A Novel Approach for Determining Permeability in Porous Media

Permeability can be grouped into three different types; absolute permeability, relative permeability, and effective permeability. Rocks have different permeability properties; some rocks permit the flow of fluids through its pores effectively, others only do so nominally. The permeability of rocks equally relates to the rock’s capacity to allow the flow of petroleum, water and gas through it. Unlike porosity, which is a function of the volume of voids over the total volume of rock fabric (usually expressed in percentage), permeability concentrates only in the simplicity that petroleum encounters as it flows between interconnected rock pores. In real life scenarios however, because of the multiphase flow (that is because not only one fluid would flow between the interconnected rock pores), different types of permeability can be encountered such as absolute permeability, relative permeability and effective permeability. In part A of this paper, absolute permeability is what is in study because it is the permeability that is dependent on reservoir rock, not taking into cognizance, the compressibility of fluid (liquid) that flows through the rock. Effective permeability is a measure of the ability of rock particle distribution and its function to allow the flow of petroleum due to different shapes that makes the rock fabric material. Finally, relative permeability describes the percentage of fluids flowing in a competitive multiple phase flow as compared to the flow of the same fluid at 100 percent saturation. A Novel Approach for Determining Permeability in Porous Media


Introduction
The main objective of this experiment is to determine the absolute permeability of sand as a porous media. Permeability (K) can be described as the ability of a rock to allow the flow of fluids, that is, oil, gas, or water. Then concept of permeability is very important in the petroleum industry in that it is applicable in the measure of resistance of a fluid that flows through it. The key results are shown in Table 1. The word "porous media" in this context is connected with sand because this work in question was carried out with sand as permeable material. Normally, permeability like this is referred to as absolute for the reason that regardless of the working fluid, K depends on the structure of the porous medium alone. Darcy's law defines the equation of permeability in terms of measurable quantities. There are four conditions necessary for Darcy's equation to be acceptable [1]. These are: However in the real life scenario it's slightly different because the flow is normally in multiphase flow instead of single phase because the engineers have to account for others fluids to be present in the porous media, e.g. water and oil flowing at the same time through porous rock.
For this reason relative permeability (Kr) is the new quantity that has to be taken in consideration due to microscopic interactions between the liquids, where local fluctuations could be caused in the pressure gradient across the sample. Therefore relative permeability (Kr) is a quantity that will account for each of the fluid present in the eventual multiphase flow, and the extent to which the fluids hinder one another. Relative permeability therefore will be related to the new (non-compressible) fluid flowing in the same rock. The rock permeability does not change, but the flow rate of the new fluid and the equivalent pressure gradient will be accounted, and described as: .
flowrate multiphase flow lative permeability Flowrate fluid at saturation ⇒ For this reason the Darcy's law has to be rewritten to account for each fluid, and the middle term of the equation below is referred to as the "mobility" of phase/fluid i and Kkri represents the total permeability of phase i as: Where: K=absolute permeability of medium Where: Particle size distribution, relates the size of the porous space, therefore this size will be dependent on the particle size, whereas if the particles are small the size between them will be small resulting in a decrease of permeability because the flow of the fluids will depend on the ability of the rock pore space to allow the flow [2].
In the other hand if the particles are bigger the space between the pores will be bigger resulting in an increase in permeability.
Porosity, relates the degree of compaction of the particle or how more or less compact are the particles because the matrix of this particle distribution will affect as well on the size of the voids between the particles.
The degree of saturation relates the percentage of water filling the voids spaces as it will affect the permeability results, because the blockage of the pores by air bubbles can reduce the permeability considerably.
This way if the degree of saturation is less than 85%, air is likely to be continuous instead of being isolated bubbles, which invalidates Darcy's law", this way is very important to eliminate air bubbles from the matrix.
Temperature, relates that the permeability will increase when the temperature increases, because the viscosity of the water decreases with the rise of temperature and vice versa, therefore is important to take note of water temperature [3].

Description Of Experimental Procedure
• The pump was switched on after all the valves were kept closed • After the experiment was started when a constant water level in the overhead tank indicated a constant trickle from the overflow pipe • Valves (1 to 4) were kept closed in order to open the manometer valves (5 to 8) • To collect any of the bed material that passed through the sieve and preventing it from returning to the system the drain tube from valve 4 was inserted into a beaker placed on the water tank • To get the water temperature a thermometer was also placed in the beaker • After the height of the bed was recorded (305) as well the water and mercury manometer zero levels • For the water go through the column in a down flow direction valves 1 and 4 were open • The flow rate (Q)was adjusted using valve 1 where the starting point was 50 cm , and the various flow rates were noted at the different manometer levels.(Attention was being made to close valves 5 and 6 in case the levels in the water manometer exceeded the scale limits, to shut off the water manometer, it didn't happen) • Finally to get the average water temperature, the water temperature was taken regularly during the proceeding

Calculating P1 and P2
For the calculation of the height of the bed in atmosphere from To convert the taken readings to cm: Diameter 38 mm=38/10=3.8 m Length 305 mm=305/10=30.5 cm Therefore the area was calculated from the following formula from: Where the slope is equal to gradient: Calculating the permeability (K) from the formula: Where m is equal to the slope or gradient of the graph, therefore:    For the calculation of the relative oil permeability (k rw ) the formula used was:

Conclusion
It can be concluded that the certain rock properties of porosity such as particle size, as well as fluid properties such as viscosity, density, etc affected the final results. For non-compressible liquids or fluids, the permeability of the rock is maintained as same irrespective of the type of fluid that flows through it. For this reason, an experiment like this is very useful in the real life because of the fact that determining the absolute permeability of a reservoir would out-rightly inform us on whether the rock material is good and viable for flow and accumulation of petroleum. The apparatus used for permeability is shown in Figure 3.
It is therefore established in this experiment that the permeability of rock is directly proportional to the permeability of the sand mentioned above in the objective. In this concept, when there is an increase in particle size, there is definitely an increase in permeability and porosity of rock sediment. It should also be highlighted that reservoirs are different due to the inconsistencies in particle sizes, degree of cementation between particles, formation of sediments by individual particles, etc.