List of top Questions asked in GATE PE

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