![10/7/2020
20
39
Optimum R2 and RMSE of test and train process of new krg and kro
R2RSSRMSEMAEEmpirical correlations-krg
0.68745.50600.20050.1294Corey [18]
0.59103.09080.15020.0978Honarpour et al. [15]
0.63982.99770.14790.0909Ibrahim and Koederitz [16]
0.62879.94510.26940.1925Kam and Rossen [37]
0.97690.15520.03460.0248New empirical correlation
R2RSSRMSEMAEEmpirical correlations-kro
0.56755.57280.20170.1367Corey [18]
0.78324.48390.18090.1355Honarpour et al. [15]
0.80453.13730.15130.1123Ibrahim and Koederitz [16]
0.57954.87080.18860.1294Kam and Rossen [37]
0.97660.22970.04170.0282New empirical correlation
40
Point-to-point analysis of
experimental data versus
predicted results for gas
phase
Point-to-point
analysis of
experimental data
versus predicted
results for oil phase](https://image.slidesharecdn.com/webinarpresentation-petroteach-201007214845/85/Classic-Measurement-vs-Image-Processing-in-Porous-Media-20-320.jpg)
![10/7/2020
21
41
Relative Permeability measurements
Experimental Kr Measurement
42
Relative Permeability measurements
No. Oil phase Gas phase
Gas flow Rate
(cc/min)
Sand size
(𝒎𝒎)
IFT
(mN/m)
Nc
Swc
(%)
Soi
(%)
Sor
(%)
krg end
points
kro end
points
1 n-C6 CO2 20 0.15 0.734 0.00126 27.5 72.40 30.9 0.432 0.999
2 n-C6 N2 20 0.25 4.11 0.00022 29.34 70.65 42.51 0.999 0.98
3 n-C6 CH4 20 0.3 1.21 0.00076 21.22 78.78 45.16 0.999 0.973
4 n-C6 CO2 55 0.15 0.734 0.00346 20.65 79.35 40.4 0.762 0.999
5 n-C6 N2 55 0.25 4.11 0.00062 29.34 70.66 42.51 0.955 0.51
6 n-C6 CH4 55 0.3 1.21 0.0021 24.37 75.63 28.36 0.999 0.999
7 n-C6 CO2 100 0.25 0.734 0.00629 31.64 68.36 26.88 0.999 0.967
8 n-C6 N2 100 0.3 4.11 0.00112 24.04 75.95 35.88 0.982 0.99
9 n-C6 CH4 100 0.15 1.21 0.00381 21.54 78.46 12.25 0.948 0.95
10 n-C7 CO2 20 0.3 2.005 0.00054 31.51 68.48 45.38 0.747 0.999
11 n-C7 N2 20 0.15 7.88 0.00014 20.65 79.35 30.66 0.999 0.999
12 n-C7 CH4 20 0.25 1.18 0.00092 27.73 72.26 45.84 0.730 0.35
13 n-C7 CO2 55 0.25 2.005 0.00149 27.39 72.61 31.25 0.336 0.999
14 n-C7 N2 55 0.3 7.88 0.00038 24.37 75.63 42.01 0.999 0.797
15 n-C7 CH4 55 0.15 1.18 0.00255 24.42 75.57 14.62 0.784 0.55
16 n-C7 CO2 100 0.3 2.005 0.00272 32.88 67.12 27.05 0.689 0.95
17 n-C7 N2 100 0.15 7.88 0.00069 20.89 79.10 17.03 0.999 0.999
18 n-C7 CH4 100 0.25 1.18 0.00463 26.70 73.30 33.09 0.965 0.587Data set No. points Experiment Rock type Gas
type
IFT condition
,mN/m
Temperature,°𝑪 Pressure ,psi Ref.
1 26 unsteady state sandstone CO2 - 95 5900 [35]
2 34 unsteady state sandstone CH4 - 95 5900 [35]
3 32 steady state sandstone CH4 0.03 21 1385 [7]
37 steady state sandstone CH4 0.43 21 1100 [7]
5 23 steady state sandstone CH4 0.23 93 1750 [36]
6 23 steady state sandstone CH4 1.03 93 1530 [36]
7 31 unsteady state sandstone CH4 0.04 38 1840 [43]
8 22 steady state sandstone CH4 0.78 37 1787 [38]
9 26 unsteady state sandstone CH4 0.14 - 6589 [37]
10 32 steady state Composite core CH4 0.4 71 1114 [39]
11 39 steady state sandstone CH4 0.14 41 2697.7 [40]
12 37 un steady state sandstone CO2 0.812 ambient 800 [41]
13 31 un steady state Carbonate CO2 0.812 ambient 800 [41]
14 47 un steady state sandstone CH4 0.04 38 1840 [42]](https://image.slidesharecdn.com/webinarpresentation-petroteach-201007214845/85/Classic-Measurement-vs-Image-Processing-in-Porous-Media-21-320.jpg)
Classic Measurement vs. Image Processing in Porous Media
- 1. 10/7/2020 1 World Class Training Solutions Outline • Brief Introduction to PetroTeach • Introducing our Distinguished Instructor Professor Azin • Webinar Presentation (45 - 60 min.) • Q&A (10 - 15 min.) 2
- 2. 10/7/2020 2 Introduction to PetroTeach Reservoir............ 3 Providing 150 training courses About 50 Distinguished Lecturer Online, Public and In-house course Download Our Catalogue ! Follow us on Social Media! 4 Tuesday 1st – 16:00 GMT Nightmare of Hydrate Blockage Professor Bahman Tohidi Wednesday 9th – 16:00 GMT Seismic Reservoir Characterization Dr. Andrew Ross Thursday 10th – 16:00 GMT Hydraulic Fracturing Jerry Rusnak Monday 14th – 17:00 GMT 3D Printing: The Future of Geology Dr. Franek Hasiuk and Dr. Sergey Ishutov Free Webinars in September Monday 21th – 17:00 GMT Elements of Fiscal Regimes and Impact on E&P Economics and Take Statistics Professor Wumi Illedare Thursday 3 rd – 16:00 GMT Advanced Petrophysics Mostafa Haggag
- 3. 10/7/2020 3 5 Wednesday 7th – 16:00 GMT Classic Measurement vs. Image Processing Professor Reza Azin Thursday 1st – 16:00 GMT Casing and Cementing Jerry Rusnak Wednesday 14th – 16:00 GMT Advanced Analysis of Carbonate System Professor Maria Mutti Monday 21th – 16:00 GMT SAGD And Solvent-SAGD Design And Analysis Dr. Mazda Irani Free Webinars in October 6 Wednesday 25th – 16:00 GMT Plug and Abandonment (P&A) of Wells Dr. Mahmoud Khalifeh Monday 9th – 16:00 GMT Electrofacies, A Guided Machine Learning For The Practice of Geomodeling David Garner Free Webinars in November Monday 30th – 16:00 GMT Capillarity in Porous Media Professor Majid Hassanizadeh Sunday 1st – 16:00 GMT BoreHole Image Application Imene Ferhat Wednesday 18th – 16:00 GMT Well Integrity Management System Fayez Makkar Wednesday 4th – 16:00 GMT Application of Artificial Intelligence and Machine Learning in Petroleum Engineering Professor Shahab D. Mohaghegh
- 4. 10/7/2020 4 7 Tuesday 1st – 16:00 GMT Fundamentals of Carbonate Reservoirs Professor Ezat Heydari Free Webinars in December Wednesday 9th – 16:00 GMT The Role of Geomodeling in The Multi-Disciplinary Team David Garner Register by email to: webinar@petro-teach.com https://www.petro-teach.com Sunday 13th – 16:00 GMT Petroleum Investment Analysis Dr. Babak Jafarizadeh Tuesday 15th – 16:00 GMT Carbon Capture, Utilization And Storage Dr. Franek Hasiuk Imaging vs. Classic Flow Measurements in Porous Media Professor. Reza Azin 7.10.2020 World Class Training Solutions www.petro-teach.com
- 5. 10/7/2020 5 Professor Reza Azin PetroTeach Distingushed Instructor • MS (1998) and BSc (1996) in Chemical Engineering and PhD degree in Petroleum Engineering (2007) • More than 20 years of experience in Academic Research, training and industrial Consulting in chemical process and petroleum reservoir • Senior lecturer and researcher in Reservoir and Chemical Process Engineering. • Focus on experimental, as well as theoretical and numerical solutions to the oil and gas industry, seeking solutions to reservoir and process engineering problems using advanced and hi-tech approaches. • Areas of interest cover oil and gas reservoir, underground gas storage, PVT analysis and modeling, surface facility design, carbon management, and process simulation. • 50+ masters and PhD theses and dissertations supervised • 80+ journal papers published; 50+ conference papers presented • Books: The Vapor Extraction (VAPEX) Process in Heavy Oil Fractured Systems (ISBN 978-3-659-30196-4) and Simulation Study of Underground Gas Storage (ISBN 978-8484-1091-0), both published by Lambert Academic Publishing (LAP), Germany Imaging vs. Classic Flow 9 • This webinar reviews some of the classical concepts in flow of fluids through porous media and introduces new experimental and numerical approaches, including imaging technologies in rock property determination, pre-Darcy flow regime, artificial intelligence application in relative permeability determination, etc. 10
- 6. 10/7/2020 6 • pre-Darcy eq. vs. Darcy eq. (Measurement, modeling) • Porosity and permeability: classic measurement vs. image processing • Relative Permeability • Phase trapping 11 12 G. O. Brown, Henry Darcy and the Making of a Law, Water Resources Research, vol. 38, no. 7, 2002 Henry Philibert Gaspard Darcy (1803–1858) An Empirical Equation Based on experiments on a loose, unconsolidated sandpack Water as the flowing fluid Steady-state flow conditions Laminar flow
- 7. 10/7/2020 7 Brinkman Flow • The Brinkman momentum equation, which originally was derived for a pressure-driven Darcy flow in porous media, then has been generalized by Brinkman to account for the inertial forces, pressure gradient, body forces, and shear stresses • Brinkman (1974) showed that the following equation is more appropriate for flow through highly permeable mediums: −𝛻𝑝 + 𝜇𝛻2 𝑣 = 𝜇 𝐾 𝑣 + 𝜌𝑔𝑐𝑜𝑠𝛼 Compare Brinkman Equation with Viscous Flow Equation: 13 −𝛻𝑝 + 𝜇𝛻2 𝑣 =0
- 8. 10/7/2020 8 Viscose velocity profile Brinkman velocity profile Darcy velocity profile y = 0.2081x2 R² = 1 0 500 1000 1500 2000 2500 0 20 40 60 80 100 120 K_DB(md) R (μm) Darcy Flow Brinkman and Viscous Flow High velocity (High Permeability) Low Radius Low velocity (Low Permeability) High Radius • Classic measurement techniques: N2 or Helium Gas volume and volume flow rate • Gas volume measured from ideal gas law • Gas volume rate correlated to pressure by Darcy Equation • Correction of Gas Perm. by Klinkenberg method 16 • Image processing • CT-Scanning • CBCT (Dental CT-Scanning) • Micro-CT scanning
- 9. 10/7/2020 9 • Image Segmentation, model reconstruction and processing 17 Farokhian, Danial, Reza Azin, and Ali Ranjbar, 2019, Application of Medical and Dental CT-Scan Technologies for Determining Porosity Distribution of the Persian Gulf coastal zone and Zagros basin Core Samples, Journal of African Earth Sciences, vol. 150, pp. 96-106 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 0.2 0.4 0.6 0.8 1 porosity(fraction) Normalized distance alonge the core Core#1 Core#8 Core#9 Core#14 Core#17 • Resolution is a challenge • CT-Scanning • CBCT (Dental CT-Scanning) • Micro-CT scanning 18 Farokhian, Danial, Reza Azin, and Ali Ranjbar, 2019, Application of Medical and Dental CT-Scan Technologies for Determining Porosity Distribution of the Persian Gulf coastal zone and Zagros basin Core Samples, Journal of African Earth Sciences, vol. 150, pp. 96-106 0 0.2 0.4 0.6 1 3 5 7 9 11 13 15 17 19 Porosity (fraction) Samplenumber Porosity Bar chart Medical CT-scan R² = 0.9073 R² = 0.8281 10 11 12 13 14 15 16 17 10 12 14 16 CT-scanporosity(%) Average porosity (laboratory method) (%) (b) Dental CT- scan Good porosity estimates by CT-scan images for sandstone and calcite carbonate Not so good for heterogeneous dolomite samples, marl and evaporates samples Higher resolution is needed to overcome phenomena like cementation and weathering that may interfere with the image processing.
- 10. 10/7/2020 10 • The linear Q-Δp relationship in Darcy Equation • pre-Darcy flow: Non-linear relationship at low flow rates • Observation: soil contamination by hydrocarbon • Low oil/gas rates in reservoir 19 Pre-Laminar: velocity increases greater than applied gradient Forchheimer: inertial effects begin Questions: Conditions for Pre-Darcy flow? Onset of Darcy flow? Effect of fluid and rock properties? Pre-Darcy flow occurs only for liquids or for liquids and gases? No flow: below a threshold gradient 12 different models are proposed for pre-Darcy flow: • Sandpack flooding setup Core flooding setup 20 Sands in the size range of 0.15-0.3 mm (corresponding to mesh 50-100) were used in experiments, making φ=33.23-38.30% and k=(0.779-2.53) Darcy Farmani, Zohreh, Reza Azin, Rouhollah Fatehi, Mehdi Escrochi, 2018, Analysis of Pre-Darcy flow for different liquids and gases, Journal of Petroleum Science and Engineering, Volume 168, pp. 17-31 Farmani, Zohreh, Danial Farokhian, Amin Izadpanahi, Fatemeh seifi, Parviz Zahedizadeh, Zohreh Safari, Azita Ghaderi, Fatemeh Kazemi, Reza Azin, 2019, Pre-Darcy flow and Klinkenberg effect in dense, consolidated carbonate formations, Geotechnical and Geological Engineering, Volume 37, Issue 4, pp 3255–3270 • Water • Condensate • Normal Hexane • Normal Heptane • N2 • CH4 • CO2
- 11. 10/7/2020 11 Effect of permeability (particle size) • Condensate • Pressure drop increases with decrease in particle sizes, revealing dependency of pressure drop to pore spaces and particle diameter. • Normal hexane • Normal heptane Flow regime Pre-Darcy Non-Darcy Liquid type u(m/s) x10-05 dp/dx (Pa/m) x105 u(m/s) x10-05 dp/dx (Pa/m) x105 water 7.08 – 23.6 0.0456 – 0.738 70.0 – 94.0 5.76 – 9.11 condensate 0.189 – 1.18 0.633 – 8.84 99.08 – 118.0 10.57 – 19.15 n-hexane 1.18 – 7.077 0.000024 – 0.847 82.6 – 118.0 6.75 – 11.67 n-heptane 0.708 – 1.65 1.97 – 6.80 118.0 – 132.1 12.85 – 17.38 For Pre-Darcy regime, pore Reynolds number (Rep) is defined which is introduced. Reynolds number analysis Darcy flow region Re p s p D u 180 Re k c p f Re s k u k 2 ( / ) k P L k f u 𝑹𝒆√𝒌 and 𝒇√𝒌 are the modified Reynolds number and modified friction factor for evaluating the permeability effect. The difference between Rep and 𝑹𝒆√𝒌 is that permeability enters in definition of 𝑹𝒆√𝒌 instead of particle diameter in the formulation of Rep 𝑅𝑒 𝑑 = 𝜌𝑢 𝐷 𝐷 𝑝 𝜇 𝑢 𝑠 = 𝜑𝑢 𝐷
- 12. 10/7/2020 12 Reynolds number analysis Liquid type Dp (mm) K x10-12 (m2) Pre-Darcy Darcy Non-Darcy 𝑹𝒆 √ 𝒌 Red Rep 𝑹𝒆 √ 𝒌 Red Rep 𝑹𝒆 √ 𝒌 Red Rep water 0.15 0.779 𝑅𝑒 √ 𝑘 < 2.3 x10-07 Red< 0.00012 Rep< 0.0001 2.3 x10-07 < 𝑅𝑒 √ 𝑘 < 7.02x10-05 0.00012 < Red< 0.036 0.0001 <Rep< 0.02 𝑅𝑒 √ 𝑘 > 7.02x10-05 Red > 0.036 Rep> 0.02 water 0.25 1440 𝑅𝑒 √ 𝑘 < 1.4 x10-05 Red< 0.0038 Rep< 0.0013 1.4 x10-05 < 𝑅𝑒 √ 𝑘 < 0.00024 0.0038 < Red< 0.066 0.0013 <Rep< 0.023 𝑅𝑒 √ 𝑘 > 0.00024 Red > 0.066 Rep> 0.023 water 0.3 2530 𝑅𝑒 √ 𝑘 < 5.06x10-05 Red< 0.006 Rep< 0.0024 5.06x10-05 < 𝑅𝑒 √ 𝑘 < 0.00067 0.006 < Red< 0.083 0.0024 <Rep< 0.032 𝑅𝑒 √ 𝑘 > 0.00067 Red > 0.083 Rep> 0.032 condensate 0.15 779 𝑅𝑒 √ 𝑘 < 2.8x10-06 Red< 0.0014 Rep< 0.0005 2.8x10-06 < 𝑅𝑒 √ 𝑘 < 0.0015 0.0014 < Red< 0.75 0.0005 <Rep< 0.251 𝑅𝑒 √ 𝑘 > 0.0015 Red > 0.75 Rep> 0.251 condensate 0.25 1440 𝑅𝑒 √ 𝑘 < 9.5x10-06 Red< 0.0056 Rep< 0.002 9.5x10-06 < 𝑅𝑒 √ 𝑘 < 0.0021 0.0056 < Red< 1.24 0.002 <Rep< 0.437 𝑅𝑒 √ 𝑘 > 0.0021 Red > 1.24 Rep > 0.437 condensate 0.3 2530 𝑅𝑒 √ 𝑘 < 3.2x10-05 Red< 0.016 Rep < 0.006 3.2x10-05 < 𝑅𝑒 √ 𝑘 < 0.0032 0.016 < Red< 1.56 0.006 < Rep< 0.597 𝑅𝑒 √ 𝑘 > 0.0032 Red > 1.56 Rep > 0.597 n-hexane 0.15 779 𝑅𝑒 √ 𝑘 < 2.1x10-05 Red< 0.011 Rep < 0.004 2.1x10-05 < 𝑅𝑒 √ 𝑘 < 0.0014 0.011 < Red< 0.754 0.004 < Rep< 0.25 𝑅𝑒 √ 𝑘 > 0.0014 Red > 0.754 Rep > 0.25 n-hexane 0.25 1440 𝑅𝑒 √ 𝑘 < 5.7x10-05 Red< 0.034 Rep < 0.012 5.7x10-05 < 𝑅𝑒 √ 𝑘 < 0.0026 0.034 < Red< 1.53 0.012 < Rep< 0.537 𝑅𝑒 √ 𝑘 > 0.0026 Red > 1.53 Rep > 0.537 n-hexane 0.3 2530 𝑅𝑒 √ 𝑘 < 0.00023 Red< 0.112 Rep < 0.043 0.00023 < 𝑅𝑒 √ 𝑘 < 0.0038 0.112 < Red< 1.87 0.043 < Rep< 0.716 𝑅𝑒 √ 𝑘 > 0.0038 Red > 1.87 Rep > 0.716 n-heptane 0.15 779 𝑅𝑒 √ 𝑘 < 1.1x10-05 Red< 0.0056 Rep < 0.0019 1.1x10-05 < 𝑅𝑒 √ 𝑘 < 0.0018 0.0056 < Red< 0.94 0.0019 < Rep< 0.313 𝑅𝑒 √ 𝑘 > 0.0018 Red > 0.94 Rep> 0.313 n-heptane 0.25 1440 𝑅𝑒 √ 𝑘 < 1.0x10-05 Red< 0.006 Rep < 0.0021 1.0x10-05 < 𝑅𝑒 √ 𝑘 < 0.0027 0.006 < Red< 1.63 0.0021 <Rep< 0.537 𝑅𝑒 √ 𝑘 > 0.0027 Red > 1.63 Rep > 0.537 n-heptane 0.3 2530 𝑅𝑒 √ 𝑘 < 4.6x10-06 Red< 0.023 Rep < 0.009 4.6x10-05 < 𝑅𝑒 √ 𝑘 < 0.0037 0.023 < Red< 1.83 0.009 <Rep< 0.7 𝑅𝑒 √ 𝑘 > 0.0037 Red > 1.83 Rep > 0.7 Effect of permeability (particle size) N2 • Since now, there is no study reported for using gases as working fluid to investigate Pre-Darcy flow. CO2 CH4 The onset of Pre-Darcy is different for each gas and occurs at a certain low superficial velocity. This onset is a function of k/𝜇 for the system.
- 13. 10/7/2020 13 A percent of mobility is defined as the ratio of mobility for Darcy equation to that for a real system which obeys Pre-Darcy flow, named here as peak or maximum mobility. For a given pressure gradient, lower Pre-Darcy velocity compared to Darcy velocity can be imagined as a lower mobility, which results in a deviation from 100% peak mobility. The horizontal line at 100% mobility indicates Darcy velocity obtained by drawing a Darcy straight line from the origin for each data point. %𝑀 = 𝑀 𝑢 𝐷 𝑀 𝑢 𝑝𝑟𝑒−𝐷 Peak Mobility ratio Pre-Darcy Flow in Dense Cores 26 • Properties of each core sample are given in Table 1. The core samples have permeability and porosity in the range of 0.011-18.53 md and 12.33-28.21 %. N2 is used as a gas phase for single-phase experiments. All tests were conducted at temperature of 98.6°F and pressure of 100 psi. Core no. Rock type Formation Length (mm) Diameter (mm) Permeability (md) Porosity (fraction) Particle diameter (mm) 1 Carbonate Asmari 0.609 0.378 0.011 0.1233 0.39 2 Carbonate Aghajari 0.632 0.376 0.054 0.1483 0.14 3 Calcite-carbonate Dalan 0.615 0.382 0.16 0.1434 0.094 4 Carbonate Asmari 0.54 0.377 0.216 0.1658 0.092 5 Chalk-salt Gachsaran 0.51 0.382 0.3 0.1607 0.074 6 Carbonate Asmari-Jahrom 0.48 0.378 0.884 0.189 0.051 7 Dolomite-Carbonate Kangan 0.53 0.38 18.53 0.2821 0.014
- 14. 10/7/2020 14 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.E+00 2.E+06 4.E+06 6.E+06 Superficialvelocity(m/s) Pressure gradient (pa/m) k=0.011 md k=0.054 md k=0.16 md k=0.216 md k=0.3 md Pre-Darcy flow in Dense Cores 0 2 4 6 8 10 12 14 16 0 20 40 60 80 100 K(md) 1/P⁻ (atm⁻¹) k=0.16 md k=0.216 md k=0.054 md k=0.884 md k=0.01 md k=0.3 md Darcy Pre- Darcy k μ g 28 • Dimensionless Reynolds number analysis is performed to characterize different flow regimes and evaluate the range of Reynolds number for different flow regimes. • Figure shows f K-C versus Rep for core#6 with k=0.884 md. Deviation from Darcy straight line at low pore Reynolds number indicates change in governing equation of fluid flow in porous media known as pre-Darcy flow. For this core, pre-Darcy flow becomes dominant when Rep< 0.004. Also, at sufficient high fluid velocity when Rep > 0.29, the second deviation from Darcy straight line was observed which is attributed to post-Darcy or non-Darcy flow. Dimensionless Reynolds number analysis
- 15. 10/7/2020 15 29 • Also, the pressure drop analysis was made using modified Reynolds number, 𝑅𝑒√𝑘 and modified friction factor,𝑓√𝑘 (Farmani et al., 2018).𝑅𝑒√𝑘 and 𝑓√𝑘 are used to evaluate permeability effect. Red is used to evaluate the effect of Darcy velocity in Reynolds number. The values of Red are reported in Table 6 for different core samples for pre-Darcy, Darcy and non-Darcy flow regimes. • 𝑅𝑒 𝑘 versus 𝑓√𝑘 is plotted in Figure 20 for core#5 with k=0.3 md. It can be seen from this Figure that deviation from Darcy straight line occurs at low pore Reynolds number and known as pre-Darcy flow. For this particular core, pre-Darcy flow regime becomes dominant when 𝑅𝑒 𝑘 <1.6x10-06. Also, at sufficient high fluid velocity, the second deviation from Darcy straight line can be observed called non-Darcy flow. In this case with k=0.3 md, when 𝑅𝑒 𝑘 > 1.1x10-04, the non-Darcy flow regime prevails. Dimensionless Reynolds number analysis Pre- Darcy Darcy Non- Darcy 30 Relative permeability concept A crucial SCAL parameter in multiphase flow through porous media The permeability of the rock to each of flowing immiscible phases (oil, water and gas) in the presence of the other phases is called effective permeability to that phase. The effective permeability of rock to a fluid is a function of its saturation in the porous media, and the effective permeability to a phase at its 100% saturation is simply equal to the absolute permeability. 𝑲 𝒓𝜶 = 𝐄𝐟𝐟𝐞𝐜𝐭𝐢𝐯𝐞 𝐩𝐞𝐫𝐦𝐞𝐚𝐛𝐢𝐥𝐢𝐭𝐲 𝐀𝐛𝐬𝐨𝐥𝐮𝐭𝐞 𝐩𝐞𝐫𝐦𝐞𝐚𝐛𝐢𝐥𝐢𝐭𝐲 = 𝑲 𝒆𝜶 𝑲 𝒂𝒃𝒔 Function of saturation
- 16. 10/7/2020 16 31 Year Relative permeability Correlations System Rock type Wettability 1949 Purcell OW/GL - - 1951 Fatt & Dykstra OW Sandstone - 1953 Burdine OW/GL Sandstone - 1954 Corey GL Sandstone - 1958 Wyllie & Gardner OW/GL Sandstone - 1958 Wahl GL Sandstone - 1958 Torcaso & Wyllie GL Sandstone - 1958 Pirson OW Sandstone Water-wet 1966 Brooks-Corey OW/GL Sandstone - 1982 Honarpour et al. OW/GL Sandstone/Carbonat e Any wettability 2000 Ibrahim and Koederitz OW/GL Sandstone/Carbonat e Any wettability 2001 MAK GL Sandstone - 2003 Kam & Rossen GL Sand pack - 2003 Al-Fattah OW Sandstone - 2006 Shen et al. OW Sandstone Intermediate- wet 2013 Mosavat et al. OW Sandstone - 2015 Xu et al. OW Sandstone Water-wet First Category O: Oil W: Water G: Gas L: Liquid Available correlations for estimation of two-phase relative permeability 32 Year Relative permeability Correlations System Rock type Wettability 1954 Corey generalized correlation OW/GL - - 1966 Brooks & Corey generalized correlation OW/GL - - 1979 Sigmund & McCaffery OW/GL Carbonate - 1984 Chierici OW/GL Sandstone - 1999 Van Genuchten-Maulem OW/GL - - 2005 LET OW/GL Composite rock - 2006 Ke OW - - 2014 Li et al. OW - - Second Category O: Oil W: Water G: Gas L: Liquid Available correlations for estimation of two-phase relative permeability Common empirical and analytical correlations of two-phase relative permeability of oil-water systems: Correlations With No Adjustable Parameters Honarpour et al. Ibrahim and Koederitz Al-Fattah Correlations With Adjustable Parameters Corey generalized correlation Brooks & Corey generalized correlation Sigmund & McCaffery Van Genuchten-Maulem Ke Chierici LET Li et al.
- 17. 10/7/2020 17 33 Common empirical and analytical correlations of two-phase relative permeability of gas-oil systems: Correlations With No Adjustable Parameters Correlations With Adjustable Parameters Corey Honarpour et al. Ibrahim and Koederitz Corey generalized correlation Brooks & Corey generalized correlation Sigmund & McCaffery Van Genuchten-Maulem Chierici LET Kam and Rossen 34 Water-Oil system Relative permeability correlation Water phase Oil phase MAE RMSE MAE RMSE Honarpour et al. 0.104348 0.127274 0.079764 0.121889 Ibrahim and Koederitz 0.043479 0.059028 0.051662 0.077921 Al-Fattah 0.031276 0.036588 0.068264 0.113995 Corey generalized correlation 0.005338 0.007964 0.019493 0.035352 Brooks & Corey generalized correlation 0.021541 0.029267 0.048436 0.061533 Sigmund & McCaffery 0.004954 0.007691 0.009031 0.016419 Chierici 0.003369 0.005415 0.011775 0.019219 Van Genuchten-Maulem 0.124280 0.163419 0.104270 0.130624 LET 0.002586 0.002818 0.010408 0.017681 Ke 0.012369 0.018535 0.063588 0.113228 Li et al. 0.004995 0.007952 0.021822 0.047743 The mean values of MAE and RMSE errors, considering total experimental data on local optimization. Results and Discussion Result related to the correlations with A & B minimum, C & D maximum error considering the total experimental data on local optimization.
- 18. 10/7/2020 18 35 Decision Tree for Water-Oil system Relative permeability Rock type Wettability Sandstone Carbonate Oil phase Water phase Oil phase Water phase LET LET Sigmund & McCaffery LET Oil-wet Intermediate-wet Water-wet Oil phase Oil phase Oil phase Water phase Water phase Water phase Sigmund & McCaffery Chierici LET LET LET LET The best values of adjustable parameters of four top models can be obtained using global optimization Model NoNwCorey gen. corr. 2.419 085 2.5022 22 BANoNwSigmund & McCaffery 0.06479 0 0.085 555 2.580 454 2.6787 36 MLBAChierici 1.00000 0 0.816 292 2.107 074 1.6022 56 ToEoLoTwEwLwLET 1.6255 96 7.4238 56 1.00000 0 1.000 000 2.581 845 1.7737 46 36 Comparison between different Kr correlations for a sample data Not all correlations fit our experimental data 1st solution: optimize the existing correlations 2nd solution: propose a new set of correlations that cover a wider range of data with a better accuracy
- 19. 10/7/2020 19 37 Gas-Oil system Developing New correlation o A generalized set of correlations to cover a wide range of rock and fluids. 𝑆 𝛼 ∗ = 𝑆 𝛼− 𝑆 𝛼 ,𝑀𝑖𝑛 𝑆 𝛼 ,𝑀𝑎𝑥− 𝑆 𝛼 ,𝑀𝑖𝑛 𝛼: 𝑔, 𝑜 𝑆 𝑜 ,𝑀𝑎𝑥= 1 − 𝑆 𝑤𝑐 − 𝑆 𝑔𝑐 𝑆 𝑔 ,𝑀𝑎𝑥= 1 − 𝑆 𝑤𝑐 − 𝑆 𝑜𝑟 𝑘 𝑟𝑜= 𝑓 𝑆 𝑜 ∗ , 𝑀𝑊, 𝐴𝑃𝐼, 𝐾 ∅ 𝑘 𝑟𝑔 = 𝑓(𝑆 𝑔 ∗ , 𝑀𝑊, 𝐴𝑃𝐼, 𝐾 ∅ ) 38 For gas phase 𝑘 𝑟𝑔 ∗ = 0.2308 𝑎 𝑔 − 1.091 𝑎 𝑔 = 4.947 ( 𝑆𝑔 ∗ 2 + 𝑏 𝑔 + 𝑐 𝑔 + 𝑑 𝑔 + 𝑒 𝑔 𝑏 𝑔 = − 0.000993 × 𝑓𝑔 × 𝐴𝑃𝐼 + 𝐿𝑛 𝐴𝑃𝐼 2 𝑀𝑊𝑔 𝑐 𝑔 = 𝐿𝑛 𝐴𝑃𝐼 − 5.741 𝑆𝑔 ∗ 𝐿𝑛 𝑀𝑊𝑔 + 0.003574 𝑘 𝑎𝑏𝑠 𝜑 𝐿𝑛 𝐿𝑛 𝐴𝑃𝐼 𝑑 𝑔 = 0.005159 (𝑀𝑊 𝑔 4 29.5531 + 0.034718 𝑘 𝑎𝑏𝑠 𝜑 + 𝑀𝑊𝑔 𝐴𝑃𝐼 4 𝑒 𝑔 = 109.4206 𝑀𝑊𝑔 𝑘 𝑎𝑏𝑠 𝜑 1 4 𝑓𝑔 = 𝐴𝑃𝐼 𝐸𝑥𝑝 −6.996025 𝑆𝑔 ∗ + 9.701419 𝑆𝑔 ∗ 4 𝐿𝑛 𝑀𝑊𝑔 𝐿𝑛 𝐴𝑃𝐼 𝐿𝑛 𝐿𝑛 𝐴𝑃𝐼 − 𝐴𝑃𝐼 For oil phase:𝑘 𝑟𝑜 ∗ = 0.09595 𝑎 𝑜 + 0.03296 𝑎 𝑜 = 𝑆 𝑜 ∗ 3.057 − 𝑏 𝑜 𝑆 𝑜 ∗ +𝜀 𝑆 𝑜 ∗+𝜀 𝑐 𝑜 3.333 − 𝑑 𝑜 𝑏 𝑜 = (𝑀𝑊 𝑔 𝑆 𝑜 ∗ − 𝑀𝑊𝑔 + 7.841𝑀𝑊𝑔 𝑀𝑊𝑔 − 2𝐴𝑃𝐼 5.504𝑀𝑊𝑔 − 0.7117 𝑘 𝑎𝑏𝑠 𝜑 + 2.135𝐴𝑃𝐼 + 2.372 𝑐 𝑜 = 7.815 − 2𝐴𝑃𝐼 + 𝑒 𝑜 4.682𝑀𝑊𝑔 − 0.5836 𝑘 𝑎𝑏𝑠 𝜑 + 1.751𝐴𝑃𝐼 + 2.006 𝑑 𝑜 = 15.47 + 𝐸𝑥𝑝 6.143𝑆 𝑜 ∗ + 𝑓𝑜 𝑘 𝑎𝑏𝑠 𝜑 − 𝐴𝑃𝐼 0.7117 𝑘 𝑎𝑏𝑠 𝜑 − 5.504𝑀𝑊𝑔 − 2.135𝐴𝑃𝐼 − 5.562 𝑒 𝑜 = (𝑀𝑊 𝑔 8.001−𝑀𝑊𝑔 + (𝑀𝑊 𝑔 7.815−𝑀𝑊𝑔 + (𝑀𝑊 𝑔 𝑆 𝑜 ∗ − (𝑀𝑊 𝑔 2 𝑘 𝑎𝑏𝑠 𝜑 − 3𝐴𝑃𝐼 𝑓𝑜 = 𝑘 𝑎𝑏𝑠 𝜑 )𝑆 𝑜 ∗ 2 + 3 𝑘 𝑎𝑏𝑠 𝜑 𝑆 𝑜 ∗ + 3 𝑘 𝑎𝑏𝑠 𝜑 − 48.59𝑀𝑊𝑔 − 60.33𝐴𝑃𝐼 𝑘 𝑟𝑔 ∗ = 𝑘 𝑟𝑔 𝑘 𝑟𝑔 ,𝑀𝑎𝑥 𝑘 𝑟𝑜 ∗ = 𝑘 𝑟𝑜 𝑘 𝑟𝑜 ,𝑀𝑎𝑥 Normalized relative permeability of gas and oil:
- 20. 10/7/2020 20 39 Optimum R2 and RMSE of test and train process of new krg and kro R2RSSRMSEMAEEmpirical correlations-krg 0.68745.50600.20050.1294Corey [18] 0.59103.09080.15020.0978Honarpour et al. [15] 0.63982.99770.14790.0909Ibrahim and Koederitz [16] 0.62879.94510.26940.1925Kam and Rossen [37] 0.97690.15520.03460.0248New empirical correlation R2RSSRMSEMAEEmpirical correlations-kro 0.56755.57280.20170.1367Corey [18] 0.78324.48390.18090.1355Honarpour et al. [15] 0.80453.13730.15130.1123Ibrahim and Koederitz [16] 0.57954.87080.18860.1294Kam and Rossen [37] 0.97660.22970.04170.0282New empirical correlation 40 Point-to-point analysis of experimental data versus predicted results for gas phase Point-to-point analysis of experimental data versus predicted results for oil phase
- 21. 10/7/2020 21 41 Relative Permeability measurements Experimental Kr Measurement 42 Relative Permeability measurements No. Oil phase Gas phase Gas flow Rate (cc/min) Sand size (𝒎𝒎) IFT (mN/m) Nc Swc (%) Soi (%) Sor (%) krg end points kro end points 1 n-C6 CO2 20 0.15 0.734 0.00126 27.5 72.40 30.9 0.432 0.999 2 n-C6 N2 20 0.25 4.11 0.00022 29.34 70.65 42.51 0.999 0.98 3 n-C6 CH4 20 0.3 1.21 0.00076 21.22 78.78 45.16 0.999 0.973 4 n-C6 CO2 55 0.15 0.734 0.00346 20.65 79.35 40.4 0.762 0.999 5 n-C6 N2 55 0.25 4.11 0.00062 29.34 70.66 42.51 0.955 0.51 6 n-C6 CH4 55 0.3 1.21 0.0021 24.37 75.63 28.36 0.999 0.999 7 n-C6 CO2 100 0.25 0.734 0.00629 31.64 68.36 26.88 0.999 0.967 8 n-C6 N2 100 0.3 4.11 0.00112 24.04 75.95 35.88 0.982 0.99 9 n-C6 CH4 100 0.15 1.21 0.00381 21.54 78.46 12.25 0.948 0.95 10 n-C7 CO2 20 0.3 2.005 0.00054 31.51 68.48 45.38 0.747 0.999 11 n-C7 N2 20 0.15 7.88 0.00014 20.65 79.35 30.66 0.999 0.999 12 n-C7 CH4 20 0.25 1.18 0.00092 27.73 72.26 45.84 0.730 0.35 13 n-C7 CO2 55 0.25 2.005 0.00149 27.39 72.61 31.25 0.336 0.999 14 n-C7 N2 55 0.3 7.88 0.00038 24.37 75.63 42.01 0.999 0.797 15 n-C7 CH4 55 0.15 1.18 0.00255 24.42 75.57 14.62 0.784 0.55 16 n-C7 CO2 100 0.3 2.005 0.00272 32.88 67.12 27.05 0.689 0.95 17 n-C7 N2 100 0.15 7.88 0.00069 20.89 79.10 17.03 0.999 0.999 18 n-C7 CH4 100 0.25 1.18 0.00463 26.70 73.30 33.09 0.965 0.587Data set No. points Experiment Rock type Gas type IFT condition ,mN/m Temperature,°𝑪 Pressure ,psi Ref. 1 26 unsteady state sandstone CO2 - 95 5900 [35] 2 34 unsteady state sandstone CH4 - 95 5900 [35] 3 32 steady state sandstone CH4 0.03 21 1385 [7] 37 steady state sandstone CH4 0.43 21 1100 [7] 5 23 steady state sandstone CH4 0.23 93 1750 [36] 6 23 steady state sandstone CH4 1.03 93 1530 [36] 7 31 unsteady state sandstone CH4 0.04 38 1840 [43] 8 22 steady state sandstone CH4 0.78 37 1787 [38] 9 26 unsteady state sandstone CH4 0.14 - 6589 [37] 10 32 steady state Composite core CH4 0.4 71 1114 [39] 11 39 steady state sandstone CH4 0.14 41 2697.7 [40] 12 37 un steady state sandstone CO2 0.812 ambient 800 [41] 13 31 un steady state Carbonate CO2 0.812 ambient 800 [41] 14 47 un steady state sandstone CH4 0.04 38 1840 [42]
- 22. 10/7/2020 22 43 Relative Permeability measurements 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 Oilrelativepermeability Gasrelativepermeability Normalized gas saturation Nc=0.00126 Nc=0.00346 Nc=0.00629 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 Oilrelativepermeability Gasrelativepermeability Normalized gas saturation Nc=0.0002 2 Nc=0.0006 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 OilRelativepermeability GasRelativepermeability Normalized gas saturation API=83 API=76 API=65.8 44 New Kr Correlations:
- 23. 10/7/2020 23 45 New Kr Correlations R² = 0.9642 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 Krg,NewCorrelation Krg, Experimental R² = 0.9744 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 Kro,NewCorrelation Kro, Experimental CCS EOR Carbon Capture and Storage Enhanced Oil Recovery EGR Enhanced Gas Condensate Recovery 46 Phase Trapping in Different Reservoir Engineering Disciplines
- 24. 10/7/2020 24 47 Phase Trapping in Oil Reservoir EOR At discovery Sand grain Oil fills pores and throat Water film coating sand grain End of water flooding Oil droplets trapped in pores Water or Gas The volume of trapped oil is a key factor in evaluating oil recovery 48 Water Condensate Gas 𝑷 𝒓𝒆𝒔. > 𝑷 𝑫𝒆𝒘 𝑺 𝒄𝒐𝒏𝒅𝒆𝒏𝒔𝒂𝒕𝒆 = 𝟎 𝑷 𝒓𝒆𝒔. < 𝑷 𝑫𝒆𝒘 𝑺 𝒄𝒐𝒏𝒅𝒆𝒏𝒔𝒂𝒕𝒆 < 𝑺 𝒄𝒓𝒊𝒕𝒊𝒄𝒂𝒍 𝑷 𝒓𝒆𝒔. < 𝑷 𝑫𝒆𝒘 𝑺 𝒄𝒐𝒏𝒅𝒆𝒏𝒔𝒂𝒕𝒆 > 𝑺 𝒄𝒓𝒊𝒕𝒊𝒄𝒂𝒍 Phase Trapping in Gas Condensate Reservoir EGR
- 25. 10/7/2020 25 Trapping Pore structure Fluid-rock interfacial properties Capillary pressure Fluid-fluid properties Relative permeabilit y Initial Saturation Properties of the fluids and the flow Pressure gradient and gravity Wettability Interfacial tension Viscosity ratio Density difference 49 Parameters Affecting Capillary Phase Trapping Column packed with sand Column fully saturated with brine (primary imbibition) Oil phase injection (primary drainage) –to reach Soi Gas injection (secondary drainage) –to reach Sor 1 2 3 4 50 Experimental Procedure in Oil-Gas System
- 26. 10/7/2020 26 51 IR 0 10 20 30 40 50 60 65 70 75 80 85 90 Sor(%) Soi (%) Kerosene/CO₂- Carbonate Pack n-Hexane/CO₂-Sand Pack n-Heptane/CO₂-Sand Pack Condensate/CO₂-Sand Pack Effect of Porosity 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 Sor(%) φ(%) n-Hexane/CO₂ (This work) n-Heptane/CO₂ (This work) Wulling et al. (2009) Tanino and blunt (2012) Aissaoui (1983) Jerauld (1997)-Fontainebleau Jerauld (1997)-Frigg Declaud (1991) Effect of IFT 20 25 30 35 40 45 50 55 0 0.5 1 1.5 2 2.5 Sor(%) IFT (mN/m) Q=3.33E-7 m³/s Q=9.17E-7 m³/s Effect of Flow Rate 20 25 30 35 40 45 50 55 60 65 0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 Sor(%) Qnw (m3/s) n- Hexane/CO ₂ n- Heptane/C O₂ 52 Effect of Capillary Number 20 25 30 35 40 45 50 55 60 65 0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05 5.00E-05 Sor(%) Nc n-Hexane/CO₂ n-Heptane/CO₂ n-Hexane/CH₄ n-Heptane/CH₄ n-Hexane/N₂ n-Heptane/N₂ 0 10 20 30 40 50 60 65 70 75 80 85 90 Sor(%) Soi (%) Kerosene/CO₂-Carbonate Pack n-Hexane/CO₂-Sand Pack n-Heptane/CO₂-Sand Pack Condensate/CO₂-Sand Pack Kerosene/CO₂-Sand Pack Ma & Youngeren Model Spiteri et al. Model IR-Match with Optimum Correlations 20 25 30 35 40 45 50 55 0 2E-09 4E-09 6E-09 8E-09 1E-08 Sor(%) Mo (m2/Pa.s) n-Hexane/CO₂ n-Heptane/CO₂ Effect of Mobility
- 27. 10/7/2020 27 Concluding Remarks • Image Processing as a tools for rock property estimation • A wide range of flowing conditions and flow regimes from pre-Darcy to post-Darcy • Relative permeability: novel correlations and new experimental data • Phase trapping in the condensate systems: experiments and optimization 53 • Farmani, Zohreh, Reza Azin, Rouhollah Fatehi, Mehdi Escrochi, 2018, Analysis of Pre-Darcy flow for different liquids and gases, Journal of Petroleum Science and Engineering, Volume 168, pp. 17-31 • Farmani, Zohreh, Danial Farokhian, Amin Izadpanahi, Fatemeh seifi, Parviz Zahedizadeh, Zohreh Safari, Azita Ghaderi, Fatemeh Kazemi, Reza Azin, 2019, Pre-Darcy flow and Klinkenberg effect in dense, consolidated carbonate formations, Geotechnical and Geological Engineering, Volume 37, Issue 4, pp 3255–3270 • Farmani, Zohreh, Reza Azin, Rouhollah Fatehi, and Mehdi Escrochi, 2018, Investigation the existence of Pre-Darcy flow in different gas systems, presented at the 80th EAGE Annual Conference and Exhibition, 11-14 June, Copenhagen, Denmark • Azin, Reza, Mohammad Mohammadi Baghmolaei, and Zahra Sakhaei, 2016, Parametric analysis of diffusivity equation in oil reservoirs, Journal of Petroleum Exploration and Production Technology (PEPT), Vol. 7, No. 1, pp. 169-179 • Farmani, Zohreh, Reza Azin, Mohamad Mohamadi-Baghmolaei, Rouhollah Fatehi, and Mehdi Escrochi, 2019, Experimental and theoretical study of gas/oil relative permeability, Computational Geosciences, Volume 23, Issue 3, pp 567–581 • Mohamadi-Baghmolaei, Mohamad, Reza Azin, Zahra Sakhei, Rezvan Mohamadi-Baghmolaei, and Shahriar Osfouri, 2016, Novel method for estimation of gas/oil relative permeabilities, Journal of Molecular Liquids, vol. 223, pp. 1185-1191 • Kazemi, Fatemeh, Reza Azin, and Shahriar Osfouri, 2020, Evaluation of Phase Trapping Models in Gas-Condensate Systems in an Unconsolidated Sandpack, Journal of Petroleum Science and Engineering, in Press 54 Selected Publications and References to this Webinar Presentation
- 28. 10/7/2020 28 AN INTEGRATED APPROACH TO PVT AND PHASE BEHAVIOR OF RESERVOIR FLUIDS (RES 435) (online) 1-3 Jun 2021 25-27 Oct. 2021 Register@petro-teach.com This course is designed to provide the audience with classical and novel approaches in phase behaviour studies of reservoir fluids. The course starts with an overview of reservoir fluids and their classification. The audience will become familiar with the role of PVT phase behavior in upstream field development plan and downstream process design. Then, the challenges and errors associated with fluid sampling are reviewed. A detailed Quality check (QC) of collected fluid samples from subsurface and surface is presented and discussed, and a unified approach is presented for sampling and recombination of gas condensate samples to obtain a representative reservoir fluid. Next, PVT correlations and Physical property estimation methods are reviewed for black oil and compositional fluid samples. Learning Objectives • General reservoir fluid classifications; An overview of the PVT phase behaviour and its importance in the upstream and downstream process design Overview of PVT test methods: CVD, CCE, DL, Flash, etc. • Challenges and Errors associated with Sampling and Recombination of Gas Condensate Fluids; A Unified Approach for Quality Control (QC) of Drill Stem Test (DST) and PVT Data • PVT correlations and Physical property estimation: Black oil and Compositional • Forward- and Backward-material balance of CVD Data • Fluid Characterization: from classical to novel approaches • Equation of State Tuning: State-of-the-Art approach; Integrated Characterization and a Tuning Strategy for the PVT Analysis of Representative Fluids Course price (Euro): • Normal registration:990+VAT • 20% DISCOUNT for PhD students, Group (≥ 3 person) and early bird registrants (1 week before) 55Imaging vs. Classic Flow 56 LegalDisclaimer,GeneralAccessTerms& Conditions This material and the information contained in it are directed to or intended for general education propose. The information presented on this material is collected, maintained and provided purely for the convenience of the reader. We have made every attempt to ensure that the information contained in this material has been obtained from reliable sources and PetroTeach is not responsible for any errors, decisions or omissions of the information. The information on this material has been incorporated in good faith and it is only for the general education and training purpose. It should not be relied upon for any specific purpose and no representation or warranty is given for its accuracy or completeness. By accessing this material, you agree that PetroTeach will not be liable for any loss incurred due to the use of the information and the material contained. The copyright for this material is solely belongs to the PetroTeach and Its Instructors. Any access to it by the general public does not imply free license to any company/organization to use it for any commercial education and projects unless it is inquired permission from PetroTeach.