Problem 1
If the capillary pressure is given in psi, the surface tension in dynes/cm, and the formation permeability in mD, derive the constant in the Leverett J-function expression presented in class.

Problem 2
Consider a capillary tube of diameter 6 x10^-6 m containing a bubble of gas that is surrounded by water to the left and oil to the right. The interfacial tension of gas-water and gas-oil are 20 dynes/cm and 70 dynes/cm, and the corresponding angles are 30 degress and 45 degress, respectively. If the pressure in the water just to the left of the gas bubble is 100kPa, calculate the pressure in the oil phase just to the right of the gas bubble in order for the bubble to remain static. Assume that gas bubble is sufficient small so that the pressure drop across its length(within the bubble) is negligible.

Problem 3
Calculate and plot the height water rises in capillary tube as a function of tube radius. Consider the water air surface tension to be 70 mN/m, the water density 0.995 g/cc with the tube diameter varying between 0.01 inches to 0.05 inches.

Problem 4
a. Use Eq. 5.30 on page 347 to reproduce and plot the laboratory capillary pressure curve for the data reported in the Example on pages 353-354 of your textbook (Tiab and Donaldson, Third Edition). Note the units of capillary pressure in Eq. 5.30 are kPa.

b. If σ_water/air = 72 dynes/cm, θ_water/air =0^o, σ_oil/water = 25 dynes/cm, θ_oil/water = 40^o, convert the laboratory measured data to field conditions. Plot the field capillary pressure data. Note these are the data for layer 1 in a reservoir containing four layer with their properties reported in the table below.

c. Calculate and plot the Levertt J-function for reservoir.

d. As stated above, assume that the reservoir contains four layers of the following properties:

calculate the capillary pressure curves for layers 2 to 4, and plot them on the same graph as the one you prepare in question b above.