List of top Questions asked in GATE PE

The porosity of a formation with matrix density of 2.65 g/cc and fluid density of 1.0 g/cc is 0.15. The formation has shear modulus of 30 GPa and bulk modulus of 36 GPa.
The compressional wave velocity in the formation is .......... \( \times 10^3 \) m/s (rounded off to two decimal places).
The hydrostatic pressure gradient in a vertical well drilled in a relaxed depositional basin is 0.452 psi/ft. Assume that the gradient of effective horizontal stress with depth is constant in the drilling zone and has a value of 9.96 × 10⁻² psi/ft. The casing shoe is at 4000 ft depth.
While drilling the bore hole below the casing shoe with 10 ppg mud, the maximum allowed standpipe pressure is .......... psi (rounded off to one decimal place).
A horizontal well is planned with two radial sections to land the target at an angle of 90°. The total vertical depth (TVD) between the surface and the target is 8000 ft. The buildup rate is 6° per 100 ft in the first section and 9° per 100 ft in the second section. The total angle built by the second section is 30°.
The distance of the first kickoff point from the surface is .......... ft (rounded off to one decimal place).
The laboratory analysis data obtained from the core is as follows:
Weight of clean dry core in air = 30 g
Weight of core completely saturated with oil = 32 g
Weight of saturated core completely immersed in oil = 24 g
If the density of oil used for saturation of core during the experiment is 0.88 g/cc, then the effective porosity of the core is .......... % (rounded off to two decimal places).
The Buckley Leverett frontal advance theory is employed to evaluate the performance of the water flooding operation in a horizontal reservoir.
The following data are given:
- Cross-sectional flow area = 40000 ft²
- Payzone thickness = 20 ft
- Porosity = 20%
- Water injection rate = 1000 rb/day
- Distance between injection and production well = 1000 ft
- Cumulative pore volume of water injected (PVWI) at breakthrough = 0.5
The time of breakthrough is .......... days (rounded off to one decimal place).
Natural gas is produced at a flow rate of 2 MMscf/day at the wellhead having temperature and pressure of 560 °R and 200 psi, respectively. The apparent molecular weight and the compressibility factor (z) of the gas are estimated to be 20 g/g-mole and 0.8, respectively, at wellhead conditions. The gas formation volume factor (\( B_g \)) at the wellhead condition is ........... × \( 10^{-2} \) ft\(^3\)/scf (rounded off to one decimal place).
The formation resistivity factor (\( F \)) is related to the formation porosity (\( \phi \)) in a water-bearing carbonate formation by the following correlation:
\[ F = 0.9 \phi^{-2} \] where \( \phi \) is in fraction. The resistivity of the invaded zone of the formation obtained by the Microspherically Focused Log (MSFL) is 4.5 \( \Omega \)m, and the resistivity of the mud-filtrate is 0.05 \( \Omega \)m. The formation porosity is .......... % (rounded off to one decimal place).
The hoisting system of a drilling rig contains seven ideal sheaves with hook load of \( 3.0 \times 10^5 \) kg. The static derrick load is .......... × \( 10^5 \) kg (rounded off to one decimal place).
The product of the roots of the equation \( x^4 + 1 = 0 \) is ....... (answer in integer).
Reservoir Quality Index (RQI) based on Kozeny-Carman equation as a function (\( f \)) of permeability (\( k \), in mD) and porosity (\( \phi \), in fraction) is given by: \[ {RQI} = C f(k, \phi) \] where, \( C \) is a constant with a value of 0.0314. If a carbonate reservoir has the permeability of 152 mD and the porosity of 0.18, then the RQI is ........ $\mu m$ (rounded off to two decimal places).
The ratio of number of production to injection wells for a regular Seven-Spot pattern is ........... (rounded off to one decimal place).
Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: P. At once, without thinking much, people rushed towards the city in hordes with the sole aim of grabbing as much gold as they could.
Q. However, little did they realize about the impending hardships they would have to face on their way to the city: miles of mud, unfriendly forests, hungry beasts and inimical local lords – all of which would reduce their chances of getting gold to almost zero.
R. All of them thought that easily they could lay their hands on gold and become wealthy overnight.
S. About a hundred years ago, the news that gold had been discovered in Kolar spread like wildfire and the whole State was in raptures.
Two cars, P and Q, start from a point X in India at 10 AM. Car P travels North with a speed of 25 km/h and car Q travels East with a speed of 30 km/h. Car P travels continuously but car Q stops for some time after travelling for one hour. If both the cars are at the same distance from X at 11:30 AM, for how long (in minutes) did car Q stop?
If HIDE and CAGE are coded as 19-23-7-11 and 5-2-17-11 respectively, then what is the code for HIGH?

For a hydrocarbon reservoir, the following parameters are used in the general material balance equation (MBE):

\[ \begin{aligned} N & = \text{Initial (original) oil in place, stb} \\ G & = \text{Initial volume of gas cap, scf} \\ m & = \text{Ratio of initial volume of gas cap to volume of oil initial in place, rb/rb} \\ S_{wi} & = \text{Initial water saturation} \\ S_{oi} & = \text{Initial oil saturation} \\ B_{oi} & = \text{Initial oil formation volume factor, rb/stb} \\ B_{gi} & = \text{Initial gas formation volume factor, rb/scf} \end{aligned} \]

The total pore volume (in rb) of the reservoir is:

The eigenvalues of the matrix \[ A = \begin{bmatrix} 3 & -1 & 1 \\ -1 & 5 & -1 \\ 1 & -1 & 3 \end{bmatrix} \] are \(\lambda_1, \lambda_2, \lambda_3\). The value of \(\lambda_1 \lambda_2 \lambda_3 (\lambda_1 + \lambda_2 + \lambda_3)\) is:

A stationary tank is cylindrical in shape with two hemispherical ends and is horizontal, as shown in the figure. \(R\) is the radius of the cylinder as well as of the hemispherical ends. The tank is half filled with an oil of density \(\rho\) and the rest of the space in the tank is occupied by air. The air pressure, inside the tank as well as outside it, is atmospheric. The acceleration due to gravity (\(g\)) acts vertically downward. The net horizontal force applied by the oil on the right hemispherical end (shown by the bold outline in the figure) is: 

If a function \(f(x)\) is continuous in the closed interval \([a, b]\) and the first derivative \(f'(x)\) exists in the open interval \((a, b)\), then according to the Lagrange's Mean Value Theorem: \[ \frac{f(b) - f(a)}{b - a} = f'(c) \] If \(a = 0, b = 1.5\), and \(f(x) = x(x - 1)(x - 2)\), then the value(s) of \(c\) in \([a, b]\) is/are:
Which of the following logging tool(s) underestimate(s) porosity in a gas-bearing formation?

The drainage oil-water capillary pressure data for a core retrieved from a homogeneous isotropic reservoir is listed in the table. The reservoir top is at 4000 ft from the surface and the water-oil contact (WOC) depth is at 4100 ft. \[ \begin{array}{|c|c|} \hline \textbf{Water saturation (\%)} & \textbf{Capillary pressure (psi)} \\ \hline 100.0 & 0.0 \\ \hline 100.0 & 5.5 \\ \hline 99.0 & 5.6 \\ \hline 89.2 & 6.4 \\ \hline 81.8 & 6.9 \\ \hline 44.2 & 11.2 \\ \hline 29.7 & 17.1 \\ \hline 25.1 & 36.0 \\ \hline \end{array} \] Assume the densities of water and oil at reservoir conditions are 1.04 g/cc and 0.84 g/cc, respectively. The acceleration due to gravity is 980 cm/s2. The interfacial tension between oil and water is 35 dynes/cm and the contact angle is 0 degree. The depth of free-water level (FWL) is at ________ ft (rounded off to one decimal place).

The effect of pressure on various properties of black oil is shown in the figure. The bubble point pressure is \(P_b\). 

Which of the following option(s) is/are CORRECT?

Which of the following definition(s) related to fire and explosion is/are CORRECT?

The formation resistivity factor \((F)\) is related to the formation porosity \((\phi)\) in a water-bearing carbonate formation by the following correlation: \[ F = 0.9 \phi^{-2} \] where \(\phi\) is in fraction. The resistivity of the invaded zone of the formation obtained by the Microspherically Focused Log (MSFL) is \(4.5 \, \Omega m\), and the resistivity of the mud-filtrate is \(0.05 \, \Omega m\). The formation porosity is ________ % (rounded off to one decimal place).

Which of the following option(s) is/are CORRECT for well testing analysis of a reservoir?

In a capillary rise experiment with a capillary tube of length \(l_1\), water rises to a height \(h\) such that \(h \lt l_1\).

If the capillary tube is cut to a length \(l_2\) such that \(l_2 \lt h\), and the experiment is repeated, which of the following statements is/are CORRECT?