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GATE (Graduate Aptitude Test in Engineering) Production & Industrial Engineering is an online examination conducted to get admission in M-Tech (Masters in Technology), ME (Master of Engineering ) and PhD at IITs (Indian Institutes of Technology), NITs (National Institutes of Technology), IIITs (Indian Institutes of Information Technology) and other universities in India. GATE exam is jointly conducted by IIT Bombay, IIT Delhi, IIT Guwahati, IIT Kanpur, IIT Kharagpur, IIT Madras, IIT Roorkee and Indian Institute for Science, Bangalore (IISC Bangalore). The exam is divided into two different parts General Aptitude (GA) and Candidate’s Selected Subject (Core Subjects). GATE Production & Industrial Engineering online mock tests help candidates in preparing for the GATE exam. By attempting GATE online mock tests candidates get familiar with the pattern of actual question paper. BrPaper provides all GATE question papers completely free. Here you can practice free online mock tests of Main exam of GATE Production & Industrial Engineering. We advise candidates to solve the online GATE Production & Industrial Engineering mock tests to get good marks in the exam. Start practicing Production & IndustrialGATE 2018 Mock tests here online for free

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Category: GATE Petroleum Engineering 2018

Question 1:

The Taylor series expansion of the function,

f (x) = \frac{- 1}{1 + x},

around 𝑥 = 0 (up to

4^{t h}

order term) is:

A	$1 + x + x^{2} + x^{3} + x^{4}$	B	$- 1 - x + x^{2} - x^{3} + x^{4}$
C	$- 1 - x + x^{2} - x^{3} + x^{4}$	D	$- 1 + x - 2 x^{2} + 3 x^{3} - 4 x^{4}$

Category: GATE Petroleum Engineering 2018

Question 2:

The inverse of the matrix

[\frac{1}{1} \frac{3}{2}] i s,

A	$[\frac{2}{1} \frac{3}{1}]$	B	$[\frac{- 1}{3} \frac{1}{- 1}]$
C	$[\frac{- 2}{1} \frac{3}{- 1}]$	D	$[\frac{2}{- 1} \frac{- 3}{1}]$

Category: GATE Petroleum Engineering 2018

Question 3:

The line integral of a vector function

\bar{F} (\bar{r})

over a curve C in a simply connected domain D in space, is defined by:

\int_{c} \bar{F} (\bar{r}) . d \bar{r} = \int_{c} (F_{1} d x + F_{2} d y + F_{3} d z)

The line integral is independent of the path in D.

F_{1}, F_{2} a n d F_{3}

are continuous, and have continuous first partial derivatives in D.𝐶′ is a closed curve in D. Which one of the following is NOT ALWAYS true in domain D?

A	$\bar{\nabla} \times \bar{F} = \bar{0}$	B	$\bar{\nabla} . \bar{F} = 0$
C	$\oint_{C'} \bar{F} (\bar{r}) . d \bar{r} = 0$	D	$\bar{F} \times \bar{F} = \bar{0}$

Category: GATE Petroleum Engineering 2018

Question 4:

Which one of the following is the integrating factor (IF) for the differential equation,

(\cos^{2} x) \frac{d y}{d x} + y = \cos x ?

A	$e^{\tan x}$	B	$e^{\cos x}$
C	$e^{- \tan x}$	D	$e^{\sin x}$

Category: GATE Petroleum Engineering 2018

Question 5:

A phase diagram of black oil is shown in the figure (Y is the critical point).

Match the following: (P) Curve XY (I) Dew point curve (Q) Curve YZ (II) Single-phase liquid (R) Phase I (III) Bubble point curve (S) Phase II (IV) Single-phase gas

P-I, Q-III, R-II, S-IV

P-III, Q-I, R-II, S-IV

P-III, Q-I, R-IV, S-II

P-I, Q-II, R-III, S-IV

Category: GATE Petroleum Engineering 2018

Question 6:

Match the following chemicals to their respective oilfield applications: (P) Hydrate inhibitor (I) Formaldehyde (Q) Well stimulation (II) Xanthan gum (R) Drilling fluid biocide (III) Methanol (S) Viscosifier (IV) Hydrochloric acid

P-IV, Q-III, R-II, S-I

P-III, Q-I, R-IV, S-II

P-I, Q-III R-IV, S-II

P-III, Q-IV, R-I, S-II

Category: GATE Petroleum Engineering 2018

Question 7:

The CH4-hydrate equilibrium curve (dashed) and CO2-hydrate equilibrium curve (solid) on a pressure-temperature plane above 0°C are shown in the figure. The two curves divide the plane into four non-overlapping regions. In which region are CO2-hydrates stable and CH4-Are hydrates unstable?

III

Category: GATE Petroleum Engineering 2018

Question 8:

The plot of the ratio of pressure to gas compressibility factor (P/Z) vs. cumulative gas production

(G_{P})

for a gas reservoir (represented by the solid curve in the figure) was shown to a reservoir engineering student.

The student made the following statements: (I) A water aquifer is attached to this gas reservoir. (II) P/Z vs. Gp curve must always be a straight line for water encroachment in a gas reservoir. (III) The ultimate gas recovery is diminished due to water encroachment. Which of the above statements is TRUE?

Only I and II

Only II and III

Only I and III

I, II, and III

Category: GATE Petroleum Engineering 2018

Question 9:

Wastewater from the oil industry consists of oil is free and emulsified forms. The oil in the free form can be recovered by:

Aerated lagoons

Trickling filters

Gravity separators

Biological oxygen pond

Category: GATE Petroleum Engineering 2018

Question 10:

A reservoir model consisting of two porous matrices M and N, separated by a fracture, is shown in the figure. The matrices are strongly water-wet and are saturated with oil of specific gravity 0.8. Water is injected only in the fracture at injection well A. If the Reynolds number for the flow in the fracture conduit is assumed to be less than unity, which one of the following force will dominate oil recovery from the porous matrix M during the water-flood operation?

Capillary force

Gravity force

Viscous force

Inertial force

Category: GATE Petroleum Engineering 2018

Question 11:

A fractional flow curve is given for a core for which the irreducible water saturation is 0.2 and the residual oil saturation is 0.3. The initial water saturation in the core is 0.3. If Welge’s method is applied to find the breakthrough saturation and fraction flow of water at breakthrough, which point should be used in the figure to draw a tangent line to the fractional flow curve.

III

Category: GATE Petroleum Engineering 2018

Question 12:

Which one of the following curves represents the behaviour of oil phase viscosity as a function of pressure in the reservoir (where,

P_{b}

is the bubble point pressure of oil)?

Curve I

Curve II

Curve III

Curve IV

Category: GATE Petroleum Engineering 2018

Question 13:

Pick out the INCORRECT statement.

Flash point is always lower than fire point.

Pour point of lube oil can be reduced by removing the wax from it.

Fracturing is a well stimulation technique.

Coal bed methane typically contains more than 60% CO2.

Category: GATE Petroleum Engineering 2018

Question 14:

Which one of the following phenomena encountered during flooding is desirable for increasing oil recovery from a reservoir?

Viscous fingering

Formation damage

Increase in mobility ratio

Decrease in capillary pressure

Category: GATE Petroleum Engineering 2018

Question 15:

C O_{2}

foams are used for enhanced oil recovery due to which of the following reasons? (I) It can be used for

C O_{2}

sequestration (II)

C O_{2}

can exist in the form of a dense fluid at reservoir conditions (III)

C O_{2}

can convert to hydrocarbon at the reservoir temperature and pressure (IV) Solubility of

C O_{2}

in oil is higher compared to gases like

N_{2}

Only I, II, and III

Only I, II, and IV

Only II, III, and IV

Only I, III, and IV

Category: GATE Petroleum Engineering 2018

Question 16:

Which one of the following is FALSE about a typical offshore deepwater oil spill?

Using boom boats to prevent spilled oil from spreading

Allowing the spill to reach the shore before clearing

Burning of spilled oil

Using a skimmer to collect the oil

Category: GATE Petroleum Engineering 2018

Question 17:

Which one of these methods is NOT commonly used to deal with the problem of soil contamination by oil spillage?

Biodegradation

Leaching out the oil

Soil recycling

Using rain water to wash the contaminants

Category: GATE Petroleum Engineering 2018

Question 18:

The factor on which the selection of an offshore platform for the reservoir does NOT depend:

Water depth

Reservoir fluid properties

Sea bed conditions

Best case weather forecast

Category: GATE Petroleum Engineering 2018

Question 19:

Which one of the following options is correct about the effects of steam stimulation in increasing the oil production rate? (I) Reduces the oil viscosity (II) Increases the formation damage (III) Reduces the interfacial tension (IV) Increases the oil viscosity

Only I and II

Only II and III

Only III and IV

Only I and III

Category: GATE Petroleum Engineering 2018

Question 20:

Which one of the following is INCORRECT about oil-based drilling muds?

Good rheological properties at higher temperatures (as high as 250oC)

Effective against corrosion

Detection of gas kick is difficult

Less inhibitive than water based muds

Category: GATE Petroleum Engineering 2018

Question 21:

Assume that vicious, gravity, and capillary are the only dominant forces for fluid flow in a given reservoir, a cone formed around the perforation zone will break into the well, when

capillary forces are more than viscous and gravity forces

viscous forces are more than gravity forces

gravity forces are more than capillary forces

viscous and gravity forces are equal

Category: GATE Petroleum Engineering 2018

Question 22:

Two complex numbers,

\tilde{K} a n d \tilde{ε}

are related as follows:

\tilde{K} = \frac{\tilde{ε}}{i ω}

where,

i = \sqrt{- 1}

and 𝜔 is a scalar. Given the principal argument of

\tilde{ε}, A r g (\tilde{ε}) = - \frac{2 π}{3},

the principal argument

\tilde{k}, A r g (\tilde{k}) =

(rounded-off to two decimal places.Use

π = 3.14)

2.10 to 2.30

2.30 to 2.50

2.50 to 2.70

2.70 to 2.90

Category: GATE Petroleum Engineering 2018

Question 23:

A cylindrical sandstone core, 7.5 cm long and 3.5 cm diameter have a grain density of3 g/

c m^{3}

. If the mass of the dry core is 200 g, the porosity of the core is __________%.(rounded-off to two decimal places)

7.00 to 7.75

7.25 to 7.75

7.50 to 7.75

7.75 to 7.75

Category: GATE Petroleum Engineering 2018

Question 24:

In an oil reservoir, the current average pressure is below the bubble point pressure of the oil. The current oil production rate is 103 m3/day and the total gas production rate is

10^{5} m^{3}

/day at STP conditions (25°C and 1 atm). The formation volume factor of the oil is

1.2 \frac{m^{3} a t r e s e r v o i r p r e s s u r e}{m^{3} a t S T P}

and that of gas is 0.01

\frac{m^{3} a t r e s e r v o i r p r e s s u r e}{m^{3} a t S T P} .

The dissolved gas-oil ratio is

10 \frac{m^{3} o f g a s a t S T P}{m^{3} o f o i l a t S T P} o f o i l .

The gas flow rate at bottom-hole conditions is ______

\times 10^{2} m^{3}

per day. (rounded-off to two decimal places)

8.90 to 9.10

8.90 to 9.20

8.90 to 9.30

8.90 to 9.40

Category: GATE Petroleum Engineering 2018

Question 25:

The exponential decline curve is to be used to estimate the oil reserves of a well. The current oil production rate is 1000

m^{3}

per day and the yearly decline rate is 6% per year. If the minimum oil flow rate economically sustainable for the well is

1 m^{3}

per day, the reserves (economically producible) associated with the well are _____ ×

10^{6} m^{3} .

(rounded-off to two decimal places. Use 1 year = 365 days)

5.50 to 5.90

5.60 to 6.00

5.70 to 6.10

5.80 to 6.20

Category: GATE Petroleum Engineering 2018

Question 26:

The probability density for three binomial distributions (D1, D2, and D3) is plotted against a number of successful trials in the given figure.

Each of the plotted distributions corresponds to a unique pair of (n, p) values, where, n is the number of trials and p is the probability of success in a trial. Three sets of (n, p) values are provided in the table.

Set	(n, p)
I	(60, 0.3)
II	(60, 0.2)
III	(24, 0.5)

Pick the correct match between the (n, p) set and the plotted distribution

Set I – D1, Set II – D2, Set III – D3

Set I – D3, Set II – D1, Set III – D2

Set I – D2, Set II – D3, Set III – D1

Set I – D2, Set II – D1, Set III – D3

Category: GATE Petroleum Engineering 2018

Question 27:

Which of the following statements are true about Natural Gas Hydrates? Natural gas hydrates: (I) are formed under low temperature and high pressure. (II) can store approximately 160 m3 of gas per m3 of hydrate at 25 oC and 1 atm. (III) the formation is an endothermic process. (IV) are potential sources of methane.

Only II, III & IV

Only I, II & III

Only I, II & IV

Only I, III & IV

Category: GATE Petroleum Engineering 2018

Question 28:

Pdf (bottom-hole well-flowing pressure) vs. Q (flow rate) plots show the inflow performance relation (IPR) and vertical lift performance (VLP) curves. Figure I showsVLP curves for two wellhead pressures Phw1 and Phw2. Figure II shows VLP curves for two well diameters D1 and D2. Which one of the following statements is true?

A	$P_{h w 1} > P_{h w 2} a n d D_{1} < D_{2}$	B	$P_{h w 1} > P_{h w 2} a n d D_{1} > D_{2}$
C	$P_{h w 1} < P_{h w 2} a n d D_{1} < D_{2}$	D	$P_{h w 1} < P_{h w 2} a n d D_{1} > D_{2}$

Category: GATE Petroleum Engineering 2018

Question 29:

Match the following: (P) Weber Number (I) Ratio of inertial force to viscous force (Q) Froude Number (II) Ratio of convective heat transfer to conductive heat transfer (R) Reynolds number (III) ratio of inertial force to interfacial force (S) Nusselt number (IV) Ratio of inertial force to gravitational force

P-III, Q-IV, R-I, S-II

P-III, Q-II, R-I, S-IV

P-II, Q-III, R-IV, S-I

P-IV, Q-III, R-I, S-II

Category: GATE Petroleum Engineering 2018

Question 30:

A dilute mixture of coal and sand particles, both of diameter 100 μm and densities 1800 kg

/ m^{3}

and 2600 kg

/ m^{3}

respectively, is to be classified by elutriation technique using water (density 1000 kg

/ m^{3}

,viscosity

10^{- 3}

Pa.s). Assuming Stokes law is applicable, the minimum settling velocity of the particles in the mixture is

(g = 9.81 m / s^{2}) :

A	$4.36 \times 10^{- 3} m / s$ 4.	B	$8.72 \times 10^{- 3} m / s$
C	$2.18 \times 10^{- 3} m / s$	D	$1.29 \times 10^{- 3} m / s$

Category: GATE Petroleum Engineering 2018

Question 31:

Oil flow rate and flowing bottom-hole pressure (FBHP) recorded with time during a multi-rate well test are shown.

Let k is the reservoir permeability, his formation thickness and μ is the viscosity of the oil.

∆ P_{D} (t)

is a constant-rate dimensionless pressure drop as a function of time. The total pressure drop till the time, t, where t >

t_{1}

, will be:

A	$\frac{q_{1 μ}}{2 πkh} ∆ P_{D} (t) + \frac{(q_{2 -} q_{1})}{2 πkh} ∆ P_{D} (t - t_{1})$	B	$\frac{q_{1 μ}}{2 πkh} ∆ P_{D} (t_{1}) + \frac{(q_{2 -} q_{1})}{2 πkh} ∆ P_{D} (t - t_{1})$
C	$\frac{q_{1 μ}}{2 πkh} ∆ P_{D} (t) + \frac{q_{2} μ}{2 πkh} ∆ P_{D} (t - t_{1})$	D	$\frac{q_{1 μ}}{2 πkh} ∆ P_{D} (t_{1}) + \frac{q_{2} μ}{2 πkh} ∆ P_{D} (t - t_{1})$

Category: GATE Petroleum Engineering 2018

Question 32:

Which one of the following options presents the correct combination? (P) Reservoir limit test (I) Communication between wells (Q) Modified isochronal test (II) Ideally zero flowing bottom hole pressure (R) Interference test (III) Extended drawdown test (S) Absolute open flow potential (IV) Drawdown and build-up test of equal duration

P-II, Q-III, R-I, S-IV

P-IV, Q-I, R-III, S-II

P-III, Q-IV, R-I, S-II

P-I, Q-III, R-IV, S-II

Category: GATE Petroleum Engineering 2018

Question 33:

Which one of the following options presents the correct combination? (P) Roller Cone bits (I) Long and widely spaced teeth (Q) PDC bits (II) Journal (Pin) angle (R) Soft formation (III) Short and wider teeth (S) Hard formation (IV) Size of the cutting (T) Back rake angle (V) 1400oC and

6 \times 10^{5}

psi

P-II, Q-V, R-I, S-III, T-IV

P-III, Q-IV, R-I, S-II, T-V

P-III, Q-II, R-IV, S-I, T-V

P-II, Q-V, R-III, S-I, T-IV

Category: GATE Petroleum Engineering 2018

Question 34:

Primary and secondary indicators of a kick in a well where the indicators are: 1) flow rate increase, 2) gas, oil or water-cut muds, 3) pit volume increase, 4) flowing well with mud pump shut-off, 5) reduction in drill-pipe weight, 6) drilling break Which one of the following presents the correct combination?

Primary (1, 3, 5) and Secondary (2, 4, 6)

Primary (1, 2, 3) and Secondary (4, 5, 6)

Primary (1, 2, 4) and Secondary (3, 5, 6)

Primary (1, 3, 4) and Secondary (2, 5, 6)

Category: GATE Petroleum Engineering 2018

Question 35:

R elative permeability curve for the two rock types (X: solid line and Y: dashed line) are shown in the diagram, where Sw is the fractional water saturation. Which one of the following statements is correct about the wettability and consolidated nature of the two rock types?

X is more consolidated and mixed wet, Y is less consolidated and water wet

X is more consolidated and water wet, Y is less consolidated and mixed wet

X is less consolidated and mixed wet, Y is more consolidated and water wet

X is less consolidated and water wet, Y is more consolidated and mixed wet

Category: GATE Petroleum Engineering 2018

Question 36:

Which one of the following options presents correct combinations of exploration method with their respective frequency of operation? (P) Seismic (I) ~

10^{6}

Hz (Q) Sonic (II) ~

10^{2}

Hz (R) Controlled Source EM (III) ~

10^{4}

Hz (S) Ultrasonic (IV) ~1 Hz

P-IV, Q-II, R-I, S-III

P-II, Q-III, R-IV, S-I

P-II, Q-I, R-IV, S-III

P-IV, Q-I, R-II, S-III

Category: GATE Petroleum Engineering 2018

Question 37:

Which one of the following options presents the correct combinations? (P) Borisov’s (I) Critical rate correlation in vertical wells with coning (Q) Schols’ (II) Horizontal good performance relation (R) Efros’ (III) Vertical good performance relation (S) Wiggins’ (IV) Critical rate correlation in horizontal wells with coning

P-II, Q-IV, R-I, S-III

P-IV, Q-III, R-II, S-I

P-IV, Q-II, R-III, S-I

P-II, Q-I, R-IV, S-III

Category: GATE Petroleum Engineering 2018

Question 38:

Which one of the following options represents the typical sequence of applying cut-offs for pay zone identification in a conventional reservoir?

porosity, saturation, shale

porosity, permeability, saturation

shale, porosity, saturation

shale, porosity, permeability

Category: GATE Petroleum Engineering 2018

Question 39:

Which one of the following options represents the correct sequence of arrival of acoustic wave energy recorded in a sonic log?

shear, surface, compressional

compressional, shear, surface

surface, shear, compressional

compressional, surface, shear

Category: GATE Petroleum Engineering 2018

Question 40:

The variation of the amount of salt in a tank with time is given by,

\frac{d x}{d t} + 0.025 x = 20,

where 𝑥 is the amount of salt in kg and 𝑡 is the time in minutes. Given that there is no salt in the tank initially, the time at which the amount of salt increases to 200 kg is __________ minutes. (rounded-off to two decimal places)

10.50 to 12.50

11.50 to 13.50

12.50 to 14.50

13.50 to 15.50

Category: GATE Petroleum Engineering 2018

Question 41:

Solve the given differential equation using the

2^{n d}

order Runge-Kutta (RK2) method:

\frac{d y}{d t} = t - \sqrt{y};

Initial condition: 𝑦(𝑡 = 0) = 4 Use the following form of RK2 method with an integration step-size, ℎ = 0.5:

k_{1} = f (t_{i}, y_{i}); k_{2} = (t_{i} + 0.5 h, y_{i} + 0.5 k_{1} h) y_{i + 1} = y_{1} + k_{2} h

The value of 𝑦(𝑡 = 0.5) =__________________. (rounded-off to two decimal places)

3.12 to 3.23

3.12 to 3.24

3.12 to 3.25

3.12 to 3.26

Category: GATE Petroleum Engineering 2018

Question 42:

A box contains 100 balls of the same size, of which, 25 are black and 75 are white. Out of 25 black balls, 5 have a red dot. A trial consists of randomly picking a ball and putting it back in the same box, i.e., sampling is done with replacement. Two such trials are done. The conditional probability that no black ball with a red dot is picked given that at least one black ball is picked, is __________. (infraction rounded-off to two decimal places)

0.75 to 0.80

0.76 to 0.80

0.77 to 0.80

0.78 to 0.80

Category: GATE Petroleum Engineering 2018

Question 43:

A cylindrical pipeline of length 30 km is transporting naphtha. Pressure sensors are attached along pipe length to detect leaks. Under steady-state, leak-free operation, there is a linear pressure drop along the length (z) of the pipeline. If a leak occurs, the pressure profile develops a kink at the leak point

z_{l e a k,}

Assume that there is only one leak-point (4 km < 𝑧leak < 27 km) and a new steady-state is reached. The steady-state pressure measurements at four locations along the pipe-length are provided in the table. The location of the leak-point using the gradient intersection method is _______________km. (rounded off to two decimal places)

𝑧 (km)	Pressure
0	$p_{0}$
4	0.84 $p_{0}$
27	0.31 $p_{0}$
30	0.25 $p_{0}$

7.10 to 7.70

7.20 to 7.80

7.30 to 7.90

7.40 to 8.00

Category: GATE Petroleum Engineering 2018

Question 44:

A dry core was subjected to the mercury injection test in the laboratory. Following are the related details: Average formation porosity = 0.2 Formation volume factor, BO = 1.2 reservoir-bbl/STB Oil APIo = 32, Specific gravity of water = 1.1 Hydrostatic gradient = 0.433 psi/ft

{(σ_{o w} \cos θ)}_{r e s}

26 dyne/cm, where

σ_{o w}

is the oil-water interfacial tension and 𝜃 is the contact angle

{(σ_{A M} \cos θ)}_{l a b}

= 367 dyne/cm, where

σ_{A M}

is air- mercury interfacial tension and 𝜃 is the contact angle Average drainage area = 80 acres (1 acre-ft = 7758 bbl) The Table shows the laboratory data for capillary pressure at different mercury saturations

Pc (Asia)	Mercury saturation $(S_{H g})$
10	0.0075
17	0.25
30	0.50
108	0.70
2000	0.85

P_{c} \frac{2 σ \cos θ}{r}

and the average water saturation (

S_{W}

) for the productive column is 0.25. The Original Oil in Place (OOIP) in the productive column where

S_{W}

≤ 0.5 is ___________ MMSTB. (rounded-off to one decimal place)

105.00 to 109.00

106.00 to 109.00

107.00 to 109.00

108.00 to 109.00

Category: GATE Petroleum Engineering 2018

Question 45:

A well is drilled with water-based mud. The water saturation in the completely flushed zone (no formation fluid residual) is given by,

S_{x o} = {(\frac{a}{ϕ^{2}} \times \frac{R_{m f}}{R_{x o}})}^{1 / 2},

where,

R_{m f}

and

R_{x o}

are the mud filtrate resistivity and flushed zone resistivity, respectively. Use, a = 1.0 and

R_{x o}

= 25

R_{m f} .

. The calculated porosity (ϕ) of the formation is ______. (infraction rounded-off to two decimal places)

0.19 to 0.21

0.21 to 0.23

0.23 to 0.25

0.25 to 0.27

Category: GATE Petroleum Engineering 2018

Question 46:

An n oil well is tested at a flow rate (Q) of 50 BOPD. The bottom hole flowing pressure (Pdf) is 500 psi. The shut-in pressure is 1000 psi. If Pdf is lowered to 300 psi and assuming Vogel’s correlation holds, the estimated flow rate in the oil well is ______BOPD (rounded-off to two decimal places). Vogel’s correlation is:

\frac{Q}{Q_{m a x}} = 1 - 0.2 (\frac{P_{w f}}{\bar{P}}) - 0.8 {(\frac{P_{w f}}{\bar{P}})}^{2}

60.00 to 63.00

61.00 to 63.00

62.00 to 63.00

63.00 to 63.00

Category: GATE Petroleum Engineering 2018

Question 47:

Using Miller, Dyes and Hutchinson (MDH) method, the skin factor of an oil well is found to be 𝑠 = – 3.5. The reservoir and fluid properties are: Formation porosity is 0.20 Total compressibility is 2.5

\times 10^{- 5} p s i a^{- 1}

Oil viscosity is 1.5 cP Wellbore radius is 0.5 ft Flowing bottom hole pressure at Δt = 0 is 2830 psi Shut-in pressure at Δt = 1 hr (PΔt=1hr) is 3000 psi The slope of the middle time region (MTR) line in the MDH plot is 190 Asia/cycle The permeability of the reservoir is __________mD. (rounded-off to two decimal places)

22.00 to 29.00

23.00 to 29.00

24.00 to 29.00

25.00 to 29.00

Category: GATE Petroleum Engineering 2018

Question 48:

An oil well (producing under expansion drive only) in a reservoir is subjected to two pressure build-up tests. The average formation thickness of the reservoir is 13 ft, the total compressibility is 1×

10^{- 5}

p s i a^{- 1}

and the porosity is 0.2. The average formation volume factor of oil is 1.3 reservoir-bbl/STB. Average reservoir pressure during the first test and the the second test was found to be 3500 psi and 3200 psi, respectively. If the oil produced between the two pressure build-up tests in 180 days is 250 STB/day, the area of the reservoir is __________acres. (rounded-off to two decimal places) (Use: 1 acre = 43560

f t^{2}

, 1 bbl = 5.615

f t^{3}

)

930.00 to 940.00

940.00 to 950.00

950.00 to 960.00

960.00 to 970.00

Category: GATE Petroleum Engineering 2018

Question 49:

A well in a very large reservoir has a wellbore radius of 10 cm. The sandstone, with a porosity of 0.25 and 12% (by grain volume) calcite (CaC

O_{3}

), is to be acidized with a preflush (HCl solution) so as to dissolve all the calcite up to a distance of 1 m from the wellbore. 1

m^{3}

of the preflush is able to dissolve 0.082

m^{3}

CaC

O_{3}

. Assume that the reaction between HCl and CaC

O_{3}

is instantaneous. The minimum preflush volume required per meter of the formation thickness is ______________

m^{3}

. (rounded off to two decimal places)

1.40 to 2.50

2.40 to 3.50

3.40 to 4.50

4.40 to 5.50

Category: GATE Petroleum Engineering 2018

Question 50:

At a particular temperature, the vapour pressure of benzene and toluene is 4 atm and 1.2 atm, respectively. The composition of the liquid at equilibrium is 0.5 moles of benzene and 0.5 moles of toluene. Assuming ideal gas and ideal solution, the equilibrium vapour phase mole fraction of benzene is ________. (rounded off to two decimal places)

0.72 to 0.80

0.72 to 0.82

0.80 to 0.82

0.82 to 0.90

Category: GATE Petroleum Engineering 2018

Question 51:

Saturated steam at 0.7 atm and 90°C condenses on a vertical pipe of 2 cm outside diameter and 40 cm length. The average condensation heat transfer coefficient on the tube is 12000 W/

m^{2} K .

. The outside surface temperature of the pipe is maintained constant at 85°C. The enthalpy values for saturated steam and condensate are 2660 kJ/kg and 375 kJ/kg, respectively. The rate of steam condensation is ____ kg/h. (rounded off to two decimal places)

2.10 to 2.40

2.10 to 2.50

2.10 to 2.60

2.10 to 2.70

Category: GATE Petroleum Engineering 2018

Question 52:

Oil is being transported between two reservoirs with the help of three parallel pipes at a steady state. The diameters of these pipes are 2 cm, 3 cm and 4 cm, respectively. The pipes are equal in length and the flow is laminar. The discharge through the 4 cm diameter pipe is 50 liters/s. The discharge through the 2 cm diameter pipe is _____ liters/s. (rounded-off to two decimal places)

3.00 to 3.20

3.20 to 3.40

3.40 to 3.60

3.60 to 3.80

Category: GATE Petroleum Engineering 2018

Question 53:

A driller finds an oil reservoir with a gas cap starting at a depth of 1000 m from the surface. The gas-oil contact was found at 1100 m depth and water-oil contact was found at 1300 m depth. The water pressure in the aquifer below the oil zone varies with depth from the surface (h, in meters) as, P = h×

10^{4}

Pa. The density of the oil is 900 kg/

m^{3}

and that of the gas is 5 kg/

m^{3}

at the reservoir condition. The minimum density of the mud needed to stop the gas kick when the driller reaches the top of the gas cap is _____kg/m3. (rounded off to two decimal places. Use g = 9.81

m / s^{2}

)

1113.00 to 1160.00

1114.00 to 1160.00

1115.00 to 1160.00

1116.00 to 1160.00

Category: GATE Petroleum Engineering 2018

Question 54:

The viscosity, μ (in Pa.s) of a power-law fluid as a function of shear rate, 𝛾̇ (in

s^{- 1}

) is given by the following relation:

μ = \frac{1}{2} |\dot{y}|

This power-law fluid lies between two infinitely large horizontal parallel plates separated by a distance (h) of

10^{- 3}

m. The top plate is moving horizontally at a velocity (v) of

10^{- 3}

m/s and the bottom plate is held stationary. Assuming laminar flow and neglecting gravity, the absolute value of steady-state shear stress acting on the bottom plate is ______ Pa. (rounded-off to two decimal places)

0.49 to 0.51

0.51 to 0.53

0.53 to 0.55

0.55 to 0.57

Category: GATE Petroleum Engineering 2018

Question 55:

A heterogeneous rectangular rock of cross-sectional area 1

m^{2}

perpendicular to the flow is being flooded by water to measure the effective permeability from cross-section AA’ to cross-section CC’.

The pressure at the cross-sections AA’, BB’, and CC’ is 2 bar, 1.5 bar, and 1 bar, respectively. The permeability in mili-Darcy and lengths AB and BC in meters are given in the figure. The effective permeability of the rock from AA’ to CC’ is ______mD. (rounded off to two decimal places)

0.50 to 1.00

1.00 to 1.50

1.50 to 2.00

2.00 to 2.50

⮜ Back Next ⮞

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Answered & Marked for Review (will be considered for evaluation)

Question 1:

The Taylor series expansion of the function,

f (x) = \frac{- 1}{1 + x},

around 𝑥 = 0 (up to

4^{t h}

order term) is:

A	$1 + x + x^{2} + x^{3} + x^{4}$	B	$- 1 - x + x^{2} - x^{3} + x^{4}$
C	$- 1 - x + x^{2} - x^{3} + x^{4}$	D	$- 1 + x - 2 x^{2} + 3 x^{3} - 4 x^{4}$

Correct Answer : B

Question 2:

The inverse of the matrix

[\frac{1}{1} \frac{3}{2}] i s,

A	$[\frac{2}{1} \frac{3}{1}]$	B	$[\frac{- 1}{3} \frac{1}{- 1}]$
C	$[\frac{- 2}{1} \frac{3}{- 1}]$	D	$[\frac{2}{- 1} \frac{- 3}{1}]$

Correct Answer : C

Question 3:

The line integral of a vector function

\bar{F} (\bar{r})

over a curve C in a simply connected domain D in space, is defined by:

\int_{c} \bar{F} (\bar{r}) . d \bar{r} = \int_{c} (F_{1} d x + F_{2} d y + F_{3} d z)

The line integral is independent of the path in D.

F_{1}, F_{2} a n d F_{3}

are continuous, and have continuous first partial derivatives in D.𝐶′ is a closed curve in D. Which one of the following is NOT ALWAYS true in domain D?

A	$\bar{\nabla} \times \bar{F} = \bar{0}$	B	$\bar{\nabla} . \bar{F} = 0$
C	$\oint_{C'} \bar{F} (\bar{r}) . d \bar{r} = 0$	D	$\bar{F} \times \bar{F} = \bar{0}$

Correct Answer : B

Question 4:

Which one of the following is the integrating factor (IF) for the differential equation,

(\cos^{2} x) \frac{d y}{d x} + y = \cos x ?

A	$e^{\tan x}$	B	$e^{\cos x}$
C	$e^{- \tan x}$	D	$e^{\sin x}$

Correct Answer : A

Question 5:

A phase diagram of black oil is shown in the figure (Y is the critical point).

Match the following: (P) Curve XY (I) Dew point curve (Q) Curve YZ (II) Single-phase liquid (R) Phase I (III) Bubble point curve (S) Phase II (IV) Single-phase gas

Correct Answer : P-III, Q-I, R-II, S-IV

Question 6:

Correct Answer : P-III, Q-IV, R-I, S-II

Question 7:

Correct Answer : II

Question 8:

The plot of the ratio of pressure to gas compressibility factor (P/Z) vs. cumulative gas production

(G_{P})

for a gas reservoir (represented by the solid curve in the figure) was shown to a reservoir engineering student.

Correct Answer : Only I and III

Question 9:

Wastewater from the oil industry consists of oil is free and emulsified forms. The oil in the free form can be recovered by:

Correct Answer : Gravity separators

Question 10:

Correct Answer : Capillary force

Question 11:

Correct Answer : IV

Question 12:

Which one of the following curves represents the behaviour of oil phase viscosity as a function of pressure in the reservoir (where,

P_{b}

is the bubble point pressure of oil)?

Correct Answer : Curve IV

Question 13:

Pick out the INCORRECT statement.

Correct Answer : Coal bed methane typically contains more than 60% CO2.

Question 14:

Which one of the following phenomena encountered during flooding is desirable for increasing oil recovery from a reservoir?

Correct Answer : Decrease in capillary pressure

Question 15:

C O_{2}

foams are used for enhanced oil recovery due to which of the following reasons? (I) It can be used for

C O_{2}

sequestration (II)

C O_{2}

can exist in the form of a dense fluid at reservoir conditions (III)

C O_{2}

can convert to hydrocarbon at the reservoir temperature and pressure (IV) Solubility of

C O_{2}

in oil is higher compared to gases like

N_{2}

Correct Answer : Only I, II, and IV

Question 16:

Which one of the following is FALSE about a typical offshore deepwater oil spill?

Correct Answer : Allowing the spill to reach the shore before clearing

Question 17:

Which one of these methods is NOT commonly used to deal with the problem of soil contamination by oil spillage?

Correct Answer : Using rain water to wash the contaminants

Question 18:

The factor on which the selection of an offshore platform for the reservoir does NOT depend:

Correct Answer : Best case weather forecast

Question 19:

Correct Answer : Only I and III

Question 20:

Which one of the following is INCORRECT about oil-based drilling muds?

Correct Answer : Less inhibitive than water based muds

Question 21:

Assume that vicious, gravity, and capillary are the only dominant forces for fluid flow in a given reservoir, a cone formed around the perforation zone will break into the well, when

Correct Answer : viscous forces are more than gravity forces

Question 22:

Two complex numbers,

\tilde{K} a n d \tilde{ε}

are related as follows:

\tilde{K} = \frac{\tilde{ε}}{i ω}

where,

i = \sqrt{- 1}

and 𝜔 is a scalar. Given the principal argument of

\tilde{ε}, A r g (\tilde{ε}) = - \frac{2 π}{3},

the principal argument

\tilde{k}, A r g (\tilde{k}) =

(rounded-off to two decimal places.Use

π = 3.14)

Correct Answer : 2.50 to 2.70

Question 23:

A cylindrical sandstone core, 7.5 cm long and 3.5 cm diameter have a grain density of3 g/

c m^{3}

. If the mass of the dry core is 200 g, the porosity of the core is __________%.(rounded-off to two decimal places)

Correct Answer : 7.25 to 7.75

Question 24:

In an oil reservoir, the current average pressure is below the bubble point pressure of the oil. The current oil production rate is 103 m3/day and the total gas production rate is

10^{5} m^{3}

/day at STP conditions (25°C and 1 atm). The formation volume factor of the oil is

1.2 \frac{m^{3} a t r e s e r v o i r p r e s s u r e}{m^{3} a t S T P}

and that of gas is 0.01

\frac{m^{3} a t r e s e r v o i r p r e s s u r e}{m^{3} a t S T P} .

The dissolved gas-oil ratio is

10 \frac{m^{3} o f g a s a t S T P}{m^{3} o f o i l a t S T P} o f o i l .

The gas flow rate at bottom-hole conditions is ______

\times 10^{2} m^{3}

per day. (rounded-off to two decimal places)

Correct Answer : 8.90 to 9.10

Question 25:

The exponential decline curve is to be used to estimate the oil reserves of a well. The current oil production rate is 1000

m^{3}

per day and the yearly decline rate is 6% per year. If the minimum oil flow rate economically sustainable for the well is

1 m^{3}

per day, the reserves (economically producible) associated with the well are _____ ×

10^{6} m^{3} .

(rounded-off to two decimal places. Use 1 year = 365 days)

Correct Answer : 5.80 to 6.20

Question 26:

The probability density for three binomial distributions (D1, D2, and D3) is plotted against a number of successful trials in the given figure.

Set	(n, p)
I	(60, 0.3)
II	(60, 0.2)
III	(24, 0.5)

Pick the correct match between the (n, p) set and the plotted distribution

Correct Answer : Set I – D3, Set II – D1, Set III – D2

Question 27:

Correct Answer : Only I, II & IV

Question 28:

A	$P_{h w 1} > P_{h w 2} a n d D_{1} < D_{2}$	B	$P_{h w 1} > P_{h w 2} a n d D_{1} > D_{2}$
C	$P_{h w 1} < P_{h w 2} a n d D_{1} < D_{2}$	D	$P_{h w 1} < P_{h w 2} a n d D_{1} > D_{2}$

Correct Answer : A

Question 29:

Correct Answer : P-III, Q-IV, R-I, S-II

Question 30:

A dilute mixture of coal and sand particles, both of diameter 100 μm and densities 1800 kg

/ m^{3}

and 2600 kg

/ m^{3}

respectively, is to be classified by elutriation technique using water (density 1000 kg

/ m^{3}

,viscosity

10^{- 3}

Pa.s). Assuming Stokes law is applicable, the minimum settling velocity of the particles in the mixture is

(g = 9.81 m / s^{2}) :

A	$4.36 \times 10^{- 3} m / s$ 4.	B	$8.72 \times 10^{- 3} m / s$
C	$2.18 \times 10^{- 3} m / s$	D	$1.29 \times 10^{- 3} m / s$

Correct Answer : A

Question 31:

Oil flow rate and flowing bottom-hole pressure (FBHP) recorded with time during a multi-rate well test are shown.

Let k is the reservoir permeability, his formation thickness and μ is the viscosity of the oil.

∆ P_{D} (t)

is a constant-rate dimensionless pressure drop as a function of time. The total pressure drop till the time, t, where t >

t_{1}

, will be:

A	$\frac{q_{1 μ}}{2 πkh} ∆ P_{D} (t) + \frac{(q_{2 -} q_{1})}{2 πkh} ∆ P_{D} (t - t_{1})$	B	$\frac{q_{1 μ}}{2 πkh} ∆ P_{D} (t_{1}) + \frac{(q_{2 -} q_{1})}{2 πkh} ∆ P_{D} (t - t_{1})$
C	$\frac{q_{1 μ}}{2 πkh} ∆ P_{D} (t) + \frac{q_{2} μ}{2 πkh} ∆ P_{D} (t - t_{1})$	D	$\frac{q_{1 μ}}{2 πkh} ∆ P_{D} (t_{1}) + \frac{q_{2} μ}{2 πkh} ∆ P_{D} (t - t_{1})$

Correct Answer : A

Question 32:

Correct Answer : P-III, Q-IV, R-I, S-II

Question 33:

6 \times 10^{5}

psi

Correct Answer : P-II, Q-V, R-I, S-III, T-IV

Question 34:

Correct Answer : Primary (1, 3, 4) and Secondary (2, 5, 6)

Question 35:

Correct Answer : X is less consolidated and mixed wet, Y is more consolidated and water wet

Question 36:

Which one of the following options presents correct combinations of exploration method with their respective frequency of operation? (P) Seismic (I) ~

10^{6}

Hz (Q) Sonic (II) ~

10^{2}

Hz (R) Controlled Source EM (III) ~

10^{4}

Hz (S) Ultrasonic (IV) ~1 Hz

Correct Answer : P-II, Q-III, R-IV, S-I

Question 37:

Correct Answer : P-II, Q-I, R-IV, S-III

Question 38:

Which one of the following options represents the typical sequence of applying cut-offs for pay zone identification in a conventional reservoir?

Correct Answer : shale, porosity, saturation

Question 39:

Which one of the following options represents the correct sequence of arrival of acoustic wave energy recorded in a sonic log?

Correct Answer : compressional, shear, surface

Question 40:

The variation of the amount of salt in a tank with time is given by,

\frac{d x}{d t} + 0.025 x = 20,

Correct Answer : 10.50 to 12.50

Question 41:

Solve the given differential equation using the

2^{n d}

order Runge-Kutta (RK2) method:

\frac{d y}{d t} = t - \sqrt{y};

Initial condition: 𝑦(𝑡 = 0) = 4 Use the following form of RK2 method with an integration step-size, ℎ = 0.5:

k_{1} = f (t_{i}, y_{i}); k_{2} = (t_{i} + 0.5 h, y_{i} + 0.5 k_{1} h) y_{i + 1} = y_{1} + k_{2} h

The value of 𝑦(𝑡 = 0.5) =__________________. (rounded-off to two decimal places)

Correct Answer : 3.12 to 3.26

Question 42:

Correct Answer : 0.76 to 0.80

Question 43:

z_{l e a k,}

𝑧 (km)	Pressure
0	$p_{0}$
4	0.84 $p_{0}$
27	0.31 $p_{0}$
30	0.25 $p_{0}$

Correct Answer : 7.20 to 7.80

Question 44:

{(σ_{o w} \cos θ)}_{r e s}

26 dyne/cm, where

σ_{o w}

is the oil-water interfacial tension and 𝜃 is the contact angle

{(σ_{A M} \cos θ)}_{l a b}

= 367 dyne/cm, where

σ_{A M}

Pc (Asia)	Mercury saturation $(S_{H g})$
10	0.0075
17	0.25
30	0.50
108	0.70
2000	0.85

P_{c} \frac{2 σ \cos θ}{r}

and the average water saturation (

S_{W}

) for the productive column is 0.25. The Original Oil in Place (OOIP) in the productive column where

S_{W}

≤ 0.5 is ___________ MMSTB. (rounded-off to one decimal place)

Correct Answer : 105.00 to 109.00

Question 45:

A well is drilled with water-based mud. The water saturation in the completely flushed zone (no formation fluid residual) is given by,

S_{x o} = {(\frac{a}{ϕ^{2}} \times \frac{R_{m f}}{R_{x o}})}^{1 / 2},

where,

R_{m f}

and

R_{x o}

are the mud filtrate resistivity and flushed zone resistivity, respectively. Use, a = 1.0 and

R_{x o}

= 25

R_{m f} .

. The calculated porosity (ϕ) of the formation is ______. (infraction rounded-off to two decimal places)

Correct Answer : 0.19 to 0.21

Question 46:

\frac{Q}{Q_{m a x}} = 1 - 0.2 (\frac{P_{w f}}{\bar{P}}) - 0.8 {(\frac{P_{w f}}{\bar{P}})}^{2}

Correct Answer : 61.00 to 63.00

Question 47:

\times 10^{- 5} p s i a^{- 1}

Correct Answer : 25.00 to 29.00

Question 48:

10^{- 5}

p s i a^{- 1}

f t^{2}

, 1 bbl = 5.615

f t^{3}

)

Correct Answer : 960.00 to 970.00

Question 49:

A well in a very large reservoir has a wellbore radius of 10 cm. The sandstone, with a porosity of 0.25 and 12% (by grain volume) calcite (CaC

O_{3}

), is to be acidized with a preflush (HCl solution) so as to dissolve all the calcite up to a distance of 1 m from the wellbore. 1

m^{3}

of the preflush is able to dissolve 0.082

m^{3}

CaC

O_{3}

. Assume that the reaction between HCl and CaC

O_{3}

is instantaneous. The minimum preflush volume required per meter of the formation thickness is ______________

m^{3}

. (rounded off to two decimal places)

Correct Answer : 4.40 to 5.50

Question 50:

Correct Answer : 0.72 to 0.80

Question 51:

Saturated steam at 0.7 atm and 90°C condenses on a vertical pipe of 2 cm outside diameter and 40 cm length. The average condensation heat transfer coefficient on the tube is 12000 W/

m^{2} K .

Correct Answer : 2.10 to 2.60

Question 52:

Correct Answer : 3.00 to 3.20

Question 53:

10^{4}

Pa. The density of the oil is 900 kg/

m^{3}

and that of the gas is 5 kg/

m^{3}

at the reservoir condition. The minimum density of the mud needed to stop the gas kick when the driller reaches the top of the gas cap is _____kg/m3. (rounded off to two decimal places. Use g = 9.81

m / s^{2}

)

Correct Answer : 1115.00 to 1160.00

Question 54:

The viscosity, μ (in Pa.s) of a power-law fluid as a function of shear rate, 𝛾̇ (in

s^{- 1}

) is given by the following relation:

μ = \frac{1}{2} |\dot{y}|

This power-law fluid lies between two infinitely large horizontal parallel plates separated by a distance (h) of

10^{- 3}

m. The top plate is moving horizontally at a velocity (v) of

10^{- 3}

Correct Answer : 0.49 to 0.51

Question 55:

A heterogeneous rectangular rock of cross-sectional area 1

m^{2}

perpendicular to the flow is being flooded by water to measure the effective permeability from cross-section AA’ to cross-section CC’.

Correct Answer : 2.00 to 2.50

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