Department of Engineering and Design,

MSc Petroleum Engineering

LAB.REPORT ON PERMEABILITY AND POROSITY EXPERIMENT

Author: TOLULOPE AFOLABI (3228764)

Academic Session: 2014/2015

Lecturer: DR. ELSA ARISTODEMU

Course Moodle: PETROPHYSICS

Mode of Study: FULL TIMEDATE: NOVEMBER 30,2014.

TABLE OF CONTENTCover page ------------------------------------ 1Table of context ------------------------------------ 2

1.0 Introduction ---------------------------------- 3

1.1 Permeability Measurement -------------------------------- 4

1.2 Aims and objectives ------------------------------ 41.3 Experimental equipment ------------------------------ 51.4 Experimental procedure and observations --------------------------- 5

i. Experiment one -------------------------------------------- 5ii. Experiment two ------------------------------------------------- 6

1.5 Experimental results and calculations --------------------------------- 61.6 Presentation and analysis of result --------------------------------- 13

1.7 Error analysis ------------------------------------ 15 1.8 Conclusion ------------------------------------- 15

1.9 References ------------------------------------------- 16

2.0 Porosity measurement ------------------------------------------- 17 2.1 Aim and objectives ------------------------------------------- 17 2.2 Experimental apparatus ------------------------------------------ 17 2.3 Experimental procedures and observation ---------------------------- 17 2.4 Results and calculations ----------------------------------------------- 18 2.5 Discussion ----------------------------------------------- 19 2.6 Conclusions --------------------------------------------- 21 2.7 Summary -------------------------------------------- 22 2.8 References ---------------------------------------------- 22 Attach notes ----------------------------------------------- 23

pg. 2

PERMEABILTY AND POROSITY

1.0 INTRODUCTION :

The topic investigated in this experiment were permeability determination of a porous media and its porosity, permeability is a measure of how well a porous media allows the flow of fluids through it, Permeability and porosity forms the two major characteristics of reservoir rocks. A reservoir rock must have the ability to allow petroleum fluids to flow through its interconnected pores. Permeability is an indication of the porous medium’s ability to permit fluid flow. Permeability and porosity forms the two major characteristics of reservoir rocks. A reservoir rock must have the ability to allow petroleum fluids to flow through its interconnected pores. The permeability of a porous medium is a measure of its resistance to the flow of a fluid through it. The fluid may be a liquid or a gas. However, the only fluid used in this experiment was water. The majority of the work was based on using sand as the permeable material.

Basically, permeability could be of three types: absolute permeability, relative permeability and

effective permeability. The relative permeability of the oil, gas and water would be;

kro = ko/k, krg = kg/k, and krw = kw/k respectively. This describes the extent to which the

fluids hinder one another.

Where:

kro is the relative permeability of the oil (Dimensionless)

ko is the effective permeability of the oil (Darcy)

k is the absolute permeability of the phase in question (Darcy)

krg is the relative permeability of the gas (Dimensionless)

kg is the effective permeability of the gas (Darcy)

krw is the relative permeability of the water (Dimensionless)

kw is the effective permeability of the water (Darcy)

The equation that defines permeability in terms of measurable quantities is Darcy’s law. This

equation is given by:

Q= AK ∆ PμL

(1)

Where:

Q is the flow rate (cm3/s)

K is permeability (Darcy)A is the cross sectional area of bed (cm2)∆ P is the pressure drop (atm)

pg. 3

μ is the viscosity of the fluid (cP)L is the length of the bed (cm)The above equation can be transposed for the permeability ‘K’ as:

K= QμLA ∆ P

(2)

Darcy equation can be written individually for each fluid/phase that flows in the pore as:

Qi = ( Kkriμi ) A ∆ Pi

L (3)

Where :

Qi = flow rate of phase i (cm3/s)

K = absolute permeability of medium (mD)Kri = the viscosity of the phase i (cP)∆P = pressure drop (atm)L = length of the medium (cm)A = cross sectional area of medium (cm2)

Porosity of a rock is the fraction of the volume of space between the solid particles of the rock to the total rock volume. The space includes all pores, cracks, vugs, inter- and intra-crystalline spaces.The porosity is conventionally given the symbol Φ, and is expressed either as a fraction varying between 0 and 1, or a percentage varying between 0% and 100%. Sometimes porosity is expressed in porosity units, which are the same as percent (i.e., 100 porosity units (pu) = 100%).Reservoirs with high porosity indicate abundant fluids in their pore spaces while those with low porosity indicates low capacity to hold fluids.Knowledge of two basic reservoir properties; porosity and permeability is essential in order to know the types of fluids, amount of fluids, rates of fluid flow and fluid recovery estimates (Tiab and Donaldson, 2012). In addition, porosity can be use quantitatively when it comes to calculating oil reservoir content volumetrically. Types of porosity are Primary porosity, Secondary, total and effective porosity.Porosity can be calculated as the pore volume of the rock divided by its bulk volume.Φ=Pore volume /bulk volume (Vp/V b)Φ=V b−V m /V b=V p /V b Porosity can be measured directly or indirectly but this laboratory measurement of core samples is a direct measurement which is generally considered to be reliable and accurate and it requires measurement of pore volume and bulk volume. The bulk volume is usually estimated by volumetric or gravimetric method, volumetric method measures the volume of displaced liquid by a rock sample when completely immersed in liquid and the gravimetric method is the mass of the sample when immersed in a known density liquid. For this experiment, three plugs extracted from sandstone core sample with known permeabilities (50mD, 100mD and 500mD) were used to carry out a direct measurement of porosity using the gravimetric and volumetric method.The experiment in details

pg. 4

1.1 PERMEABILITY MEASUREMENT1.2 AIMS AND OBJECTIVES:The objectives of the laboratory practical were to determine the absolute permeability of sand in porous media, and to determine the relative permeability of multi-phase flow (water and oil) using darcy and corey equations

This experiment was important because knowledge of it would show how well a porous media

allows fluids to flow through it, and as petroleum engineers, one of the interest in reservoir rocks

is how easily petroleum will flow through them to the wellbore from where they are transported

to the surface.

1.3 EXPERIMENTAL EQUIPMENTIn order to carry out the experiment, a permeability/fluidisation studies apparatus manufactured and supplied by Armfield (ltd) was used. See figure 1 below.

pg. 5

Manometer

Packed bed sand medium

Flow meter

Thermometer

Figure 1: Picture of experimental equipment

1.4 EXPERIMENTAL PROCEDURE AND OBSERVATIONSi. EXPERIMENT ONE

Part A

Flow rates were varied (not above 500 cm3/min, so as not to cause fluidisation) and the corresponding pressure drops were recorded.At the beginning of the experiment, all the valves were kept closed and then the pump was switched on. At a point, a trickle from the overflow pipe indicated a constant water level in the overhead tank, the experiment was started. Keeping the inlet and outlet valves closed, the manometer valves were opened. The drain tube from valve 4 was inserted into a beaker placed on the water tank to prevent any of the bed material that passed through the sieve returning to the system. A thermometer was then placed in the beaker to indicate the water temperature, and the temperature read after which bed height (L) was recorded along with the water & mercury manometer zero levels.Valves 1 and 4 were opened to admit water through the column in a down flow direction.Valve 1 was then used to adjust the flow rate (Q) and the manometer levels were both recorded for the various flow rate. The temperature was recorded at the beginning of the experiment and at the end of the experiment to obtain the water average temperature.Part B We didn’t carry out this experiment but experimental data were given for pressure drop and flow rates for two fluids; oil and water at different saturations. Here the two fluids were injected simultaneously in the cylinder of the sand sample which was assumed to be the same sample used in part one.

ii EXPERIMENT TWOThis type of permeability is absolute. For this experiment, the bed heights were varied at different flowrates. In this case, the sand samples were poured into a measuring cylinder to various heights (125mm, 215mm and 305m), with known density of the fluid (water) the difference in fluid pressures were calculated from h1 – h2. In both cases, it was observed that the differential pressure increased with increase in flowrate which is in agreement with Darcy’s law.

1.5 EXPERIMENTAL RESULTS AND CALCULATIONS:The experimental results and calculated results shown in tables below. Table1. Experimental results for absolute permeability determination

No of Runs 

Flow rate (cm3/min)

P1 (mmH2O) P2 (mmH2O) ∆P (mmH2O)

1 50 245 268 23

2 100 230 286 56

3 150 214 305 91

4 200 194 327 112

5 250 183 340 140

pg. 6

6 300 163 364 201

7 350 148 383 236

8 400 125 407 282

9 450 101 436 335

10 500 83 459 376

Table2. Measured values and calculation of results (Glass beads)

Length of the bed (cm) 31.5

Diameter of the bed (cm) 3.8

Area of the bed (cm2) 11.34

Average temperature ( C)⁰ 22.5

Pressure at zero flow rate (mmH2O)P1 = 248P2 = 268

Permeability (Darcy) 0.591D

Gradient of graph 4.74 *10-3 atm/cm3/s

Table 3. Calculated results for absolute permeability determination.

No of runFlow rate (cm3/s)

P1 (* 10-3 atm)

P2 (* 10-3 atm)

∆P K (Darcy)(*10-3 atm)

 0.83 23.71 25.38 1.67 1.66

1

 1.67 22.26 27.68 5.42 0.51

2

 2.5 20.71 29.51 8.8 0.32

3

 3.33 18.78 31.65 12.87 0.22

4

 4.17 17.71 32.9 15.19 0.18

5

 5 15.78 35.22 19.44 0.14

6

 5.83 14.32 37.06 22.74 0.12

7

 6.67 12.09 39.39 27.3 0.102

8

 7.5 9.77 42.19 32.42 0.086

9

10 8.33 8.03 44.42 36.39 0.076

pg. 7

0 1 2 3 4 5 6 7 8 90

5

10

15

20

25

30

35

40

45

Flow rate (cm3/s)

Pre

ssu

re g

rad

ien

t (*

10-

3 at

m)

Figure 2: Graph of pressure gradient against flow rate

CALCULATIONS:(a) Experiment 1 (absolute permeability determination) as shown in the table and

graph above(i) Change in pressure ΔP: When P1 = 245 mmH2O and P2 = 268 mmH2O

Therefore, ΔP=h2−h1=268−245=23 mm( H 2O )

To convert change in pressure from mmH2O to atm.

Therefore 23mmH2O can be written as

ΔP=ρ .g .h=1000×9. 81×23×10−3

100000=22 .56×10−3atm

(ii) Gradient of the graph in figure 1: Change∈ pressure drop(atm)

Change∈flow rate(cm3/seconds)

Converting from cm3/min tocm3 /sec : For example when Q = 100cm3/min

Q=100 cm3 /min60 sec/min

=1 . 67 cm3 /sec

Gradient = ∆(∆ P)

∆ Q =

(32.42−8.8 )∗10−3

7.55−2.5 = 4.7 * 10-3 atm/cm3/s

(iii) Absolute permeability: Using equation 2: K= μLA ∆ P

Where:

pg. 8

μ = 1 cP, Length of bed (L) = 315 mm = 31.5cm, Diameter of bed (d) = 38mm = 3.8cm Area of

bed, A=πd2

4=

3 .14×(3.8 )2

4=11. 34cm2

K= μA

LΔP

= μA

LGradient

= 1

11. 3431 . 5

4 .7×10−3 ¿591 millidarcy = 0.59 Darcy

Case Qw(cc/s) Qo(cc.s) ∆P (atm) kw krw ko kro

80%W, 20% O 5 2 0.03 189.12 0.316 2.36 0.004

60% W, 40% O 4 3 0.05 37.23 0.063 114.65 0.197

40%W, 60% O 3 4 0.06 2.36 0.004 301.41 0.51

20% W,80% O 2 5 0.08 0 0 591 1

1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 00

0.2

0.4

0.6

0.8

1

1.2

krwKro

Water saturation sw (%)

Rela

tive

perm

eabi

lity

krw

, kro

pg. 9

Irreducible water saturation

Residual oil saturation

No water flows No oil

flows

Table 4. Calculated results for relative permeability determination using Corey’s law.

Figure 3: Relative permeability curve for oil and water using Corey’s law

(b)(i) Test 2; Sample calculations for Relative permeability using Corey’s law; table and graph are shown aboveEquation for relative permeability of oil,

Kro = ( 1−Sw1−Swc )

4

From the table Sw = 0.8, Swc = 0.2

Kro = (1−0.81−0.2

¿¿4 = 0.004

Effective permeability of oil Ko = Kro *KWhere Kro = 0.004, K= 591mD0.004*591= 2.364

Equation for relative permeability of water , Krw=( Sw−Swc1−Swc )

4

Krw = ( 0.8−0.21−0.2 )

4

=0.32

Effective permeability of water Kw = Krw *KWhere Krw = 0.32, K= 591mD0.32*591= 189.12

Table 5. Calculated results of relative permeability using Darcy Law

Case Qw(cc/s) Qo(cc.s) ∆P (atm) kw krw ko kro

80%W, 20% O 5 2 0.03 463.0 0.78 463.0 0.78

60% W, 40% O 4 3 0.05 222.2 0.376 416.7 0.71

40%W, 60% O 3 4 0.06 138.9 0.235 463.0 0.78

20% W,80% O 2 5 0.08 69.44 0.118 434.0 0.73

pg. 10

10 20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Krwkro

Water saturation sw (%)

Rela

tive

perm

eabi

lity

krw

, kro

Figure 4: Relative permeability curve for oil and water using Darcy’s law

(b)(ii) Relative permeability using Darcy’s law as shown in the table and graph above

Equation for Qi = ( Kkriμi ) A ∆ Pi

L

Transposing for Kri= Qi× µi× LK × A ×∆ P

Permeability of water phase for run1 , Krw= 5×1×31.5591× 11.34× 0.03

=0.78

Kw = Krw × KKw = 0.78×591 =463mD

Permeability of oil p h ase for run1, Kro= 2 × 2.5× 31.5591×11.34 × 0.03

=0.78

Kw = Krw × KKw = 0.78×591 = 463mD

Table 6: Experimental results for second permeability experiment

pg. 11

Table 7,

calculated results for absolute permeability determination for second permeability experiment

pg. 12

L (mm) P1 (mmH2O) P2 (mmH2O) ∆P (mmH2O)Flowrate (cm3/min)

     80

125 80 68 12

      

10072 58 15

      

12065 55 20

215 70 50 20 80

  82 59 23 100

  96 66 30 120

305 79 47 32 80

  75 36 35 100

  64 25 39 120

L (cm)

H1 (cmH2O)

H2 (cmH2O)

ΔP (cmH2O)

Flowrate (cm3/sec)

ΔP(m)ΔP (atm)

K (mD)

K (Darcy)

12.5 80 68 12 1.33 0.12 0.012 94.58 0.0946

12.5 72 58 15 1.66 0.15 0.015 75.67 0.0757

12.5 65 55 20 2 0.20 0.019 56.75 0.0567

21.5 70 50 20 1.33 0.20 0.019 97.61 0.098

21.5 82 59 23 1.66 0.23 0.022 84.88 0.085

21.5 96 66 30 2 0.30 0.029 65.07 0.065

30.5 79 47 32 1.33 0.32 0.031 86.54 0.086

30.5 75 36 35 1.66 0.35 0.034 79.13 0.079

30.5 64 25 39 2 0.39 0.038 71.01 0.071

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.10

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

f(x) = 0.0145231412236412 x − 0.000524534901989903

f(x) = 0.0116098596673597 x − 0.00409575658004159

f(x) = 0.0101532188892189 x + 0.0174271925809326

L = 30.5Linear (L = 30.5)L = 12.5Linear (L = 12.5)L = 21.5Linear (L = 21.5)

Flowrate (cm3/sec)

ΔP (a

tm)

Figure 5: Graph of pressure gradient against flow rate

(b) Experiment 2 (varying bed heights)(i) Calculation of difference in fluid pressure:

Density of the fluid (1000kg/m3), pressure gradient can be calculated from ΔP=ρ .g . hWhere ρ = 1000kg/m3, g = 9.81m/s2 h = h1 – h2 = (80 – 68)cm = 12cm = 0.12m

∴∆ P=1000∗9.81∗0.12100000

=12∗10−3atm

(ii) Absolute permeability: Using equation 2: K= μLA ∆ P

Where: μ = 1 cP, Length of bed (L) = 125mm = 12.5cm, Diameter of bed (d) = 38mm = 3.8cm and gradient for L=12.5 is 0.0116 as displayed in figure 5

pg. 13

Area of bed, A=πd2

4=

3 .14×(3.8 )2

4=11. 34cm2

K= μA

LΔP

= μA

LGradient

= 1

11. 3412 . 5

11. 6×10−3 ¿95.03 millidarcy = 0.0953 Darcy

Same calculation for when L=21.5cm and L=30.5cm

1.6 PRESENTATION AND ANALYSIS OF RESULT:In figure 1, as the flow rate increases, there was corresponding increase in the pressure gradient as observed, one can deduce a direct correlation and relationship between flow rate and pressure difference. This can also be seen from table 3 when the flow rate was 0.83 cm 3/sec (50 cm3/min), the pressure gradient was 1.67 atm. (23 mm H2O), also when the flow rate was increased to 1.67 cm3/s (100 cm3/min), pressure gradient increased to 5.42 atm.(56 mmH2O) which was consistence throughout the experiment, pressure gradient increased to 5.42 atm. (56 mm H2O) giving rise to a straight line plot of pressure gradient against flow as shown in figure 1.In table 3 and 7, as the pressure gradient increases, there was a reduction in permeability. This is in support of the assumption on absolute permeability of porous medium is independent of the fluid used. It must be noted, that this assumption will only be true, if viscous flow prevail. That is the rate of the flowing fluid is sufficiently low to be directly proportional to the potential gradient (Honarpour and Mahmood, 1988).

In part B; relative permeability determination, it was observed that relative permeability is a function of saturation of the phases present in the medium unlike the case of absolute permeability where the pores of the medium are 100% saturated with a particular type of fluid.

It can be seen from the relative permeability curve in figure 3 that the relative permeability of the sand medium to water was sharply decreasing when the water saturation was reduced. This could be due to the occupation of the larger pores or flow paths by the oil phase; that is the water phase has been displaced by the oil phase.

When this happens, it is said that a wet fluid has been displaced by a non-wetting fluid, and this process is called drainage. The relative permeability in figure 3 curve also shows that the relative permeability of the oil phase approaches unity whereas that for the water phase is restricted. Thus at the same saturation, the value of the oil phase relative permeability was greater than that of the water phase.

Referring to figure 4, a relative permeability curve was plotted for the values of the relative permeabilities of oil and water versus water saturation calculated using Darcy’s law. It can be seen that there was a similar sort of behaviour for the water phase but not for the oil phase, this infers that Darcy’s law is not suitable when the flow is not a single phase flow.For the second experiment where the bed heights were varied, at a particular flowrate with varying bed height, there was an increase in the differential pressure (∆P), this can be seen in table 7, when the flowrate was 1.33cm3/s at a bed height of 12.50cm, the differential pressure was 0.012atm compared to when the flowrate was still 1.33cm3/s with a bed height of 21. 50cm

pg. 14

where the differential pressure was 0.019atm. This follows through when the flowrate remained the same but at a bed height of 30.50cm where the differential pressure increased to 0.031atm.At a particular bed height with increased flowrate, the differential pressure also increased accordingly too. In terms of the permeability, comparing both permeabilities obtained from both experiments; the one in the first experiment were the bed height was constant was higher than the second experiment were the bed heights were varied. The reason for this could be that the first experiment could be likened to highly compacted sandstones while the second one could be likened to low compacted sandstone sandstones,From the experiment, the absolute permeability of the sand porous media for the first experiment (when the bed height was kept constant) was estimated to be 591millidarcy. When the bed heights were varied, the estimated absolute permeability carried accordingly. For bed height of 12.5 cm, the absolute permeability was 95.02millidarcy, for bed height of 21.5cm, the absolute permeability was 130.75 millidarcy, for bed height of 30.5cm, and the absolute permeability was 263.69millidarcy. In addition, it was found that the values of permeability for the second experiment were smaller than those ones for the first experiment.

It was also found that using Corey’s law, a relative permeability curve can be drawn for fluids

(oil and water) flowing through a porous media. Based on the curve, it was found that relative permeability is saturation dependent. The proportional relationship between the flow rate, viscosity, length of rock bed sample, permeability, cross sectional area of the rock bed sample and the pressure was observed.

1.7 ERROR ANALYSIS:The following errors could have arosen in this experiment;

(1) Systematic error: The packed sand bed may not be representative of the reservoir rock because reservoir rocks are not homogeneous rather they are heterogeneous.

(2) Human and random error: There may be a temptation to select the best parts of the sand medium for testing and also inability to take accurate reading on the manometer

(3) Systematic error; The permeability of the sand medium may be altered probably when they were gotten from the original sample, or even when they were cleaned and packed

1.8 CONCLUSION:At the end of this experiment, the following conclusions can be drawn:(i) For absolute permeability determination, the medium must be 100% saturated with a

particular type of fluid.

(ii) The higher the permeability, the easier it will be for fluids to flow and, hence the higher the

production rate from a particular well (OPITO, 2011). The permeable material that was

used in this lab was a packed bed medium of sand

(iii) Absolute permeability does not depend on the properties of the flowing fluid; it only depends on the properties of the medium.

(iv) The quality of a reservoir as determined by permeability in millidarcy (mD) may be judged as poor if k < 1, fair if 1< k < 10, moderate if 10 < k < 50, good if 50 < k < 250 and very good if k > 250

pg. 15

mD. Since there was a permeability of 50mD and above for sand samples from the experiment, it will make a good reservoir

(v) During the flow of fluid through a porous medium, there is proportional relationship between the flow rate and the pressure gradient.

(vi) Relative permeability is dependent on the saturation of the different phases in the medium.(vii) There is a proportional relationship between flow rate, viscosity, length of rock bed

sample, permeability, cross sectional area of the rock bed sample and pressure gradient.

1.9 REFERENCES

Honarpour, M and Mahmood, S.M. (1988) Relative-Permeability Measurements: an Overview. Journal of Petroleum Technology. Vol.40, No. 8. Texas: Society of Petroleum Engineers. pp 963-966Aristodemu, E. (2014) lab notes for permeability measurement. Ekwere, J.P (2012) Advanced petrophysics ; geology, porosity, absolute permeability, Heterogeneity and geostatistics. Vol 3 1st ed. Live Oak Book Company. Chapter threeTarek, A. (2010) Reservoir Engineering Handbook. 4th ed. Oxford: Elsevier Inc. Chapter 4 & 5. Tiab, D and Donaldson, E.C. (2012) Petrophysics: theory and practice of measuring reservoir rock and fluid transport properties. 3rd ed. Oxford: Gulf Professional Publishing. Chapter 3. OPITO (2011) Oil Well Drilling Technology Workbook: Petroleum Open Learning. Aberden: OPITO.

pg. 16

2.0 POROSITY MEASURMENT2.1 AIM AND OBJECTIVES The main objective of this laboratory work was to estimate some porosity data (bulk volume and pore volume) and ultimately used them to calculate the porosity for the different samples provided, using three core samples that were given and calculating the porosity employing the method of direct measurement and using the buoyancy method by applying Archimede’s principle.

2.2 EXPERIMENTAL EQUIPMENT AND FUNCTIONSThe following equipment were used in carrying out the experiment: Vernier Caliper: to measure the length and diameter of the plug sample, calibrated in inches

and millimetres Electronic balance: to weigh the samples, samples were taken in grammes Beaker containing distilled water to saturate core samples Clamp: to aid the immersing of samples into beaker containing distilled water (the mass of

the beaker, water, and metal wire was subtracted by using the balance tare) Vacuum chamber accelerator: to displace air in the samples Saturated cloth or tissue: to dry any excess fluid from the saturated sample before being

weighed

dessicator

pg. 17

Vacuum chamber

Fig.3 Picture of vaccum chamber connected to dessicator

EXPERIMEN

2.3 EXPERIMENTAL PROCEDURES AND OBSERVATION

pg. 18

0.248cm 2.49cm 2.57cm 2.49cm

5.19cm 5.07 cm 5.03cm

K = 50mD

Figure 4 Drawing of Core Samples

K = 500mD K = 100mD

For the geometric estimation of the bulk volume:The diameter and length of the three (3) cylindrical core samples (K = 50mD, K = 100mD, K = 500mD) were taken using a Vernier calliper which was calibrated in inches. The values gotten were then converted to centimeters (cm) using the relationship below1 inch = 2.54 cmFor instance, the diameter recorded for K50 was 0.981inch, conversion to cm equal 0.981*2.54= 2.49cm, this was applicable for all the length measurements.The volume of the core samples was calculated using the volume of a cylinder given below Volume of core sample = π r2h Where r = radius of the core sample = diameter /2 h = height (in this case, it is the length of core sample)π = 3.14

For estimation of the pore volume: The three (3) core dry samples were each weighed using a digital mass spectrometer to determine their masses, the masses were recorded in gramme as dry sample mass after which they were then saturated with distilled water. This was done by placing the core samples in a beaker containing distilled water; the beaker was then placed in a vacuum chamber so as to accelerate the displacement of the air in the rock by water, this is called imbitions. After saturation, the core samples were again weighed to determine the saturated sample mass. The mass of water in the pore was then calculated using the formula below:Mass of water∈ pore∈the pore volume , M w=Saturated sample mass – dry samplemass

While the pore volume was calculated using the relationship below:Pore volume =Mass of water∈ pore∈the pore volume ¿density of water Where density of water, ρ = 1.0g/cm3

The porosity of each of the samples was also determined using equation 1.

Estimation of the bulk volume by buoyancyIn this method, A metal wire was suspended from a clamp and placed in a beaker containing water, then both beaker and suspended wire was placed on the mass spectrometer. The combined mass of the beaker and the wire was zeroed using the balance tare. Each of the samples was then placed on the suspended wire and their individual masses recorded. While doing this, it was ensured that the core samples do not touch the body of the beaker as this could affect the readings. The bulk volume of each of the sample was then computed by dividing their masses by the density of water (density of water, ρ = 1.0g/cm3).

2.4 RESULTS AND CALCULATIONS

SAMPLE CALCULATIONS

(i) Geometrical Estimate of the Bulk Volume, (Vb) as shown in table 1 belowTo calculate the volume of the three (3) core cylindrical samples, the formula for the volume of a cylinder is used. This is given below

pg. 19

Volume of a cylinder = π r2hWhere: Where r = radius = diameter/2h = height (in this case length) For the K = 50mD, the bulk volume, (Vb (k50)), was calculated as

V b (k 50 )=3.142×( 2.492 )

2

×5.07

= 25.49cm3 Same procedure was repeated for the other two samples

Table 1: Geometrical Estimation of the Bulk Volume

Sample Diameter (inches)

Diameter (cm)

Length (inches)

Length (cm)

Volume (cm3)

50mD 0.981 2.49 2.0461 5.19 25.49

100mD 1.0131 2.57 1.998 5.07 26.52

500mD 0.981 2.49 1.979 5.03 24.70

.(ii) Estimation of the Pore Volume, (Vp) as ahown in table 2To do this, the mass of water (Mw) in the pore volume was first calculated, is calculated using the formula below:M w=Saturated sample mass – Dry sample massFor sample K = 50, Mw = 56.91g – 52.70 = 3.72gSame procedure was repeated for the other two samplesTo calculate for the volume of the pore (Vp) = the mass of water∈the pore volume /density of water = 3.72g/1.0g cm-3 = 3.72cm3

Then porosity was estimated as Φ,=V p /V bWhere Vb = bulk volume for sampleFor example, for sample K = 50, Φ = 3.72cm3/25.49.52 cm3 = 0.164 or 16.4%Same procedure was repeated for the other two samples

Table 2: Estimation of the Pore Volume

Sample Dry sample mass (g)

Saturated sample mass (g)

Mass of water (g)

Volume of water (cm3)

Porosity

50mD 52.70 56.42 3.72 3.72 0.146

pg. 20

100mD 52.22 55.91 3.69 3.69 0.139

500mD 48.60 52.83 4.23 4.23 0.171

(iii) Estimation of the bulk volume by Buoyancy as shown in table 3 The bulk volume (Vb) from the buoyancy mass of displaced water was calculated usingV b=buoyancy mass of displaced water /density of water

Where density of water, ρ = 1.0g cm-3

For sample K = 50mDVb = 24.93g/1.0g cm-3 = 24.93cm3

While the porosity was calculated asPorosity , Φ=volume of pore /volume of bulkFor sample K = 50 Φ = 3.72cm3/24.93cm3

= 0.149 or 14.9%Same procedure was repeated for the other two samples.

Table 3: Estimation of the Bulk Volume by Buoyancy

Sample Bouyancy mass of displaced water (g)

Bulk volume (cm3) Porosity

50 md 24.93 24.93 0.149

100 md 24.76 24.76 0.149

500 md 24.17 24.17 0.175

2.5 DISCUSSIONFrom calculations done in the experiment carried out, it was observed that the bulk volumes of the core samples estimated using the two methods that is calculations using direct core measurements and the buoyancy method are not exactly the same, for K= 50mD and K=500mD the differences in their measurements are of negligible values while K= 100mD has a difference of 1.76cm3 as shown in table 4 below

Table 4: Comparing bulk volumes estimated by different methods

Sample Bulk volume Estimated By Direct Measurement (cm3)

Bulk volume Estimated by Buoyancy (cm3)

K = 50mD25.49 24.93

K = 100mD26.52 24.76

K = 500mD 24.17

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24.70

The inconsistency in the result could be due to experimental errors. From theory, porosity experiments require that the sample are saturated in vacuum desiccator for up to an hour, for this experiment however the saturation period lasted for only 20minutes.

Despite discrepancies with bulk volume figures, the extrapolated porosity from both experimental methods are approximately the same for the three samples using the buoyancy method. This can be seen table 5 as shown below

Table 5: Comparing porosities estimated by different methods

Sample Porosity Estimated By Direct Measurement (%)

Porosity Estimated by Buoyancy (%)

K = 50mD 14.6 14.9

K = 100mD 13.9 14.9

K = 500mD 17.1 17.5

On a theoretical basis, sample K = 500mD has an average porosity of 0.173, K = 100mD (0.144) and K= 50 (0.148), the reduction of porosity of these samples could be as result of compaction, the cementation of the rock sample and the degree of saturation.

Theoretically, another reason for the discrepancy in the values of the porosity obtained by direct measurement and that obtained by the buoyancy method is because the buoyancy method measures effective or connected porosity as it depends on the saturation of the rock samples with a fluid.

In practical situations, the buoyancy (Archimedes) method of estimating bulk volume could be accurate in better quality rocks if effective pore spaces can be completely saturated. On the other hand, in poorer quality rocks, it could be difficult to completely saturate the sample. In addition, saturating fluid may react with minerals in the core (e.g. swelling clays). Variations in grain packing could lead core samples not to have the type of regular shape that may give more accuracy to the direct measurement method.

2.6 CONCLUSIONS

At the end of the experiment, the following conclusions can be drawn: Geometric method of bulk volume estimation for porosity determination can be

effectively applied for regularly shaped cores. Comparing the direct measurement (geometric) method and the buoyancy method, it can

be concluded that the buoyancy method could be more accurate. This is because, the direct measurement or geometric method can only be effectively applied for regularly

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shaped cores or core plugs, and this does not paint a true picture of the shapes of the various core samples that can be encountered in the Field or lab in real life.

For the gravimetric or buoyancy method, it could be more accurate in better quality rocks if effective pore spaces can be completely saturated. Otherwise, in poorer quality rocks, it could be difficult to completely saturate the samples.

The inconsistency between both methods of bulk volume estimation can be negligible since they are not too much.

Even though the 500mD sample had a higher porosity than the 50mD and 100mD, there is still lack of correspondence between these two important reservoir properties; porosity and permeability.

The porosity data obtained in this experiment varied as a result of factors such as cementation, particle shape and sizes which made the 500mD sample had a higher porosity than 50mD and 100mD samples.

The 500mD sample with a porosity value of 17.1% (for volumetric estimate) and 17.5. 3% (for the buoyancy method) has a higher capacity to store or contain fluids (oil, gas, and water) than the 50mD and 100mD samples.

2.7 SUMMARY

Porosity data are very important to Petroleum Engineers as they are used to classify reservoirs and to estimate the potential volume of hydrocarbons in a reservoir. Thus reservoirs with high porosity indicate abundant fluids in their pore spaces while those with low porosity indicates low capacity to hold fluids.From the experiment, it was found that Sample K = 500mD has a porosity of 0.173 K = 100mD and K= 50mD has almost same porosity; 0.148 and 0.144 respectively. This shows K= 500mD has the capacity to store fluids than the others. After a careful laboratory study of these samples, it can be concluded that sample K = 500mD is more porous than the other samples.Also the 500mD sample had a higher porosity than the 50mD and 100mD samples, there is actually no specifically defined relationship between porosity and permeability, although there could be a qualitative relationship between both properties but not quantitative.According to Diab and Donaldson (2012), “it is possible to have a very high porosity without having any permeability at all, as in the case of pumice stone (where the effective porosity is nearly zero), and also in clays and shales

2.8 REFERENCES

Aristodemu, E. (2014) lab notes for porosity measurement. Cone, M. P., and Kersey, D. G. (1992) Porosity: Part 5. Laboratoy Methods. AAPG. [Online] Available from: http://archives.datapages.com/data/specpubs/

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Ekwere, J.P (2012) Advanced petrophysics ; geology, porosity, absolute permeability, Heterogeneity and geostatistics. Vol 3 1st ed. Live Oak Book Company. Chapter threeSchlumberger Oil Field Glossary (2012). [Online] Available from: http://www.glossary.oilfield.slb.com/en/Terms/p/porosity.aspx [accessed 4th November 2014]. Tiab, D., and Donaldson, E.C. (2012) Petrophysics: theory and practice of measuring reservoir rock and fluid transport properties. 3rd ed. Oxford: Gulf Professional Publishing.

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