# Mathematical relationship between porosity and permeability lab

### Porosity and Permeability

ISSN: CODEN: JMESCN Relationships between porosity and permeability of calcarenite rocks based on laboratory measurements Abdelaali. The permeability of a porous medium can be determined from the samples Klinkenberg () postulated, on the basis of his laboratory Straight line equation #2 for relationship between effect of permeability on Klinkenberg effect .. its Relation to 3-D Preferential Flow Occurring in Agricultural Soils. Two separate characteristics of rocks control how effective they are as aquifers: Porosity is a measure of how much of a rock is open space. This space can be.

Theory shows relationship between the response function and permeability; and either matrix permeability or effective fracture flow aperture may be determined from the calibration charts and tables provided [23, 24]. The response function is related to permeability k: For each sample point 3— 6 measurements were made, in order to ensure the quality of the data. For each sample point, an average of the measurements was calculated and used as the representative value for that point.

Six rock samples were tested, and values of the permeability, particle and bulk densities, and porosity are listed in Table 1. Petrophysical properties of calcarenite rocks. For each specimen, the permeability and particle and bulk densities were measured, and porosity calculated.

The morphology of the porous medium obtained by mercury porosimetry gives an appearance pore distribution of the material.

The samples have sufficient volume to be representative of the material. The results are shown in Figures and Table 2. Results and discussion The results of permeability and porosity of the rocks were analyzed using the least squares regression method. The equation of best fit line and coefficient of determination R2 were determined for each regression.

The values of permeability of the calcarenite rocks were correlated with the porosity of the rocks. A very strong correlation between permeability and porosity of the rocks was found. It can be observed that there is linear relation between the permeability of rocks with porosity of the calcarenite rocks.

The results of regression equations and the coefficient of determination are presented in Figure 1. JMESCN Permeability and porosity are in a close relationship that depends on the amount of void space in the tested material. It is widely accepted that permeability is greatly affected by microstructure, which is, in this context, defined in terms of pore and crack structures.

So it could be supposed that with increasing porosity, the permeability should increase as well. But there are some other facts to note when speaking about this relationship. Therefore, permeability of porous material is influenced not only by porosity, but also by shape and arrangement of pores, or by the amount of clayey component [25, 26].

It is necessary to distinguish between total and effective porosity. We are not able to make assumptions on permeability of tested material from values of total porosity, due to the fact that it is the total void space in the rock. A rock may be highly porous, but if the voids are not interconnected, fluids within the closed isolated pores cannot leak, e.

The pore size distribution is very important petrophysical property controlling the fluid flow. To clarify the relationship between permeability and porosity; pore size and pore size distribution were determined for selected rock samples.

## Porosity and Permeability Lab

Pore dimensions cover a very wide range. Within our research, two samples of calcarenite, which have approximately the same order values of permeability, but different porosities, were tested by mercury porosimetry for pore size distribution.

Permeability versus porosity of calcarenite rocks. Figures 2 and 3 show the polymodal nature of the pore size distribution of the studied stones. The relevant features here are the number and kind of pore families, rather than pore volume frequency. As we can see from Figures 2 and 3, sample 2 has a more uniform distribution in the range of pore size.

The megapores of this sample should not exceed It has a very broad spectrum of porosity with significant mesoporosity. The prevailing part of pores belongs to the megapores, which can create main transport ways for liquid.

In the case of sample 3, the distribution of pore size is different. The dominant part of pores belongs to the mesoporosity, and microporosity, which is also very important.

Pore size distribution of sample 2. Pore size distribution of sample 3. JMESCN The distribution of pore volumes of sample 2 is unimodal a single dominant family of pores resulting in a single point of inflection in the curve of injectionit is possible to determine a radius access or threshold pore: It is graphically determined on the first injection curve as the radius corresponding to the inflection point of the curve or by the method of tangents [21, 22].

The threshold pore can also be viewed on the curves representing the increment of mercury injected for each access radius. The injection curves with multiple turning points illustrate multimodal porous networks where several families ray access to the pores coexists.

Average pore diameter is usually used as a representative parameter of the pore size distribution. Cores are dried in an oven or extracted by a Soxhlet extractor and then they are subsequently dried. The core is inserted in a core holder. A pressure applied on the surface of the core as confining pressure. An appropriate pressure gradient is adjusted across the core sample and the rate of flow of air through the plug is observed.

A straight line is fitted to the data points. But at ultralow flow rates, the flow rate is not proportional to pressure drop. This deviation shows that the pressure drop in turbulent flow is higher than viscous flow.

## Measurement of Permeability

By increasing the pressure drop we can reach to a maximum flow rate capacity of the medium, after that flow rate will not increase by increasing the pressure drop. Plot of Experimental Results for Calculation of Permeability The same experiment can be done with water or other liquids. In this case the core sample should be fully saturated with the testing liquid. When liquid is used as the testing fluid, care must be taken that it does not react with the solids in the core sample. The permeability of a core sample measured by flowing air is always greater than the permeability obtained when a liquid is the flowing fluid.

Klinkenberg postulated, on the basis of his laboratory experiments, that liquids had a zero velocity at the sand grain surface, while gases exhibited some finite velocity at the sand grain surface. This resulted in a higher flow rate for the gas at a given pressure differential. Correction can be applied for the change in permeability because the reduction in confining pressure on the sample.

Example The following data obtained during a routine permeability test at 70oF. Rocks which contain fractures in situ separate along natural plane of weakness when cored. Therefore the conductivity of such fractures will not be included in the laboratory data. 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.

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. 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.

At the end of this experiment, the following conclusions can be drawn: 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.

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.

Journal of Petroleum Technology. Society of Petroleum Engineers. P Advanced petrophysics ; geology, porosity, absolute permeability, Heterogeneity and geostatistics.

### Porosity and Permeability Lab

Vol 3 1st ed. Live Oak Book Company. Chapter three Tarek, A. Tiab, D and Donaldson, E. 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: Estimation of the bulk volume by buoyancy In 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. Estimation of the Bulk Volume by Buoyancy pg. 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: 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. 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.

This is because, the direct measurement or geometric method can only be effectively applied for regularly 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.