GATE 2025 Question Paper Petroleum Engineering (PE)

GATE
2025
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.

General Aptitude
Q.1 – Q.5 Carry ONE mark Each

Q.1 Fish : Shoal :: Lion : _______

Select the correct option to complete the analogy.

(A) Pride

(B) School

(C) Forest

(D) Series

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Q.2 Identify the grammatically correct sentence:

(A) It is I who am responsible for this fiasco.

(B) It is myself who is responsible for this fiasco.

(C) It is I who is responsible for this fiasco.

(D) It is I who are responsible for this fiasco.

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Q.3 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?

(A) 10

(B) 12

(C) 15

(D) 18

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Q.4 The ceiling function of a real number 𝑥, denoted by 𝑐𝑒(𝑥), is defined as the smallest
integer that is greater than or equal to 𝑥. Similarly, the floor function, denoted by
𝑓𝑙(𝑥), is defined as the largest integer that is smaller than or equal to 𝑥. Which one
of the following statements is NOT correct for all possible values of 𝑥?

(A) 𝑐𝑒(𝑥) ≥ 𝑥

(B) 𝑓𝑙(𝑥) ≤ 𝑥

(C) 𝑐𝑒(𝑥) ≥ 𝑓𝑙(𝑥)

(D) 𝑓𝑙(𝑥) < 𝑐𝑒(𝑥)

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Q.5 P and Q play chess frequently against each other. Of these matches, P has won 80%
of the matches, drawn 15% of the matches and lost 5% of the matches.

If they play 3 more matches, what is the probability of P winning exactly 2 of these
3 matches?

(A) 48
125

(B) 16
125

(C) 16
25

(D) 25
48

Organizing Institute: IIT Roorkee Page 5 of 38

Q.6 – Q.10 Carry TWO marks Each

Q.6 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.

(A) P→Q→R→S

(B) Q→S→R→P

(C) S→Q→P→R

(D) S→P→R→Q

Organizing Institute: IIT Roorkee Page 6 of 38

Q.7 If HIDE and CAGE are coded as 19-23-7-11 and 5-2-17-11 respectively, then what
is the code for HIGH?

(A) 5-17-1-2

(B) 17-19-13-17

(C) 13-3-1-2

(D) 19-23-17-19

Organizing Institute: IIT Roorkee Page 7 of 38

Q.8 The given figure is reflected about the horizontal dashed line and then rotated
clockwise by 90° about an axis perpendicular to the plane of the figure.

Which one of the following options correctly shows the resultant figure?

Note: The figures shown are representative.

(A)

(B)

(C)

(D)

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Q.9 Which one of the following options has the correct sequence of objects arranged in
the increasing number of mirror lines (lines of symmetry)?

(A) Circle; Square; Equilateral triangle; Isosceles triangle

(B) Isosceles triangle; Equilateral triangle; Square; Circle

(C) Equilateral triangle; Isosceles triangle; Square; Circle

(D) Isosceles triangle; Square; Equilateral triangle; Circle

Q.10 A final year student appears for placement interview in two companies, S and T.
Based on her interview performance, she estimates the probability of receiving job
offers from companies S and T to be 0.8 and 0.6, respectively. Let 𝑝 be the
probability that she receives job offers from both the companies. Select the most
appropriate option.

(A) 0 ≤ 𝑝 ≤ 0.2

(B) 0.4 ≤ 𝑝 ≤ 0.6

(C) 0.2 ≤ 𝑝 ≤ 0.4

(D) 0.6 ≤ 𝑝 ≤ 1.0

Organizing Institute: IIT Roorkee Page 9 of 38

Q.11 – Q.35 Carry ONE mark Each

Q.11 Four fair coins are tossed simultaneously. The probability that at least one tail turns
up is

(A) 1
16

(B) 15
16

(C) 7
8

(D) 1
2

Q.12 Let 𝑨 ̂ and 𝑩
⃗⃗ = 2𝒊̂ − 𝒋̂ + 𝒌 ̂ are unit vectors. The projection
⃗⃗ = 𝒊̂ + 𝒋̂, where 𝒊̂, 𝒋̂, and 𝒌
of ⃗𝑩
⃗ on ⃗𝑨
⃗ is

(A) 1
√12

(B) 1
√6

(C) √6

(D) 1
√2

Organizing Institute: IIT Roorkee Page 10 of 38

Q.13 𝑐𝑜𝑠 𝑥
The value of 𝑙𝑖𝑚 ( 𝜋 ) is
𝑥→𝜋⁄2 𝑥−
2

(A) 1

(B) −1

(C) 0

(D) 𝜋

Q.14 Which ONE of the following CANNOT be obtained from pressure transient
analysis in well testing?

(A) Formation damage

(B) Average reservoir pressure

(C) Solution gas-oil ratio

(D) Drainage pore volume

Organizing Institute: IIT Roorkee Page 11 of 38

Q.15 The primary objective of the electrostatic grid in electrostatic heater-treater used in
crude oil processing is to

(A) separate sand particles.

(B) promote coalescence of water droplets.

(C) generate electrical energy from the kinetic energy of the feed.

(D) prevent corrosion by the cathodic protection.

Q.16 The maximum Polished Rod Load (PRL) in the operation of the sucker rod pump
is observed near the

(A) top of the stroke and the traveling valve is open.

(B) top of the stroke and the traveling valve is closed.

(C) bottom of the stroke and the traveling valve is open.

(D) bottom of the stroke and the traveling valve is closed.

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Q.17 Four curves designated as I, II, III, and IV are shown in the figure. 𝑃𝑏 is the bubble
point pressure of a crude oil at the given temperature.

Which ONE of the following options correctly depicts the solubility of asphaltene
(𝑞𝑎 ) in the crude oil with pressure (P) at a given temperature?

I
𝑞 →

II

III

IV
𝑃 𝑃 →

(A) I

(B) II

(C) III

(D) IV

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Q.18 𝐶1 , 𝐶2 , and 𝐶3 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?

(A) 𝐶3 < 𝐶2 < 𝐶1

(B) 𝐶2 < 𝐶1 < 𝐶3

(C) 𝐶1 < 𝐶2 = 𝐶3

(D) 𝐶1 = 𝐶2 < 𝐶3

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Q.19 Four curves designated as I, II, III, and IV are shown in the figure. q f is the
bottomhole oil flow rate, q s is the surface oil flow rate, and Bo is the oil formation
volume factor.

Which ONE of the following curves depicts the minimum wellbore storage effect?

1.0
IV III II I
qf
qs

Time

(A) I

(B) II

(C) III

(D) IV

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Q.20 Match the entries in GROUP I with the entries in GROUP II.

GROUP I GROUP II

(P) Liquid hold-up (I) Water removal

(Q) Liquid carryover (II) Free gas escaping with liquid phase

(R) Gas blowby (III) Free liquid escaping with gas phase

(S) Gas dehydration (IV) Fraction of pipe volume occupied by liquid

(A) P – III; Q – IV; R – I; S – II

(B) P – IV; Q – III; R – II; S – I

(C) P – I; Q – II; R – IV; S – III

(D) P – IV; Q – II; R – III; S – I

Q.21 Which ONE of the following rocks shows the highest reading in the natural gamma
ray log?

(A) Dolomite

(B) Anhydrite

(C) Oil Shale

(D) Limestone

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Q.22 Crude oil denser than pure water has the API gravity

(A) less than 10.

(B) between 10 and 20.

(C) between 20 and 60.

(D) more than 60.

Q.23 Which ONE of the following options is CORRECT in relation to the standard drill
pipe?

(A) Nominal weight is equal to the actual weight.

(B) Nominal weight is less than the actual weight.

(C) Nominal weight is greater than the actual weight.

(D) Nominal weight is twice the actual weight.

Organizing Institute: IIT Roorkee Page 17 of 38

Q.24 Four different multilateral well patterns (Forked, Branched, Dual opening and
Splayed) are shown in the figure.

Which ONE of the following options correctly identifies the multilateral well
patterns?

I II III IV

(A) I – Forked; II – Branched; III – Dual Opening; IV – Splayed

(B) I – Dual Opening; II – Branched; III – Forked; IV – Splayed

(C) I – Dual Opening; II – Splayed; III – Forked; IV – Branched

(D) I – Branched; II – Dual Opening; III – Splayed; IV – Forked

Organizing Institute: IIT Roorkee Page 18 of 38

For a hydrocarbon reservoir, the following parameters are used in the general
Q.25 material balance equation (MBE).

N = Initial (original) oil in place, stb
G = Initial volume of gas cap, scf
m = Ratio of initial volume of gas cap to volume of oil initial in place, rb/rb
𝑆𝑤𝑖 = Initial water saturation
𝑆𝑜𝑖 = Initial oil saturation
𝐵𝑜𝑖 = Initial oil formation volume factor, rb/stb
𝐵𝑔𝑖 = Initial gas formation volume factor, rb/scf

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

(A) 𝐺 𝐵𝑔𝑖 (1 + 𝑚)
1 − 𝑆𝑜𝑖

(B) 𝑁 𝐵𝑜𝑖 (1 − 𝑚)
1 − 𝑆𝑜𝑖

(C) 𝑁 𝐵𝑜𝑖 (1 + 𝑚)
1 − 𝑆𝑤𝑖

(D) 𝐺 𝐵𝑔𝑖 (1 − 𝑚)
1 − 𝑆𝑤𝑖

Q.26 Which of the following statement(s) is/are CORRECT?

(A) Gradient of temperature is a vector.

(B) Gradient of pressure is a vector.

(C) Divergence of velocity is a vector.

(D) Gradient of velocity is a scalar.

Organizing Institute: IIT Roorkee Page 19 of 38

Q.27 Which of the following statement(s) is/are CORRECT about the chemicals used for
the processing of sour crude oil and natural gas?

(A) Amine solutions cannot be regenerated after removal of H2S from natural gas.

(B) Amine solutions in liquid form absorb H2S from natural gas.

(C ) Glycols become corrosive in the presence of oxygen.

(D) Iron sponges cannot be used for H2S removal.

Q.28 Consider the following diffusivity equation for the radial flow of a fluid in an
infinite and homogeneous reservoir.

1𝜕 𝜕𝑃 1 𝜕𝑃
(𝑟 ) =
𝑟 𝜕𝑟 𝜕𝑟 𝜂 𝜕𝑡

where, 𝑃 denotes pressure, r is the radial distance from the centre of the wellbore,
𝑡 denotes time, and, 𝜂 is the diffusivity constant. The initial pressure of the reservoir
is 𝑃𝑖 .

The condition(s) used in the derivation of analytical solution of the above equation
for pressure transient analysis in an infinite acting reservoir is/are:

(A) At time 𝑡 = 0, 𝑃 = 𝑃𝑖 for all 𝑟.

(B) Wellbore is treated as a line source.

(C) As 𝑟 → ∞, 𝑃 → 𝑃𝑖 for all 𝑡.

(D) 𝜕𝑃
At any radius 𝑟 and time 𝑡, the pressure gradient is constant.
𝜕𝑟

Organizing Institute: IIT Roorkee Page 20 of 38

Q.29 Which of the following offshore drilling platform(s) has/have legs on the seabed?

(A) Jack up

(B) Tension leg

(C) Concrete gravity

(D) Semi-submersible

Q.30 Which of the following statement(s) is/are CORRECT about polymer flooding?

(A) Viscous fingering in the reservoir decreases.

(B) Viscosity of the displaced fluid increases.

(C) Mobility of the displacing fluid increases.

(D) Mobility ratio decreases.

Q.31 The hoisting system of a drilling rig contains seven ideal sheaves with hook load of
3.0 × 105 kg.

The static derrick load is ________ × 105 kg (rounded off to one decimal place).

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Q.32 The product of the roots of the equation 𝑥 4 + 1 = 0 is _______(answer in
integer).

Q.33 Reservoir Quality Index (RQI) based on Kozeny-Carman equation as a function
(𝑓) of permeability (𝑘 in mD) and porosity (𝜙 in fraction) is given by

𝑅𝑄𝐼 = 𝐶 𝑓(𝑘, 𝜙)

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 ________ µm (rounded off to two decimal places).

Q.34 The ratio of number of production to injection wells for a regular Seven-Spot pattern
is _______ (rounded off to one decimal place).

Q.35 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 (Bg) at the wellhead condition
is __________× 10−2 ft3/scf (rounded off to one decimal place).

Organizing Institute: IIT Roorkee Page 22 of 38

Q.36 – Q.65 Carry TWO marks Each

Q.36 𝑑𝑦
If 𝑑𝑥 + 𝑦 = 𝑥, and y (0) = 0, then the value of y (1) is

(A) 𝑒

(B) 1
𝑒

(C) 1

(D) −1

Q.37 Let 𝑓(𝑥) = 𝑙𝑛 𝑥. The first derivative 𝑓′(𝑥) is to be calculated at 𝑥 = 1 using
numerical differentiation. 𝑓′(1) is calculated using first order forward difference
′ ′
(𝑓𝐹𝐷 ), first order backward difference (𝑓𝐵𝐷 ), and second order central difference
′
(𝑓𝐶𝐷 ), using interval width h = 0.1.
′ ′ ′
The CORRECT order of the values of 𝑓𝐹𝐷 , 𝑓𝐵𝐷 , and 𝑓𝐶𝐷 is

′ ′ ′
(A) 𝑓𝐹𝐷 > 𝑓𝐶𝐷 > 𝑓𝐵𝐷

′ ′ ′
(B) 𝑓𝐶𝐷 > 𝑓𝐵𝐷 > 𝑓𝐹𝐷

′ ′ ′
(C) 𝑓𝐵𝐷 > 𝑓𝐹𝐷 > 𝑓𝐶𝐷

′ ′ ′
(D) 𝑓𝐵𝐷 > 𝑓𝐶𝐷 > 𝑓𝐹𝐷

Organizing Institute: IIT Roorkee Page 23 of 38

Q.38 Three different pressure profiles are shown in the figure. CSD is Casing Setting
Depth.

Match the entries in GROUP I with the entries in GROUP II.

GROUP I GROUP II

(P) Profile 1 (I) Reduced wellbore integrity due to weak formation

(Q) Profile 2 (II) Reduced wellbore integrity due to weak casing

(R) Profile 3 (III) Full wellbore integrity

Pressure → Pressure→ Pressure →

C3 C3 C2
C1 C1
Depth →

Depth →

Depth →
C2 C2 C1

C3
CSD →

C4 C4 C4

Profile 1 Profile 2 Profile 3
C1: Resulting burst pressure ( )
C2: Pressure inside the casing/open hole ( )
C3: Burst strength of casing ( )
C4: Fracture strength ( )

(A) P – I; Q – II; R – III

(B) P – II; Q – III; R – I

(C) P – III; Q – I; R – II

(D) P – II; Q – I; R – III

Organizing Institute: IIT Roorkee Page 24 of 38

Q.39 Match the well logging methods in GROUP I with their corresponding measured
parameters in GROUP II.

GROUP I GROUP II

(P) Neutron log (I) Resistivity in the flushed/invaded zone

(Q) Density log (II) Hydrogen ion concentration in the formation

(R) Microspherically (III) Interval transit time of a compressional wave
Focused Log (MSFL)

(S) Sonic log (IV) Electron density of the formation

(A) P – IV; Q – I; R – II; S – III

(B) P – II; Q – IV; R – I; S – III

(C) P – II; Q – III; R – IV ; S – I

(D) P – III; Q – IV; R – I; S – II

Organizing Institute: IIT Roorkee Page 25 of 38

Q.40 A drilling fluid with time-dependent rheology is used for the rotary drilling of a
reservoir. The following equation describes the dependence of shear stress (𝜏) on
shear rate (𝛾̇ ).

𝜇0 𝑑𝜏
𝜏+ = 𝜇0 𝛾̇
𝛼 𝑑𝑡
where, 𝜇0 and 𝛼 are constants.

If the rotation of the drill pipe is stopped at time 𝑡 = 0, then the relaxation behavior
of the fluid stress with time is

(A) 𝜇 𝑡
− 0
𝜏∝ 𝑒 𝛼

(B) 𝜇0 𝑡
𝜏∝ 𝑒 𝛼

(C) 𝛼𝑡
−𝜇
𝜏∝ 𝑒 0

(D) 𝛼𝑡
𝜇
𝜏∝ 𝑒 0

Organizing Institute: IIT Roorkee Page 26 of 38

Q.41 Classification of kerogen is based on the relative amount of Carbon (C), Hydrogen
(H) and Oxygen (O).

Which ONE of the following options is CORRECT about Type II kerogen?

(A) It is low in aliphatic compounds and H:C ratio < 0.84.

(B) It is rich in aliphatic compounds and H:C ratio < 0.84.

(C ) It is low in aliphatic compounds and H:C ratio > 1.0.

(D) It is rich in aliphatic compounds and H:C ratio > 1.0.

Q.42 3 −1 1
The eigenvalues of the matrix [−1 5 −1] are 𝜆1 , 𝜆2 , and 𝜆3 .
1 −1 3
The value of 𝜆1 𝜆2 𝜆3 (𝜆1 + 𝜆2 + 𝜆3 ) is

(A) 11

(B) 45

(C) 396

(D) 495

Organizing Institute: IIT Roorkee Page 27 of 38

Q.43 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 𝜌 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

Air
𝑔
Oil R

(A) 1
𝜌𝑔𝑅3
2

(B) 2
𝜌𝑔𝑅3
3

(C) 3
𝜌𝑔𝑅3
4

(D) 1
𝜌𝑔𝑅3
3

Organizing Institute: IIT Roorkee Page 28 of 38

Q.44 If a function 𝑓(𝑥) is continuous in the closed interval [ , ] and the first derivative
𝑓′(𝑥) exists in the open interval ( , ), then according to the Lagrange’s mean value
theorem

𝑓( ) − 𝑓( )
= 𝑓′(𝑐)
−
If a = 0, b = 1.5, and 𝑓(𝑥) = 𝑥(𝑥 − 1)(𝑥 − 2), then the value(s) of c in [ , ] is/are

(A) 0.50

(B) 0.75

(C) 1.00

(D) 1.50

Q.45 Which of the following logging tool(s) underestimate(s) porosity in a gas-bearing
formation?

(A) Neutron log

(B) Nuclear Magnetic Resonance (NMR) log

(C) Sonic log

(D) Density log

Organizing Institute: IIT Roorkee Page 29 of 38

Q.46 The effect of pressure on various properties of black oil is shown in the figure.
The bubble point pressure is 𝑃b .

Curve 1
Oil Property →
Curve 2

Curve 3

Pb
Pressure →

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

(A) Curve 1 represents solution gas-oil ratio.

(B) Curve 2 represents oil viscosity.

(C) Curve 3 represents oil formation volume factor.

(D) Curve 3 represents oil density.

Organizing Institute: IIT Roorkee Page 30 of 38

Q. 47 Which of the following definition(s) related to fire and explosion is/are CORRECT?

(A) Fire point is the lowest temperature at which the vapour above a liquid will continue
to burn once ignited.

(B) Deflagration is the explosion in which the reaction front moves at a speed greater
than the speed of sound in the unreacted medium.

(C) Detonation is the explosion in which the reaction front moves at a speed less than
the speed of sound in the unreacted medium.

(D) Flash point of a liquid is the lowest temperature at which it gives enough vapour to
form an ignitable mixture with air.

Q.48 Which of the following option(s) is/are CORRECT for well testing analysis of a
reservoir?

(A) Permeability, skin and reservoir geometry are calculated using data from pseudo
steady state.

(B) Permeability, skin and reservoir geometry are calculated using data from transient
state.

(C) Reservoir geometry is calculated using data from pseudo steady state.

(D) Absolute open flow potential is calculated from back pressure test for a gas well.

Organizing Institute: IIT Roorkee Page 31 of 38

Q.49 In a capillary rise experiment with a capillary tube of length l1, water rises to a height
h such that h < l1.
If the capillary tube is cut to a length l2 such that l2 < h, and the experiment is
repeated, which of the following statements is/are CORRECT?

(A) Water overflows from the top of the tube.

(B) Water does not overflow from the top of the tube.

(C) At equilibrium, radius of curvature of meniscus are same in both the experiments.

(D) At equilibrium, radius of curvature of meniscus are different in both the
experiments.

Q.50 The formation resistivity factor (𝐹 ) is related to the formation porosity (𝜙) in a
water-bearing carbonate formation by the following correlation

𝐹 = 0.9𝜙 −2
where 𝜙 is in fraction. The resistivity of the invaded zone of the formation obtained
by the Microspherically Focused Log (MSFL) is 4.5 Ωm, and the resistivity of the
mud-filtrate is 0.05 Ωm.

The formation porosity is ________% (rounded off to one decimal place).

Organizing Institute: IIT Roorkee Page 32 of 38

Q.51 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.

Water saturation (%) Capillary pressure (psi)

100.0 0.0

100.0 5.5

99.0 5.6

89.2 6.4

81.8 6.9

44.2 11.2

29.7 17.1

25.1 36.0

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.

The depth of free-water level (FWL) is at _________ ft (rounded off to one
decimal place).

(Use: 1 psi = 68950 dynes/cm2 ; 1 ft = 30.5 cm)

Q.52 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 ________× 103 m/s (rounded
off to two decimal places).

Organizing Institute: IIT Roorkee Page 33 of 38

Q.53 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).

(Note: 1 ppg mud is equivalent to 0.052 psi/ft.)

Q.54 A vertical well is drilled up to a depth of 4000 ft. Further drilling starts with 10 ppg
of fresh mud and 50000 lbf weight on bit (WOB). An equivalent circulation density
(ECD) of 10.75 ppg was recorded. The total circulation pressure loss is estimated
to be 110 psi. The still density is 65.5 ppg.

The decrease in hook load is _________ lbf (rounded off to one decimal place).

(Note: 1 ppg mud is equivalent to 0.052 psi/ft.)

Q.55 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).

Organizing Institute: IIT Roorkee Page 34 of 38

The laboratory analysis data obtained from the core is as follows:
Q.56
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
Q.57
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).
(Use: 1 acre = 43560 ft2 and 1 bbl = 5.615 ft3)

Q.58 A hydraulically fractured vertical well has fracture permeability of 4000 mD,
reservoir permeability of 80 mD, fracture width of 0.12 in, and fracture half-length
of 1000 ft.

Dimensionless fracture conductivity is _________× 10−4 (rounded off to one
decimal place).

Organizing Institute: IIT Roorkee Page 35 of 38

Q.59 An electrical submersible pump is to be installed to lift oil of 30o API in a 10000 ft
deep well. The oil formation volume factor (Bo) is 1.25 rb/stb. The desired flow rate
is 8000 stb/day. Minimum suction pressure of the chosen pump is 200 psi. Inflow
performance relationship shows a flowing bottomhole pressure of 2820 psi at the
desired flow rate.

Assuming casing pressure and weight of the gas in the annulus to be negligible, the
minimum pump setting depth is _________ ft (rounded off to one decimal place).

Q.60 Log-log plot of pressure drop (𝛥𝑝) versus time (𝑡) obtained using well test data is
matched with one of the Grigarten type curves. Thereafter, a point on the type curve
is chosen with 𝑃𝐷 = 10 and 𝑡𝐷 ⁄𝐶𝐷 = 100, where 𝑃𝐷 , 𝑡𝐷 , and 𝐶𝐷 are dimensionless
pressure, dimensionless time, and dimensionless wellbore storage, respectively.
The corresponding match point on the log-log plot is 𝛥𝑝 = 250 psi and 𝑡 = 10 hrs.
Oil flow rate is 500 rb/day. Viscosity of oil is 1.5 cP. Thickness of the reservoir is
10 ft and formation volume factor of oil is 1.2 rb/stb.

The permeability of the reservoir is __________ mD (rounded off to one decimal
place).

Q.61 Correlation equations for gas compressibility factor (𝑧) and viscosity (𝜇) as
functions of pressure (𝑝) are as given below.

𝑧 = 𝐶1 𝑝−0.25 ; 𝜇 = 𝐶2 𝑝1.25
where, 𝐶1 and 𝐶2 are constants, consistent with the field units (pressure 𝑝 in psi, and
viscosity 𝜇 in cP), and have values 1.96 and 7 × 10−4 , respectively.

Real gas pseudo pressure corresponding to a pressure of 2500 psi
is _________× 106 psi2 /cP (rounded off to two decimal places).

Organizing Institute: IIT Roorkee Page 36 of 38

Q.62 An isotropic and homogeneous oil reservoir has a porosity of 20%, thickness of
20 ft and total compressibility of 15 × 10−6 psi−1. Variation of flowing bottomhole
pressure (𝑝𝑤𝑓 ) with time (𝑡) under pseudo steady state of a drawdown test in the
well (under radial flow condition) is given as

𝑝𝑤𝑓 = 2850 − 5𝑡
The pressure is in psi and time is in hours. During the well test, the oil flow rate is
1800 rb/day.

The drainage area of the reservoir is ___________ acres (rounded off to two
decimal places).

(Use: 1 acre = 43560 ft2)

Q.63 A production tubing string of length 1500 m is tightly held by packers to prevent
any expansion in either direction. Production of hot gases from the reservoir
increases the temperature of the tubing by 20 oC. The Young’s modulus of elasticity
of the tubing material is 3000 N/m2, and the linear coefficient of thermal expansion
is 5 × 10−6 per oC.

Assuming no radial expansion, and neglecting the weight of the gas in the tubing
and its viscosity, the increase in the stress of the tubing due to temperature rise
is _______ N/m2 (rounded off to two decimal places).

Q.64 A homogeneous rock layer Q of density 2600 kg/m3 is lying below homogeneous
rock layer P of density 2400 kg/m3. A compressional wave travels from P to Q. On
reaching the interface of P and Q, this wave is incident normally and gets reflected
and refracted. The velocity of the compressional wave is 2.7 km/s in the rock layer
P and 3.5 km/s in layer Q.

The ratio of reflection coefficient to the transmission coefficient at the interface
is ______________(rounded off to two decimal places).

Organizing Institute: IIT Roorkee Page 37 of 38

Q.65 A Newtonian fluid is transported through a smooth horizontal pipe of diameter 1 m
at a flow rate of 3.14 m3 ⁄s. The length of the pipe is 1 km. The viscosity of the oil
is 0.02 Pa.s and its density is 800 kg⁄m3 . Consider the Darcy friction factor (𝑓) for
turbulent flow in a smooth pipe is given as

0.316
𝑓=
𝑅𝑒 0.25
where Re is the Reynolds number.

Assuming fully-developed flow in the pipe, the pressure drop due to the frictional
effect is _______ kPa (rounded off to two decimal places).

Organizing Institute: IIT Roorkee Page 38 of 38

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