Q.1.The diffusivity equation in terms of radial coordinates for slightly compressible fluids, which is the equation forming the basis for much welltest analysis, is shown below

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Explain the meaning of each of the terms in this equation. Name one assumption made in deriving this equation.

Q.2.Name three boundary conditions commonly used to explain different reservoir types.Sketch a log-log pressure + derivative plot for a heavily, naturally fractured reservoir.

Q.3. We have the oil flow rate vs. time shown below:

Time (h)01.53691218244872

Pressure (psi)5050494349374935492949274923492149164912

Oil viscosity = 0.5 cP, Oil formation volume factor = 1.75 RB/stb, oil rate =500 bopd, formation thickness = 60 ft, porosity = 0.2, compressibility = 1.5 x 10-5, rw = 0.16 ft and Skin = 0.0.With the software provided (welltest analysis-drawdown-sv), vary the permeability (k) value to match the data and thus obtain the permeability of the formation.

Q.4. A pressure build up test was carried out for 100 hours with an initial pressure of 4905 psi with the results shown in the table below:

Time (h)0102030405060708090100

Pressure (psi)49054916492549314937494249464950495349574960

Oil viscosity = 0.5 cP, Oil formation volume factor = 1.80 RB/stb, oil rate =400 bopd, formation thickness = 50 ft, porosity = 0.2, compressibility = 1.5 x 10-5, rw = 0.16 ft and Skin = 0.0. Initial reservoir pressure was 5000 psi. With the software provided (welltest analysis-buildup-sv), vary the permeability (k) value to match the data and thus obtain the permeability of the formation.