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PGE 310 FALL 2005 EXAM 1
Work all five problems. Show your work on the exam paper. All questions are self-explanatory. If you think you need more data or information, then assume some values; write down your assumption, explain why you made it, and continue to work the problem. 1. (20 points). The pressure of gas leaving a compressor Pout (psia) depends on the mass g -4 ^ Pout & & flow rate m (ton/day) through the compressor W = 1.34 10 m PinVin g -1 Pin and the power input W (hp) according to the equation at the right: ^ Here Vin is the specific volume of the gas going into the compressor in ft3/lbmol; g is the ratio of specific heat capacities for the gas; Pin is the inlet pressure to the compressor (psia). Values for several operating parameters are
g -1 g
^ ~ ~
^ ~ - 1~ ~
Gas gravity g (ratio of specific heats) Inlet temperature to compressor Inlet pressure to compressor Inlet specific volume of the gas
0.7 1.3 540 degrees Rankine 50 psia 275 ft3/lbmol
You wish to apply Goal Seek to determine the outlet pressure when the mass flow rate is 12 ton/day and the power input is 15 hp. Enter values and formulae as appropriate in the worksheet below that would enable you to use Goal Seek for the computation. Note: do not attempt to compute a value for the outlet pressure just set up the worksheet so that you could compute a value.
2. (10 points). You created a spreadsheet in Problem 1. Suppose now that you invoke Goal Seek, causing the dialog box below to appear. Fill in the dialog box appropriately to compute the outlet pressure at the conditions prescribed in Problem 1.
3. A simplified analysis of the production of heavy oil from a steam-flooded reservoir yields two governing equations: an energy balance, given by Qsteam DH vap Y qoil = C p,oil (Treservoir - Tinit ) C p,oil ( t - t init ) and Darcy's law for steady radial flow, given by ^ 2.4 kh P - Pwf Treservoir qoil = - 1~ m 0 ln re T0 rw P is 800 psia. Wells are being produced at a The average reservoir pressure bottomhole pressure Pwf of 600 psia. A graphical solution for these conditions at time t = 125 days is shown below.
8 Darcy's Law 7 6 5 4 3 2 1 0 350 400 450 reservoir temperature, K 500 550 Energy balance
oil production rate, bbl/d
a. (15 points) What is the reservoir temperature at t = 125 days? The point of intersection is at q = 2.2 b/d and T = 438 K.
b. (20 points) If Pwf is reduced to 400 psi, the drawdown P - Pwf increases by a factor of two. Will the oil production rate i. increase by a factor of two; ii. increase by less than a factor of two; iii. decrease by a factor of two; Circle your answer and support it by carefully plotting the appropriate curve on the graph. No credit for answers without a plot. The equation for Darcy's law shows that doubling the drawdown will double the flow rate at any given reservoir temperature. The equation for the energy balance does not depend on drawdown, so it will not change. The graph for this situation is easily constructed from the existing plot: for several values of temperature, take the flow rate on the existing Darcy's law curve and double it. Connecting these points gives the graph for the larger drawdown. The point of intersection of this curve with the existing energy balance curve gives the new flow rate, about 3.2 b/d. It is larger than the old value, 2.2 b/d, but by less than a factor of two.
Frequency of Hurricanes (All Categories) Making Landfall in US 3
Number of hurricanes year per (averaged over a decade)
2.5 2 1.5 1 0.5 0 1850 1900 Year 1950 2000
4. (10 points) The possibility of hurricanes complicates the design of Gulf of Mexico production facilities. a. Considering the figure above (source: NOAA Technical Memorandum NWS TPC-4, August 2005), do you expect hurricanes to strike the US with greater frequency or smaller frequency in the next 10 years? Several interpretations of the data are possible. Peaks occur every 50 years or so, and so one might expect we are headed into another peak. Alternatively, the peak may be happening now, and in the next ten years there would be fewer storms. Simple extrapolation of recent data would suggest fewer storms. b. Is your answer data driven or model driven? This discussion is data driven. We are not considering any physical explanations for hurricane frequency, such as trends in the average sea-surface temperature.
5. (25 points) Forecasts of the demand for oil often require a proxy for human health and happiness. A spreadsheet, part of which is shown below, contains the Human Development Index (HDI) for the world's countries for several years, along with the Gross Domestic Product (GDP) for two years. You wish to determine whether an increase in HDI for a country is always associated with an increase in GDP. Create a formula (or set of formulae) that will return the word "YES" in column H, if the country's HDI was greater in 2001 than in 1990 and the country's GDP was greater in 2001 than in 1990. If these conditions are not met, the formula should return the word "NO".
country human development index GDP, $ does HDI correlate with GDP? 1990 2001 166905413632 221578800000 =IF(AND(I5,J5),"YES","NO") 8372942848 10499360000 =IF(AND(I6,J6),"YES","NO") 239762669568 300794500000 =IF(AND(I7,J7),"YES","NO") 388042948608 518382300000 =IF(AND(I8,J8),"YES","NO") 370921897984 511556000000 =IF(AND(I9,J9),"YES","NO") 227997761536 302216700000 =IF(AND(I10,J10),"YES","NO") 9762099953664 10881610000000 =IF(AND(I11,J11),"YES","NO") 706646638592 834390200000 =IF(AND(I12,J12),"YES","NO") 4763832811520 4326444000000 =IF(AND(I13,J13),"YES","NO") 240122970112 309465100000 =IF(AND(I14,J14),"YES","NO") 158452072448 212404200000 =IF(AND(I15,J15),"YES","NO") 94812880896 148553000000 =IF(AND(I16,J16),"YES","NO") did HDI increase? did GDP increase? =IF(E5>C5,TRUE,FALSE) =IF(G5>F5,TRUE,FALSE) =IF(E6>C6,TRUE,FALSE) =IF(G6>F6,TRUE,FALSE) =IF(E7>C7,TRUE,FALSE) =IF(G7>F7,TRUE,FALSE) =IF(E8>C8,TRUE,FALSE) =IF(G8>F8,TRUE,FALSE) =IF(E9>C9,TRUE,FALSE) =IF(G9>F9,TRUE,FALSE) =IF(E10>C10,TRUE,FALSE) IF(G10>F10,TRUE,FALSE) = =IF(E11>C11,TRUE,FALSE) IF(G11>F11,TRUE,FALSE) = =IF(E12>C12,TRUE,FALSE) IF(G12>F12,TRUE,FALSE) = =IF(E13>C13,TRUE,FALSE) IF(G13>F13,TRUE,FALSE) = =IF(E14>C14,TRUE,FALSE) IF(G14>F14,TRUE,FALSE) = =IF(E15>C15,TRUE,FALSE) IF(G15>F15,TRUE,FALSE) = =IF(E16>C16,TRUE,FALSE) IF(G16>F16,TRUE,FALSE) =
Norway Iceland Sweden Australia Netherlands Belgium United States Canada Japan Switzerland Denmark Ireland
1990 0.9 0.912 0.893 0.886 0.904 0.892 0.911 0.924 0.906 0.904 0.893 0.871
1995 0.924 0.918 0.924 0.926 0.925 0.923 0.923 0.929 0.92 0.912 0.91 0.895
2001 0.944 0.942 0.941 0.939 0.938 0.937 0.937 0.937 0.932 0.932 0.93 0.93