Liquid Permeability of Porous Media

1. 0Summary This experiment is conducted to determine the liquid permeability of porous media. The apparatus used in the experiment is the liquid permeameter. The liquid used in this experiment is water. Three membrane samples of different thickness (0. 1, 0. 2, 0. 3 cm) are used as the porous media. The determination of the permeability is carried out using elevated pressure test. Each sample is tested for 5 times at different values of pressure gradient which are 5, 10, 15, 20 and 30 psi.In order to obtain more accurate data, ensure that the membrane samples to be test is fixed tightly and covers the o-ring of the sample chamber completely. Values of volumetric flow rates are obtained from the apparatus itself. For pressure gradient of 5 psi and 30 psi, the average permeability for PP1 membrane sample are 0. 23993 cm2 @ 2. 33993? 10-5 m2 and 0. 096196 cm2 @ 9. 6196? 10-6 m2 respectively. For PP3 membrane sample, the average permeability are 0. 52692 cm2 and 0. 19841 cm2 for pressur e gradient of 5 psi and 30 psi.For PP5 membrane sample, the average permeability are 1. 0541 cm2 and 0. 29489 cm2 for pressure gradient of 5 psi and 30 psi. The values of permeability obtained are then compared by plotting graphs of volumetric flow rate over cross sectional (q/A) against pressure gradient over thickness (? P/L). The gradient of the straight line from the graph is  µ/k. For PP1 sample membrane, the permeability obtained from the graph is k= 0. 000148 m2 for ? P=5psi and k= 0. 000062 m2 for ? P= 30 psi.Permeability obtained from the graph is compared with ones obtained from the liquid permeameter apparatus. Reynolds number for the tests at ? P=5psi is 5. 3913? 10-5 and for ? P= 30 psi is 1. 1147? 10-4. Laminar flow conditions exist so that Darcy’s equation is applicable. 2. 0 Introduction When fluid flows through a medium, the flow is affected by the property of the medium that allows the flow of the fluid through it. The property of the medium is called perm eability. Permeability which is symbolized as k is the measure of the ability of a medium to transfer fluids.Permeability affects flow processes of fluids. An effective flow process can occur if the permeability of the medium where the fluids pass through is high. Concept of permeability is important in the oil and gas industry in which the permeability characteristic of rocks are determined in order to extract oil and gas from the subsurface reservoir. For example, sandstones are permeable and can transmit fluid effectively. This types of stones possessed large and many connected pores. They may content high quantity of oil.Shales and siltstones composed of fine grains and have less connected pores causing them to be less permeable or impermeable. Permeability of a medium can be easily determined from equipment with high technology. It is important to know the factors or component which may affect permeability in order to prove or increase the permeability. This might benefits the industry which involves extraction processes. Experimental results are important because to increase the efficiency of processes involving permeability it is dependent on the data or results. 3. 0 Aims/ObjectivesThe experiment is conducted to objective of this experiment is to determine the permeability of the porous media, to create conditions so that Darcy’s equation can be used and to compare the average permeability for different pressure gradient and types of tested samples as well as to relate permeability with various components of Darcy’s equation. 4. 0 Theory Permeability is property of the porous medium and is a measure of the ability of the medium to allow fluids to pass through it. Permeability concept is widely used to determine the flow characteristics of hydrocarbons  in  oil  and  gas  reservoirs.Medium or rocks that possess high permeability can allow fluids to pass through it in large quantity over time. This is indicated form high volumetri c flow rate. To quantify permeability, assume that there is a medium with cross-sectional area (A) and thickness (L). A fluid of dynamic viscosity ( µ) is allowed to flow through the medium. The change in pressure that occurs during the flow is ? P and the volumetric flow rate (q) is the amount of fluid that can flow through the medium over a period of time with respect to the ? P. Permeability (k) is related to all the components by the Darcy’s equation. Darcy’s equation: q=kA?P µL †¦.. (1) The SI unit for permeability, k is m2. Permeability is also measured in Darcy, D. 1 D is approximately 10-12m2. Factors affecting permeability are membrane solubility, pressure, concentration and temperature of the molecules or solutes. Permeability is also affected by size of the molecules of the fluids that passing through the medium. Darcy’s equation is valid for any Newtonian fluids and is only applicable for laminar flow. The laminar flow is always achieved by groundwater but not always achieved by gas flows. Laminar flow can be determined by computing the Reynolds number of the flow. Re= ? vD µ 5. 0 Apparatus i.Liquid permeameter apparatus ii. Liquid hose iii. Yellow chip pullers iv. Membranes of different thickness, 0. 1, 0. 2 and 0. 3 cm v. Water 6. 0 Procedures i. 3 membrane samples of different thickness (0. 1, 0. 2, 0. 3cm) are prepared. The samples are cut bigger than the o-ring so that they will cover the ring completely and to ensure perfect sealing. ii. The liquid hose attached to the sample chamber lid is disconnected. The lid is unscrewed and removed. The chamber insert and adapter plates are taken out. The o-rings is checked for dryness. iii. Under Group on the main CapWin menu, a new group is created by clicking on New Group. iv.Under Execute on the main CapWin menu, Autotest F2 is selected. Autotest settings screen is opened. Test Type is clicked and Liquid Permeametry is selected from the Test Selection box. Then, Elevat ed Pressure Test option is selected. v. At the Autotest screen, several information are keyed in. The fields are as below. Output File Name-user designated End User-user designated Test Reference-Liquid Permeametry; Elevated Pressure Test Sample ID-user designated Lot Number-user designated Operator-user designated Fluid-Water Surface Tension Diameter-3cm for all 3 samples Thickness-0. 1, 0. 2, 0. 3 cm vi. Done on the Autotest screen is clicked. ii. The screened adapter plate is placed in the bottom of the sample chamber. The plate is aligned on three chamber pins. The sample is placed on the top of the screened plate. The o-ring of the screened plate is checked so that it seals against the sample. Top adapter plate is place on the sample chamber. viii. The chamber insert is placed into the chamber. The insert should not be lower than the sample chamber height. ix. Start Test button is clicked. Starting pressure, maximum pressure, point step pressure, maximum wait between points and maximum number of points are keyed in. Continue button is clicked after each value has been entered. . Sample chamber is filled with water. The lid is screwed and hand-tightened. Liquid fill hose with quick connect fitting is attached to the sample chamber lid. xi. Click Ok on the Autotest screen and the test is started. xii. When the test has ended, a Test Done dialogue box appeared and clicked Ok. xiii. Test results may be viewed and analyzed using CapRep. Select Report from the main CapWin menu and clicked on Execute Report to access the data from the test. xiv. Steps (iii) to (xiii) are repeated for different pressure gradient (10, 15, 20, and 30) and two other samples with thickness 0. 2 cm and 0. 3 cm. 7. 0 ResultFor PP1 sample with diameter, d= 3cm and thickness, L= 0. 1cm. Differential Pressure (psi)| Average Permeability| 5| 0. 23993| 10| 0. 17461| 15| 0. 13315| 20| 0. 11792| 30| 0. 096196| For PP3 sample with diameter, d= 3cm and thickness, L= 0. 2cm. Differential Pressur e (psi)| Average Permeability| 5| 0. 52692| 10| 0. 36709| 15| 0. 33807| 20| 0. 26133| 30| 0. 19841| For PP5 sample with diameter, d= 3cm and thickness, L= 0. 3 cm. Differential Pressure (psi)| Average Permeability| 5| 1. 0541| 10| 0. 70806| 15| 0. 50627| 20| 0. 37001| 30| 0. 29489| 8. 0 Calculations i) PP1 sample with diameter, d= 3cm and thickness, L=0. cm at ? P= 5psi. From the plotted graph, q/A against ? P/L, a straight line obtained gives a gradient of 0. 148. From the gradient of graph, we can compute the permeability, k. Gradient = y2-y1x2-x1 = 4-127-6. 9 = 0. 148 Gradient = k µ 0. 148 = k0. 001 Pa. s , k = 0. 000148 m2 @ 1. 48? 10-4 m2 The permeability, k obtained from the CapWin software is 0. 23993 cm2 @ 2. 33993? 10-5 m2. ii) PP1 sample with diameter, d= 3cm and thickness, L=0. 1cm at ? P= 30psi. From the plotted graph, q/A against ? P/L, a straight line obtained gives a gradient of 0. 148. From the gradient of graph, we can compute the permeability, k.Gradient = y2-y1x 2-x1 = 12-6195-98 Gradient = k µ 0. 062 = k0. 001 Pa. s , k = 0. 000062 m2 @ 6. 2? 10-5 m2 The permeability, k obtained from the CapWin software is 0. 096196 cm2 @ 9. 6196? 10-6 m2. iii) Calculations of Reynolds number At ? P= 5 psi, q= 2. 5424? 10-6 m3/s, V= 1. 7971? 10-9m/s, ? =1000kg/m3 Re= ? VD µ=10001. 7971? 10-9(0. 03)0. 001= 5. 3913? 10-5 (laminar flow) At ? P= 30 psi, q= 5. 2564? 10-6 m3/s, V= 3. 7155? 10-9m/s, ? =1000kg/m3 Re= ? VD µ=10003. 7155? 10-9(0. 03)0. 001= 1. 1147? 10-4 (laminar flow) 9. 0 Discussion Permeability of PP1 sample membrane at ? P = 5 psi and ?P = 30 psi are k = 0. 23993 cm2 @ 2. 33993? 10-5 m2 and k = 0. 096196 cm2 @ 9. 6196? 10-6 m2 respectively. By plotting graphs of q/A against ? P/L, the compute permeability is 1. 48? 10-4 m2 at ? P = 5 psi and 6. 2? 10-5 m2 at ? P = 30 psi. The values are different as being compared. This might due to the different techniques involved in computing the values of permeability. The values from the liquid permea meter are more accurate as the values are computed as the test runs. Compared to the ones computed by plotting the graph, there might be some minor errors that make the values to be different from each other.Apart from that, the apparatus might not function effectively or might be having some problems. Besides that, the sample membranes used are the old ones. As they are often used for testing, this might change or alter their permeability values as they oftenly pass through by fluids. For the tests, laminar flows did occur. Laminar flow occurs at the region in which the points from the graph intersect the straight line plotted. For both ? P = 5 psi and ? P = 30 psi, laminar flow did occur. For ? P = 5 psi, the Reynolds number is 5. 3913? 10-5 which is representative for laminar flow. For ?P = 30 psi, the Reynolds number is 1. 1147? 10-4 which is also representative for laminar flow. For graph at ? P = 5 psi, there is only one point that intersects the straight line (best line of fi t) plotted. This is because the pressure gradient is low so there is not much data for permeability is acquired as the test runs. It is different for graph at ? P = 30 psi, there are several points that are intersect or join by the straight line plotted. As the pressure is elevated to 30 psi, there are many data obtained for permeability at different pressures as the pressure increasing to 30 psi.As laminar flow is proven to occur in the test, so Darcy’s equation can be used. From the Darcy’s equation, we can relate that permeability of a medium is directly proportional to volumetric flow rate, dynamic viscosity of fluid and thickness of medium and is inversely proportional to pressure gradient. For membrane sample PP1 with thickness of 0. 1 cm, we can see that the average permeability of the membrane is decreasing with increasing pressure gradient. This case occurs for other two membrane samples, PP3; thickness of 0. 2 cm and PP5; thickness of 0. 3 cm.Permeability dec rease as pressure gradient increase because the fluid, in this case water have to overcome certain pressure as they flow through the membrane samples. The pressure gradient acts as resistance to the flow. The higher the resistance, little or less fluid can flow through the medium over a given time. It is also shown that for the same pressure gradient by using membranes with different thickness, the average permeability is higher for sample which is thicker. The different between the three membrane samples is only the thickness. They are of same cross-sectional area.As fluid flow they overcoming the same pressure gradient, same cross-sectional area, the amount of fluid that can be passed through is much dependent on the thickness. When the fluid passes through membranes with large thickness, they are experiencing much effect through the membranes causing the permeability to be higher than the ones obtained with small thickness. 10. 0 Conclusions The objectives of this experiment are achieved. The permeability of three membrane samples are obtained from the liquid permeameter-elevated pressure tests. The permeability of the PP1 sample at ? P = 5 psi and ? P = 30 psi are k = 0. 3993 cm2 @ 2. 33993? 10-5 m2 and k = 0. 096196 cm2 @ 9. 6196? 10-6 m2 respectively. Laminar flow conditions are also created where Darcy’s equation can be used. From the data obtained from the tests, we are able to deduce relationship between permeability and other components of Darcy’s equation. Although the compared values are differing from the each other, we can say that the experiment is still a success as we are able to achieve the main objectives. 11. 0 Recommendations In order to get more accurate results, ensure that the apparatus used (liquid permeameter) is in good condition and is maintained regularly.Besides that, using new or fresh membrane samples can improve the results. Not necessarily that for every test to use new ones but replacing old ones with new ones a s when they are in bad condition would help. The average permeability value would be more accurate and the values obtained from the graph would be of not much difference. 12. 0 References i) Brown, G. (n. d. ). Darcy's Law. Retrieved October 03, 2012, from Darcy's Law Basics and More: http://biosystems. okstate. edu/darcy/LaLoi/basics. htm ii) Darcy's Law. (n. d. ). Retrieved October 03, 2012, from Darcy's Law: http://www. ldeo. columbia. du/~martins/hydro/lectures/darcy. html iii) Laminar Flow. (n. d. ). Retrieved October 03, 2012, from Hyper Physics: http://hyperphysics. phy-astr. gsu. edu/hbase/pfric. html iv) Laminar, Transitional or Turbulent Flow. (n. d. ). Retrieved October 03, 2012, from The Engineering ToolBox: http://www. engineeringtoolbox. com/laminar-transitional-turbulent-flow-d_577. html v) Oilfield Glossary. (2012). Retrieved October 03, 2012, from Schlumberger: http://www. glossary. oilfield. slb. com/Display. cfm? Term=permeability vi) Permeability. (n. d. ). Retri eved October 03, 2012, from NDT Resource Center: http://www. ndt-ed. rg/EducationResources/CommunityCollege/MagParticle/Physics/Permeability. htm 13. 0 Appendices Graph1: q/A against ? P/L at ? P=5psi Graph 2: q/A against ? P/L at ? P= 30 psi Figure 1: Liquid permeameter Figure 2: Sample chamber Figure 3: Pressure cylinder Figure 4: Fluid bin Figure 5: The discharge port of water Figure 6: Yellow chip pullers For ? P = 5psi, ?P/L| q/A| 0| 0| 15. 919| 3. 1536| 19. 185| 3. 4128| 22. 623| 3. 6631| 26. 519| 3. 9394| 29. 866| 4. 1191| 32. 784| 4. 1995| For ? P = 30 psi, ?P/L| q/A| ? P/L| q/A| ? P/L| q/A| 0| 0| 74. 1191| 6. 529| 142. 874| 8. 724| 5. 4528| 2. 274| 77. 339| 6. 8886| 146. 066| 8. 948| 12. 8498| 2. 9474| 81. 186| 6. 7182| 150. 051| 9. 209| 15. 9759| 3. 1624| 84. 434| 7. 2454| 153. 216| 9. 497| 19. 0896| 3. 4502| 88. 364| 7. 1371| 156. 263| 9. 495| 22. 5177| 3. 7128| 91. 687| 7. 0481| 159. 821| 9. 957| 26. 6236| 4. 057| 94. 541| 6. 9633| 163. 875| 9. 468| 29. 9179| 4. 1482| 97 . 858| 7. 126| 167. 619| 9. 357| 32. 471| 4. 2458| 98. 775| 8. 4774| 170. 453| 9. 444| 35. 9619| 4. 449| 100. 678| 7. 2947| 173. 287| 9. 683| 39. 2052| 4. 7036| 104. 677| 7. 94| 176. 741| 9. 692| 44. 044| 5. 186| 107. 986| 7. 9996| 180. 85| 10| 47. 068| 5. 1119| 116. 322| 8. 1839| 184. 373| 10. 5| 49. 7694| 5. 697| 118. 307| 8. 042| 187. 213| 10| 53. 2892| 5. 3991| 122. 31| 8. 399| 190. 655| 11. 1| 56. 6594| 5. 51| 125. 161| 8. 437| 193. 936| 10. 19| 59. 9503| 5. 8797| 128. 615| 8. 379| 198. 032| 10. 3| 63. 3005| 6. 0421| 132. 325| 8. 492| 201. 679| 10| 66. 792| 6. 2865| 135. 517| 8. 692| 205. 078| 10| 69. 7064| 6. 1141| 138. 523| 8. 76| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |