HERIOT WATT UNIVERSITYDEPARTMENT OF PETROLEUM ENGINEERING

Examination for the Degree ofMeng in Petroleum Engineering

Reservoir Engineering 1

Tuesday09.30 - 13.30

NOTES FOR CANDIDATES

1. This is a Closed Book Examination.

2. 15 minutes reading time is provided from 09.15 09.30.

3. Examination Papers will be marked anonymously. See separate instruction forcompletion of Script Book front covers and attachment of loose pages. Do not write yourname on any loose pages which are submitted as part of your answer.

4. This paper consists of 2 Sections:- A and B

5. Section A:- Attempt all QuestionsSection B:- Attempt 4 numbered Questions.

6. Section A:- 20% of marksSection B:- 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 numericalquestions. No marks can be given for an incorrect answer if the method of calculation isnot presented.

9. Answers must be written in separate, coloured books as follows:

Section A:- BlueSection B:- 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 relationto the prediction of the behaviour of natural and injected water drive systems. The answer shouldbe 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 pointand bubble point pressure of a reservoir fluid. Explain briefly how the equations are used, whenthe 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 equationin reservoir engineering.

(3)

A7 Describe the method by which the line source solution may be adapted to accommodate a zone ofreduced permeability around a wellbore (a skin).

(3)

SECTION B

B1(i) Draw a pressure temperature diagram for a retrograde-gas condensate fluid and indicate thekey 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 conditionsare 240oF and 8500 psia.

When the reservoir was initially tested, a condensate to gas ratio of 80 stock tank barrels permillion SCF of gas was obtained. The produced gas and condensate compositions were as follows:

Compositions of Produced Fluids(Mole fractions)

Gas Condensate

C1 Methane 0.89

C3 Propane 0.07 0.21

C5 N-Pentane 0.04 0.61

C8 Octane 0.18

The reservoir pore volume is considered to be 5 x 1011 cu ft with a connate water saturation of 0.17.

Calculate the condensate fluids produced (STB) and the gas produced (SCF) in producing the reservoirdown to a pressure of 6750 psia.

1 bbl = 5.615 cu ftoR = 460+oF1 lb mole = 379.4 SCFR = 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 aPVT 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 reservoirtemperature. The system composition remained constant throughout the test.

Table 1(System constant)

Pressure Volume Pressure Volume psig cc psig cc

5000 162.54 1591 168.394500 163.21 1573 169.084000 163.90 1555 169.853500 164.64 1515 171.563000 165.43 1435 174.972500 166.32 1341 180.112000 167.21 1234 186.951900 167.40 1113 197.281800 167.60 989 211.041700 167.80 854 231.711601 168.00 728 259.31

In another test on the fluid a sample of oil at its bubble point pressure and reservoir temperature in a PVTcell were passed through a two stage separator at 100 psig and 75oF and 0 psig and 60oF. 34 cc of oil weredisplaced from the PVT cell and 27.4 cc of oil were collected from the last separator stage. 4976 cc of gaswere 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 gasproduced at each stage removed and the remaining oil volume measured. The total gas produced atstandard conditions was recorded and is presented in Table 2.

Table 2Pressure in Cumulative Volume of Oil PVT Cell Gas Produced in Cell

psig cc cc(standard conditions)

Bubble Point 0 184.801400 2044 182.351200 4438 179.371000 6732 176.52800 9076 173.670 26,928 @ 60oC 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 ofa reservoir after natural water drive or water injection.

(5 marks)

(iii) Core samples have been obtained from a well and air-mercury capillary pressure curvesgenerated 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 = 1.03Specific of oil = 0.80Density of water = 62.4 lb/ft3

Air-mercury capillaryPressure = 10 x water-oil capillary

pressureOil formation volume factor = 1.22

(12 marks)

B4(i) Water drive reservoirs are said to be rate sensitive. Explain briefly this statement withrespect to different aquifer characteristics

(4 marks)

(ii) Explain briefly how the constant terminal pressure solution of the Hurst and van Everdingenunsteady state theory can be used to predict water influx into an oil reservoir with a decliningreservoir pressure.

(4 marks)

(iii) A water drive reservoir extends to a radius of 15,000 ft. Sealing faults restrict the shape ofthe reservoir to form only a part of the full radial system. The supporting acquifer is considered toextend 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) 0 6 12 18 24Pressure (psia) 6700 6688 6642 6584 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 = 180 mD

w= 0.6 cp

porosity = 0.19water compressibility = 3 x 10-6 psi-1

pore/rock compressibility = 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

= 1.119cRo2h

pW

D

where

We

= cumulative water influx (bbls)

p= pressure drop (psi)

WD

= dimensionless water influxc = compressibility of the acquifer (psi-1)R

o= radius of oil reservoir (ft)

h = thickness of acquifer (ft) = porosity

Charts are supplied of dimensionless water influx WD versus dimensionless time t

D (see 2 attachments)

where:

tD

= 2 30902.

ktcRw

t = time (years)k = permeability (millidarcies)

w= 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 reservoirpressure. The outer boundary of the reservoir is closed. Describe the development of the pressureprofile from the well to the outer boundary as production continues. Assume single phase flowand that the whole oil reservoir can be produced with no technical or economic limitations.

(5)

(ii) A well flows at a constant rate of 200stm3/day. Calculate the bottomhole flowing pressureat 8 hours after the start of production. The well is vertical, perforated along the full thickness ofthe reservoir.

Data

porosity, _ 25%formation volume factor for oil, B

o1.30rm3/stm3

net thickness of formation, h 50mviscosity of reservoir oil, _ 2.2x10-3 Pascompressibility, c 0.8x10-9Pa-1

permeability, k 120mDwellbore radius, r

w0.15m

external radius, re

650minitial reservoir pressure, P

i270bar

well flowrate (constant) 200stm3/dayskin factor 0

(15)

B6 A well has been on production in an oil reservoir. For the following data, calculate the bottomholeflowing pressure, P

wf for

(i) steady state conditions (6)(ii) semi steady state conditions (6)

and briefly describe the main differences in the flow regimes (8)

Data

formation volume factor for oil, Bo

1.42rm3/stm3

net thickness of formation, h 60mviscosity of reservoir oil, _ 1.3x10-3 Paspermeability, k 100mDwellbore radius, r

w0.15m

external radius, re

530maverage reservoir pressure, P 270.0barwell flowrate (constant) 220 stm3/dayskin factor 0