HERIOT WATT UNIVERSITY DEPARTMENT OF PETROLEUM ENGINEERING Examination for the Degree of Meng in Petroleum Engineering Reservoir Engineering 1 Tuesday 09.30 09. 30 - 13.30 13.30
NOTES FOR CANDIDA CANDIDATES TES 1.
This is is a Closed Bo Book Ex Examination.
2.
15 mi minu nute tess rea readi ding ng ti time me is pr prov ovid ided ed fr from om 09 09.1 .15 5 – 09 09.3 .30. 0.
3. Exami Exa mina nati tion on Pap Papers ers wi will ll be mar marked ked an anony onymo mousl usly y. Se Seee sepa separat ratee in instr struct uctio ion n for for completion of Script Book 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 answer.. 4.
This Th is pa pape perr co cons nsis ists ts of 2 Se Sect ctio ions ns::- A an and dB
5.
Section A:Section B:-
Attempt all Questions Attempt 4 numbered Questions.
6.
Section A:Section B:-
20% of marks 80% of marks
Marks for Questions and parts are indicated in brackets 7.
This Th is ex exam amin inat atio ion n rep repre rese sent ntss 100 100% % of of the the Cl Clas asss ass asses essm smen ent. t.
8. State Sta te cle clearl arly y any any assum assumpti ptions ons use used d and and inte interme rmedia diate te cal calcul culati ations ons mad madee in in numer numerica icall questions. No marks can be given given for an incorrect answer answer if the method of of calculation is is not presented. 9.
Answ An swer erss must must be be writ writte ten n in in sepa separa rate te,, colo colour ured ed boo books ks as as foll follow ows: s:
Section A:Section B:-
Blue Green
SECTION A
A1
Explain briefly what you understand by:
(a)
the compositional model description and
(b)
the black oil model description for the characterisation of a reservoir fluid. (2)
A2
Explain briefly the importance of characterising the permeability variations in a reservoir in relation to the prediction of the behaviour of natural and injected water drive systems. The answer should be limited to the behaviour in the vertical plane rather than the areal plane (3)
A3
Derive the instantaneous gas-oil ratio equation. (3)
A4
Derive two equations in terms of composition and equilibrium ratios to determine the dew point and bubble point pressure of a reservoir fluid. Explain briefly how the equations are used, when the temperature of the reservoir and composition of the fluid are known. (3)
A5
(i)
Explain briefly what is meant by (a)
a normal pressured reservoir
(b)
an overpressured reservoir (3)
A6
Briefly explain the need for the development of transient flow solutions to the diffusivity equation in reservoir engineering. (3)
A7
Describe the method by which the line source solution may be adapted to accommodate a zone of reduced permeability around a wellbore (a skin). (3)
SECTION B
B1 (i) Draw a pressure temperature diagram for a retrograde-gas condensate fluid and indicate the key features. What is gas cycling and why in some cases is it used? (6 marks) (ii) The dew point pressure of a condensate gas field is 6250 psia. The initial reservoir conditions are 240oF and 8500 psia. When the reservoir was initially tested, a condensate to gas ratio of 80 s tock tank barrels per million SCF of gas was obtained. The produced gas and condensate compositions were as follows: Compositions of Produced Fluids (Mole fractions)
C1 Methane C3 Propane C5 N-Pentane C8 Octane
Gas
Condensate
0.89 0.07 0.04 —
— 0.21 0.61 0.18
The reservoir pore volume is considered to be 5 x 10 11 cu ft with a connate water saturation of 0.17. Calculate the condensate fluids produced (STB) and the gas produced (SCF) in producing the reservoir down to a pressure of 6750 psia. 1 bbl o R 1 lb mole R
= = = =
5.615 cu ft 460+oF 379.4 SCF 10.73 psi cu ft/lb mole oR
See Attachment B1 (Table and Figure) (14 marks) B2 (i) Explain briefly the three following tests carried out on reservoir fluid samples in relation to a PVT study, and comment on their application. (a)
Relative Volume (Flash Vaporisation Test)
(b)
Separator Test
(c)
Differential Test (6 marks)
(ii) Explain briefly the constant volume depletion test for gas condensate (4 marks)
(iii) Table 1 gives the results for a volume/pressure investigation of a reservoir fluid at reservoir temperature. The system composition remained constant throughout the test.
Table 1 (System constant) Pressure psig
Volume cc
Pressure psig
Volume cc
5000 4500 4000 3500 3000 2500 2000 1900 1800 1700 1601
162.54 163.21 163.90 164.64 165.43 166.32 167.21 167.40 167.60 167.80 168.00
1591 1573 1555 1515 1435 1341 1234 1113 989 854 728
168.39 169.08 169.85 171.56 174.97 180.11 186.95 197.28 211.04 231.71 259.31
In another test on the fluid a sample of oil at its bubble point pressure and reservoir temperature in a PVT cell were passed through a two stage separator at 100 psig and 75 oF and 0 psig and 60oF. 34 cc of oil were displaced from the PVT cell and 27.4 cc of oil were collected from the last separator stage. 4976 cc of gas were collected at standard conditions during the test. In a further test the pressure in a PVT cell at reservoir temperature was reduced in stages and the gas produced at each stage removed and the remaining oil volume measured. The total gas produced at standard conditions was recorded and is presented in Table 2.
Table 2 Pressure in PVT Cell psig
Bubble Point 1400 1200 1000 800 0
Cumulative Gas Produced cc (standard conditions) 0 2044 4438 6732 9076 26,928 @ 60oC
Volume of Oil in Cell cc
184.80 182.35 179.37 176.52 173.67 140
(a)
Determine the bubble point pressure of the reservoir fluid at reservoir temperature.
(b)
The oil formation volume factor at 3650 psig (c) The solution gas-oil ratio at 3650 psig and 2700 psig (d) The solution gas-oil ratio at 1200 psig (e) The total formation volume factors at 3650 psig and 1200 psig. (10 marks)
B3 (i) In the context of capillary pressure define the free water level. (3 marks) (ii) Explain briefly the reason for significant oil saturation remaining in the water swept zones of a reservoir after natural water drive or water injection. (5 marks) (iii) Core samples have been obtained from a well and air-mercury capillary pressure curves generated for an oil reservoir system (see attachment Figure 1). The lowest limit of 100% S w was found at the bottom of the well in rock type A as shown in the attachment Figure 2. (a) Determine the free water level and indicate it on the well diagram provided. (b) Construct the water saturation profile in the space provided. (c) Calculate the oil-in-place per unit cross-section over the thickness of the reservoir. Data:
Specific gravity of water Specific of oil Density of water Air-mercury capillary Pressure
= = =
1.03 0.80 62.4 lb/ft3
=
10 x water-oil capillary pressure 1.22
Oil formation volume factor =
(12 marks) B4 (i) Water drive reservoirs are said to be ‘rate sensitive’. Explain briefly this statement with respect to different aquifer characteristics (4 marks) (ii) Explain briefly how the constant terminal pressure solution of the Hurst and van Everdingen unsteady state theory can be used to predict water influx into an oil reservo ir with a declining reservoir pressure. (4 marks) (iii) A water drive reservoir extends to a radius of 15,000 ft. Sealing faults restrict the shape of the reservoir to form only a part of the full radial system. The supporting acquifer is considered to extend to 90,000 ft. The reservoir shape is given below. Over the first two years of production the pressure decline is expected to be as follows: Time (months) Pressure (psia)
0 6700
6 6688
12 6642
18 6584
24 6508
After the first 6 months 80,000 bbls of water were calculated to have influxed from the acquifer.
The properties common to the reservoir and acquifer are as follows: K µw porosity water compressibility pore/rock compressibility
= = = = =
180 mD 0.6 cp 0.19 3 x 10-6 psi-1 4 x 10-6 psi-1
(a)
Calculate the thickness of the acquifer sands
(b)
Calculate the cumulative water influx at the end of 12 months, 18 months and 24 months.
The Hurst & van Everdinger equation for a full radial system is: We =
1.119∅cR o2h∆ pWD
where We ∆ p WD c R o h ∅
= = = = = = =
cumulative water influx (bbls) pressure drop (psi) dimensionless water influx compressibility of the acquifer (psi -1) radius of oil reservoir (ft) thickness of acquifer (ft) porosity
Charts are supplied of dimensionless water influx W D versus dimensionless time t D (see 2 attachments) where:
tD
=
t = k = µw =
2.309
kt
µ w φcR 20
time (years) permeability (millidarcies) viscosity (cp) (12 marks)
B5 (i) A radial oil reservoir of constant thickness has a single vertical well situated at its centre, perforated the full thickness of the reservoir. The pressure everywhere is the initial reservoir pressure. The outer boundary of the reservoir is closed. Describe the development of the pressure profile from the well to the outer boundary as productio n continues. Assume single phase flow and that the whole oil reservoir can be produced with no technical or economic limitations. (5) (ii) A well flows at a constant rate of 200stm 3/day. Calculate the bottomhole flowing pressure at 8 hours after the start of production. The well is vertical, perforated along the full thickness of the reservoir.
Data porosity, _ formation volume factor for oil, B o net thickness of formation, h viscosity of reservoir oil, _ compressibility, c permeability, k wellbore radius, r w external radius, r e initial reservoir pressure, P i well flowrate (constant) skin factor
25% 1.30rm 3/stm3 50m 2.2x10 -3 Pas 0.8x10-9Pa-1 120mD 0.15m 650m 270bar 200stm 3/day 0
(15)
B6 A well has been on production in an oil reservoir. For the following data, calculate the bottomhole flowing pressure, P wf for (i) steady state conditions (ii) semi steady state conditions
(6) (6)
and briefly describe the main differences in the flow regimes
(8)
Data formation volume factor for oil, B o net thickness of formation, h viscosity of reservoir oil, _ permeability, k wellbore radius, r w external radius, r e average reservoir pressure, P well flowrate (constant) skin factor
1.42rm 3/stm3 60m 1.3x10 -3 Pas 100mD 0.15m 530m 270.0bar 220 stm 3/day 0
