Permeability Of Core Plugs (Lab Report Sample)

Objectives
The main objective in this experiment is to attain the permeability of core plugs 3A and 3B using the PERG-200 and air as the flow. Other objectives include using 3 different flow rates to prevent miscalculations and incorporating the measurements obtain in Darcy’s formula to obtain the values.
Theory
Flowing air is used to calculate for permeability of the core samples, which is measured in Darcy or other equivalents of the Darcy like millidarcy, microdary and nanodarcy. Darcy was the initial person to work on permeability by examining the flow of water through a sample. By reducing the pressure of water flow, the water would then flow from one side of the sample to the other. He summed up his findings with the following formula:
q=KAμP1-P2L
The law assumes that:
Steady state: everything maintains a state of relative equilibrium or changes with time.
Laminar: assumes Re is R=LvDμ which is less than 2000
Linear: in regards to pressure, the drop must occur continuously over that period to obtain a steady.
Incompressible fluid: water is recommended because in a large range of pressures, it does not undergo a change in volume.
Darcy’s units will be the same as 1 Darcy when:
* A is equal to 1 cm2.
* q is equal to 1ccsec.
* P1-P2=1 atm.
* L=1 cm.
However, time, mass, length, number of moles, temperature, luminous intensity and electric current cannot be broken down. These dimensions are significant because they are prerequisites for other dimensions. All in all, they use independent units other than the Darcy units but their dimensions are the same. A good example for this explanation is pressure. It can be measured in pascal or psi units but the dimensions are equal. The dimension breakdown for permeability can be attained by:
k=qμL(A)(P1-P2)
Meanwhile viscosity is equivalent to 1 cp it should be broken down as follows to simplify the analysis process: 1 cp=10-3Pa.s. But, because Pa as a unit of pressure will not be broken down further. With pressure units on the top and bottom of the formula, the units will cancel each other therefore simplifying the analysis process: k= L3TPT[L]L2[P]=L2
As seen above, the dimension breakdown for permeability indicates that permeability and area share similar dimensional analysis and therefore they are equal.
1 Darcy=9.869×10-13 m.
each m2=3 ft×3ft.
In reference to the assumptions presented before for the Darcy law of calculating permeability, two assumptions must be let go during this experiment. The reason behind this is one, gas is compressible and two, a steady state cannot be attained in compressibility thus there will be a difference in the volumes in and out the passage area.
Due to the above reasons, a setback is presented in the calculations and it must be corrected to achieve the objective. So, the average pressure for the two inlets must be taken down and merged into Boyle’s law. This step will enable to transition the liquid permeability formula into a gas permeability equation as follows:
1 Liquid permeability formula qm=kAμ(P1-P2)L
2 Boyle’s law P1V1=P2V2=PmVm=P1q1=P2q2=Pmqm
3 Reshuffling Boyle’s law qm=P2q2Pm
4 Through the impression of Boyle’s law Pm=P1+P22
5 qm can be presented as qm=P2q2P1+P22=2P2q2P1+P2
6 Substitute qm to Liquid permeability formula as: qm=kAμP1-P2L
2P2q2P1+P2=kAμP1-P2L
7 To obtain the gas permeability formula, multiply both sides with P1+P2 then divide both sides by 2P2 to get: q2=kAμP12-P222P2L
Finally, gas permeability is given by: kg=2μgqgPaLAP1+P22P1-P22
Gas is the popularly preferred element in calculating permeability because it consumes less time. When using liquids, the sample must be 100% saturated and the process itself consumes a lot of time. Another reason gas is preferred is because it is less messy and finally, its interaction with the sample does not affect the sample properties like in the case of liquids.
Despite the impact of the reasons given above not being addressed, gas is quick because it causes the gas slip effect. The more pressure exerted during the experiment, the lower the permeability will be. To obtain the liquid permeability, the gas permeability can also be calculated using the Klinkenberg effect. Nevertheless, relevant measurements of kg and Pm must be noted down. Consequently, the values will be used to construct graphs as illustrated below.
-633730230505kgThe intercept value is Liquid or absolute Permeability The linear equation of the line is kg=kL(1+bPm) where b is Klinkenberg factor1Pm00kgThe intercept value is Liquid or absolute Permeability The linear equation of the line is kg=kL(1+bPm) where b is Klinkenberg factor1Pm
The Klinkenberg effect is determined by the type of gas used, pore size and the average distance covered between collisions. Therefore, the graph above is constructed to attain the Klinkenberg formula and liquid permeability respectively. During the experiment, P2 integrates the surrounding’s pressure which is equivalent to 1, as it stays open throughout the test.
Procedure
The PERG-200 shown below was used to conduct the experiment:
27908251149350027501852889250Figure SEQ Figure \* ARABIC 1: PERG-200 tool00Figure SEQ Figure \* ARABIC 1: PERG-200 tool
3096260236220GAS FLOW RATE00GAS FLOW RATE4424045241300UPSTREAM PRESSURE00UPSTREAM PRESSURE302958523939500
46374051663700.00000.0032391351657350.00000.00121539028003500
379730018415CORE HOLDERINLET00CORE HOLDERINLET12128501555115Figure SEQ Figure \* ARABIC 2:Cup holder00Figure SEQ Figure \* ARABIC 2:Cup holder121285013208000
4566285172720V100V12959735174625REGULATOR00REGULATOR183896016891000428688517335500
5055235996950033089859969500
Core plugs 3A and 3B are measured again.
Core plus 3A is inserted into the rubber holder
The rubber holder is then placed in the core holder and immersed in the cup and closed
The pressure is adjusted (it can be any value but not on overload)
After 20-40 seconds of observation, check if the flow rate has stabilized. If not, either -0.1 or + 0.1