List of top Questions asked in GATE Petroleum Engineering

$ C_1, C_2, $ and $ C_3 $ are the Dietz shape factors of three reservoirs with circular, square, and rectangular shape of drainage area, respectively. The well is located at the geometric center of the reservoir. Which ONE of the following options is CORRECT about the shape factors?

An underwater riser with an outer diameter of 250 mm and wall thickness of 20 mm is subjected to tension and pressure. The effective tension is $1200$ kN wherein the internal and external pressures of the riser are $25$ MPa and $6$ MPa, respectively. The true wall tension in the riser is $\times 10^{6}$ N (rounded to two decimal places).

A shell-and-tube heat exchanger is used for cooling crude oil from $400~\text{K}$ to $360~\text{K}$. Crude oil flows through the tube at $3650~\text{kg/h}$. Water enters the shell side at $310~\text{K}$ and has a flow rate of $1600~\text{kg/h}$. Assume $c_{p,\text{oil}}=2.5~\text{kJ/(kg.K)}$, $c_{p,\text{w}}=4.187~\text{kJ/(kg.K)}$, overall $U=300~\text{W/(m}^2\!\cdot\!\text{K)}$, and countercurrent flow. The required heat–transfer area is ............... m$^2$ (rounded to one decimal place).

A four–column semi–submersible floater is located offshore. The diameter of each column is $5~\text{m}$. Consider the total displaced weight of seawater of the semi–submersible as $4000~\text{tonnes}$. Assume added mass contribution as $50\%$ of the semi–submersible weight, and seawater density as $1025~\text{kg/m}^3$. (Acceleration due to gravity $=9.81~\text{m/s}^2$.) The natural period of oscillation of the floater in vertical mode is __________ seconds (rounded to one decimal place).

An oil droplet is to be mobilized by injecting water through a pore throat. The oil–water interface has the rear radius of curvature $r_A = 25\times10^{-6}\ \text{m}$ and the forward radius of curvature $r_B = 5\times10^{-6}\ \text{m}$. The pore is completely water-wet (contact angle $=0^\circ$) and interfacial tension is $\sigma = 0.025\ \text{N/m}$. The minimum pressure drop required to mobilize the trapped oil droplet is ________ N/m$^2$ (nearest integer).

Crude oil having density and viscosity of $850\ \text{kg/m}^3$ and $2\times10^{-3}\ \text{Pa}\!\cdot\!\text{s}$, respectively, is flowing at an average velocity of $0.35\ \text{m/s}$ through a horizontal capillary tube. The inside diameter and length of the capillary tube are $2.5\times10^{-3}\ \text{m}$ and $0.30\ \text{m}$, respectively. The Fanning friction factor is $f=\dfrac{16}{\mathrm{Re}}$. The pressure drop across the capillary tube is ________ Pa (rounded to one decimal place).

A non-Newtonian drilling fluid (Bingham plastic) is between two flat parallel rectangular plates of area $10\ \mathrm{cm^2}$ each, separated by $1\ \mathrm{cm}$. A force of $300$ dyne is required to initiate motion of the upper plate. A force of $600$ dyne keeps the plate moving at a constant velocity of $10\ \mathrm{cm/s}$. The constitutive law is \[ \tau_{yx} = \mu_p \dot{\gamma} + \tau^o_{yx}. \] Find the Bingham plastic viscosity $\mu_p$ in dyne$\cdot$s/cm$^2$ (rounded to the nearest integer).

A kill mud of appropriate density is required to be injected in a well such that the shut-in pressure is $6.8 \times 10^{6}\ \mathrm{Pa}$ at a depth of $3500\ \mathrm{m}$. Here, the shut-in pressure is the quantity by which the bottom-hole pressure exceeds the hydrostatic pressure of the original mud at the given depth. The density of the original mud is $1100\ \mathrm{kg/m^3}$. The density of the kill mud is _________ kg/m$^3$ (rounded to two decimal places).

Consider a micellar displacement process in a homogeneous reservoir with a porosity of 30%. The volume of the microemulsion slug to be injected is 4% of the pore volume. The slug contains 4 vol% surfactant. The density of the rock and the surfactant is $2.7~\text{g/cm}^3$ and $1.1~\text{g/cm}^3$, respectively.

Assuming that the average surfactant adsorption is 0.25 mg/g of the reservoir rock, the fraction of the injected surfactant that will be adsorbed is ............. (rounded to two decimal places).

A compressional acoustic wave takes $55~\mu s$ to travel $0.3048~\text{m}$ through a rock formation having bulk modulus of $37.5~\text{GPa}$ and shear modulus of $31~\text{GPa}$. The bulk density of the rock is ............. kg/m$^{3}$ (rounded to two decimal places).

After well completion, a discovery well in an oil reservoir is produced for a short period and then closed for pressure build-up test. The production history before shut-in is given below. The Horner’s pseudo-producing time, $t_{pH}$, is ............... hr (rounded to nearest integer).

Production rate (STB/day)	Duration (days)
500	5
550	7
400	8

Consider 1D oil--water flow with $k_{ro}^o=1,\ k_{rw}^o=0.2,\ S_{wr}=0.2,\ S_{or}=0.4$. Oil and water viscosities are $5$ cP and $1$ cP. With \[ k_{ro}=k_{ro}^o(1-S_w^*),\quad k_{rw}=k_{rw}^o(S_w^*),\quad S_w^*=\frac{S_w-S_{wr}}{1-S_{or}-S_{wr}}, \] the total relative mobility at $S_w=0.4$ is _________ cP$^{-1}$ (rounded to one decimal place).

An empty steel pipeline with massless endcaps has an outer diameter, $D$, and thickness, $t$. The density of steel is $7850\ \mathrm{kg/m^3}$. The critical $D/t$ ratio at which the pipeline starts floating in seawater of density $1025\ \mathrm{kg/m^3}$ is _________ (rounded to two decimal places).

Figure shows an inextensible catenary mooring cable in still water. The submerged weight (per meter length), and the anchor radius are 100 kg/m and 50 m, respectively. If horizontal tension ($T_h$) in the catenary is 1600 kg, the catenary length (AB) is ............. m (rounded to two decimal places).

The directional derivative of $f = x^{3} + 4y^{2} + z^{2}$ at the point $P(2,1,3)$ in the direction of the vector $\vec{V} = 3\hat{\imath} - 4\hat{k}$ is ............. (rounded to one decimal place).

Using Simpson’s one-third rule (with step size $h=0.25$), the area under the curve $y = e^{-x^{3}}$, from $x=0$ to $x=1$ is ............. (rounded to two decimal places).

A build-up test is characterized by production at constant rate over time $t_p$, followed by shut-in period of $\Delta t$. A plot of shut-in bottom hole pressure ($P_{ws}$) with $\log \left(\dfrac{t_p+\Delta t}{\Delta t}\right)$ for pressure build-up test data is shown in the figure. Which of the following statement(s) is/are TRUE?

Match the entries between Group-I and Group-II for seismic data acquisition, processing and interpretation.

Schematic of phase diagrams for a pure gas hydrate system of methane (CH$_4$), carbon dioxide (CO$_2$), hydrogen sulphide (H$_2$S) and nitrogen (N$_2$) between the lower and upper quadruple points are shown in the figure. Arrowheads indicate the stable hydrate region for a particular gas hydrate system. Match the phase diagram with the corresponding pure gas hydrate.

The figure shows a schematic representation of the organic solid phase diagram for wax, hydrate, and asphaltene deposition around the bubble point of a sample reservoir fluid. Arrowheads indicate the stable region for a corresponding organic solid. Match the phase diagram with organic solids.

Match the flow regimes associated with a vertically fractured well in a reservoir.

Consider the following accident scenario: Failure of a drain connection on a rich oil line at the base of an absorber tower in a gas producing plant allowed the release of rich oil and gas. The resulting vapor cloud ignited from the ignition system of an engine-driven recompressor. The absorber tower eventually collapsed across a pipe rack. The breakage of the pipelines added more fuel to the fire and led to the total destruction of the plant. The resulting fire burnt for 3 days.