Porosity-permeability correlations

Generally, as permeability decreases, increasing pressure drops are required across a package in order to maintain a desired flow rate. The density differences in a yam package result in permeability variations, which directly affect flow behaviour within the package. The correlation between package density and permeability was discussed by Denton, who addressed this correlation for cotton yam packages. Porosity-permeability correlations for other types of fibrous porous media are also available from the literature. " Consideration of these works is beyond the scope of the material presented here. 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

Accurate interpretation of the formation properties (porosity, permeability and irreducible water saturation) requires reliable estimates of NMR fluid properties or the relationship between diffusivity and relaxation time. Estimation of oil viscosity and solution-gas content require their correlation with NMR measurable fluid properties. These include the hydrogen index, bulk fluid relaxation time and bulk fluid diffusivity [8]. 

Fig. 3.2. Generalized field correlations of porosity, permeability and density with depth and distribution in the Oued el-Mya and Ghadames Basins (based on statistical processing of reservoir petrophysical data)...

Here, Ap is the pressure drop across a microchannel heat sink subject to an impinging jet and p, Vq, e, K, Ce, H, Re, Wc, and Ar are density, impinging velocity at the inlet of the microchannel heat sink, fluid dynamic viscosity, porosity, permeability, Ergun coefficient, channel height, Reynolds number, channel width, and aspect ratio, respectively. The correlations for the pressure drop and the thermal resistance were compared with experimental results, and both match with experimental results within 10 %. 

Permeability, which characterizes the ability of rocks to allow the movement of fluids contained in their pores, is one of the most important parameters describing the porous media. Normally, in order to measure the permeability, the sample must have a simple geometric shape (e.g. cylinder or cube) and certain dimensions. On the other hand, measurements of porosity, pore-size distribution, and specific surface area do not require special geometric dimensions. The correlations among permeability and other easier-to-measure parameters, therefore, have been studied theoretically and experimentally. In practice, the most often reported correlation is that between the permeability and porosity The coefficient of correlation for porosity-permeability relationship varies from sample to sample, with a better correlation if the porosity used in the calculation is measured when a core contains the irreducible fluid. Porosity does not reflect the number and width of fractures, the pore sizes and topological structure, whereas the specific surface area does. Thus, it appears advisable to relate permeability simultaneously to porosity, specific surface area, irreducible water/oil saturation, grain size/pore size/throat size distribution, tortuosity, etc. 

Bastos, A.C., Dillon, L.D., Vasquez, G.F., Soares, J.A., 1998. Core derived acoustic, porosity and permeability correlations for computation pseudo-logs. In Harvey, P.K., Lovell, M.A. (Eds.), Core-Log Integration. Geological Society, London, pp. 141-146. Special Publ. 136. 

SWS are useful to obtain direct indications of hydrocarbons (under UV light) and to differentiate between oil and gas. The technique is applied extensively to sample microfossils and pollen for stratigraphic analysis (age dating, correlation, depositional environment). Qualitative inspection of porosity is possible, but very often the sampling process results in a severe crushing of the sample thus obscuring the true porosity and permeability. 

If appropriate, correlation panels may contain additional information such as depositional environments, porosities and permeabilities, saturations, lithological descriptions and indications of which intervals have been cored. 

Some variables often have dependencies, such as reservoir porosity and permeability (a positive correlation) or the capital cost of a specific equipment item and its lifetime maintenance cost (a negative correlation). We can test the linear dependency of two variables (say x and y) by calculating the covariance between the two variables (o ) and the correlation coefficient (r) ... 

Permeability and porosity are related to each other if the porosity is zero the permeability is zero. Although a correlation between these two parameters may exist, permeability cannot be predicted from porosity alone, since additional parameters that contain more information about the pore structure are needed. These additional parameters are tortuosity and cormectivity. 

NMR has proven to be a valuable tool for formation evaluation by well logging, downhole fluid analysis and laboratory rock characterization. It gives a direct measure of porosity as the response is only from the fluids in the pore space of the rock. The relaxation time distribution correlates with the pore size distribution. This correlation makes it possible to estimate permeability and irreducible water saturation. When more than one fluid is present in the rock, the fluids can be identified based on the difference in the fluid diffusivity in addition to relaxation times. Interpretation of NMR responses has been greatly advanced with the ability to display two distributions simultaneously. 

We have developed a method to spatially resolve permeability distributions. We use MRI to determine spatially resolved velocity distributions, and solve an associated system and parameter identification problem to determine the permeability distribution. Not only is such information essential for investigating complex processes within permeable media, it can provide the means for determining improved correlations for predicting permeability from other measurements, such as porosity and NMR relaxation [17-19]. 

Separators are characterized by structural and functional properties the former describes what they are and the latter how they perform. The structural properties include chemical (molecular) and microcrystalline nature, thickness, pore size, pore size distribution, porosity, and various chemical and physical properties such as chemical stability, and electrolyte uptake. The functional properties of interest are electrical resistivity, permeability, and transport number. It is useful to characterize separator materials in terms of their structural and functional properties and to establish a correlation of these properties with their performance in batteries. A variety of techniques are used to evaluate separators. Some of these techniques are discussed in this section. 

Figure 11.4. Data of compressibilities and porosities of filter cakes, (a) Parameters of the correlation a = a0(hP)n for resistivity of CaSi03 filter cakes at two rates and two concentrations (Rushton and Katsoulas, 1984). (b) Resistivity as a function of pressure measured in a compressibility-permeability (CP) cell [Grace, Chem. Eng. Prog. 49, 303, 367, 427 (1953)]. (c) Porosity as a function of pressure for the same six materials (Grace, loc. tit.).

The determination of open porosity (or fluid permeability) as given in ISO Standard 4022 is not expensive, and by this way the permeability of a sintered metal element can be correlated with its effective gap indicating the grade of flameproofness. 

To calculate the reduction in the concentration of surfactant in the fluid by adsorption it is necessary to have an estimation of the inner surface area of the reservoir. This parameter is related to the porosity of the medium and to its permeability. Attempts have been made to correlate these two quantities but the results have been unsuccessful, because there are parameters characteristic of each particular porous medium involved in the description of the problem (14). For our analysis we adopted the approach of Kozeny and Carman (15). These authors defined a parameter called the "equivalent hydraulic radius of the porous medium" which represents the surface area exposed to the fluid per unit volume of rock. They obtained the following relationship between the permeability, k, and the porosity, 0 ... 

Applications of ultrasonic techniques to solid-gas systems rely on the fact that velocity and attenuation of US-waves in porous materials is closely related to pore size, porosity, tortuosity, permeability and flux resistivity. Thus, the flux resistivity of acoustic absorbents oan be related to US attenuation [118,119], while the velocity of slow longitudinal US is related to pore tortuosity and diffusion, and transport properties, of other porous materials [120]. Ultrasound attenuation is very sensitive to the presence of an external agent suoh as moisture in the pore space [121] and has been used to monitor wetting and drying prooesses [122] on the other hand, US velocity has been used to measure the elastic coefficients of different types of paper and correlate them with properties such as tensile breaking strength, compressive strength, etc. [123]. 

The aspect of hole filling by plasma deposition can be demonstrated by the transport characteristics of LCVD-prepared membranes. First, the porosity as porous media calculated from the gas permeability dependence on the applied pressure can be correlated to the salt rejection of the composite membrane as shown in Figure 34.13. The effective porosity s/, where s is the porosity and q is the tortuosity factor, is measured in dry state and may not directly correlate to the porosity of the membranes in wet state. The effective porosity of LCVD-prepared membranes was measured before the reverse osmosis experiment. The decrease of porosity (as porous media) is clearly reflected in the increase in salt rejection in reverse osmosis. 

In the capillary flow, the flow capacity is defined by capillary radius R. In porous media, the flow capacity is defined by permeability k and porosity ( ). Now we have to correlate these parameters. 

Core analysis data are displayed as continuous logs in Fig. 2. Porosity varies from > 0 to 19%. Permeability varies from <0.1 mD to > 5000 mD. Porosity and permeability are highest where the rocks are most coarse grained. However, again the correlation is not perfect the tops of the sandbodies tend to have low porosity and permeability values relative to the middle and lower portions of sandbodies (Fig. 2). Consequently, grain size and facies variations cannot be used in isolation to understand or predict variations in reservoir quality. 

Fig. 8. Combination diagram of grain size data (derived from core description, Fig. 2) and mineral proportions, porosity and permeability (derived from wireline log analysis). There is excellent correlation between quartz proportion and reservoir quality. The correlation of these with grain size is complex. The tops of some sandbodies have a high dolomite content and correspondingly poor reservoir quality (e.g. 2470-2471 m). Sandbodies are numbered for reference to Fig. 9. Core analysis porosity and permeability data (dashed and faint) have been added to the diagram for comparison with the wireline-derived data.

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