List of practice Questions

In a three-dimensional \( xyz \)-space, if \( \vec{v} = 3z \hat{i} + 2z \hat{j} + z \hat{k} \), and \( \text{curl}(\vec{v}) = a \hat{i} + b \hat{j} + c \hat{k} \), then the value of \( (a + b + c) \) is ________________ (in integer).

If Z is the standard normal variable having mean 0 and standard deviation 1, then the probability of occurrence of Z in the range of –3 to 3 is ________________ (rounded off to three decimal places). Given: \[ \text{erf}(z) \approx \tanh \left( \frac{167z}{148} + \frac{11z^3}{109} \right) \]

The local minimum value of the real function \[ f(x) = 2x^3 - 21x^2 + 36x - 20 \] is __________ (in integer).

Consider the following ordinary differential equation: \[ \frac{dy}{dx} = x^2y \] The initial value is \( y(0) = 1 \) and the step-size is 0.1. Solving this differential equation by Euler’s first-order method, the value of \( y(0.2) \) is ____________ (rounded off to three decimal places).

In a horizontal circular pipe, liquid and gas are flowing concurrently at the same superficial velocity. However, the average velocity of the gas is greater than the average velocity of liquid. If the slip velocity is equal to the superficial velocity of each of the phases, the fractional liquid holdup is ____________ (rounded off to two decimal places).

A 1 kg-mol bottled gas consists of the following composition at 30\(^\circ\)C. The equilibrium vapour composition of n-Butane in mol % is ____________ (rounded off to two decimal places).

Well testing is to be conducted on the bounded sandstone reservoirs as shown in the figures. All the reservoirs have the same drainage area, rock and fluid properties, and well bore conditions. Which of the following statements are CORRECT for the given reservoirs?

The following data are given for an oil well scheduled for a drawdown test.

Total compressibility = \( 20 \times 10^{-6} \, \text{psi}^{-1} \)
Oil compressibility = \( 100 \times 10^{-6} \, \text{psi}^{-1} \)
Volume of fluid in the wellbore = 180 rb
Average oil density in the wellbore = 45 lb/ft\(^3\)
Tubing outer diameter = 2 inch
Casing inner diameter = 7.675 inch
Porosity = 15%
Wellbore radius = 0.25 ft
Oil viscosity = 2 cP
Pay zone thickness = 50 ft
Skin factor = 0
Permeability = 30 mD
If the well is tested at a constant rate, the ‘Wellbore Storage Effect’ would sustain for ______________ hours (rounded off to two decimal places).

During the core analysis, the following data are measured at laboratory and reservoir conditions.

The capillary pressure at the laboratory condition is 50 psi. The calculated capillary pressure using the Leverett J-function at the reservoir condition is ________________ psi (rounded off to two decimal places).

The total oil production rate (measured at the bottom hole conditions) from a volumetric reservoir is 200 bbl/day (1 bbl = 5.615 ft\(^3\)) at the flowing bottom hole pressure (FBHP) of 3000 psi. The reservoir has the following properties:

Considering a radial flow under pseudo steady state, the bottom hole pressure after 180 days is ________________ psi (rounded off to two decimal places).

An incompressible fluid (density = 40 lb/ft\(^3\)) flows at a steady state through a linear porous media with the following properties:

Length (L) = 1500 ft
Height (H) = 15 ft
Width (W) = 30 ft
Permeability = 150 mD
Viscosity = 1.5 cP
Inlet pressure (P\(_1\)) = 1600 psi
Outlet pressure (P\(_2\)) = 1590 psi
Porosity = 18%

The absolute value of the difference between the actual fluid velocity (ft/day) at \( \theta = 0^\circ \) and \( \theta = 10^\circ \) is ______________ (rounded off to three decimal places).

An oil well (wellbore radius = 0.5 inch) in a heavy oil reservoir (drainage radius = 745 ft, oil viscosity = 500 cP) is being operated at 200 rb/day and 150 psi under the radial steady state flow regime. A huff and puff steam injection is planned to reduce the oil viscosity to 35 cP. The steam soaks into the reservoir up to a distance of 65 ft from the centre of the wellbore. The new production rate at the downhole condition after the steam stimulation is ____________ rb/day (rounded off to two decimal places).

A real gas is produced from a gas reservoir at a constant temperature of 30°C. The compressibility factor (\(Z\)) is observed to change with pressure (\(P\)) at a rate of \[ \left( \frac{\partial Z}{\partial P} \right)_T = Z^2 \] The difference in the compressibility of the real gas from the ideal gas at a given pressure (\(P\)) and temperature (\(T\)) is:

Which ONE of the following options is the CORRECT match of contaminants and their effluent treatment techniques?

Capillary pressure (\(P_c\)) vs water saturation (\(S_w\)) curves for different sandstone reservoirs (I, II, III and IV) are given in the following figure.

Which reservoir has the most uniform pore size distribution?

Flow tests are conducted for oil well in reservoirs P, Q, R and S having different parameters as given in the following table. In all the four cases the wells are tested at 1200 stb/day.

Identify the reservoir in which the pressure transient reaches earliest at a point 2000 ft away from the wellbore.

Identify the CORRECT match for the flow regimes (Group 1) with the corresponding slopes of the pressure derivative (Group 2) used in the type curve analysis.

The log data obtained for a particular well section are shown in the following figures. Identify the CORRECT interpretations for different zones.

The flammable gas detector works on which of the following phenomena?

A drilling mud with high gel strength is undesirable because it

A homogeneous sandstone reservoir is under a radial steady state flow. The wellbore radius is 0.1 m. The formation near the wellbore is damaged up to 0.9 m from the sand face. The permeability impairment results in \( k/k_s = 5 \), where \( k \) is the permeability in the undamaged region and \( k_s \) is that of the damaged region. The value of skin factor is (rounded off to two decimal places) ______________.

A reservoir is producing oil at 7000 stb/day with a producing gas to oil ratio (GOR) of 2000 scf/stb. At a certain point of time, the reservoir pressure is monitored and decided to be maintained at a constant pressure of 2500 psi using water injection. The PVT properties estimated at 2500 psi are:

Bubble point pressure = 3000 psi
Oil formation volume factor = 1.2 rb/stb
Water formation volume factor = 1.0 rb/stb
Gas formation volume factor = 0.0012 rb/scf
Solution GOR = 300 scf/stb
The initial water injection rate (stb/day) required to maintain oil production at 7000 stb/day is ________________ (rounded off to the nearest integer).