Question

To maximize production and minimize pumping costs, crude oil is heated to reduce its viscosity during transportation from a production field. (1) Consider a pipe-in-pipe configuration consisting of concentric steel tubes with an intervening insulating material. The inner tube is used to transport warm crude oil through cold ocean water. The inner steel pipe (k, =45 W/m K) has an inside diameter of D 150 mm and wall thickness t, = 20 mm while the outer steel pipe has an inside diameter of D = 250mm and wall thickness = 4.Determine the maximum allowable crude oil temperature to ensure the polyurethane foam insulation (kp =0.03 W/m-K) between the two pipes does not exceed its maximum service temperature of T 70°C. The ocean water is at T 5°C and provides an external convection heat transfer coefficient of h 500 W/m2-K. The convection coefficient associated with the flowing crude oil is h, = 450 W/m2-K. (2) It is proposed to enhance the performance of the pipe-in-pipe device by replacing a thin (r, = 10 mm) section of polyurethane located at the outside of the inner pipe with an aerogel insulation material (k, =0.012 W/m-K). Determine the maximum allowable crude oil temperature to ensure maximum polyurethane temperatures are below T mas = 70°C. Physical Properties Mathematical Functions Step 1 Determine the convection heat transfer resistance on the inside of the pipe per unit length, in m-K/W. Rconv m-K/W Step 2 Determine the conduction resistance of the polyurethane per unit length without the aerogel, in m-K/W. Rconda m-K/W Step 3 Determine the conduction resistance of the polyu rethane per unit length when aerogel is used, in m-K/W. m-K/W R 1,condp.ae= Step 4 Determine the maximum crude oil temperature if no aerogel is used, in °C T =i Step 5 Determine the maximum crude oil temperature if aerogel is used, in °C. PIC COLLAGE T = i

Answer 1

aThe case with ouut the aeTogel WWY. M Ronyi Rtylondsi Ritondp MNA RondRtconvo 9 7o0i-TmaysP obs Tmax pTos O Reondip+R't, cond sat Ruo RcoT,itR'tonda (Fmap-Too,oRbconwit R'trodis)mas i t Too,i (Rycondpt R,conds2+ R'conv,o) O.004716 m-KlW 450 Tix0 15 RCond n [250 Ci50r20) R.046 m-K Rtxondisi= lm{li50+20/ 150] 0.000443 m-k 2Tメ45 Rtycond S2 250+201250 0 00027m-k 2T1X45 Rtcono 500XTT x0.27 0.002358 m-k To 10--50.004716t0-oo0443) (R.046t 0-00021+0.002358) +TO Too 10.ac b) -Thermal esistance yetwork with bmis0120+101 50+RO T-012) 158 -k T4 m- K Rpond P n(250180] RTXO 03 Too(RConV i + R,onbsit R1condag) Tooi (Tmax,P Rt,cond/p + R, COndsa t R4,(onvo +Tmax, p O 004T6 T O 000443 t 0758) + 70 (10-(X J.74 t0.00027 t0.002 358 Too, i 102.8°C