CHAPTER 1 FLUID FLOW THROUGH POROUS MEDIA Example 1
An incompressible fluid flow in a linear porous media with the following properties; L = 2000 ft Ø = 15% k = 100 md P2 = 1990 psia P1 = 2000 psia width = 300 ft h = 20 ft µ = 2 cp Calculate; a) Flowrate in bbl/day b) Apparent fluid velocity in ft/day c) Actual fluid velocity in ft/day Example 2
An incompressible fluid flows in a linear porous media with the following properties; L = 2500 ft
Ø = 17%
h = 30 ft
µ = 2 cp
width = 500 ft
inlet pressure = 2100 psia
k = 50 md
Q = 4 bbl/day
ρ = 45 lb/ft
3
Calculate and plot the pressure profile throughout t hroughout the linear system. Example 3
Assume that the porous media in Example 1 is tilted with a dip angle of 5 o. The incompressible fluid has a density of 42 lb/ft 3. Calculate; a) Flowrate in bbl/day b) Apparent fluid velocity in ft/day c) Actual fluid velocity in ft/day Example 4
A slightly compressible liquid with the average compressibility of 21 x 10 -5 psi -1 flows in a linear porous media with the following properties; L = 2000 ft k = 100 md P1 = 2000 psia h = 20 ft
Ø = 15% P2 = 1990 psia width = 300 ft µ = 2 cp
Calculate the flowrate at both ends of the formation.
Example 5
A gas of 0.7 specific gravity is flowing in a linear reservoir system at 150oF. The upstream and downstream pressures are 2000 and 1800 psia, respectively. The system has the following properties; L = 2000 ft k = 40 md width = 300 ft h = 15 ft Ø = 15% Calculate gas flowrate. Example 6
A natural gas with a specific gravity of 0.72 is flowing in linear porous media at 140 oF. The upstream and downstream pressures are 2100 and 1894.73 psia, respectively. The cross sectional area is constant at 4500 ft2. The total length is 2500 ft with an absolute permeability of 60 md. Calculate the gas flowrate is SCF/day. (Psc = 14.7 psia, T sc = 520oR). Example 7
Assuming steady state and an incompressible fluid, calculate the oil flowrate under the following condition; Pe = 2500 psia
rw = 0.3 ft
h = 30 ft
Pwf = 2000 psia
µo = 2 cp
k = 60 md
re = 745 ft
Bo = 1.4 bbl/STB
Then, plot the pressure profile in the formation (use 50 ft interval). Example 8
An oil well in X field is producing at a stabilized rate of 600 STB/day at a stabilized bottom-hole flowing pressure of 1800 psia. Analysis of pressure build up test indicates that the pay zone is characterized by a permeability of 120 md and a uniform thickness of 25 ft. The well drains an area of approximately 40 acres. Q o = 600 STB/day
A = 40 acres
Pwf = 1800 psia
rw = 0.25 ft
k = 120 md
µo = 2.5 cp
h = 25 ft
Bo = 1.25 bbl/STB
Calculate the pressure profile and list the pressure drop across 1 ft intervals from r w to 1.25 ft, 4 to 5 ft, 19 to 20 ft, 99 to 100 ft, and 744 to 745 ft.
Example 9
The following data is available on a well in X field; Pe = 2506 psia
co = 25 x 10-6 psi-1
h = 25 ft
re = 745 ft
Pwf = 1800 psia
k = 0.12 Darcy
Bo = 1.25 bbl/STB
rw = 0.25 ft
µo = 2.5 cp
Assuming slightly compressible fluid, calculate the oil flowrate.
Example 10
The PVT data from a gas well in the X field is given as follow; P, psia
0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400
µg, cp
z
0.0127 0.01286 0.01390 0.01530 0.01680 0.01840 0.02010 0.02170 0.02340 0.02500 0.02660 0.02831
1 0.937 0.882 0.832 0.794 0.770 0.763 0.775 0.797 0.827 0.860 0.896
The well is producing at a stabilized bottom-hole flowing pressure of 3600 psia. The wellbore radius is 0.3 ft. the following additional data is available; k = 65 md
h = 15 ft
Pe = 4400 psia
re = 1000 ft
Calculate the gas flowrate by using a) Real-gas potential solution b) Pressure-squared method
T = 600oR
Example 11
An oil well is producing at a constant flowrate of 300 STB/day under unsteady state flow conditions. The reservoir has the following rock and fluid properties; Bo = 1.25 bbl/STB
Ø = 15%
ct = 12 x 10-6 psi-1
k = 60 md
Pi = 4000 psia
rw = 0.25 ft
h = 15 ft
a) Calculate the pressure at radii of 0.25, 5, 10, 50, 100, 500, 1000, 1500, 2000 and 2500 ft for 1 hour. Plot P vs r. b) Repeat for t = 12 and 24 hours. Plot P vs r. Example 12
An oil well is producing at constant oil flowrate of 120 STB/day under a semisteady-state flow regime. Well testing data indicates that the pressure is declining at a constant rate of 0.04655 psi/hour. The following additional data is available; h = 72 ft
Ø = 25%
Bo = 1.3 bbl/STB
ct = 25 x 10-6 psi-1
Calculate the well drainage area. Example 13
An oil well is developed on the center of a 40 acre square drilling pattern. The well is producing at a constant flowrate of 100 STB/day under a semisteady-state condition. The reservoir has the following properties; Ø = 15%
h = 30 ft
k = 20 md
CA = 30.8828 -6
µ = 1.5 cp
Bo = 1.2 bbl/STB
ct = 25 x 10 psi
Pi = 4500 psia
rw = 0.25 ft
A = 40 acres
-1
a) Calculate and plot the bottom-hole flowing pressure as a function of time (t = 1, 10, 50, 100, 200 hours) b) Calculate the pressure decline rate
Pseudo critical properties of miscellaneous natural gases and condensate well fluids
The Z−factor correlation chart of Standing and Katz
Exponential Integral Table
