Exercise 1The following table gives porosity and permeability measured on core plugs from a reservoir.

Depth h Porosity k(ft) (ft) (%) (md)

2880 1 29.5 15002881 1 28.9 12712882 1 28.5 12392883 1 28.1 11842884 1 28.8 18912885 1 27.9 15002886 1 29.2 12712887 1 29.0 15652888 1 29.7 13252889 1 27.4 9672890 1 27.8 7172891 1 28.0 7282892 1 27.5 6002893 1 22.2 5542894 1 20.3 1302895 1 21.5 2182896 1 25.5 4662897 1 24.9 6842898 1 27.2 6002899 1 23.7 3362900 1 21.9 1502901 1 22.0 2772902 1 19.4 782903 1 17.4 1012904 1 18.4 822905 1 16.7 822906 1 16.9 492907 1 17.1 362908 1 15.9 232909 1 16.5 202910 1 13.0 102911 1 16.8 562912 1 17.3 492913 1 17.8 262914 1 17.8 332915 1 15.6 262916 1 17.4 362917 1 17.3 422918 1 16.8 332919 1 16.6 392920 1 17.2 52

2921 1 16.9 562922 1 15.2 332923 1 16.1 462924 1 17.4 362925 1 14.8 292926 1 15.7 332927 1 15.7 232928 1 15.6 332929 1 15.5 32

Find the mean, the median (P50), P90, P10 and the mode of the distribution of porosity (for the mode lump by intervals of 1%).Find a correlation between porosity and permeability.

Compare the averages. Compare VDP for porosity and permeability.

Exercise 2: Darcy’s Law1- Consider a cylindrical core plug that has a radius of 0.5 in. and a length of 2 in. Suppose the core is flooded with an oil that has viscosity = 0.5 cp, formation volume factor = 1.0 RB/STB,and a measured flow rate = 0.1 BOPD. If the pressure drop from the inlet to the outlet is 20 psia, what is the permeability of the plug?.Hint: Express area A in sq. ft. and length L in ft. Solve Darcy’s Law for permeability.Q= C.k.A.ΔP/(LμB) where the coefficient C = 0,001127 with k in md, μ in cp, A in sq.ft, P in psi, Lin ft, Q in BOPD, B in reservoir volume per surface volume.2- Suppose that water (viscosity = 1.0 cp, FVF = 1.0 RB/STB was used instead of oil. Use the permeability calculated to estimate the water flow rate, assuming the same permeability to single phase flow.

Exercise 3: Equivalent permeability1- Calculate the equivalent linear permeability of 4 parallel beds having equal widths & lengths:Bed Thickness (ft) k (md)

1 5 2502 8 2003 15 1304 20 80

2- Calculate the equivalent permeability a radial system comprised of 3 zones with the following characteristicsZone Inner radius (ft)Outer radius (ftk (md)

1 0.25 5 102 5 150 803 150 750 150

Exercise 4: Darcy’s Law in a tilted reservoir1- An incompressible fluid flows in a linear porous medium with the following properties:

Calculate flowrate in bbl/d, apparent fluid velocity & its real velocity in ft/d.2- Assume that this medium is tilted with a dip angle of 5°. The incompressible fluid has a density of 42 lb/ft3. Calculate the same as in 1.

Exercise 5: Skin Effect (Vertical or Horizontal well)

Calculate the arithmetic, the harmonic and the geometric averages and the ratio VDP

= ka/kh (Dykstra-Parsons heterogeneity index) for porosity and permeability.

L = 2000 ft, h = 20 ft, width = 300 ft, k = 100 mD, φ = 15%, μ = 2 cp, ΔP = 10 psi.

Exercise 6: Oil wellAn oil well with a radius of 0.25 ft is producing at a stabilized rate of 600 stb/d at a stabilized bottom-hole flowing pressure of 1800 psi. The pay zone, 25 ft thick, has a permeability of 120 md, and the drainage area of about 40 acres is roughly circular. The oil has a Bo of 1.25 rb/stb and a viscosity of 2.5 cp at reservoir temperature. Calculate the pressure profile and list the pressure drop across 1 ft at the intervals 4-5 ft, 19-20 ft, 99-100 ft, 1 ft interval at the boundary of the drainage area.

Exercise 7: Gas wellThe PVT data from a gas well is given below:

400 0.01286 0.937 800 0.01390 0.8821200 0.01530 0.8321600 0.01680 0.7942000 0.01840 0.7702400 0.02010 0.7632800 0.02170 0.7753200 0.02340 0.7973600 0.02500 0.8274000 0.02660 0.8604400 0.02831 0.896The well, with a radius of 0.3 ft, is producing at a stabilized flowing pressure of 3600 psi and the pressure is 4400 psi at the boundary of the drainage area which has a radius of 1000 ft. The reservoir is 15 ft thick; its temperature is 140 °F and its permeability is 65 md. Calculate the gas flow rate in Mscf/d.

Exercise 8: Equivalent tube or fissureA porous medium has a length of 100 ft, a section of 30ft×10ft, a porosity of 10% and a permeability of 10 md. Calculate the diameter of an equivalent tube or the aperture of an equivalent fracture (parallel either to its width or to its height) and the equivalent porosity.

Exercise 9Assuming a log-normal distribution of permeability, calculate the Dykstra-Parsons coefficient of variation defined as: VDP = exp(-(ln(kA/kH))1/2) for the following distribution (kA: arithmetic average, kH harmonic average)

k (md)1 352 483 1484 2025 906 4187 7758 609 682

10 47211 12512 300

Calculate the skin factor due to radial damage with: rw (wellbore radius) = 0.328 ft, permeability impairment: k/ks = 5, damage penetration = 0.5 ft.

P (psia) μg (cp) Z

0 0.01270 1.000

13 13814 19115 350

kAkHVDP

Exercise 101- Consider a cylindrical core plug that has a radius of 0.5 in. and a length of 2 in. Suppose the core is flooded with an oil that has viscosity = 0.5 cp, formation volume factor = 1.0 RB/STB, and a measured flow rate = 0.1 BOPDIf the pressure drop from the inlet to the outlet is 20 psia, what is the permeability of the plug?.Hint: Express area A in sq. ft. and length L in ft. Solve Darcy’s Law for permeability.Q= C.k.A.ΔP/(LμB) where the coefficient C =0,001127 with k in md, μ in cp, A in sq.ft, P in psi, Lin ft, Q in BOPD, B in reservoir volumeper surface volume.2- Suppose that water (viscosity = 1.0 cp, FVF = 1.0 RB/STB was used indtead of oil. Use the permeability c

Exercise 11A build-up test has been performed on a well completed over the whole pay zone in a reservoir formed of 4 layers, with the following thicknesses and permeabilities measured on cores :Layer # 1 2 3Thickness (ft 5 10 15Porosity (%) 16 13.3 11.6Sw (%) 15 20 22k (md) 20 8 4What would be the permeability expected from the B-U test?What are the shares of the 4 layers in total flowrate?Compare depletion rates for the 4 layers.

The following table gives porosity and permeability measured on core plugs from a reservoir.

Find the mean, the median (P50), P90, P10 and the mode of the distribution of porosity (for the mode lump by intervals of 1%).

1- Consider a cylindrical core plug that has a radius of 0.5 in. and a length of 2 in. Suppose the core is flooded with an oil that has viscosity = 0.5 cp, formation volume factor = 1.0 RB/STB,

If the pressure drop from the inlet to the outlet is 20 psia, what is the permeability of the plug?.

Q= C.k.A.ΔP/(LμB) where the coefficient C = 0,001127 with k in md, μ in cp, A in sq.ft, P in psi, Lin ft, Q in BOPD, B in reservoir volume per surface volume.2- Suppose that water (viscosity = 1.0 cp, FVF = 1.0 RB/STB was used instead of oil. Use the permeability calculated to estimate the water flow rate, assuming the same permeability to single phase flow.

1- Calculate the equivalent linear permeability of 4 parallel beds having equal widths & lengths:

2- Calculate the equivalent permeability a radial system comprised of 3 zones with the following characteristics

2- Assume that this medium is tilted with a dip angle of 5°. The incompressible fluid has a density of 42 lb/ft3. Calculate the same as in 1.

DP = ka/kh (Dykstra-Parsons heterogeneity index) for porosity and permeability.

An oil well with a radius of 0.25 ft is producing at a stabilized rate of 600 stb/d at a stabilized bottom-hole flowing pressure of 1800 psi. The pay zone, 25 ft thick, has a permeability of 120 md, and the drainage area of about 40 acres is roughly circular. The oil has a Bo of 1.25 rb/stb and a viscosity of 2.5 cp at reservoir temperature. Calculate the pressure profile and list the pressure drop across 1 ft at the intervals 4-5 ft, 19-20 ft, 99-100 ft, 1 ft interval at the boundary of the drainage area.

The well, with a radius of 0.3 ft, is producing at a stabilized flowing pressure of 3600 psi and the pressure is 4400 psi at the boundary of the drainage area which has a radius of 1000 ft. The reservoir is 15 ft thick; its temperature is 140 °F and its permeability is 65 md. Calculate the gas flow rate in Mscf/d.

A porous medium has a length of 100 ft, a section of 30ft×10ft, a porosity of 10% and a permeability of 10 md. Calculate the diameter of an equivalent tube or the aperture of an equivalent fracture (parallel either to its width or to its height) and the equivalent porosity.

Assuming a log-normal distribution of permeability, calculate the Dykstra-Parsons coefficient of variation defined as: VDP = exp(-(ln(kA/kH))1/2) for the following distribution (kA: arithmetic average, kH harmonic average)

Calculate the skin factor due to radial damage with: rw (wellbore radius) = 0.328 ft, permeability impairment: k/ks = 5, damage penetration = 0.5 ft.

1- Consider a cylindrical core plug that has a radius of 0.5 in. and a length of 2 in. Suppose the core is flooded with an oil that has viscosity = 0.5 cp, formation volume factor = 1.0 RB/STB, and a measured flow rate = 0.1 BOPDIf the pressure drop from the inlet to the outlet is 20 psia, what is the permeability of the plug?.Hint: Express area A in sq. ft. and length L in ft. Solve Darcy’s Law for permeability.Q= C.k.A.ΔP/(LμB) where the coefficient C =0,001127 with k in md, μ in cp, A in sq.ft, P in psi, Lin ft, Q in BOPD, B in reservoir volumeper surface volume.2- Suppose that water (viscosity = 1.0 cp, FVF = 1.0 RB/STB was used indtead of oil. Use the permeability c

A build-up test has been performed on a well completed over the whole pay zone in a reservoir formed of 4 layers, with the following thicknesses and permeabilities

45

16.32222

1- Consider a cylindrical core plug that has a radius of 0.5 in. and a length of 2 in. Suppose the core is flooded with an oil that has viscosity = 0.5 cp, formation volume factor = 1.0 RB/STB,

2- Suppose that water (viscosity = 1.0 cp, FVF = 1.0 RB/STB was used instead of oil. Use the permeability calculated to estimate the water flow rate, assuming the same permeability to single phase flow.

An oil well with a radius of 0.25 ft is producing at a stabilized rate of 600 stb/d at a stabilized bottom-hole flowing pressure of 1800 psi. The pay zone, 25 ft thick, has a permeability of 120 md, and the drainage area of about 40 acres is roughly circular. The oil has a Bo of 1.25 rb/stb and a viscosity of 2.5 cp at reservoir temperature. Calculate the pressure profile and list the pressure drop across 1 ft at the intervals 4-5 ft, 19-20 ft, 99-100 ft, 1 ft interval at the boundary of the drainage area.

An oil well with a radius of 0.25 ft is producing at a stabilized rate of 600 stb/d at a stabilized bottom-hole flowing pressure of 1800 psi. The pay zone, 25 ft thick, has a permeability of 120 md, and the drainage area of about 40 acres is roughly circular. The oil has a Bo of 1.25 rb/stb and a viscosity of 2.5 cp at reservoir temperature. Calculate the pressure profile and list the pressure drop across 1 ft at the intervals 4-5 ft, 19-20 ft, 99-100 ft, 1 ft interval at the boundary of the drainage area.

An oil well with a radius of 0.25 ft is producing at a stabilized rate of 600 stb/d at a stabilized bottom-hole flowing pressure of 1800 psi. The pay zone, 25 ft thick, has a permeability of 120 md, and the drainage area of about 40 acres is roughly circular. The oil has a Bo of 1.25 rb/stb and a viscosity of 2.5 cp at reservoir temperature. Calculate the pressure profile and list the pressure drop across 1 ft at the intervals 4-5 ft, 19-20 ft, 99-100 ft, 1 ft interval at the boundary of the drainage area.

An oil well with a radius of 0.25 ft is producing at a stabilized rate of 600 stb/d at a stabilized bottom-hole flowing pressure of 1800 psi. The pay zone, 25 ft thick, has a permeability of 120 md, and the drainage area of about 40 acres is roughly circular. The oil has a Bo of 1.25 rb/stb and a viscosity of 2.5 cp at reservoir temperature. Calculate the pressure profile and list the pressure drop across 1 ft at the intervals 4-5 ft, 19-20 ft, 99-100 ft, 1 ft interval at the boundary of the drainage area.