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1 Course: Class: HERIOT-WATT UNIVERSITY DEPARTMENT OF PETROLEUM ENGINEERING Examination for the Degree of MEng in Petroleum Engineering Reservoir Engineering 1 Tuesday 6th January NOTES FOR CANDIDATES 1. This is a Closed Book Examination minutes reading time is provided from Examination Papers will be marked anonymously. See separate instructions for completion of Script Book front covers and attachment of loose pages. Do not write your name on any loose pages which are submitted as part of your answer. 4. This Paper consists of 3 Sections:- A, B and C. 5. Section A:- Attempt all Questions Sections B & C:- Attempt 4 numbered Questions with at least 1 Question from each Section 6. Section A:- 20% of marks Section B / C:- 80% of marks Marks for Questions and parts are indicated in [brackets] 7. This Examination represents 100% of the Class assessment. 8 State clearly any assumptions used and intermediate calculations made in numerical questions. No marks can be given for an incorrect answer if the method of calculation is not presented. 9. Answers must be written in separate, coloured books as follows:- Section A:- Section B:- Section C:- Blue Green Yellow

2 SECTION A A1 Define:- (i) (ii) (iii) (iv) Gas formation-volume factor Oil formation-volume factor Total formation-volume factor Solution gas-oil ratio [2] A2 Explain briefly what you understand by:- (i) Compositional model description for the characterisation of a reservoir fluid. (ii) Black oil description for the characterisation of a reservoir fluid. [3] A3 Draw the pressure - temperature phase diagram for a gas condensate reservoir indicating the following:- (i) (ii) (iii) (iv) (v) Bubble point and dew point lines Critical point Cricondentherm Lines of constant proportion of liquid-gas Region of retrograde condensation. [3] A4 Derive an equation for the average permeability, resulting from radial circular flow into a well from layers of different permeabilities and thicknesses. From where would such an average be obtained? [3] A5 List the rock properties that should be determined in a rock-mechanicaloriented, special core analysis programme. [3]

3 A6 Describe the nature of a partially communicating fault and how pressure data may be used to identify the transmissibility index of such features. [3] A7 Explain the difference between a steady-state and a semi-steady-state productivity index. [3]

4 SECTION B B8 (a) Methane is a significant component in reservoir fluids. Using a sketch for a binary of methane and n-decane (C10), illustrate the impact of methane on the critical point loci of C1-C10 binary mixtures. What is the significance of this diagram? [6] (b) A wet gas is producing at 40,000 SCF/STB, from a reservoir which has been estimated from petrophysics to have a volume of 1.1 x 1010 cu ft. and has a pressure of 3,000 psia and a temperature of 250 F The composition of the producing gas is given below:- Component (MW) Composition (Mole fraction) Gas Condensate Methane (16.04) Ethane (30.07) Propane (44.09) N-butane (58.12) N-pentane (72.15) Hexane (86.17) Heptane plus (114.2) (equivalent to octane) (i) (ii) (iii) What is the composition of the reservoir gas? What are the reserves of gas and condensate at 3,000 psia? How much gas will have been produced, when the pressure has dropped to 2,000 psia? [14] R = 10.72cu ft.psi/lb mole. R 1lb mole = SCF 1bbl = 5.615cu ft

5 B9 (a) You have been given a PVT report for an oil sample. (i) (ii) The bubble point pressure at reservoir temperature The solution gas-oil ratios and the oil formation volume factors above the bubble point and below the bubble point. [10] (b) A laboratory cell, contained 290cc of reservoir liquid at its bubble point of 2100 psia at 145 F. 21cc of mercury were removed from the cell and the pressure dropped to 1700 psia. Mercury was then re-injected at constant temperature and pressure and SCF of gas was removed leaving 270cc of liquid in the cell. The process was repeated reducing the pressure to 14.7 psia and the temperature to 60 F. Then 0.45 SCF of gas was removed and 207.5cc of liquid remained in the cell. List the procedures and calculations you would take to determine:- Determine:- (i) and Rs at the bubble point. (ii) Bo, Bt, Bg, Rs and z at 1,700 psia and 145 F (iii) Bt at 2100 psia and 145 F [10] B10 Using field examples, describe the various rock-mechanical phenomena which can be activated in producing reservoirs, and explain the impact of these phenomena on reservoir development and management strategies. [20]

6 B11 (a) For low permeability rocks, the measured permeability of the rock, using gas as the fluid is more than it is using a liquid. Comment briefly on this and how the permeability of a rock can be obtained using gas as the fluid. [4] (b) The system below represents the common arrangement for measuring the permeability of a core plug using a gas. Derive an equation to calculate the gas permeabilities of a rock using the above system. [6] (c) What is the free water level? Explain briefly why, because of capillary pressure, it is possible to have water saturations of large values, up to 100%, above the oil-water contact and above layers with lower water saturations. [4] (d) Capillary pressure data are obtained from core samples which represent a small part of the reservoir. Leverett derived a J Function using the Poiseuille equation for laminar flow:- r P q = π 4 8µL to relate Capillary pressure (Pc), to Permeability (k), and Porosity (ø). Derive the 'J' function and comment on one of its limiting assumptions. [6]

7 B12 (a) Identify the various elements in the material balance equation below:- ( N N ) B = NB B [ NR ( N N ) R G ] p o oi g si p s ps [( G G ) B GB ] ( W W B ) pc g gi e p w NB ( 1 m) p c S c f + wc w oi + ( WinjBw GinjBg) 1 S + wc with a line above the symbols of the equation e.g. ( W W B ) = net water inf lux e p w [3] (b) Simplify the material balance equation above so that it can be used for an undersaturated reservoir without waterdrive and water production. Modify the simplified equation so that it can be used to express the recovery at the bubble point in terms of the effective compressibility of the reservoir system.. [4] (c) To predict the performance of a solution gas drive reservoir we require both the instantaneous gas-oil ratio equation and an equation to express the average oil saturation. Derive the instantaneous gas-oil ratio equation and use the equation to explain briefly the shape of the producing GOR of a depletion type reservoir from a pressure above the bubble point to one significantly below the bubble point pressure. [6] (d) Tarner s method and Tracy's modification of Tarner's method use the Material Balance equation, the Instantaneous GOR equation and the Saturation equation to predict oil production as a function of pressure for a solution gas drive reservoir from the bubble point pressure. Describe briefly, in a step by step procedure, the application of one of these methods. [7]

8 SECTION C C13 A tight formation of horizontal permeability, k y, equal to 0.5md and thickness, h, of 150ft is to be developed for oil production. The choice lies between horizontal wells or vertical wells with hydraulic fracturing. The rock mechanics suggest that an infinite-conductivity fracture of halflength, x f, equal to 300ft will be feasible. Determine the length of a horizontal well, L, which will have a comparable semi-steady-state productivity index (PI) to the fractured, vertical well. Additional Well Data:- Formation vertical permeability, k z = 0.01md Oil viscosity, µ 0 = 1.5cp Oil formation volume factor, B 0 = 1.25 Wellbore radius, r w = 0.3ft Equivalent cylindrical external radius of reservoir drainage compartment, r e = 10,000ft. [20] C14 A particular formation has been shown to be amenable to acid treatment which can increase the rock permeability from the intrinsic value of 5md to an improved value of 17md due to its effect on interstitial clay. In a formation of 80ft thickness and 20% porosity, estimate how much the well productivity index will be increased if 1000bbl of acid are injected into the formation, assuming piston displacement of connate water and oil to a residual saturation of Additional reservoir data:- Connate water saturation, S wc = 0.25 Oil formation volume factor, B 0 = 1.2 Oil viscosity, µ 0 = 0.8cp Drainage area external radius, r e = 5000ft Wellbore radius, r w = 0.3ft [20]

9 C15 Discuss how the wireline formation tester can give information on dynamic aquifer effects and indicate where other phenomena can give similar pressure-depth plots to those associated with a dynamic aquifer. Why is it important to know if dynamic aquifer effects are present? [20] End of Paper

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14 Course: Class: HERIOT-WATT UNIVERSITY DEPARTMENT OF PETROLEUM ENGINEERING Examination for the Degree of MEng in Petroleum Engineering Reservoir Engineering 1 Friday 8 January NOTES FOR CANDIDATES 1. This is a Closed Book Examination minutes reading time is provided from Examination Papers will be marked anonymously. See separate instructions for completion of Script Book front covers and attachment of loose pages. Do not write your name on any loose pages which are submitted as part of your answer. 4. This Paper consists of 3 Sections:- A, B and C. 5. Section A:- Attempt all Questions Sections B & C:- Attempt 4 numbered Questions with at least 1 Question from each Section 6. Section A:- 20% of marks Section B / C:- 80% of marks Marks for Questions and parts are indicated in [brackets] 7. This Examination represents 100% of the Class assessment. 8 State clearly any assumptions used and intermediate calculations made in numerical questions. No marks can be given for an incorrect answer if the method of calculation is not presented. 9. Answers must be written in separate, coloured books as follows:- Section A:- Section B:- Section C:- Blue Green Yellow

15 SECTION A A1 Define: (i) (ii) (iii) (iv) The gas formation volume factor The oil formation-volume factor The total formation volume factor The solution gas-oil ratio [2] A2 A3 Derive an equation in terms of equilibrium ratios and composition to predict liquid and vapour ratios and compositions resulting from the flash separation of a reservoir fluid. Explain briefly the application of the equation when the reservoir fluid composition, temperature, and the pressure of the separation are known. [3] Derive the instantaneous gas-oil ratio equation and plot the shape of the producing GOR versus pressure for a solution gas drive reservoir [3] A4 A5 A6 With the aid of a diagram, comment on the fluid pressure gradients in an oil reservoir with a gas cap with a supporting aquifer for a normally pressured reservoir. Illustrate the gradient for an overpressured reservoir. [3] Briefly describe how the permeability sensitivity of rocks to stress can be measured in the laboratory, and draw a graphical, normalised, representation of the results you would expect to see for sandstones with high, medium and low permeabilties measured at ambient conditions. [3] Discuss the common mechanisms of formation damage occurring during drilling. [3] A7 Discuss the concept of a critical rate in coning situations. [3]

16 B8 (a) SECTION B Draw a Pressure-Temperature phase diagram to illustrate the phase behaviour of a gas condensate fluid. [2] (b) (c) Explain briefly gas cycling with reference to gas condensate reservoirs. [3] A wet gas reservoir is producing gas and condensate with the compositions given below at a gas-oil ratio of 25,000 SCF/STB. The average reservoir temperature is 260 F and the initial reservoir pressure is 8520 psia. The pore volume of the reservoir is considered to be 9.5 x 10 8 cu ft and the average water saturation is 19%. (i) (ii) (iii) Calculate the composition of the reservoir fluid Calculate the inplace reserves in SCF of gas and STB condensate of the reservoir at the original pressure. Calculate the production of gas and condensate when the reservoir pressure has declined to 4260psia. 1bbl = cu ft 0 F = 460 R 1lb mole = SCF R = psi cu ft/lb mole R Composition of Produced Fluids (Mole fraction) [15] Gas Condensate Attachments C1 Methane C3 Propane C5 n-pentane C8 Octane

17 B9 (a) (b) (c) After natural water drive or injected water drive residual oil is left within that part of the rock contacted by the water. Comment briefly with the aid of a sketch why this might be. [5] Miscible gas injection can be used to recover the residual oil after a water flood. Explain briefly what miscible gas injection is and why in some cases gas injected is alternated with water injection in a WAG (water alternating gas ) process. [5] An edge water drive reservoir extends to a radius of 8,000 ft. Sealing faults are such that the water influx only forms part of a full radial system as the sketch below illustrates. The supporting aquifer extends to a radius of 40,000ft. Over the first two years of production the pressure decline is expected to be as follows: Time( months) Pressure(psia) After the first 6 month period 23,200 bbls. of water were estimated to have influxed from the aquifer. The properties common to the oil reservoir and the adjoining aquifer are as follows: permeability k = 120 milli darcies water viscosity µw = 0.8 cp porosity = 0.2 effective water compressibility = 1 x 10-6 psi-1 (i) (ii) Calculate the average thickness of the aquifer sands. The cumulative water influx after 12, 18 and 24 months. The Hurst & van Everdingen equation for a full radial flow system is: [10]

18 W 2 = φcR h pw e o D where We p WD c Ro h Ø = cumulative water influx (bbls) = pressure drop(psi) = dimensionless water influx = compressibility of the aquifer (psi-1) = radius of the oil reservoir (ft) = average thickness of the aquifer sands. (ft) = porosity Charts are supplied of dimensionless water influx WD versus dimensionless time td (see 2 attachments) where t D = 2 kt. 309 µ φcr 2 w o t = time ( years) k = permeability (millidarcies) µw = viscosity (cp) Aquifer Radius 40,000ft Oil Reservoir Radius 8,000ft Angle - 135º

19 B10 (a) (b) (c) Describe briefly the drive mechanisms associated with producing an undersaturated oil reservoir, without a supporting aquifer, down to a pressure well below the bubble point. [6] Explain briefly why surface samples from a wet gas or condensate reservoir can be unrepresentative if collected too early after a shut down or major well disturbance. What suggestions would you give to get more representative samples. [4] Table 1 gives the results for a constant mass study on an oil sample. In the test the volume of live oil was measured as a function of pressure. The temperature was maintained at the reservoir temperature of 220 F. In another test a sample of the same oil in a PVT cell,at its bubble point and at 220 F was passed through a two stage separator at 500 psig and 160 F and 0 psig and 60 F. 38 cc of oil were removed from the PVT cell and cc of oil were collected from the final separator. A total amount of 3492 cc of gas at 60 F and 0 psig were collected from both stages of the separation process. In a further test a differential liberation procedure was carried out on a sample of the oil at 220 F and the volumes of oil remaining and standard volumes of gas liberated at each stage were recorded. The results are presented in Table 2. From the results of these tests assuming separator conditions of 500 psig and 160 F and 0 psig and 60 F determine: (i) (ii) (iii) (iv) The bubble point pressure of the reservoir fluid at 220 F The oil formation volume factor at 4400 psig and 3925 psig. The solution gas to oil ratio at 4400 psig and 3925 psig. The oil formation volume factor and solution gas to oil ratio you would use for reservoir calculations at 1605 psig. (v) The total formation volume factor at 3300 psig. [10]

20 Table 1 Constant Mass Study of Reservoir fluid at 220 ºF Pressure (psig) Volume of Oil in Cell (cc) Pressure (psig) Volume of Oil in Cell (cc) Pressure (psig) Volume of Oil in Cell (cc)

21 Table 2 Differential test at 220 ºF Pressure (psig) Cumulative Gas Produced Volume of Oil in Cell 60 º F & 0 psig (cc at pressure) Bubble point pressure

22 B11 (a) (b) In reserve estimates what do you understand by Proven, Probable and Possible reserves. [6] A well penetrates an oil reservoir from which core samples have been collected and capillary pressure curves generated using the air-mercury method. The capillary pressure data for the specific rock types are given in the attached figure. The lowest 100% Sw saturation level was found at the bottom of the well in rock A as indicated. (i) Determine the free water level and indicate it on the diagram. [2] (ii) Construct the water saturation profile on the saturation height diagram. [7] (iii) Estimate the oil -in place per unit cross section area over the reservoir thickness. [5] Data The specific gravities of water and oil relative to water density at 60 F are 1.03 & 0.8 respectively. The density of water at 60 F is 62.4 lbm/cu.ft. Air/mercury capillary pressure = 10 x capillary pressure water/ oil. 1 bbl = cu. ft 1 lbf = 1 lbm x g. psi = lbf / sq inch

23 B12 You have been appointed as the engineering manager of a reservoir. Given that you appreciate the importance of allowing for the activation of rock mechanical phenomena ( stress-sensitivity) in the management of the reservoir, explain how you would screen the reservoir for stress - sensitivity at the reservoir scale by listing and describing: (a) the relevant rock mechanical phenomena to be considered, and their impact on reservoir performance (b) the data set required to conduct the screening process (c) the software tools necessary [9] [9] [2]

24 Section C C13 A super well has been devised for high permeability reservoirs in which individual vertical wells are drilled in two concentric circles as shown in the diagram. Each ring has the same number of wells but staggered in position as shown. Yaxley has given an expression for the Dietz shape factor for a well in a triangular drainage area, also shown as a diagram. Sketch the approximate shape of the well drainage areas for the super well configuration and show how Yaxley s formula may be used to obtain the productivity index of the wells in the inner and outer rings. C A = γ 4A 4π re 3 ro r o + θ exp ln 2ln θ 4 πθo 2π sin θ where A = re = r θπ π θ e or Derive the Hawkins equation for the damage skin factor in an openhole completion. Supposing the skin factor, S, has been measured in a transient well test what additional information could be used to estimate the depth of damage, r a, and hence the damage zone permeability, k a. [20]

25 Closed Outer Boundary 16 Well "Super Well" in a Large Circular Reservoir

26 C14 A two layer reservoir is produced commingled as shown in the diagram and it is desired to balance the production by the use of variable chokes; here balanced production implies that the rate from a layer is proportional to its thickness i.e. q 1 /h 1 = q 2 /h 2. This is the basis of smart wells used to optimise production behaviour. Each choke diameter may be continuously varied from fully open to closed. Given a vertical lift curve for the well i.e. a plot of bottom-hole flowing prerssure, p wf, versus well total flow-rate, q, where q = q 1 + q 2, show how the choke settings may be calculated to give maximum balanced production. Assume that the choke performance is given by an equation of the form: q i = C ch A t 2 p ρ 1 σ 2 where p = pressure drop over choke q i = flow-rate through device C ch = discharge coefficient (constant) A t = throat area = πd 2 t /4 σ = D t D p D t = throat diameter D p = pipe diameter [20] C15 Describe the phenomenon of supercharging and the procedures which may be used to obtain a useful WFT survey in a low permeability reservoir [20] End of Paper

27 q Balanced Production Using Variable Chokes Layer 1 S 1 k 1 h 1 p 1 q 1 Layer 2 q 2 S 2 k 2 h 2 p 2 q = q 1 + q 2 Q14

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29 BEHAVIOUR OF OIL FIELD HYDROCARBON SYSTEMS Compressibility Factor, z Pseudo Reduced Pressure, Pr Pseudo Reduced Temperature Compressibility of Natural Gases (Jan. 1, 1941) Pseudo Reduced Pressure, Pr

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