection = 573 samples
Selected samples = 323 samples
Sample Selection criteria:
MICP data exhibit a suitably smooth trend
MICP data exhibit a clear displacement pressure
Permeability is directly measured, not estimated from other parameters.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

49. Data Collection and Analysis – pd, l, Swi
Brooks-Corey pc model
Data-model matching using regression
Solver Module in Microsoft Excel (2013)
Minimizing sum squared residuals
Visually verify the match with plots
Semi-log plot of pc versus Sw
Log-log plot of pc versus Sw*
Observed deviation of MICP data from the Brooks-Corey pc model
Deviation at low Sw
The selection of data range is subjective
Focus on low pc data range
The process is robust and consistent
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

50. Data Collection and Analysis – pd, l, Swi
< pd < psia
< l < (dim-less)
< Swi < (fraction)
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

51. Semi-Analytical Model
Models Comparison
Statistical Variable
Semi-Analytical Model
Swanson Model
Sum of Squared Residuals
367 ln(md)2
392 ln(md)2
Mean Squared Error
ln(md)2
ln(md)2
Residual Standard Error
ln(md)
ln(md)
R-Squared
0.9467
0.9431
95% of the data are within
A factor of 9.1
A factor of 10.4
Within a factor of 2
58%
56%
The new semi-analytical model is better than the optimized Swanson model in all statistical measures.
The new semi-analytical model can give a better permeability prediction.
Bigger variation at k < 1 md are observed in both models
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

52. Regression analysis – Semi-analytical model
Evaluate the impact from the MICP data quality
Good MICP quality sample
Poor MICP quality sample
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

53. Regression analysis – Semi-analytical model
The model can equally well applied to both sample groups
Good MICP quality sample
Poor MICP quality sample
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

54. Relationship between the Semi-Analytical Correlation Model and the Swanson Model
Found a strong correlation between the Swanson-l term and the Huet-l term over the entire range of l-values in our data sets.
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016 Texas A&M University | College Station, TX The Development and Application of a New Semi-Analytical Model to Estimate Permeability from Mercury Injection Capillary Pressure

55. Brooks-Corey Log-log Plot of Sample #71
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

56. Estimation Function for Pore-Size Distribution Index
Eq. D6:
Eq. D7:
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

57. Correlation of Huet and Swanson Models
Swanson correlation model:
Substituting [Sb/pc]A into the Swanson model:
Isolating the l-term in the Huet model:
Brooks-Corey/Swanson l-identity
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

58. Introduction: Brooks-Corey (1964) & Swanson (1981)
Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure

59. J-Function Sarin APISAKSIRIKUL | M.S. Defense | 10 March 2016
Texas A&M University | College Station, TX
The Development and Application of a New Semi-Analytical Model
to Estimate Permeability from Mercury Injection Capillary Pressure