UBC Theses and Dissertations
Non-Newtonian oil flow through porous media Fariss, Tariq Fariss al-
A mathematical and experimental investigation was made of the flow through porous media of non-Newtonian fluids with yield stresses. The analysis of the problem was made in three parts: 1) Two models were developed to describe the flow through porous media of a power-law fluid with yield stress, la) Darcy's law was modified by coupling the Herschel-Bulkley rheological model with the capillary flow model and hydraulic gradient description of a porous medium to generate a generalized form of the flow equation as: [See Thesis for Chemical Diagrams] 2a) An oil which exhibited a rheological behaviour which was well described by the Herschel-Bulkley model was developed by adding paraffin wax to Newtonian oils. Two oils were used, Clarus-B and Clarus-C oils supplied by Shell Canada Company, with 2.5%, 4% and 5% paraffin wax for the preliminary tests. Crude oil from the Peace River field in Alberta was also found to exhibit the same behaviour. 2b) The flow characteristics of the test oils and the crude oil were measured using a rotational viscometer (Haake Rotovisco RV-12). 3) The three types of waxy oils were tested in two sand beds of 91 and 100 cm length with two sizes of particles 0.077 and 0.128 cm respectively, thus giving D[sub c]/D[sub p] ratios of 62.7 and 79.4 and porosities of 0.36 and 0.44. The flow behaviours of the waxy oils through the porous medium were determined over a wide range of flow rates (0.0057-17.4 ml/sec), Reynolds numbers (3.38 x 10⁻⁸- 0.33), pressure drops (3.11 - 299.6 kPa) , friction factors (8.9 x 10² - 2.86 x 10⁹), yield stresses (0.71 - 69.37 dyne/cm²), and temperatures (2-20°C). The experimental results show agreement with the mathematical models in the range of flow rates investigated. An average error of 3.64% and 5.5% was obtained with Clarus C and B respectively. The crude oil gave an average error 3.9%. The logarithmic least square fit of the f* - R*[sub e] correlation gave a correlation coefficient of 0.98 for the two artificial waxy oils, while the crude oil showed excellent fit for the correlation in a wide range of Reynolds numbers in the laminar region. There was some scatter in the data which was explained by sensitivity of the fitting parameter- (K) to small errors in the measurements of the rheological parameters n, τ[sub o] and H.
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