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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
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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
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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
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 Spring '08
 dicarlo
 Heat, Orders of magnitude, MD, power law shear

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