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# Midterm2010.KEY - NAME UT EID MIDTERM EXAM PGE 421K SPRING...

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NAME ___________________ SIGNATURE _____________________ UT EID ___________________ MIDTERM EXAM PGE 421K SPRING 2010 Open book and open notes. Answer all five questions on the exam paper; use your own engineering paper only if you need more space. Put your name and EID on any engineering paper you turn in. If you think you need more information to solve a problem, make a plausible assumption, write it down, and continue working. No credit for answers with inappropriate units. 1) Two immiscible, incompressible fluids are flowing in the control volume pictured below. Each mass flow rate and refers to the combined rate of both fluids. There are exactly two components A and B in system. For t 1 < t < t 2 , the rate of generation of component A in the control volume is negative. Which of the following must be true during the interval t 1 < t < t 2 ? Circle all that apply. 10 pts a. Net rate of accumulation of A in the CV is positive. b. Net rate of accumulation of total mass in the CV is positive. c. Net rate of accumulation of A in the CV is negative. d. Net rate of generation of B in the CV is positive. e. Net rate of transport of B across the CV boundaries is negative. We have , and during the time interval in question we also have . Since , where w A is the mass fraction of A in the streams flowing across the CV boundaries, it follows that the rate of accumulation of A in the CV is negative. Thus (a) cannot be true and (c) must be true. For the total mass in the CV, we have , because the rate of generation of total mass must be zero. Therefore (b) cannot be true. Because there are exactly two components in the system, the rate of destruction of A must equal the rate of creation of B . That is, , , so . Therefore (d) must be true. The rate of transport of component B across the CV boundaries is , so (e) must be true. 2 0 m Control Volume 1 0 m

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2) Work all four parts (a) - (d). Vast quantities of brine in deep, overpressured formations in south Texas contain dissolved methane. The binary system (CH 4 – H 2 O) phase diagrams for two temperatures are shown below (one set with linear x-axis, the other with logarithmic). Your company has acquired rights to a formation that is 12,000 ft deep. The aquifer conditions are 11500 psia and 280°F. A sample of the brine has been retrieved. Laboratory measurements indicate its bubble point is 5000 psia; its density, heat capacity and viscosity at reservoir conditions are 1100 kg/m 3 , 4.25 J/g/K and 0.44 cP. 30 points a) Estimate the concentration of CH 4 in the brine at aquifer conditions. Give your answer as a mole fraction. The bubble point tells you the pressure at which first bubble of gas forms from the brine at reservoir temperature. The intersection of P = 5000 psia and the bubble point curve (left hand curve on the P-x diagrams) shows the mole fraction of CH 4 would be 0.01 if the aquifer temperature were 250 F and 0.004 if the aquifer were at 300 F. Note it is much easier to determine the mole fraction from the log scale curves. Interpolation indicates that the mole fraction of CH 4 in our 280°F aquifer is about 0.007.
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Midterm2010.KEY - NAME UT EID MIDTERM EXAM PGE 421K SPRING...

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