Looking for assistance with some Reservoir Engineering questions.
Reservoir Engineering Coursework Questions -1
1. Rock Properties
A permeability test was performed on a cleaned core sample and gave the following results:
Flow rate = 500 cm3 in 200 secs
Upstream pressure = 3.5 atm
Downstream pressure = 1.8 atm
Fluid viscosity = 0.6 cP
Cross-sectional area = 19.6 cmL
Length of core = 6 cm
(i) What is the absolute permeability of the core in mD?
(ii) For mostly the same parameters as in (i) above, what would the upstream pressure need to be if the core sample had an absolute permeability of 50mD?
For the core sample in (ii), if the relative permeability to oil at Swc were found to be 0.61, what would be the effective permeability to oil be at connate water saturation?
2. Rock Properties
A normally pressured low GOR oil reservoir has an initial reservoir pressure at datum depth of 4,815.0 psia and a bubble-point pressure of 730.0 psia. The back-pressure created by the operating pressure of the separator plus the pressure losses due to friction in the surface piping is 320.0 psig. The average oil and water gradients are 0.35 psigift. and 0.45 psigift, respectively. Atmospheric pressure is 14.7 psia.
(i) What is the vertical datum depth of the reservoir in feet?
(ii) What is the maximum bottom-hole drawdown at datum depth available to produce this reservoir?
(iii) If the connected pore volume is 800 IVINIbbl and the connate water is 27%, what volume of oil would be produced by a simple depletion mechanism down to the minimum flowing bottom-hole pressure?
Neglect the effects of gas and assume the oil, water and formation compressibilities are 14 x 3.2 x 10-6 and 3 x 10-6 psi-1, respectively.
(iv) What was the 0IIP and what is the recovery factor obtained from a simple depletion drive in this reservoir down to the minimum flowing bottom-hole pressure?
(v) How might we increase the recovery factor?
3. Rock Properties
A core sample of sandstone rock having a porosity of 17% was tested to determine its capillary pressure - saturation relationship. At Sw = 0.48, the capillary pressure (at reservoir conditions) was found to be 4.6 psia. The density difference between the reservoir water and the oil was 16.8 lblcu.ft.
Find the height above the free water level ("FWL") at which a value of Sw = 48% exists.
4. Fluid Properties
Using Kay's rules for mixtures and the Standing and Katz chart read to 3 decimal places, determine
(1) The compressibility factor for a natural gas having a composition of 86.0 molecYcp methane, 8.0 mole% ethane and 6.0 mole% propane at initial reservoir conditions of 180 °F and 6,050 psia.
(ii) The value of z at 180 degrees F and 1,500 psia.
(iii) If the production wells stop flowing at au average reservoir pressure of 1,500 psia, what would be the gas recovery factor from this reservoir by natural depletion, ignoring rock and formation water compressibilities, the effect of condensate and assuming.
no aquifer influx,
Bgi = (Zi Ti STD P / Pi STD T) where zi is the initial gas compressibility factor,
Ti is the initial reservoir temp in degrees Rankine,
Pi is the initial reservoir pressure in psia, STIR P is 14.7 psia, STD T is 520 degrees Rankine;
Bga = (z. Ti STD P Pa STD T) for any pressure "a" and
RF = (1/Bgi - 1/Bg) 1 (11Bgi)?
Component |
yi |
Pci |
Tci |
|
|
|
Psia °F |
methane |
0.86 |
666_4 |
-116.7 |
ethane |
0.08 |
706_5 |
89.9 |
propane |
0.06 |
616_0 |
206.1 |
5. Material Balance
utidersaturated oil reservoir is produced to below its Bubble Point Pressure by depletion only. The compressibility of water and the compressibility of the fomiation can be ignored. For the reservoir properties given below and stating all assumptions relied upon. use a material balance approach to calculate:
the stock tank oil initially in place.
(ii) the oil volume to be recovered by an undersaturated drive.
(iii) the oil volume to be recovered to the final reservoir pressure if 15 MM res-bbl water were injected and 1.25 MMstb water were produced at the surface. Assume Bw = 1.02 rb/stb.
Initial reservoir pressure, 5,050 psia Bubble point pressure, 2,230 psia Final reservoir pressure, 1,470 psia Swc, 25%
Cumulative oil produced. 41.17 MMstb
Cumulative gas produced, 110.565 Bcf
Psia |
Bo |
Rs |
Bg |
|
Rb/stb |
scf/stb |
rb/scf |
5,050 |
1.3 |
800 |
|
2,230 |
1.32.20 |
800 |
0.00135 |
1,470 |
1.132 |
230 |
0.00214 |
6. Material Balance
The material balance concept for a gas reservoir can be stated as:
Gas in reservoir initially - gas produced = gas remaining, or
Production = Expansion + Net Influx
For
G = gas initially in place at surface conditions:.
Gp = production at surface conditions-,
Bpi and Bg as the gas formation volume factors for initial and later conditions (at Gp production); influx as net influx = (We - Wp.Bw), where
We is in reservoir volumes, ignore the effects of connate water and formation compressibilities and derive a general material balance equation for a gas reservoir that has the form Production = Expansion + Net Influx.
7. Well Testing
A new development oil production well tested at a constant rate of 739 stb/d for 70 hours.
Reservoir data are:
Initial reservoir pressure, Pi Net formation thickness, h Porosity
Boi
Oil viscosity
Total compressibility, Ct Wellbore radius, rw,
|
5.012 psia. 30 ft
18%
L31 rb/stb 0_8 cP
15 x 10-6psi-1
0_35 ft
|
Flowing Time. t hours
|
Bottom-hole Flowing Pressure, Pwf psia
|
|
|
0
|
5012
|
1
|
4800
|
2
|
4260
|
3
|
4108
|
4
|
4019
|
6
|
3900
|
10
|
3751
|
15
|
3627
|
20
|
3538
|
25
|
3466
|
30
|
3404
|
35
|
3360
|
40
|
3276
|
45
|
3210
|
50
|
3140
|
60
|
3030
|
70
|
2927
|
(i) Create a fully labelled semi-log plot and show the Horner line. slope m and P...vfllir origin and values1
(ii) Determine the Effective Permeability, the Skin Factor. the Observed and Ideal well Productivity Index;
(iii) What does the value of the skin factor calculated for (ii) indicate)?
(iv) Once the well test is complete, would you release the rig or use it for a workover on this well?
(v) Considering the Darcy equation and the rock and fluid properties of a particular reservoir and excluding a simple increase in dP, suggest four operational strategies you might use to increase the daily production rate from a particular well location?
Reservoir Engineering Coursework Questions - 2
1. A reservoir has an initial oil volume of 60 MIAbbls at 2000psia. The oil volume increases to 60.3 101bbls as pressure is reduced from 2000 psia to 1.500 psia. Determine the compressibility of the oil and state what can be deduced about the lower pressure value of 1500 psia.
2. An oil well produced 100 Mivlstb of oil at a rate of 1000 stb/d prior to shut-in for a pressure build up survey. Froml the pressure and reservoir data given below determine the effective permeability and skin factor.
Data
Oil flow rate = 1000 stb/d
Initial Reservoir Pressure = 7800 psia Wellbore radius = 0.33 ft
Formation thickness = 100 ft
Porosity = 2.5 €'/0
Oil viscosity = 1.2 cp
Oil Formation Volume Factor = 1.13 rbistb Total compressibility = 20 x 10-6 psi-1
m = 60 psi/log cycle
Pressure 1 hour after shut-in (from straight line portion of buildup curve) = 4892 psia
Final flowing bottom hole pressure = 4412 psia
3. (a) The following table gives composition data for a gas stream which is to be exported from an offshore oilfield by pipeline:
Component moloto
Methane 82.5
Ethane 10.5
Propane 4.6
Isobutane 1.6
n-butane 0.8
Determine:
1) the specific gravity of the gas (molar mass of air = 28.96)
(ii) the density of the gas at the pipeline entry conditions of 2260 psia and 66°F
(b) What is an equation of state (EOS) and what is meant by the Principle of Corresponding States? Explain the use of this principle as the basis of the method used to obtain your answers to part (a) of this question. What are the main limitations on the accuracy of the z-factor chart used for your calculations?
4. A saturated oil reservoir with a large gas cap had an initial pressure of 3250 psia. From data obtained during exploration and appraisal drilling, it was estimated that the ratio of initial gas cap volume to initial oil volume (measured at reservoir conditions) was 0.380. The reservoir was produced without the use of any secondary recovery and natural water drive was found to be insignificant (due to the low permeability of the aquifer).
When the reservoir pressure had fallen to 2400 psia the cumulative production figures were as follows:-
Oil 35.68 x 10 5th
Gas .58.26 x 109 scf
Water negligible
PVT data for the reservoir fluid is shown below:-
Pressure Bo Rs Bg
(psia) (rbistb) (scf/stb) (rb/scf)
3250 1.5830 890 0.00094
2400 1.4365 628 0.00140
Showing clearly the steps in your calculations and stating any assumptions made, determine:
0) the initial oil in place (stb);
(ii) the initial gas in place in the gas cap (scf)
5. A well test has been carried out on Well E002. The well produced 9500 stb of oil and was then shut-in for a pressure buildup. The well is located close to where a fault has been mapped.
From the Horner buildup plot and the additional data given below, determine the follolAring:
(i) The effective permeability.
(ii) The distance to the fault.
Additional Data
Oil flow rate = 2580 stb/d
Formation thickness = 670 ft
Oil viscosity = 1.22 cp
Porosity =22 °AD
Oil Formation Volume Factor = 1.31 rb/stb Total compressibility = 15 x 10-6 psi-1
(Note: Wel!bore storage effects are negligible)
From the Homer buildup plot (see below) the intersection of the early and late time straight line trends occurred when:
log(tp + Δtx)Δtx = 1.287
(tp is the total producing time in hours and Δtx is the closed in time at which the linear extrapolations of the early and late straight line trends inter-sect.)
6. A sample of gas obtained during drilling operations on a new gas field gave the following composition data when analysed:-
Component methane
ethane
propane
iso-butane
n-butane
isopentane n-pentane
|
moI %
74.3
8.1
5.8
4.6
3.7
1.9
1.6
|
Determine:(i) the value of the gas formation volume factor, B (in rb/scfl at the initial reservoir conditions of 7800 psia and 1850F;
(ii) the density of the gas (in Ib/ft3) for the same conditions.
Component methane 74.3
ethane 8.1
propane 5.8
iso-butane 4.6
n-butane 3.7
isopentane 1.9
n-pentane 1.6
Determine:
(i) the value of the gas formation volume factor, Bgi (in rb/scfl at the initial reservoir conditions of 7800 psia and 1850F;
(ii) the density of the gas (in Ib/ft3) for the same conditions.
7. The table below gives PVT data for a reservoir fluid sample from a black oil reservoir with an initial reservoir pressure of 3870 psia. It was expected on the basis of geological data that natural water drive would be insignificant, and the field was produced without the use of any water injection or gas reinjection.
When the reservoir pressure had fallen to the bubble-point value of 3300 psia the cumulative oil production was 2.41.5 x 10 stb with negligible water production. Does this data support the assumption of negligible water drive for this reservoir? State clearly the assumptions and the reasoning on which your answer is based.
Pressure (psia)
3870
3300 (ph')
|
PVT Data
(rb/stb)
1.2930
1_3150
|
Fts
(scfistb)
480
480
|
Bg
(rb/scf)
0.00095
|
Reservoir and Fluid Data
Bulk volume of reservoir Average reservoir porosity Connate water saturation Formation compressibility Connate water compressibility
|
90,000 acre-ft 25.2%
21.4%
7.50 x 10-6/psi 3.2.5 x 10-6/psi
|
8. (a) A small undersaturated offshore black oil reservoir was brought into production with an initial reservoir pressure of 4,800 psia. Natural water influx into the reservoir was negligible and production was by depletion drive without the use of secondary recovery. When the reservoir pressure had dropped to the bubble point value of 2,500 psia the cumulative oil production was found to be 1.40 MMstb with negligible water production. Using the reservoir and fluid data shown below and stating clearly any assumptions made determine the stock tank oil initially in place.
(b) Production was continued, again without any secondary recovery, and when reservoir pressure had fallen to 1,600 psia the cumulative oil production (measured from the opening of the reservoir) was 3.60 MMstb, but no reliable figure was available for the gas production (owing to metering problems). Determine for these final conditions:
(i) the cumulative gas production;
(ii) the final free gas saturation in the reservoir.
PVT Data
Pressure Bo R, Bg
(psia) (rb/stb) (scf/stb) (rb/scf)
4,800 1.2950 520
2,500 1.3345 520 0.00096
1,600 1.2136 310 0.00229
Other Fluid and Reservoir Data
Swe 16.2%
c. 3.20 x 10-6/psi
cf 7.65 x 10-6/psi
9. A sample of gas obtained during exploratory drilling on a new field gave the following composition data on analysis:
Component mo1%
Methane 86.2
ethane 9.5
propane 2.5
isobutane 1.0
n-butane 0.8
The gas is to be exported from the field by pipeline. Determine:
i) the density of the gas (in Ibift3) at entry to the export pipeline where the conditions are 2,000 Asia and 70°F;
ii) the specific gravity of the gas. (Molar mass of air = 28.96) (Critical property data and compressibility chart supplied).
10. Given the following Sonic and Density log data for a sandstone matrix:
Δtlog = 99 p sec/ft (in the zone of interest)
Δtf = 250 μ sec/ft
Δtma = 76 p. sec/ft
ρb = 2.38 g/cm3(in the zone of interest)
ρma = 2.58 g/cm3
ρf = 1.10 g/cm3
Calculate porosity using the sonic and density weighted average equations.
(ii) Explain any difference or similarity in the porosity calculated from the Sonic and Density data in part Q3(a)(i) above.
11. An oilfield has been producing for 5 years at an average rate of 10,000 stb of oil per day. Water injection was started at the beginning of the third year at an average rate of 6,000 stb of water per day. Average water production has been 3000 stb of water per day since the start of production.
You are given the following reser-voir data:
Pi 4500 psia
Pb 1,950 psia
Pcurrent 3500 psia
Boi 1.25 rb/stb
Bo ©current Pr 1.29 rb/stb
Bw 1.03 rb/stb
N 50,000 acre-ft
Porosity 18%
Swc 20%
(i) Calculate the net fluid withdrawal (F) from the reservoir.
(ii) Estimate the aquifer influx volume.
List all your assumptions and indicate all units for parts 1(i) & (ii) above.
12. A sample of natural gas of from a newly-discovered field during exploratory drilling operations gave the following composition data on analysis:
Component
|
Mol%
|
methane
|
66..5
|
ethane
|
7.2
|
propane
|
3.4
|
iso butane
|
1.1
|
ri-butane
|
0.8
|
carbon dioxide
|
.5.2
|
hydrogen
|
15.8
|
|
100%
|
Determine:
1) the value of the gas formation volume factor Bg (in rh/scf) for the initial reservoir conditions of 6,500 psis and 210°F;
(ii) the specific gravity of the gas (molar mass of air = 28.96).
Use the Wichert and Aziz temperature correction factor (E) for sour gases:
ε = 120 (A0.9 - A1.6) + 1.5 (B0.5 - B4.0) (°R)
where
A = sum of mole fractions of carbon dioxide and hydrogen sulphide and
B = mole fraction of hydrogen sulphide.
This is used to correct the pseudo critical conditions as follows:
Tpc (corr) = Tpc - ε
Ppc (corr) = PpcTpc(corr)/Tpc + B(1- B)ε
where Tpc, = pseudo critical temperature and Ppc, = pseudo critical pressure