## 2

If we choose one of these (e.g., plastic), then the required lab diameter is set by Eq. (2-11):

~ ("m\ J0.00006\ , Dm = f f) =(48in-\0)Wj = 1-6in-

Since the roughness values are only approximate, so is this value of Dm. Thus we could choose a convenient size pipe for the model with a diameter of the order of 1.6 in. (for example, from Appendix F, we see that a Schedule 40, 11 in. pipe has a diameter of 1.61 in., which is fortuitous).

We now have five remaining unknowns—Qm, pm, pm, Lm and (AP)f— and only two remaining equations, so we still have three "arbitrary" choices. Of course, we will choose a pipe length for the model that is much less than the 700 miles in the field, but it only has to be much longer than its diameter to avoid end effects. Thus we can choose any convenient length that will fit into the lab (say 50 ft), which still leaves two "arbitrary" unknowns to specify. Since there are two fluid properties to specify (p and P), this means that we can choose (arbitrarily) any (Newtonian) fluid for the lab test. Water is the most convenient, available, and inexpensive fluid, and if we use it (p = 1 cP, p = 1 g/cm3) we will have used up all our "arbitrary" choices. The remaining two unknowns, Qm and (AP)f, are determined by the two remaining equations. From Eq. (2-12), p. V Dm V mm \ = (106 bbl y V16 V10

944bbl/day

/994bbl\ /42gal\/ 1 \ Qm = ((^bT) (,1440 min/day J = 27 ' 5gal/min(gpm)

Note that if the same units are used for the variables in both the model and the field, no conversion factors are needed, because only ratios are involved.

Now our experiment has been designed: We will use plastic pipe with an inside diameter of 1.6 in. and length of 50 ft and pump water through it at a rate of 27.5 gpm. Then we measure the pressure drop through this pipe and use our final equation to scaleup this value to find the field pressure drop. If the measured pressure drop with this system in the lab is, say, 1.2 psi, then the pressure drop in the field pipeline, from Eq. (2-13), would be

3480 psi

106 944

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