Reservoir Engineering (Home work 3) (05/03/2010)
Due 05/10/2010 下禮拜要交喔 請大家加油!!!
7.2 A sand body is 1500ft long, 300ft wide, and 12ft thick. It has a uniform
permeability of 345md to oil at 17% connate water saturation. The porosity is
32%. The oil has a reservoir viscosity of 3.2cp and Bo of 1.25 bbl/STB at the
bubble point.
(a) If flow takes place above the bubble-point pressure, what pressure drop will cause
100 reservoir bbl/day to flow through the sand body, assuming the fluid behaves
essentially as an incompressible fluid? What for 200 reservoir bbl/day?
(b) What is the apparent velocity of the oil in feet per day at the 100 bbl/day flow
rate?
(c) What is the actual average velocity?
(d) What time will be required for complete displacement of the oil from the sand?
(e) What pressure gradient exists in the sand?
(f) What will be the effect of raising both the upstream and downstream pressures by,
say, 1000 psi?
(g) Considering the oil as a fluid with a very high compressibility of 65(10)-6 psi-1,
how much greater is the flow rate at the downstream end than the upstream end at
100 bbl/day?
(h) What pressure drop will be required to flow 100 bbl/day, measured at the
upstream pressure, through the sand if the compressibility of the oil is 65(10)-6
psi-1 ? Consider the oil to be a slightly compressible fluid.
(i) What will be the downstream flow rate?
(j) What conclusion can be drawn from these calculations concerning the use of the
incompressible flow equation for the flow of slightly compressible liquids, even
with high compressibilities?
7.7
(a) Three beds of equal cross section have permeabilities of 50, 200, and 500 md and
lengths of 40, 10, and 75 ft, respectively. What is the average permeability of the
beds placed in series?
(b) What are the ratios of the pressure drop across the individual beds for liquid
flow?
(c) For gas flow will the overall pressure drop through beds in series be the same for
flow in either direction? Will the individual pressure drops be the same?
(d) The gas flow constant for a given linear system is 900, so that p12-p22 = 900 L/k.
If the upstream pressure is 500 psia, calculate the pressure drops in each of two
beds for series flow in both directions. The one bed is 10 ft long and 100 md; the
second is 70 ft and 900 md.
(e) A producing formation from top to bottom consists of 10 ft of 350 md sand, 4 in.
of 0.5 md shale , 4 ft of 1230 md sand, 2 in. of 2.4 md shale, and 8 ft of 520 md
sand. What is the average vertical permeability?
(f) If the 8 ft of 520 md sand is in the lower part of the formation and carries water,
what well completion technique will you use to keep the water-oil ratio low for
the well? Discuss the effect of the magnitude of the lateral extend of the shale
breaks on the well production.
7.8
(a) Three beds of 40, 100, and 800 md, and 4, 6, and 10 ft thick, respectively, are
conducting fluid in parallel flow. If all are of equal length and width, what is the
average permeability?
(b) In what ratio are the separate flows in the three beds?