List of top Questions asked in GATE PE

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.

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).

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 drilling mud with high gel strength is undesirable because it

An oil well is drilled using an 8.5-inch drill bit at a penetration rate of 30 ft/hr. The rotary speed is 20 rpm and the weight on the bit is 3500 lb. The value of the ‘d’ exponent for the drilled section is ________________ (rounded off to two decimal places).

A vertical wellbore is drilled with a 12.25-inch drill bit. While drilling, the bit could drill a total rock volume of 385 ft\(^3\) in 6.5 hr. After drilling, the hole diameter throughout the depth is found to be 12.49 inch. The average rate of penetration is ____________ ft/hr (rounded off to two decimal places).

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

Which of the following properties of Matrix \(A = \begin{bmatrix} 1 & 0.5 & 0 \\ 0.5 & 1 & 0.5 \\ 0 & 0.5 & 1 \end{bmatrix}\) are CORRECT?

The logging tool(s) preferred for the measurement of formation resistivity in a well drilled with oil-based mud is/are:

Which of the following are NOT CORRECT during the operating cycle of a ‘sucker rod pump’?

Simpson’s one-third rule will give the exact value of the integral \[ I=\int_a^b \left[ b_0 + b_1 x + b_2 x^2 + \cdots + b_n x^n \right] dx \] (where \(a, b, b_0, b_1, b_2, \ldots, b_n\) are numeric constants), if the values of \(n\) are:

The liquid shrinkage curves for different types of crude oil are shown in the following figure.

Which curve represents the Black Oil?

The dynamic mud inflow rate and mud outflow rate profiles are shown in the following figure. Identify the ``Hole ballooning’’ and the ``Lost circulation’’ phenomena.

‘Cupola’ offshore storage tank is an example of:

The formation volume factors of oil and water are \(B_o\) and \(B_w\), respectively. The CORRECT relationship between the fractional water cut at the surface condition \(f_{ws}\) and the fractional water cut at the reservoir condition \(f_w\) is:

Which ONE of the following is used to support the packer against the casing while expanding the rubber sealing element?

Let \( \vec{F}(x,y) = e^x \sin x\, \hat{i + x\, \hat{j} \) for \((x,y)\in \mathbb{R}^2\). If \(C\) is the circle \(x^2 + y^2 = 4\) oriented anticlockwise, then \[ \oint_C \vec{F} \cdot d\vec{R} \] equals:}

The value of \[ \lim_{x \to 0} \left[ \frac{1}{x} \ln(1+x) \right] \] is:

The general equation for the production rate decline can be expressed as \[ \frac{1}{q} \frac{dq}{dt} = -bq^d \] where, b and d are empirical constants, and q is the production rate.
Match the value of \(d\) (Group 1) with the appropriate decline curves (Group 2).

The following second order ordinary differential equation has the boundary conditions: \[ y(0) = 0, \quad y(1) = 1 \] The type of the above boundary conditions is: