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 +1.979.229.2702 sarin_a@tamu.edu 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

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

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

Capillary Pressure ALWAYS use Equation Editor 3. 𝑝 𝑐 = 2𝜎𝑐𝑜𝑠𝜃 𝑟 Washburn (1921): Leverett (1940): 𝐽( 𝑆 𝑤 )= 𝑝 𝑐 𝜎𝑐𝑜𝑠𝜃 𝑘/𝜙 𝑘=10.66 (𝜎𝑐𝑜𝑠𝜃) 2 𝐹𝜙 0 1 1 𝑝 𝑐 2 𝑑 𝑆 𝑤 Purcell (1949): 𝑘=0.136 𝜙 4.4 𝑆 𝑤𝑖 2 Timur (1968): Winland (1980): log 𝑅 35 =0.732 +0.588log𝑘 −0.864log𝜙 𝑘=389 𝑆 𝑏 𝑝 𝑐 𝐴 1.691 Swanson (1981): 𝑘=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

Thomeer MICP Model (1960) 𝑺 𝒃 𝑺 𝒃∞ =𝐞𝐱𝐩 − 𝑭 𝒈 𝐥𝐧 𝒑 𝒄 𝒑 𝒅 ALWAYS use Equation Editor 3. 𝑺 𝒃 𝑺 𝒃∞ =𝐞𝐱𝐩 − 𝑭 𝒈 𝐥𝐧 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

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 𝒘 ∗ ) −𝟏/𝝀 𝑺 𝒘 ∗ = 𝑺 𝒘 − 𝑺 𝒘𝒊 𝟏− 𝑺 𝒘𝒊 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

Swanson Correlation (1981) Cite References… Follow same guidance on x-axis and y-axis as in thesis. ALWAYS use Equation Editor 3. 𝒌 𝒂 =𝟑𝟖𝟗 𝑺 𝒃 𝒑 𝒄 𝑨 𝟏.𝟔𝟗𝟏 Air permeability 𝒌 𝒘 =𝟐𝟗𝟎 𝑺 𝒃 𝒑 𝒄 𝑨 𝟏.𝟗𝟎𝟏 Brine permeability 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

Equivalence of Brooks-Corey and Thomeer-Swanson Models Brooks-Corey Model Thomeer-Swanson Model 𝒑 𝒄 = 𝒑 𝒅 ( 𝑺 𝒘 ∗ ) −𝟏/𝝀 Follow same guidance on x-axis and y-axis as in thesis. 𝒑 𝒄 = 𝒑 𝒅 𝝓− 𝑺 𝒃 𝟏− 𝑺 𝒘𝒊 −𝟏/𝝀 𝝓 −𝟏/𝝀 ALWAYS use Equation Editor 3. 𝑺 𝒃 𝒑 𝒄 = 𝝓 −𝟏/𝝀 𝒑 𝒅 𝝓− 𝑺 𝒃 𝟏− 𝑺 𝒘𝒊 −𝟏/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

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 ) (𝟏− 𝑺 𝒘𝒊 )𝝓 ( 𝑺 𝒃 ) 𝑨 =𝟏𝟎𝟎𝝓(𝟏− 𝑺 𝒘𝒊 ) 𝝀 𝝀+𝟏 𝑺 𝒘𝒊 =𝟏− ( 𝑺 𝒃 ) 𝑨 𝟏𝟎𝟎𝝓 𝟏+𝝀 𝝀 ( 𝒑 𝒄 ) 𝑨 = 𝒑 𝒅 𝟏 𝝀+𝟏 −𝟏/𝝀 𝝀= 𝒏 𝟏 + 𝒏 𝟐 𝒚 𝑫 + 𝒏 𝟑 𝒚 𝑫 𝟐 + 𝒏 𝟒 𝒚 𝑫 𝟑 + 𝒏 𝟓 𝒚 𝑫 𝟒 𝒅 𝟏 + 𝒅 𝟐 𝒚 𝑫 + 𝒅 𝟑 𝒚 𝑫 𝟐 + 𝒅 𝟒 𝒚 𝑫 𝟑 + 𝒅 𝟓 𝒚 𝑫 𝟒 Coefficient Optimized Value n1 0.000013 d1 -3.424593 n2 -4.338365 d2 3.995668 n3 0.322016 d3 0.000049 n4 -0.105426 d4 -0.149015 n5 -0.129459 d5 -0.405945 𝒚 𝑫 = 𝒆− ( 𝒑 𝒄 ) 𝑨 𝒑 𝒅 𝒆−𝟏 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

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

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

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

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

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

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 +1.979.229.2702 sarin_a@tamu.edu 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

References Huet, C. C. 2005. Semi-Analytical Estimates of Permeability Obtained from Capillary Pressure. MS thesis, Texas A&M University, College Station, Texas (December 2005). Wu, T. 2004. Permeability Prediction and Drainage Capillary Pressure Simulation in Sandstone Reservoirs. Dissertation, Texas A&M University, College Station, Texas (December 2004). Thomeer, J.H.M. 1960. Introduction of a Pore Geometrical Factor Defined by the Capillary Pressure Curve. JPT 12(3): 73-77. doi:10.2118/1324-G. Brooks, R.H., Corey, A. T. 1964. Hydraulic Properties of Porous Media 3(3), Colorado State University Hydrology Papers. Swanson, B. F. 1981. A Simple Correlation Between Permeabilities and Mercury Capillary Pressures. Journal of Petroleum Technology 33 (12): 2498-2504. doi:10.2118/8234-PA. Comisky, J. T., Newsham, K., Rushing, J. A. et al. 2007. 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., 11-14 November. SPE-110050-MS. doi:10.2118/110050-MS. Rezaee, R., Saeedi, A., Clennell, Ben. 2011. Tight Gas Sands Permeability Estimation From Mercury Injection Capillary Pressure and Nuclear Magnetic Resonance Data. Journal of Petroleum Science and Engineering 88 - 89: 92-99. doi:10.1016/j.petrol.2011.12.014. Blasingame, T.A.: “Petrophysics Lecture 4 – Capillary Pressure, ” Petroleum Engineering 620 Course Notes, Texas A&M University (2014). Leverett, M. 1941. Capillary behavior in porous solids. Transactions of the AIME. 142(01): 152-169. 2016 Student Paper Contest | 30 January 2016 Texas A&M University | College Station, TX Brooks-Corey MICP Model Parameters Determination Sarin APISAKSIRIKUL

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

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

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

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

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

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

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

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