List of practice Questions

Pressure (p) as function of radius (r) and time (t) can be found from the analytical solution of radial diffusivity equation for homogenous and isotropic reservoir following Darcy law. For this solution, if dp/dt is treated as constant, which of the following correctly describe(s) the state(s) of pressure change?
Which of the following statements is/are CORRECT about the floating production, storage, and offloading systems (FPSOs)?
For a radioactive material, if N is the number of nuclei present at time t, and \(\lambda\) is decay constant, which of the following is/are CORRECT representation(s) of the rate of decay?
Which of the following logging methods is/are NOT used for investigation in Cement Bond Logging (CBL)?
The solution of the given expression is _______. \[ \lim_{x \to \pi/2} \frac{\sin(\cos x) - \cos x}{\pi/2 - x} \]
A circular reservoir with a well in the centre is producing oil at a constant rate under pseudo steady state. The rate of pressure change measured at the wellbore is 1.0 psi/day. Pressure at the external radius of the reservoir at a certain time was 3500 psi. After 500 days, the pressure (in psi) at the external radius will be __________.
When 92 ml of distilled water (density = 1.0 g/cm3) is mixed with 23 grams of NaCl salt, the density of the resultant brine solution is 1.15 g/cm3. The volume of the brine solution (in ml) is _________.
An oil has a density of 50 lbm/ft3 at Standard Temperature and Pressure (STP) conditions. The density of the oil (in oAPI) is ________. [Given: water density is 62.4 lbm/ft3 at STP]
Which of the following is the correct representation of the given expression?
\[ \frac{(1+i)^8}{(1-i)^6} \]
The values of a function \(f(x)\) at three different values of \(x\) are given below:
\(f(0.90) = 7.75\), \(f(1.00) = 9.00\), \(f(1.10) = 10.35\).
Using the central difference approximation method, which is the CORRECT estimate of the first differential \(f'(1.00)\) and second differential \(f''(1.00)\) respectively?
Consider a random continuous variable \(x\) and its cumulative distribution function \(F(x)\). Which of the following options describes the Probability Density Function (PDF) of \(x\)?
Choose the CORRECT match of sedimentary rocks in GROUP X with their processes/mechanisms of formation in GROUP Y.
GROUP XGROUP Y
(P) Evaporite(I) Physical process mainly consisting of lithification/cementation of deposition
(Q) Sandstone(II) Chemical process and depositions by marine living organisms
(R) Limestone(III) Anaerobic deposition of organic materials in mud bed
(S) Siltstone(IV) Evaporation and precipitation of marine water
Which of the following logging methods in a borehole will provide the highest depth of investigation for a given marine formation?
Choose the CORRECT match of fire detection systems in GROUP X with their working mechanisms in GROUP Y.

GROUP X
(P) Fusible plug loops
(Q) Thermal and smoke detection system
(R) Gas detection system

GROUP Y
(I) Detects rise in temperature caused by fire and visible/invisible particles of combustion
(II) Functions based on drop in pressure that activates fire shutdown
(III) Detects flammables
The sectional view of three different damaged regions (marked P, Q and R) near the vicinity of a perforation is shown in the figure above. Choose the correct option matching the entries in GROUP X with the corresponding terms in GROUP Y.

GROUP X
P
Q
R

GROUP Y
(I) Grain fracturing
(II) Charge and core debris
(III) Compacted pulverized zone
Real gas pseudo pressure is used to derive the diffusivity equation for a highly compressible fluid, for which viscosity \(\mu\) and gas compressibility factor \(Z\) are functions of pressure \(p\). Which of the following represents the partial derivative of the real gas pseudo pressure with respect to time \(t\)?
Stokes' law is used to calculate the settling rate of barite in drilling fluid for two batches, P and Q. The particle size of batch P is 75 micrometers and the particle size of batch Q is 25 micrometers. The particle settling rate in the drilling fluid for batch P is ________ times that for batch Q.
Which of the following approaches is/are used to get the response of a Formation Micro Scanner (FMS) log?
Which of the following conditions is/are inferred using cross plots of neutron porosity (\(\phi_N\)) and density porosity (\(\phi_D\))?
Which of the following is/are obtained using a core sample?
Pressure change and derivative type curves (Bourdet type curves) are used in well test analysis. Which of the following statements is/are CORRECT about these type curves?
Which of the following is/are objective(s) of a safety system in offshore production platforms?
A wellbore has true vertical depth (TVD) of 10000 ft. The pore pressure of formation fluid in the permeable stratum at bottom of wellbore is 6500 psig. Which is/are the acceptable average static mud density value(s) (in lbm/gal) to prevent flow of formation fluid into wellbore?
[Given: 1 lbm/gal mud = 0.052 psi/ft]
Which of the following statements is/are CORRECT about the skin factor?
Consider a vector function \( \vec{F} = (y-z+2)\hat{i} + (yz+8)\hat{j} - xz\hat{k} \), on the surface (S) in the XY plane at \( z = 0 \) (as shown in the figure).
Considering Stokes theorem for space, the ABSOLUTE value of the surface integral \[ \iint_S (\nabla \times \vec{F}) \cdot \hat{n}\, dS \] is __________. (Answer in integer)

(Consider \( \hat{i}, \hat{j}, \hat{k} \), and \( \hat{n} \) as unit vectors)