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Brooks-Corey MICP Model Parameters Determination

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1 Brooks-Corey MICP Model Parameters Determination
2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Department of Petroleum Engineering Texas A&M University College Station, TX (USA) Sarin Apisaksirikul 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

2 Outline Capillary Pressure Thomeer MICP Model Brooks-Corey MICP Model
Swanson Correlation Equivalence of Brooks-Corey and Thomeer-Swanson Models Method to Determine Brooks-Corey MICP Model Parameters Examples Discussion Conclusion 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

3 Capillary Pressure Cite References…
2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

4 Capillary Pressure ALWAYS use Equation Editor 3. 𝑝 𝑐 = 2πœŽπ‘π‘œπ‘ πœƒ π‘Ÿ
Washburn (1921): Leverett (1940): 𝐽( 𝑆 𝑀 )= 𝑝 𝑐 πœŽπ‘π‘œπ‘ πœƒ π‘˜/πœ™ π‘˜=10.66 (πœŽπ‘π‘œπ‘ πœƒ) 2 πΉπœ™ 𝑝 𝑐 2 𝑑 𝑆 𝑀 Purcell (1949): π‘˜= πœ™ 𝑆 𝑀𝑖 2 Timur (1968): Winland (1980): log 𝑅 35 =0.732 +0.588logπ‘˜ βˆ’0.864logπœ™ π‘˜= 𝑆 𝑏 𝑝 𝑐 𝐴 1.691 Swanson (1981): π‘˜=226 𝑙 𝑐 2 𝐹 Katz&Thompson (1986): 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

5 Thomeer MICP Model (1960) 𝑺 𝒃 𝑺 π’ƒβˆž =𝐞𝐱𝐩 βˆ’ 𝑭 π’ˆ π₯𝐧 𝒑 𝒄 𝒑 𝒅
ALWAYS use Equation Editor 3. 𝑺 𝒃 𝑺 π’ƒβˆž =𝐞𝐱𝐩 βˆ’ 𝑭 π’ˆ π₯𝐧 𝒑 𝒄 𝒑 𝒅 Fg = Pore geometrical factor pc = Capillary pressure pd = Minimum "threshold" pressure at which a continuous phase exists in a porous medium Sb = Percent bulk volume occupied by mercury at a given capillary pressure Sb∞ mercury at infinite capillary Cite References… 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

6 Brooks-Corey MICP Model (1964)
Cite References… ALWAYS use Equation Editor 3. l = Pore-size distribution index. Sw* = Effective saturation function. Sw = Wetting phase saturation. Swi = Irreducible wetting phase saturation. pc = Capillary pressure. pd = Minimum "threshold" pressure at which a continuous phase exists in a porous medium. 𝒑 𝒄 = 𝒑 𝒅 ( 𝑺 π’˜ βˆ— ) βˆ’πŸ/𝝀 𝑺 π’˜ βˆ— = 𝑺 π’˜ βˆ’ 𝑺 π’˜π’Š πŸβˆ’ 𝑺 π’˜π’Š 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

7 Swanson Correlation (1981)
Cite References… Follow same guidance on x-axis and y-axis as in thesis. ALWAYS use Equation Editor 3. π’Œ 𝒂 =πŸ‘πŸ–πŸ— 𝑺 𝒃 𝒑 𝒄 𝑨 𝟏.πŸ”πŸ—πŸ Air permeability π’Œ π’˜ =πŸπŸ—πŸŽ 𝑺 𝒃 𝒑 𝒄 𝑨 𝟏.πŸ—πŸŽπŸ Brine permeability 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

8 Equivalence of Brooks-Corey and Thomeer-Swanson Models
Brooks-Corey Model Thomeer-Swanson Model 𝒑 𝒄 = 𝒑 𝒅 ( 𝑺 π’˜ βˆ— ) βˆ’πŸ/𝝀 Follow same guidance on x-axis and y-axis as in thesis. 𝒑 𝒄 = 𝒑 𝒅 π“βˆ’ 𝑺 𝒃 πŸβˆ’ 𝑺 π’˜π’Š βˆ’πŸ/𝝀 𝝓 βˆ’πŸ/𝝀 ALWAYS use Equation Editor 3. 𝑺 𝒃 𝒑 𝒄 = 𝝓 βˆ’πŸ/𝝀 𝒑 𝒅 π“βˆ’ 𝑺 𝒃 πŸβˆ’ 𝑺 π’˜π’Š βˆ’πŸ/𝝀 𝑺 𝒃 𝑺 𝒃 𝒑 𝒄 𝑨 = 𝒅 𝒅 𝑺 𝒃 𝑺 𝒃 𝒑 𝒄 =𝟎 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

9 Equivalence of Brooks-Corey and Thomeer-Swanson Models
ALWAYS use Equation Editor 3. 𝑺 𝒃 𝒑 𝒄 𝑨 =𝟏𝟎𝟎 𝟏 𝒑 𝒅 𝝀 𝟏+𝝀 (𝟏+ 𝟏 𝝀 ) (πŸβˆ’ 𝑺 π’˜π’Š )𝝓 ( 𝑺 𝒃 ) 𝑨 =πŸπŸŽπŸŽπ“(πŸβˆ’ 𝑺 π’˜π’Š ) 𝝀 𝝀+𝟏 𝑺 π’˜π’Š =πŸβˆ’ ( 𝑺 𝒃 ) 𝑨 πŸπŸŽπŸŽπ“ 𝟏+𝝀 𝝀 ( 𝒑 𝒄 ) 𝑨 = 𝒑 𝒅 𝟏 𝝀+𝟏 βˆ’πŸ/𝝀 𝝀= 𝒏 𝟏 + 𝒏 𝟐 π’š 𝑫 + 𝒏 πŸ‘ π’š 𝑫 𝟐 + 𝒏 πŸ’ π’š 𝑫 πŸ‘ + 𝒏 πŸ“ π’š 𝑫 πŸ’ 𝒅 𝟏 + 𝒅 𝟐 π’š 𝑫 + 𝒅 πŸ‘ π’š 𝑫 𝟐 + 𝒅 πŸ’ π’š 𝑫 πŸ‘ + 𝒅 πŸ“ π’š 𝑫 πŸ’ Coefficient Optimized Value n1 d1 n2 d2 n3 d3 n4 d4 n5 d5 π’š 𝑫 = π’†βˆ’ ( 𝒑 𝒄 ) 𝑨 𝒑 𝒅 π’†βˆ’πŸ 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

10 Proposed Method pd 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. Follow same guidance on x-axis and y-axis as in thesis. (Sb/pc)A (Sb)A Follow same guidance on x-axis and y-axis as in thesis. 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

11 Example 1 Sample #71 High quality MICP data set.
pd and the Swanson Apex (Sb/pc)A can easily be identified. Both models capture the trend of the MICP data. Follow same guidance on x-axis and y-axis as in thesis. Follow same guidance on x-axis and y-axis as in thesis. 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

12 Example 2 Sample #132 High quality MICP data set.
pd and the Swanson Apex (Sb/pc)A can easily be identified. The MICP data does not match the Brooks-Corey model at low Sw. Follow same guidance on x-axis and y-axis as in thesis. Follow same guidance on x-axis and y-axis as in thesis. 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

13 Discussion This method allows the determination of Swi and l directly from the clearly defined parameters such as pd and (Sb/pc)A. This method facilitates Brooks-Corey model matching over the use of regression. Many samples have MICP data deviated from Brooks-Corey model, especially at low Sw. This method helps identify if the MICP data follow Brooks-Corey model or not. Theoretically, l can be ranged from 0 to infinity. Our study found that l is never higher than 10 and unlikely to be higher than 5. We need to work on these … I would like to limit 1 line/bullet. We need to work on grammar and structure of words. 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

14 Conclusion Capillary pressure critically affects reservoir initial fluid distribution and hydrocarbon recovery during primary or enhanced production. Relationship between capillary pressure, saturation, rock properties (porosity, permeability) exists. Brooks-Corey MICP model is widely accepted model to relate capillary pressure and wetting phase saturation. Brooks-Corey MICP model parameters are obtained by model matching using regression. Time consuming Subjective, many possible realizations Our proposed method facilitates the Brooks-Corey MICP model parameters determination. Direct calculation from the well defined parameters of displacement pressure and Swanson Apex. We need to work on these … I would like to limit 1 line/bullet. We need to work on grammar and structure of words. 2015 Student Paper Contest | 31 January 2015 Texas A&M University | College Station, TX Complexity of Permeability Determination in Shale Gas Reservoirs Sarin APISAKSIRIKUL

15 Brooks-Corey MICP Model Parameters Determination
2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Department of Petroleum Engineering Texas A&M University College Station, TX (USA) Sarin Apisaksirikul 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

16 References Huet, C. C Semi-Analytical Estimates of Permeability Obtained from Capillary Pressure. MS thesis, Texas A&M University, College Station, Texas (December 2005). Wu, T Permeability Prediction and Drainage Capillary Pressure Simulation in Sandstone Reservoirs. Dissertation, Texas A&M University, College Station, Texas (December 2004). Thomeer, J.H.M Introduction of a Pore Geometrical Factor Defined by the Capillary Pressure Curve. JPT 12(3): doi: /1324-G. Brooks, R.H., Corey, A. T Hydraulic Properties of Porous Media 3(3), Colorado State University Hydrology Papers. Swanson, B. F A Simple Correlation Between Permeabilities and Mercury Capillary Pressures. Journal of Petroleum Technology 33 (12): doi: /8234-PA. Comisky, J. T., Newsham, K., Rushing, J. A. et al A Comparative Study of Capillary-Pressure-Based Empirical Models for Estimating Absolute Permeability in Tight Gas Sands. Presented at the SPE Annual Technical Conference and Exhibition, Anaheim, California, U.S.A., November. SPE MS. doi: / MS. Rezaee, R., Saeedi, A., Clennell, Ben Tight Gas Sands Permeability Estimation From Mercury Injection Capillary Pressure and Nuclear Magnetic Resonance Data. Journal of Petroleum Science and Engineering : doi: /j.petrol Blasingame, T.A.: β€œPetrophysics Lecture 4 – Capillary Pressure, ” Petroleum Engineering 620 Course Notes, Texas A&M University (2014). Leverett, M Capillary behavior in porous solids. Transactions of the AIME (01): 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

17 Derivation of the relationship between Swanson’s parameter and the Brooks-Corey model parameters
2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

18 Derivation of the relationship between Swanson’s parameter and the Brooks-Corey model parameters
2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

19 Derivation of the relationship between Swanson’s parameter and the Brooks-Corey model parameters
2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

20 Derivation of the relationship between Swanson’s parameter and the Brooks-Corey model parameters
2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

21 Derivation of the relationship between Swanson’s parameter and the Brooks-Corey model parameters
2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

22 Derivation of the relationship between Swanson’s parameter and the Brooks-Corey model parameters
2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

23 Estimation Function for Pore-Size Distribution Index (l)
Eq. D6: Eq. D7: 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

24 Brooks-Corey Log-log Plot of Sample #71 and #132
2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

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