PETROLEUM ENGINEERING LABORATORY IIIPET 527EXPERIMENT 2: PERMEABILITY DETERMINATION (FLUIDIZED BED)OLUWASIJUWOMI TOYOSI DAVID13CN015642FOR THE PARTIAL REQUIREMENT OF PET 527, SUBITTED TO DEPARTMENT OF PETROLEUM ENGINEERING, COVENANT UNIVERSITY, OTA.ABSTRACTThis report is aimed at the determination of permeability from a fluidized bed. The ability of a reservoir to transmit fluid is largely dependent on the porous and permeable media. The ease at which fluids can flow through a rock is also dependent on the interconnection between the pore spaces. Some of the factors that are considered is the pressure in the rock. The capacity of reservoir rocks to allow the transmission of fluid is known as permeability. In this report we are aimed at calculating the permeability using a fluidized bed. This report is divided into 4 chapters. Chapter1 is the Introduction to what permeability and its parameters, chapter 2 is Experiment which involves the procedures used in achieving required result. Chapter 3 is the analysis of results gotten from the Experiment. Chapter 4, includes the observations and conclusion made.CHAPTER ONEINTRODUCTIONThe experiment carried out explains the theory of the flow of fluid through a porous media. This is therefore necessary that a pressure drop occurs along the total length of the material in use. Some factors that contribute to the change in pressure, and this may include the velocity of fluid, the viscosity of the fluid and cross-sectional area. Permeability is said to be the ability for a reservoir rock to transmit fluid under a potential gradient.The value of permeability (k), for a specified reservoir rock is dependent on the diameter of the pores (d) and also the connection that exist between the rock pore spaces. Permeability can be linked to various variables such as the rock type, and the variation with the stress and temperature, but not dependent on the effect of the fluid on the flowrate, the viscosity of the fluid is very important and be in terms of the darcy equation. Fluidization is a process whereby a granular material (porous media) is converted from a static solid-like state to a dynamic fluid-like state. This process occurs when a fluid (liquid or gas) is passed up through the granular material. This is a process similar to liquefaction. In fluidization, a bed of particles is converted to a fluid state by means of an upward flow of gas (or liquid).The experiment carried by darcy brought about the Darcy’s Law equation stated below;q=(kA?P )/??LWhere:q= Flow rate of the fluid, m3/s?=Viscosity of the fluid,kg/ms ?P=Pressure Drop,N/m2 ?L=Length of Material in use,m A= Cross-sectional Area, m2Listed below are the assumptions made by the Darcy law; The core plug is saturated with a single-phase fluid. Density of the flowing fluid is constant The system under goes a steady state flow (Qin = Qout) The flow is under laminar regime. The flow of fluid is under viscous regime, i.e. the flow rate is so low that it is proportional to pressure difference The fluid does not react with the porous medium. For fluidized bed, the Kozeny-Carman equation (or Carman-Kozeny equation) is often used in the field of fluid dynamics to determine pressure drop of a fluid flowing it. This equation predicts the relationship that exist between the permeability and the average grain diameter.Kozeny-Carman equation: ?? =d^2/180 ?^3/?(1-?)?^2 Where:k= Permeability, m2d=Grain Diameter, m ?=PorosityCHAPTER TWO EXPERIMENTAPPARATUS/EQUIPMENT USEDThe Apparatus used for this Experiment is the Armfield W3 Permeability/Fluidization Apparatus Fig 1: W3 Permeability/Fluidization ApparatusThe Permeability/Fluidisation Apparatus is designed for determining the flow characteristics through a porous media such as a bed of particles. The apparatus can also be used for a part of the testing of media for water and waste filtration. Concisely, the apparatus can be used to determine the following: Pressure drop correlations for flow through packed beds Verification of Kozeny Carman;s Equation Characteristics of a fluidized bed Permeability MeasurementsOther equipment used are: Beaker ThermometerPROCEDURECONDUCTING THE EXPERIMENT1. I closed all valve V1, V2, V3 and V4 and while I opened valves V5 and V6. On the other hand the valves V7 and V8 were closed before the experiment 2. The channel was not too firm. And the consolidation was in such a way that any form of vibration would cause the channel level is drop.3. I placed the drain tube from valve V4 into a beaker so as to drain the water flowing through it. I then inserted a thermometer into the beaker to read the temperature of the water leaving the apparatus. 5. I then noted the level of the media surface/permeable bed as L. I also recorded the water levels in the manometers a and b. 6. I then opened valves V1 and V4 to allow water flow downwards through the permeable bed. I adjusted the valves for four settings of flow- 50, 150, 200 and 250cm3/min on the flow meter and I recorded the readings on the manometer. 7. I then took readings with decreasing flow back to zero (250,200,150,100,50,0). Which included the reading of the Temperature. PRECAUTIONS I ensured that the tubing to the manometer was full of water and it was void of any air bubbles clear of air bubbles. I prevented parallax error of the manometer and flow meter by reading values accurately and not at an angle. I ensured there was proper lighting in the room to be able to read values accurately. At the conclusion of the experiment, I disconnected the water supply to the constant head tank and drain the contents of the tank.CHAPTER FOUR RESULTS AND ANALYSISRECORDED VALUES Mass of the Material, MM = 565g = 0.565kg Density of the Mateial, pM = 1522.89kg/m3 Length of the Permeable Bed, L = 3.29mm = 0.329m Mean Temperature of the water, T = 280C Density of Water = 996.26kg/m3 Dynamic Viscosity of Water = 0.8363kg/msCalculated Values Cross-sectional area of flow (m2), ?? = (?D^2)/4= (??(0.038)?^2)/4 = (4.537 X ?10?^(-3))/4= 1.1343 X 10-3m2 Bulk volume of material (m3), VB = AL = 1.1343 X 10-3m2 X 0.329m = 3.73 X 10-4m3 Grain volume of material (m3), ???? = M_M/?_M = 0.565/2500 m3 = 0.000226 m3 = 2.26 X 10-4m35. Pore volume of material (m3), VP = VB – VG = 3.73 X 10-4m3 – 2.26 X 10-4m3 = 1.47 X 10-4m3 Porosity (%), ?? = V_P/V_B = (1.47 X ?10?^(-4))/(3.73 X ?10?^(-4) ) = 0.3805 = 39.41% 7. TABLE OF RESULTSQ (cm3/min) Q (m3/s) V=(m/s) =Q/A Manometer Readings (mm) Manometer Difference ?h (mmH2O) (a-b) ?P (N/m2) A b =9.81 × ?W × ?h 0 0.000E+00 0.000E+00 213 255 0.042 410.550 8.3E-07 7.32E-4 187 285 0.098 957.8100 1.67E-06 1.47E-03 159 321 0.162 1583150 2.5E-06 2.2E-03 130 363 0.233 2277200 3.33E-06 2.94E-03 104 401 0.297 2903250 4.17E-06 3.68E-03 74 446 0.372 3636 Q (cm3/min) Q (m3/s) V=(m/s) =Q/A Manometer Readings (mm) Manometer Difference ?h (mmH2O) (a-b) ?P (N/m2) A b =9.81 × ?W × ?h 250 4.17E-06 0.000E+00 74 446 0.372 3635.672200 3.33E-06 7.32E-4 91 416 0.326 3186.099150 2.5E-06 1.47E-03 118 373 0.255 2492.194100 1.67E-06 2.2E-03 150 330 0.18 1759.19650 8.33E-06 2.94E-03 181 292 0.111 1084.8370 0 3.68E-03 211 255 0.044 430.0257 10. Permeability (m2), ?? =(?_w X ?L)/(A X m) = =(0.8746 X 0.329)/(0.001134 X 887645.8705) = 2.73 × 10-4m21 Darcy m2x Darcy = 2.73 × 10-4m211. From Kozeny-Carman equation: ?? =d^2/180 ?^3/?(1-?)?^2 (1.35*?10?^(-3))/180 ?0.3941?^3/?(1-0.3941)?^2 k=1.688 × 10-9Average grain diameter (m), ?? = ?(180k ?(1-?)?^2/?) ?(180(1.25 × 10-6)?(1-0.3941)?^2/0.3941)D = 5.32 × 10-4 mm12. Answersa) Porosity, (%)= 0.5362%b) Permeability, k (Darcy)= (1.668* ?10?^(-9))/(0.987*?10?^(-12) ) = 1689.96 Darcyc) Average grain diameter, d (millimeters) = CHAPTER FIVEOBSERVATIONS AND CONCLUSIONSOBSERVATIONSI observed that at high flow rates where the flow regime was not laminar, Darcy’s Law and Kozeny-Carman Equation did not accurately predict pressure drop trend with length.Due to the hazards involved in handling mercury, water was used in the manometer for safety reasons.CONCLUSIONSThe experiment carried out made an observation that the permeability is a dynamic property a reservoir rock as regards to flow. Also it was known that the pressure drop across the material was directly proportional to the velocity of the fluid (flowrate) as far as properties such as Cross-sectional area is constant.
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