Department of Petroleum Engineering Texas A&M University College Station, TX (USA )

1. 10 March 2016Texas 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 +1.979.229.2702 sarin_a@tamu.edu 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: • 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 Huetk-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. 2004. 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 (10 - 40 days). • Centrifuge Method • Shorter time to reach equilibrium. • Uses reservoir fluids. • 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-pcRelations • 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) 285-302. 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-pcRelation 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-pcRelation 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-pcRelation Huet (2005) • Semi-Analytical Model: • 89 MICP data sets • Petrophysical Characteristics: • 0.0041 < k < 8340 md • 0.003 < f < 0.34 (fraction) • 0.007 < Swi < 0.33 (fraction) • 2.32 < pd < 2176 psia Huet, C. C. 2005. 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 10-7 < k < 8.3 x 103 md • 0.009 < f < 0.371 (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 3.2.3. 2015. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/. 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. 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 3.97of the predicted permeability) • k< 1 md: factor of 12.70 (95% chance that the measured permeability is within a factor of 12.70of 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: • Swanson model: (log form) • Perform regression using R statistical software (2015) • R: A Language and Environment for Statistical Computing, version 3.2.3. 2015. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/. 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. 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 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. 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. 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 Discussion: • Used Huet and Swanson models with exponents forced = 2. • Correlation model reverse-calculated to yield l (as a consistency check). Swanson model correlated with 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

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]Aand 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. 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 Swi • 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 lfrom (pc)A obtained in Step 5 and pd obtained in Step 1. • Solve for Swifrom l obtained in Step 6. pd (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≤ 2.7183 (i.e., Exp(1)) • 0 ≤ l ≤ infinity (assumed pd≤ (pc)A) • -infinity ≤ Swi≤ 1 (requires attention, Swican 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 < 1x104md. • Statistics: • k≥ 1 md: factor of 3.97 (95% chance that the measured permeability is within a factor of 3.97 of the predicted permeability) • k< 1 md: factor of 12.70 (95% chance that the measured permeability is within a factor of 12.70 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 < 0.001 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): 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-pcRelation: 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 LeverettJ-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-pcRelation: 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-pcRelation: 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 saturation • Information from pc curve: Nakornthap, K., Evans, R. D. 1986. Temperature-Dependent Relative Permeability and Its Effect on Oil Displacement by Thermal Methods. SPE Reservoir Engineering 1 (03): 230 - 242. SPE-11217-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-pcRelation: Katz-Thompson (1986) Katz, A., Thompson, A. 1986. Quantitative Prediction of Permeability in Porous Rock. Physical review B 34 (11): 8179. • Model: Percolation and conductance • Key parameters: • lc= characteristic length, represent largest pore size • le = electrical conductance • lh= hydraulic conductance • Information from pc curve: length scales determination from mercury injection capillary pressure data: a. length scale of le, b. length scale of lh 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-pcRelation: 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. 2013. Combining Electrical Measurements and Mercury Porosimetry to Predict Permeability. Petrophysics 54 (06): 531-537. 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-pcRelation: Empirical model • Kwon-Pickett (1975): • Winland(1980): 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-pcRelation: Empirical model • Thomeer(1983): • Guoet al. (2004): Xiao, L., Liu, X.-P., Zou, C.-C. et al. 2014. Comparative Study of Models for Predicting Permeability from Nuclear Magnetic Resonance (Nmr) Logs in Two Chinese Tight Sandstone Reservoirs. ActaGeophysica 62 (1): 116-141. 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 • 2.10 < pd < 9046 psia • 0.15 < l< 5.22 (dim-less) • 0.00 < Swi < 0.62 (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