# GATE Exam 2019 Petroleum Engineering (PE) Question Paper With Answer Key

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(C) to whom

(D) that

2.  Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(C) 4

(D) 2 and 3

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(C) 33.1

(D) 72.8

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(C) 7

(D) 10

(A) defeated

(B) defeating

(C) defeat

(D) defeatist

Q. 6 – Q. 10 carry two marks each.

6.  Since the last one year, after a 125 basis point reduction in repo rate by the Reserve Bank of India, banking institutions have been making a demand to reduce interest rates on small saving schemes. Finally, the government announced yesterday a reduction in interest rates on small saving schemes to bring them on par with fixed deposit interest rates.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

7. In a country of 1400 million population, 70% own mobile phones. Among the mobile phone owners, only 294 million access the Internet. Among these Internet users, only half buy goods from e-commerce portals. What is the percentage of these buyers in the country?

(A) 10.50

(B) 14.70

(C) 15.00

(D) 50.00

8. The nomenclature of Hindustani music has changed over the centuries. Since the medieval period dhrupad styles were identified as baanis. Terms like gayaki and baaj were used to refer to vocal and instrumental styles, respectively. With the institutionalization of music education the term gharana became acceptable. Gharana originally referred to hereditary musicians from a particular lineage, including disciples and grand disciples.

Which one of the following pairings is NOT correct?

(B) gayaki, vocal

(C) baaj, institution

(D) gharana, lineage

9. Two trains started at 7AM from the same point. The first train travelled north at a speed of 80km/h and the second train travelled south at a speed of 100 km/h. The time at which they were 540 km apart is AM.

(A) 9

(B) 10

(C) 11

(D) 11.30

10.  “I read somewhere that in ancient times the prestige of a kingdom depended upon the number of taxes that it was able to levy on its people. It was very much like the prestige of a head-hunter in his own community.”

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(C) the number of taxes he could levy

(D) the number of heads he could gather

Petroleum Engineering

Q.1 – Q. 25 carry one mark each.

1. Let 𝑟 and 𝜃 be the modulus and argument of the complex number 𝑧 = 1 + 𝑖, respectively. Then (𝑟, 𝜃) equals

(A) (√2, 𝜋/4)

(B) (2, 𝜋/2)

(C) (2, 𝜋/3)

(D) (√2, 𝜋)

2. Let 𝜆1 and 𝜆2 be the two eigenvalues of the matrix  Then, 𝜆1 + 𝜆2 and 𝜆1𝜆2, are respectively

(A) 1 and 1

(B) 1 and −1

(C) −1 and 1

(D) −1 and −1

3. The Laplace transform of the function 𝑓(𝑡) = 𝑒−𝑡 is given by

4. The relative decline rate of oil is given by  where q is the oil production rate, a (> 0) is the decline rate and b is a constant. The equation gives harmonic decline curve when b is

(A) 1.5

(B) 1

(C) 0.5

(D) 0

5. Which one of the following provides a vertical stab for the flow lines and annulus access lines from multiple wells in offshore subsea completion?

(A) Moon pool deck

(B) Spider beams

(C) Telescopic joints

(D) Manifold

6. In a faulted reservoir, the principle of superposition for the pressure drop using diffusivity equation is applicable. This is due to

(A) high Reynolds number flow in the well.

(B) constant permeability.

(C) pressure dependent viscosity.

(D) linearity of the diffusivity equation.

7. Which one of the following parameters is measured using routine core analysis (RCA)?

(A) Porosity

(B) Relative permeability

(C) Capillary pressure

(D) Wettability

8. Match the following:

(A) P-II, Q-IV, R-III, S-I

(B) P-III, Q-I, R-IV, S-II

(C) P-II, Q-III, R-IV, S-I

(D) P-III, Q-IV, R-I, S-II

9. Which one of the following rocks and reservoir fluids are arranged in the decreasing order of their electrical resistivity? Assume that rocks have equal porosity and are filled with brine.

(A) Shale > Brine > Sandstone > Limestone > Gas

(B) Gas > Shale > Sandstone > Limestone > Brine

(C) Gas > Limestone > Sandstone > Shale > Brine

(D) Shale > Brine > Limestone > Sandstone > Gas

10. Which one of the following is the correct sequence of events for hydrocarbon generation in the subsurface?

(A) Catagenesis → Metagenesis → Diagenesis

(B) Catagenesis → Diagenesis → Metagenesis

(C) Diagenesis → Catagenesis → Metagenesis

(D) Diagenesis → Metagenesis → Catagenesis

11. Match the following:

(A) P-II, Q-I, R-III

(B) P-I, Q-III, R-II

(C) P-III, Q-II, R-I

(D) P-III, Q-I, R-II

12 Match the following for drill pipe failure :

(A) P-III, Q-IV, R-I, S-II

(B) P-II, Q-I, R-IV, S-III

(C) P-I, Q-II, R-III, S-IV

(D) P-IV, Q-III, R-II, S-I

13. Which one of the following flow regimes is more favorable for gas lift operation?

(A) Bubbly flow

(B) Annular flow

(C) Churn flow

(D) Stratified flow

14. H2S gas is

(A) acidic.

(B) non-corrosive.

(C) lighter than air.

(D) non-flammable.

15. Which one of the following offshore platforms DOES NOT use buoyant columns or pontoons?

(A) Tension leg platforms

(B) Jack up platforms

(C) Spar platforms

(D) Semi-submersible platforms

16. In which one of the following offshore platforms, the condition of the sea floor is a vital consideration?

(A) Drill ship platforms

(B) Tension leg platforms

(C) Concrete gravity platforms

17. The ‘Klinkenberg effect’ is related to

(A) viscous fingering during water flooding in oil reservoirs.

(B) hysteresis effect in relative permeability during drainage and imbibition process.

(C) oil viscosity dependence on temperature.

(D) slippage of gas phase at the sand grain surface.

18. Favourable conditions for formation of gas hydrates are

(A) high temperature and high pressure.

(B) high temperature and low pressure.

(C) low temperature and high pressure.

(D) low temperature and low pressure.

19. Match the following quantities with their dimensions:

(A) P-III, Q-II, R-IV, S-I

(B) P-II, Q-I, R-IV, S-III

(C) P-III, Q-I, R-IV, S-II

(D) P-I, Q-II, R-III, S-IV

20. The plot of dissolved gas oil ratio (RS), defined as the “ratio of STP volume of gas dissolved in the oil at pressure P, to the volume of the oil at STP” is given below.

For the same oil, the plot of produced gas oil ratio (RP) defined as the “ratio of STP volume of the gas liberated from the oil at pressure P, to the volume of the oil at STP” is

21. Which one of the following denotes a regular four-spot flood pattern?

∆ represents injection well

O represents production well

(A)

(B)

(C)

(D)

22. The value of  is____(round off to 2 decimal places).

23. Let  If AX = Y, then a + b equals ______.

24. Let  where i, j and k are cartesian unit vectors. If  is perpendicular to v, then a equals _________.

25. If the neutron log porosity (ϕN) is 0.09 and density log porosity (ϕD) is 0.24 in the cross-over region, then the average porosity of the gas bearing region is ____ (round off to 2 decimal places).

Q.26 – Q. 55 carry two marks each.

26. The general solution of the differential equation  is (here C1 and C21 are arbitrary constants)

(A) y = C1ex + C2e−x

(B) y = C1xex + C2xe2x

(C) y = C1ex + C2xe−x

(D) y = C1ex + C2xex

27. Consider the following system of linear equations (where 𝑝 and 𝑞 are constants)

x1 + x2 + x3 = 1

x1 – x2 + 2x3 = p

3x1 – x2 + 5x3 = q

This system has at least one solution for any p and q satisfying

(A) 2𝑝 −                𝑞 + 1 = 0.

(B) 2𝑞 + 𝑝 + 1 = 0.

(C) 2𝑝 +                𝑞 − 1 = 0.

(D) 2𝑞 + 𝑝 − 1 = 0.

28. Three reservoirs P, Q and R have identical geometry and rock properties. The plot of the height of the transition zone (h) above the free water level (FWL) against the water saturation (Sw) is given in the figure. Assume 𝜎 cos 𝜃 for all the three fluid combinations remains the same. Which one of the following is the correct match of the reservoir fluids with the reservoir (𝜎 is the interfacial tension between the respective fluid phases and 𝜃 is the contact angle).

(A) P: low density oil – water, Q: gas – water, R: high density oil – water

(B) P: gas – water , Q: low density oil – water, R: high density oil – water

(C) P: high density oil – water, Q: low density oil – water, R: gas – water

(D) P: gas – water, Q: high density oil – water, R: low density oil – water

29. The fractional flow (fw) versus water saturation (Sw) curve for an imbibition process (neglecting the capillary forces) in a given core for three different inclinations is shown in the figure.

Which one of the following is the correct representation of the fractional flow curves?

(A) P: Down-dip,              Q: No-dip,           R: Up-dip

(B) P: Down-dip,               Q: Up-dip,           R: No-dip

(C) P: No-dip,                     Q: Down-dip,     R: Up-dip

(D) P:Up-dip,                     Q: No-dip,           R: Down-dip

30. Match the following:

(A) P-IV, Q-II, R-I, S-III

(B) P-III, Q-I, R-IV, S-II

(C) P-II, Q-IV, R-I, S-III

(D) P-II, Q-IV, R-III, S-I

31. Match the following:

(A) P-I, Q-IV, R-III, S-II

(B) P-I, Q-II, R-IV, S-III

(C) P- IV, Q-III, R-I, S-II

(D) P-IV, Q-I, R-II, S-III

32. An exploratory well encountered three reservoir formations S1 (perfectly cemented), S2 (poorly cemented) and S3 (fractured). The Formation Factor (F) is governed by the equation 𝐹 = 𝑎𝜙𝑚, where ‘𝜙’ is the porosity and ‘m’ is the cementation factor. The constant ‘a’, linked to tortuosity is assumed to be 1 for all the formations. The log-log plot between Formation Factor (F) and porosity (𝜙) is shown.

Which one of the following represents the correct match of the formations with their respective plots?

(A) S1-P, S2-Q, S3-R

(B) S1-R, S2-P, S3-Q

(C) S1-P, S2-R, S3-Q

(D) S1-R, S2-Q, S3-P

33. Typical parameters obtained in the pyrolysis experiment of the source rock materials are shown in the Figure. Which one of the following is NOT true about pyrolysis in source rock analysis?

(A) Peak S1 represents volatilization of existing hydrocarbons.

(B) Peak S2 represents breakdown of kerogen and generation of hydrocarbons.

(C) Peak S3 represents Tmax, the temperature at which most hydrocarbons are generated.

(D) S1/(S1+S2) represents the production index.

34. A single well encounters multiple clean sands of exactly the same thickness, porosity and permeability. Rw is the formation fluid resistivity and Rmf is the mud filtrate resistivity.

Which one of the following match the relation between Rw and Rmf to that of Self  Potential (SP) log deflection?

(A) P-I, Q-III, R-II

(B) P-III, Q-I, R-II

(C) P-II, Q-I, R-III

(D) P-I, Q-II, R-III

35. Which one of the following options is NOT a part of the mudlogs prepared by the drill-site geologist?

(A) Rate of Penetration (ROP)

(B) Chromatograph showing presence of C1 to C5 concentration

(C) Lithology from drill cutting and its interpretation

(D) Reservoir unit delineation based on volume of shale (Vsh)

36. Match the following:

(A) P-II, Q-I, R-IV, S-III

(B) P-IV, Q-II, R-III, S-I

(C) P-II, Q-I, R-III, S-IV

(D) P-IV, Q-III, R-II, S-I

37. A box contains 2 red and 3 black balls. Three balls are randomly chosen from the box and are placed in a bag. Then the probability that there are 1 red and 2 black balls in the bag, is _______.

38. The values of a function 𝑓(𝑥) over the interval [0,4] are given in the table below:

Then, according to the trapezoidal rule, the value of the integral  is  _______(round off to 2 decimal places).

39. Oil is produced at a constant rate from a well in a bounded reservoir. The variation of the bottom-hole pressure with time is shown in the given Table. The magnitude of the slope of the pressure vs time curve that you would use to find the drainage area is ____ psi/day    (round off to 1 decimal place).

40. In a core flood experiment of immiscible and incompressible displacement  of oil  (𝜇𝑜 =  1 cP) with water (𝜇𝑤 = 1 cP), only axial flow is observed. The relative permeability of water is given by 𝑘𝑟𝑤 = 𝑆2w , where 𝑆 is water saturation. The relative permeability of oil is given by 𝑘𝑟𝑜 = (1 − 𝑆𝑤)2. The gravity and capillary pressure are neglected. From the fractional flow and water saturation relationship, the saturation of water at the flood front is______ % (round off to 1 decimal place).

41. In an oil well, the pressure at the gas oil contact (GOC) at a depth of 2000 m is 205 bar (gauge), as shown in the figure.

The static oil pressure gradient is 0.08 bar/m in the pay zone. If a constant hydrostatic pressure gradient of 0.1 bar/m prevails throughout the subsurface, then the thickness of the oil column is _____ m (round off to 1 decimal place).

42. Oil is produced  at  a  constant rate of10 m3/day from a reservoir for 500 days. The producing gas oil ratio (GOR) is constant at  for the first 100 days. Then, the producing  gas  oil  ratio  increases  linearly  and  on  the  500th   day  the  measured  GOR is   The  cumulative  produced  gas  oil  ratio  after  500  days  of  production  is______ (round off to 1 decimal place). Assume that all volumes are measured at

43. A pressure build-up test was conducted in a well after 1000 days of producing oil at a constant rate of 0.01 reservoir-m3/s. The two shut-in bottom-hole pressure readings taken at 0.5 day and 1 day after shut-in are 150 × 105 Pa and 151 × 105 Pa, respectively. These pressure points correspond to the linear region of the Horner’s plot. The reservoir thickness is 100 m and oil viscosity is 0.001 Pa.s. The permeability of the reservoir is ______ mD (round off to 1 decimal place). [1 mD = 10−15 m2].

44. In an oil reservoir, the residual oil saturation in the volume flooded with polymer solution is 20%. The initial water saturation is 20%. The volumetric sweep efficiency is 50%. The maximum possible recovery factor for the reservoir is _______ % (round off to 1 decimal place).

45. An electrical submersible pump (ESP) delivers well fluid with 100% watercut. In the ESP, the impeller diameter is 0.1 m and speed is 3600 rpm. The total head developed by the ESP is 300 m (water column height). If the stage efficiency of the ESP is 60%, then the minimum number of stages required is ______ (round off to nearest integer). [g = 9.81 m/s2]

46. In a counter flow heat exchanger, hot fluid enters at 100°C and leaves at 50°C. Cold fluidenters at 30°C and leaves at 40°C. If heat losses are ignored, then the logarithmic mean temperature difference (LMTD) is _______°C (round off to 1 decimal place).

47. A model porous block of cross sectional area (A) and length (L) is made up of N independent capillaries of equal radii (r) and length (L). The porosity of the block is 10%, and the permeability for a laminar, incompressible and steady state flow is 0.02 mD. If the flow is only through the capillaries, then the value of r is _______ x 10−6 cm (round off to 1 decimal place). [1 mD = 10−15 m2 ].

48. A model porous medium of 5 cylindrical capillaries of radii varying from 60 to 100 micrometers (refer Table) is subjected to Mercury Injection Capillary Pressure (MICP) treatment. The capillaries are being filled in an increasing order of their entry pressure. The magnitude of  ,where 𝜎 is the interfacial tension and 𝜃 is the contact angle. The minimum applied mercury pressure to achieve 50% mercury saturation in the sample is _______ × 103 dyne/cm2 (round off to 1 decimal place).

49. The sonic log parameters from an exploratory well in a reservoir are as follows: Measured P-wave transit time (∆𝑡𝑙𝑜𝑔) = 85 µs/ft

True resistivity (Rt) = 10 ohm-m Matrix transit time (∆𝑡𝑚𝑎) = 45 µs/ft

Fluid transit time (∆𝑡𝑓𝑙) = 205 µs/ft

Formation water resistivity at reservoir temperature (Rw) = 0.1 ohm-m

The hydrocarbon saturation (in percentage) in the reservoir is ______(round off to 1 decimal place).

[Hint: Wyllie time average equation is ∆𝑡𝑙𝑜𝑔 = (1 − 𝜑)∆𝑡𝑚𝑎 + 𝜑∆𝑡𝑓𝑙 and formation water resistivity has the correlation  , where Sw is water saturation, 𝜑 is porosity]

50. A vertical well of 8000 ft is producing below bubble point pressure. Oil and water each is produced at the rate of 500 bbl/day. The indicated bottom hole pressure is 3000 psi. If the same gas to liquid ratio (GLR) is maintained, using the given figure, the new bottom hole pressure at 5000 ft is ______psi.

51. In a drilling rig, the crown block and the traveling block have three and two sheaves, respectively. A single wireline connects the hoisting drum to the deadline anchor as shown in the figure. Neglect the weight of the pulleys and the wireline, and friction between the sheaves and wireline. The ratio of the deadline load to static crown load is ______(round off to 2 decimal places).

52. Cement weighing 100 kg is mixed with 50 liters of water. The specific gravity of cement is 3.14 and the density of water is 1000 kg/m3. Neglecting volume changes, the resulting density of the slurry is __________ kg/m3 (round off to 1 decimal place).

53. In an active water drive during a certain period, the rate of production and reservoir pressure remain constant. The water influx into the reservoir from the aquifer is 6000 bbl/day. The surface oil and water production rates are 3000 STB/day and 1500 STB/day, respectively. The current production gas to oil ratio is 825 SCF/STB, and the formation volume factors at the current pressure for oil, water and gas are 1.375 bbl/STB, 1.04 bbl/STB and 0.007 bbl/STB, respectively. The solution gas to oil ratio at the current pressure is _______SCF/STB (round off to 1 decimal place).

54. In a water flooding experiment, the pressure gradients in the displacing and displaced phases are 400 psi/ft and 350 psi/ft, respectively. Assume that the displacement front is stable in the absence of capillary and gravity forces. Consider that only water flows upstream and only oil flows downstream of the displacement front. Then the mobility ratio for this immiscible displacement process is ______ (round off to 2 decimal places).

55. In a pressure draw-down testing, the well bore flowing pressure (𝑃𝑤𝑓) is given by

The following data is given in the oil field units,

Initial reservoir pressure (𝑃𝑖) = 5000 psia

Pressure after 1 hr of production (P1hr) = 4000 psia

Oil flow rate (q) = 500 STB/day

Porosity (∅) = 0.25

Viscosity of oil (𝜇) = 2 cP

Formation volume factor of oil (B) = 1.2 bbl/STB

Formation thickness (h) = 20 ft

Total compressibility (𝑐) = 30 × 10−6 psi-1

Well bore radius (𝑟𝑤) = 0.3 ft

The slope of 𝑃𝑤𝑓 versus log t is −100 psi/cycle. Then, the skin factor (S) for this well is ________ (round off to 1 decimal place).

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