permebility and porosity

MSc. PETROLEUM ENGINEERRING

EAB_7_152 Petro Physics

Dr. Elsa Aristodemou

Permeability and Porosity

By

Muhammad Kamal

Student ID # 3325610

Submission Date: 30/11/2014

Muhammad Kamal (3325610)

FORMATION PERMEABILITY

ABSTRACT:

We can find Absolute Permeability of the porous medium using Darcy Equation and by plotting a graph between pressure gradient and flow rate. The Graph shows the linear relationship between Q and Delta P, means that as the flow rate increases delta P also increases. We can find Relative Permeability of the medium using Darcy Method and Corey Method and plot the graphs between Relative Permeability of oil and Relative Permeability of water with respect to Water Saturation. We can also measure permeability by measuring different Heights of three different lengths of sand packing for three different flow rates.

We can calculate the porosity of sandstone core samples by calculating bulk volume and pore volume.

INTRODUCTION:

Permeability is the ability of porous media to pass a fluid through its pores and it is affected by Grain Packing, Grain Angularity and Grain size Distribution.

We have to calculate the absolute permeability of the porous medium using Darcy equation which is

K=QµL/A∆ P

Where k=Permeability, Q=Flow Rate(cm3/s), µ=viscosity, L=Length(cm), A=Area(cm2), ∆ P=Pressure Drop(atm) By putting all the values in above equation we can get the value of absolute permeability k.

We can also get absolute permeability by equation

K=µL/A.Gradient

All the values are known except Gradient which we get by drawing a graph between flow rate(cm3/s) vs ∆ P(atm). By drawing a graph between Q and ∆ P we got a linear relationship between them.

Same Experiment is used to determine the relative permeability of Oil and Water. We can use Darcy Equation to determine relative permeability of oil and water.

Qi=[Kkri/µi]*A∆ Pi/L

We can use Corey Equation to determine Relative permeability of oil and water in absence of Darcy Equation.

Kro= [1-Sw/I-Swc]4


Where Kro is Relative Permeability of oil. Once we get the value of Kro ,we can find Ko by using the formula Ko=Kro*K

Similarly for Relative Permeability of Water we have

Krw=[Sw-Swc/1-Swc]4

Once we get the value of Krw we can find Kw by using the formula Kw=Krw*K

We also have three samples of sand. We can measure different heights of three different sand samples for three different flow rate and measure the permeability. We can also plot the graphs of Q vs ∆ P for three sand samples and find the gradient of each sample. Once we find three gradients then we can find permeability easily.

PROCEDURE:

First of all we closed all the valves and switch on the pump. After that we open the Manometer valves to measure the pressure difference at different flow rates. Thermometer is placed in a beaker to measure the Temperature of water. We can slowly increase the flow rates and measures the corresponding pressures and temperatures. We continue our procedure and take atleast 10 Readings.


RESULTS & DISCUSSION:

PART A In part A we calculate two permeability. One by Darcy Law and second by drawing a graph between ∆ P(atm) vs Q(cm3/s).

1. Calculations for Absolute Permeability using Darcy Law

Flow Rate (cm3/min)

Flow Rate (cm3/s)

Pressure P1 (mm)

Pressure P2 (mm)

ΔP (P2-P1) (mm)

ΔP =ρgh/10^5 (atm)

Temperature (C°)

Permeabiltiy (Darcy)

50 0.8333 242 261 19 0.0018639 18 1241.92100 1.6667 225 280 55 0.0053955 18.3 858.05150 2.5000 209 297 88 0.0086328 18.6 804.43200 3.3333 187 323 136 0.0133416 18.8 694.01250 4.1667 169 343 174 0.0170694 19 678.06300 5.0000 154 362 208 0.0204048 18.9 680.67350 5.8333 130 390 260 0.025506 18.8 635.29400 6.6667 108 415 307 0.0301167 18.5 614.89450 7.5000 89 436 347 0.0340407 18.5 612.01500 8.3333 63 466 403 0.0395343 18.5 585.52

Average permeability 740.4856137

First of all convert the flow rate cm3/min into cm3/s by dividing it with 60. Convert ∆ P(mm) into ∆ P(atm) by P=1000*g*h/105

P=1000*9.81*(19*10-3)m/105

P=0.001863 atm We can find permeability by Darcy Law using Equation

K=QµL/A∆ P

By putting the first calculation from the above table we have

K=0.8333*1*31.5/11.34*0.0018639

K=1241.92 Darcy


Area of Bed (cm2) 11.34Length of Bed (cm) 31.5

Average temperature (C°) 18.59Viscosity of water (cp) 1

Gradient of Graph 0.005Permeability (darcy) 555.55

2. Calculations for Absolute Permeability by drawing graph between ∆ P(atm) vs Q(cm3/s)

Graph shows that there is a linear relationship between ∆ P and Flow rate. It means that when Flow rate increases ∆ P also increases and vice versa.

We know that

K=µL/A.Gradient

y=mx+c (from the graph m=0.005 which is our Gradient)Put the values in above Equation,we getK=(1*31.5)/(11.34*0.005)

K=555.55

PART BIn part B we calculate Relative Permeability of Oil and Water using Darcy Method and Corey Method.Calculation for Relative Permeability of Oil and Water using Darcy Method:


Graph shows that relative permeability of water increases as water saturation increases, at 20 % water saturation Krw is 0.125, as the water saturation increases Krw also increases and at 80% saturation value of Krw is maximum which is 0.8333 but relative permeability of oil is maximum at 40% and 80% of water saturation and minimum at 60% saturation and not much depends on water saturation. We can also see from the graph that at 80% water saturation Relative Permeability of oil and water is same that is 0.833342

We know that

Qi=[Kkri/µi]*A∆ Pi/L

For oil

Qo=[Kkro/µo]*A∆ P/L

Qo=[555.55*kro/2.5]*11.34*0.03/31.5Qo=2 µo=2.5Kro=0.8333

Ko=kro*K


Case Sw Qw, cc/s Qo, cc/s ΔP, atm kw krw ko kro80% W, 20% O 0.8 5 2 0.03 482.2573 0.833342 482.2573 0.83334260% W, 40% O 0.6 4 3 0.05 231.4835 0.400004 434.0316 0.75000840% W, 60% O 0.4 3 4 0.06 144.6772 0.250003 482.2573 0.83334220% W, 80% O 0.2 2 5 0.08 72.3386 0.125001 452.1162 0.781258

Darcy Method

Ko=0.8333*555.55Ko=482.2573

Similarly we can find rest of the readings by same method. For krw only Qw=5, µw=1

rest of the procedure is same. Calculation for Relative Permeability of Oil and Water using Corey Method:

Graph shows that relative permeability of water increases slowly and goes to maximum when water saturation is 80%.it also shows that relative permeability of oil decreases with the increase in water saturation. At 20% saturation Kro is maximum but its value decrease to 0.0039 at 80% water saturation. At 60% saturation value of Krw and Kro is same which is 0.625

We know that

Kro= [1-Sw/I-Swc]4

Sw=0.8 Swc=0.2 put the values in above equation kro=0.003909 ko=kro*K


Case Sw Qw, cc/s Qo, cc/s ΔP, atm kw krw ko kro80% W, 20% O 0.8 5 2 0.03 175.7795 0.316406 2.170117 0.00390660% W, 40% O 0.6 4 3 0.05 34.72188 0.0625 34.72188 0.062540% W, 60% O 0.4 3 4 0.06 2.170117 0.003906 175.7795 0.31640620% W, 80% O 0.2 2 5 0.08 0 0 555.55 1

Corey Method

Ko=0.003909*555.55 ko=2.1701 Similarly we can calculate rest of kro by putting Sw=0.6,0.4,0.2 and Swc=0.2

We know that

Krw=[Sw-Swc/1-Swc]4

Sw=0.8 Swc=0.2 put the values in above equation krw=0.3164 kw=krw*K Kw=175.77 Similarly we can calculate rest of krw by putting Sw=0.6,0.4,0.2 and Swc=0.2

PART C

We calculate the permeability of three different lengths with three different flow rates.


Therefore by the help of graphs we can find the gradients and by using the gradients we can find the permeability.

CONCLUSION:

From the results that we obtain from calculations and graphs, we concluded that the Absolute Permeability decreases by increasing the flow rates and we can find linear relationship, if we draw a graph between ∆ P(atm) Vs Q(cm3/s).

We also concluded that for relative permeability of oil and water, Corey method is more accurate than Darcy method because Corey method gives accurate reading and both Kro and Krw depends on water saturation whereas in Darcy method Kro is independent on water saturation.


L (cm)h1

(cm)h2

(cm)Δh=h1-h2

(cm) ΔP (atm) Qcm3/min Q cm3/s K (Darcy)

Average Permeability

(Darcy)Gradient from

the graphAbsolute Permeability

from graph 12.5 7.2 5.4 1.8 0.0017658 80 1.33 832.3312.5 5.5 3.4 2.1 0.0020601 100 1.67 891.7812.5 9.6 7 2.6 0.0025506 120 2.00 864.3421.5 8.1 4.9 3.2 0.0031392 80 1.33 805.2821.5 10.9 7.4 3.5 0.0034335 100 1.67 920.3221.5 16.1 12.5 3.6 0.0035316 120 2.00 1073.7030.5 10.5 6.8 3.7 0.0036297 80 1.33 988.0030.5 10.9 6.8 4.1 0.0040221 100 1.67 1114.5130.5 11.6 7.3 4.3 0.0042183 120 2.00 1275.20

Sand 1

sand 2

sand 3

918.58

3159.91

2988.44

862.82

1125.90

933.10

0.0012

0.0006

0.0009

POROSITY

ABSTRACT:

In the laboratory, we have three rock samples (50,100,500 milli Darcy) made up of sandstone material. We have to find the bulk volume of these three rock samples from geometrical as well as buoyancy point of view. We also have to find the pore volume of the rock samples and from pore volume and bulk volume we can find the Porosity of the rock samples.

PROCEDURE:

Using Vernier Calliper we can find diameter and length of each of the rock sample. We weight the rock samples and saturate them with distilled water and put in vacuum

chamber to displace the air in the rock samples. We will provide vacuum to the rock samples for 10 minutes to accelerate the displacement

in the core sample. After that we can find saturated mass of the samples and the difference of saturated mass

and dry sample mass gives the mass of water. We can find bulk volume by buoyancy method as weeL. For this we have to submerge the

rock samples in beaker containing distilled water and make sure that the core is not touching to the walls of the beaker.

We have to subtract the weight of the beaker and water by using balance tare.

RESULTS AND DISCUSSION:

Muhammad Kamal (3325610) Sample

Diameter (mm)

Diameter (cm)

Length (mm)

Length (cm)

Volume (cm3)

50 mD 25.2 2.52 52.5 5.25 26.171 100 mD 24.9 2.49 51 5.1 24.822 500 mD 24.9 2.49 49.9 4.99 24.286

Geometrical Estimate of the Bulk Volume

D=2.52cm L=5.25cm Vb=3.14*r2*h r=D/2 Vb=26.171cm3

Porosity=Vp/Vb Porosity=2.90/26.17 Porosity=11%

CONCLUSION:


SampleDry

sample (g)

Saturated sample mass (g)

Mass of Water

(g)

Pore Volume (cm3)

Bulk Volume (cm3)

Porosity (%)

50 mD 52.66 55.56 2.9 2.9 26.17 11.08 100 mD 52.19 55.07 2.88 2.88 24.82 11.60 500 mD 48.59 52.48 3.89 3.89 24.29 16.02

Estimate of the Pore Volume and Porosity

SampleBouyancy mass

of displaced water (g)

Bulk Volume (cm3)

Pore Volume (cm3)

Porosity (%)

50 mD 24.55 24.55 2.9 11.81 100 mD 24.37 24.37 2.88 11.82 100 mD 23.8 23.8 3.89 16.34

Estimate of the Bulk Volume & Porosity by Buoyancy

After calculating Bulk volume and pore volume, We can find the porosity by using geometrical method as well as by buoyancy method. From the calculations , we can predict that there is a minute increase in porosity for buoyancy method.


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