mid3_solution - PGE 322K — TRANSPORT PHENOMENA Fall 2008...

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Unformatted text preview: PGE 322K — TRANSPORT PHENOMENA Fall 2008 EXAM 3 . Nov 17,2008 Except where noted, do all calculations in SI units ' BEWARE OF UNNECESSARY INFORMATION. ? DO NOT SPEND TOO LONG ON ANY ONE PROBLEM. DO NOT LEAVE ANY PROBLEM BLANK! YOU CAN START ANWERS FROM EQUATIONS IN BSL, JUST GIVE THE EQUATION NUMBER T0tal:100 pts NAME Solfi’fiofi 394’ Fall 2008 1. (20 pts) Your technician gives you the following data for flow through a certain porous medium. He has measured the flux (11), as a function of the head drop (AH) or sample length (L) for a power law shear thinning fluid, a Bingham fluid, and a power law shear thickening fluid. Unfortunately he forgot to label the graphs. You need to help him by labeling each graph with the fluid it corresponds to. w; Hp"; (r AH AH Q) (dole/i“ "smogch omeetw 3&ng U mug/L U Fall 2008 i i i i E i g . D {NuHUUn-Str 909‘ K1 We 4. (gpts) Flow away from an injection well. The process of drilling destroys the rock to make the well bore. This destructive process creates fines which migrate and lower the permeability of the rock near the well bore; this is known as the skin. Assume that your original reservoir rock had a permeability of 300 mD. The migration of fines has reduced the permeability of the rock within the first 1 cm of the well bore. Your well bore is 10 cm in diameter, you are injecting water, and your formation is 10 m thick. You inject water (viscosity = 10'3 Pa 5) at a rate of :1 0:5 m3/sec. You measure the head drop 1m from the center of the well bore and find it tobe 104 Pa. Calculate the permeability of the 1 cm thick skin. (Hint: There are two ways to go about this problem, one is a shell balance; the other way is to notice the parallels between this problem and another transport problem (not necessarily fluid flow) in ESL. If you use the second method state the parallels between the example problem and this problem). Side view Well bore Top view of the well bore and the surrounding rock Impermeable Rock Reservoir 300 mD Impermeable Rock txfi L 6H .1. 1M ‘\ r L JR 55" ‘ ka H r0 “1 ‘\ Fall 2008 gwm 3mm; 7E. vmuab Tame «D 50mg, 90¢ ' K \ ,. _ _ n R Q h (‘0'; 50—" r\’€)<-‘~\ I ( -\o a "'3 . ’ ABme :\o :m’ . Hgkwak ” 3 Q 1 \C)3 M Aka, 7.1T Mo)(\o‘\ \ AM, 4‘ L» L00 Z W T ( “’ 3&6“) ‘3 \o ‘10 \ ‘L 4 \3 ,L (a W13 «- qhflym‘ _ (Ll? mo H .J3’ 06L (,GT « ~1 ' r . \ L1 (& ' A)” x V LP” “Wm w :SN “0 CWWV out m cm 60,, m wfiow W, Wawey (b‘l mower A sue/k» WQ No “AT “mm Sufckx bWuX; CNS/3 you F 3 a Q/mL go‘s-2v ; BN9 you at») axon (fl EL 0" (ff F _ -K AH M“ +45% can“, 425. (SW 7; W sue. (Jars H44 : A. Q r (A ~ o cm «7 s. M “1' L“ " .f: >3“ Lyn/r) «:6 w me one? KL Fa112008 WM m\> 0°51“ (5E. 06TBtN¥D‘ MD “150ka (’0Q_ Water bath with T=TO _ Constant heat Newton’s law of cooling generation of Sn applies at surface with heat transfer coefficient h 3) (40 pts) Consider a spherical nuclear element (radius R) where the heat generation per unit volume per unit time is uniform Within the element (i.e. no r dependence like chapter 10.3 in ESL) and is given the value Sn. There also is no cladding, and the outside of the element is in a water bath of temperature T0. Newton’s law of cooling applies at the surface with a heat transfer coefficient h. Derive a formula for the steady state temperature distribution T(r) within the sphere. sith (swat. “4“” “w” an» ’V QWMWV‘Q 1 &°“’ amt + w‘orsn = we“er ‘ CM“ 6‘3 - -énr <i «=0 e :35? = " “t” *7" ...
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This note was uploaded on 11/18/2010 for the course PGE 322K taught by Professor Dicarlo during the Spring '08 term at University of Texas.

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mid3_solution - PGE 322K — TRANSPORT PHENOMENA Fall 2008...

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