What is the absolute permeability of the core and what

Question

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 cm^L

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                     B_o                    R_s                          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(t_p + Δt_x)Δt_x = 1.287

(tp is the total producing time in hours and Δt_x 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, B_gi (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             B_o                     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:

Δt_log = 99 p sec/ft (in the zone of interest)
Δt_f = 250 μ sec/ft
Δt_ma  = 76 p. sec/ft
ρ_b = 2.38 g/cm³(in the zone of interest)
ρ_ma = 2.58 g/cm³
ρ_f = 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:
P_i          4500 psia
P_b         1,950 psia
P_current  3500 psia
B_oi        1.25 rb/stb
B_o ©current Pr 1.29 rb/stb
B_w             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 (A^0.9 - A^1.6) + 1.5 (B^0.5 - B^4.0) (°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:

T_pc (corr) = T_pc - ε

P_pc (corr) = P_pcT_pc(corr)/T_pc + B(1- B)ε

where T_pc, = pseudo critical temperature and P_pc, = pseudo critical pressure