# Influence Of Pore Geometry Biology Essay

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Pressure and saturation are of two important parameters to be considered to evaluate the electrical properties of reservoir rock. As confining pressure can cause pore space of the rock to collapse and rock properties to change, it is necessary to examine in details how much the pressure and saturation changes affect the electrical properties. Investigations of electrical properties of sandstones and carbonates are the main focus in this work. The effects of pore geometries, confining pressure, and partial water saturation on electrical properties are investigated. The new electrical dispersion models from 0.01 Hz until 0.2 MHz for shaly sandstone are also developed.

Petrographic image analysis is carried out to asses pore geometry of the media. Circularity, gamma, pore aspect ratio, pore size distribution and pore angle distribution are calculated to evaluate their effect on electrical dispersion. Confining pressure and water saturation observation are then evaluated to obtain their impact on pore structure and complex resistivity.

The result of this work shows that surface conductivity plays as a dominant factor particularly in shaly media and it is indicated by electrical resistivity dispersion in low water saturation. When evaluating surface conductivity, the pore geometry has to be considered because large structure is easier to saturate rather than small structure. Moreover, the high water salinity can significantly reduce diffusive layer thickness and if the pore radii are very small, the diffusive layer thickness will touch each other and block the anion movement.

In addition to these results, it is found that pore radius distribution provides more contribution to the electrical resistivity dispersion and becomes a basis to extract porosity from resistivity. Confining pressure only contributes small changes in pore geometry of media and the use of imaginary resistivity gives a better detection on it. Modified D-model and Archie's model are developed to calculate the dielectric permittivity and effective conductivity in high water salinity saturated-rock as a function of water saturation degree.

Keywords: Surface conductivity, pore geometry, confining pressure, partial water saturation, electrical dispersion model

## 1. Introduction

The knowledge of water saturation and its distribution is very important in hydrocarbon recovery assessment. The how and when reservoir monitoring is conducted requires some deep investigations on the physical properties that much govern or change during production. If the changes are large enough, the time-lapse reservoir monitoring can be employed to map fluid distribution, pressure, temperature and fluid front. One of the physical properties that may show significant changes during production is its electrical properties. However, the variation of pore geometries and pore throats as well as inhomogeneous distribution of microporosity may cause the water not to displace oil uniformly throughout the rock. Thus, the distribution of water before and after being produced may be quite different. For this reason, saturated and unsaturated fluid mechanism as well as pressure and pore geometry are the physical basis to understand the electrical responses of reservoir rock when recovery is addressed.

The effect of brine salinity in brine-rock interaction supposes to be considered. One of the issues published by Tang (1998) is formation damage due to misusage of brine water for waterflooding. When the fresh water or low salinity brine is injected to the core sample, the fines can detach from the surface and move with the flowing liquid. The fine agent includes clay minerals such as kaolinite, illite, chlorite and montmorllonite.

For more than 15 years, study on electrical properties of rock has been increased particularly on effect of saturation, pore structure, wettability, shale content, electrical modeling and dispersion. The application of the method is usually dedicated for formation evaluation, reservoir monitoring, study of steam flood effect and so forth. Lima and Sharma (1990, 1992) study the grain conductivity by considering self-similar mixtures of conductive grain. Later, they generalize the result to evaluate Maxwell-Wegner theory for membrane polarization in shaly sandstones. Suman and Knight (1997) study the presence of thin film during saturation either in water-wet or oil-wet system. Their result show that the saturation exponent n of Archie's model may differ for those systems. The influence of grains shape, pore and oil droplet disperse in a dispersion model of carbonate rock is investigated by Seleznev (2005). He establishes the new model that is incorporated the rock microstructures. The flatter grain component is believed to cause higher dielectric dispersion and lower effective mixture conductivity. Meanwhile Rey and Jongmans (2007) study the particle shape and orientation effect on resistivity. They find that the aligned elongated resistive particle such as pebbles embedded in conductive might induce anisotropy.

Most of the previous work is in low salinity water, GPR frequency and in clean sand media. Whereas, when dealing with high water salinity the effect of saturation degree should be taken into account, especially in shaly sand media. Furthermore, surface conductivity, pore geometry and electrical dispersion needs to be studied more detail as it may correlate to porosity.

Generally, electrical properties of the rock are divided into to two folds; they are a response of volumetric or a grain-fluid interfacing. Real resistivity is considered both in volumetric and interlayer response, meanwhile imaginary resistivity due to interlayer effect only (Schon, 1998). Numerous researches note the interrelationship of real part resistivity to transport properties of the rock (Milsch et.al, 2008; Tong et.al, 2006). For practically purposes, hitherto, the Archie's model (1942) is still used as a tool to estimate fluid saturation in resistivity logging. Nevertheless, the present of clay minerals either dispersed or coated the grain-solid cause inaccurate of Archie's water saturation prediction. The main factor is believed due to the electrical double layer (EDL) having a capacitive feature and may storing the electricity on the surface of clay. These charges are very significant in low frequency where is the dielectric permittivity has an anomalous great in frequency less than 0.1 KHz (Ruffet et.al, 1991). The charges stacking makes possible since the relaxation time is sufficient before the electrical field direction change notably. Furthermore, the present of clay minerals throughout the rock may cause membrane polarization. This occurs when clay surface partially block ionic solution. Negative charges on clay minerals tend to capture the electrolyte cations and move to anions in the other way.

Numerous researchers note that the high water salinity is mainly influenced by a bulk volume of conduction process while low salinity is influenced by interlayer or fluid-grain surface conductivity (Kulenkampff and Schopper, 1988; Revil and Glover, 1997; Ruffet et.al, 1991; Schon, 1998). However, a preliminary study by Khairy et.al (2009) indicates that even in high water salinity, EDL still dominantly contributes in low water saturation degree. This phenomenon is due to the more saline water will lead to the decreasing in the thickness of double layer. Therefore, conductivity of the rock in this case should be considered incorporating both of the volumetric and surface conductivity simultaneously as water saturation is increased. The new proposed model must take into account of saturation factor and surface conductivity.

This work underlines four points to be evaluated in their relationship to electrical properties; they are: water saturation degree, confining pressure, pore geometry and surface conductivity. The conductivity and dielectric model are developed to account surface conductivity in shaly media.

## 2. Methodology

2.1. Sample Preparation

In order to investigate pore geometry effect to electrical properties, few samples are selected which represent various pore size distributions. There are nine samples studied consisting of five samples of sandstone and four samples of carbonate rock. The samples have different porosity ranging from 12.54 % until 31.94% and permeability ranging from 17.5 mD until 5091 mD as listed in Table 1. Meanwhile Table 2 and Table 3 describe the XRD result and petrographic sample description respectively. In this work, most of carbonate rocks have extremely larger pore size compared to sandstones.

The first step is to shape sedimentary core samples that fit with core-holder. The core samples are cut and shaped in accordance with the core-holder size. After core cleaning to remove salt and oil within the rock, those samples are measured of their porosity and permeability.

The saturated-unsaturated water fluid is determined by reweighting the sample once the samples immersed and dried up in a certain time. After proper drying and the partial water saturated justification, the samples are installed in the instrument. The core samples are wiped to ensure there is no water drop at each step of saturation. The degree of saturation is then calculated by

(1)

where q and f are volumetric water and porosity respectively. The volumetric water is defined as

(2)

Synthetic brine water is established to support this work with salinity of 80,000 ppm. The fluid conductivity and TDS are 100.3 mS/cm and 50.2 g/L respectively.

To test the samples whether can retain with overburden pressure, the cores are tested by analyzing their sonic velocity whilst the confining pressure is increased and decreased from 0 until 3000 psi. The P-wave and both Sv and Sh waves are recorded in order to determine the impact of the stress (Figure 1). If the velocities are in the same path while pressure is increased and decreased, it is considered the samples can retain the pressure. The complete results of pressure test are attached in Appendix A.

2.2 Complex Resistivity Measurement

Prior to installing in the instrument, the samples are jacketed by flexible rubber to avoid mixing of external fluid pressure (simulating overburden) with internal fluid pressure (simulating pore pressure). To measure resistivity, electrode must be carefully aligned on either end of the sample. The voltage electrode touches the insulating pad and the current contacts on the samples. Standard electrode materials consist of porous silver membrane filters manufactured by Osmonics Inc.

The measurement of resistivity can be established by means of two or four electrodes configuration. According to Boitnott (2008) the high impedance samples will be better to use two electrodes rather than four electrodes mode. Most of sandstones in this work use two electrodes mode while the rest by four electrodes. Resistivity observation is evaluated during overburden pressure is increased from 0 until 3000 psig with the interval every 1000 psig. The frequency setup from 0.01 Hz - 0.2 MHz automatically in logarithmic swept. Totally, there are 59 points of frequencies for each execution. This mechanism is performed repeatedly until full water brine saturation is achieved. The same process is employed for unsaturated system. To make sure the evaporation is insignificant, the samples are weighted before and after measurement.

Input files for the system are core length, diameter, density and pore fluid conductivity. The measurement of electrical property of rock in this work is made in a serial mode. The complex impedance Z* is

(3)

where Rs is the series resistance and Xs is the reactance. The complex resistivity can be calculated as

(4)

where A and t are cross-sectional area and thickness respectively. The complex dielectric permittivity is then formulated

(5)

where w is angular frequency and eo is the vacuum permittivity (8.85 x 10-12 F/m).

Quality of the data measurement is adjusted by balancing the Z-meter interface box with the reference resistor. Measurement quality is enhanced by selecting the reference resistor that most closely matches the effective (low frequency) resistance of the sample. This effectively balances the voltages measured by the two amplifiers. In addition, correcting for parasitic impedances at high frequencies require the reference resistor to be equal to or larger than the effective resistance of the sample. The effective resistance of the sample could be estimated by noting the current setting of the reference resistor switch and comparing the amplitudes of the signals measured on the oscilloscope. Non-linearity due to the presence of strong brine at low frequencies is balanced by reducing sinusoidal signal amplitude.

An electrode polarization that may occur in low frequency is identified by plotting complex resistivity in Argand plot. The semicircle data represent as a response of the sample and the resistivity data less than characteristic frequency represent as electrode polarizations (Knight and Nur, 1987). Figures 2 is the example of the electrode polarization identification plot. The results of measurement are tabulated in Appendix-B.

2.3 Petrographic Image Analysis

In order to quantify pore space and its geometry, petrographic image analysis is conducted. The thin sections are produced and the images are classified into solid matrix and pore space. Petrographic analyses starts from rock coring, cutting, grinding and preparing thin sections with thickness of 0.03 mm. The samples are then impregnated with blue dyed epoxy. The result of this step includes parameter that quantitatively describes pore space and its shape such as pore radius distribution, aspect ratio, pore angle, circularity and gamma. This result acts as a basis to correlate electrical dispersion with geometry of the pore.

The crucial step to recognize pore space is image segmentation. Image segmentation refers to the task to distinguish the pore space from its matrix on digital images. Traditional segmentation microphotograph is usually preceded by converting the thin image into binary image. This can be facilitated based on the color band in hue-saturation-value (HSV) color space. The technique to classify pore image based on color filtering is used in this step. The weakness of this method exhibits when the image of pore quality saturation is inconsistent or has many impurities such as bubbles or oil artifact. To cope with this particular weakness, it is proposed that the sequences of image processing have to be applied prior to recognizing pore image from the background (Figure 3a-d). Image of the sample is firstly adjusted to correct the contrast and its color level (Figure 3b). Range of blue color is then determined as a filtering criterion. Multiple pore selection with carefully adjusting pore-matrix boundary is the third step. Next, the pore layer is saturated with white color whereas the other layer is saturated with black (Figure 3c). Merging these two layers and threshold are the two last steps of the image converting. Finally, filtering is applied to clean impurities and micro artifact less than 100 pixels (Figure 3d). To calculate pore geometry it is helped by standard image processing package (Image J version 1.41). The results of binary pictures from thin sections are attached in Appendix C.

## 3. Experimental Result and Discussion

3.1 Effect of Pressure

Electrical resistivity decreases very slightly when confining pressure is increased from 1000 psi to 3000 psi for all sandstone and carbonate samples. Dispersion curve of electrical resistivity on those types of rocks exhibits insignificant changes in high water saturation (more than 20%) as shown in Figure 4a-i for sample of sandstones (BR-1, P03) and carbonate (158). The frequency of less than 10 KHz produces the dispersion curve (due to Maxwell-Wagner effect) and could easily be observed in low-water saturation only. Whole of those rocks notice that at more than 10 KHz, where the electrical polarization at fluid-solid more intensively vibrates, the separation is difficult to be identified. Due to pressure, the effect of low resistivity changes reflects a small decrease in pore volume.

Based on the observation, it appears that the imaginary resistivity, compared to the real part, has a more sensitive behavior in responding to confining pressure. The result is tabulated in Table 4 and Figure 5a show the average imaginary resistivity (at 100 Hz) in responding to confining pressure rapidly changes than real resistivity averagely more than 30%. This means that the imaginary resistivity reading has better characterization to pore geometry changes due to confining pressure at low-water saturation. Similar result exposes by Kullenkamp and Schopper (1988) that note imaginary resistivity has more interrelationships with specific surface area. In other word, the real resistivity is more responsible to the bulk volumetric fluid while imaginary due to water-solid interfacing. Figure 5b and 5c also show the same trend where the real part resistivity cannot recognize the pressure effect on the rock. In contrast, the imaginary resistivity is sufficiently sensitive to differentiate pressure changes supplied on the rock.

3.2 Partial Water Saturation Effect

Referring to the experimental result, it is observed that the electrical dispersion relationship to the water saturation might be observed in low water saturation only (Figure 6). When the water fully fills the pore space, the dispersion effect in low saturation is very small. This reflects that bulk fluid volumetric now controls the path of the electrical current. In other word, the dispersion curve reflects water-coating grain or an interlayer effect.

Since the higher water salinity will reduce the thickness of electrical double layer, thus the electrical double layer tends to be less important for water saturation increment. However, because of the lack of saturation density data, it is difficult to judge the exact saturation border. Averagely, the dispersion can be observed for the water saturation less than 20%. The simplest alternative way to evaluate the border can be seen in the plot of dielectric permittivity as tested in sample P03 and P19 (Figure 7). The relatively low variation in dielectric permittivity after certain saturation refers to the pore condition fully covered by water. According to Klein and Swift (1977), the water fluid only does not contribute to the permittivity dispersion in great effect. Thus, the interaction between solid and fluid should be playing a major contribution to the electrical dispersion. The scenario of water saturation and its relationship with electrical dispersion is depicted in Figure 8.

To examine a dynamic fluid process, the sample is proceeded to have partially saturated-unsaturated water fluid. Figure 9 exhibits a plot of resistivity dispersion in saturation-unsaturated process. As the brine water partially leaves the pore space, the resistivity increases notably. However, unsaturated-resistivity is always lower than the other. The presence of irremovable conductive salt-water film coating the solid-grain acts as an agent of electrical current. Thus, although the water leaves most of the pore space, the resistivity may become lower than imbibitions.

The water-solid interfacing behavior is more easily analyzed by looking at the imaginary resistivity. Figure 10a-b shows the plot of real and imaginary resistivity during the drainage-imbibitions in 100 Hz frequency. Before the whole of solid grain is coated by water film, the electrical resistivity decreases un-smoothly (imbibitions). Reducing the water saturation after imbibitions yields the increase (drainage) of the electrical resistivity monotony at every step of pressure. Both drainage and imbibitions path satisfy the power equation.

3.3 Pore Geometry Effect

Polarizability of the inclusion is a function of the electromagnetic properties of its material as well as the inclusion of geometry. This takes into account by depolarization factor that explains how the inclusion polarization is diminished according to the particle's shapes. In term of pore space, the polarization occurs on the boundary of the pore wall. This polarization effectively characterized by its pore radius and water saturation.

A numbers of histogram are produced to quantify the pore geometry they are (see Appendix C):

Pore radius parameter is defined as

(6)

where A is area of particular pore. This definition has the assumption that pore shape is close to the circular. Since the optical microscope can only be resolved more than thin section thickness, in this particular analysis the separation of micropore to macropore is assumed as 30 mm (Anselmetti et.al, 1998).

Gamma parameter is defined as

(7)

where P and A are perimeter and area of the pore respectively. Gamma parameter describes how close the shape of the object approaches that of the circle. This parameter is 1 for a perfect circle and is significantly higher for elongated objects such as cracks and fractures.

Aspect ratio is defined as

(8)

where dmax and dmin are major and minor axes of ellipsoid fitted around the object. These parameters also indicate some aspects of roundness. In contrast to gamma, they clearly distinguish elongated features from star-shaped features, but they produce ambiguities when distinguishing, for example, solid circles from stars.

Circularity is defined as

(9)

This parameter gives a value of 1.0 for perfect circle. If the value approaches 0, it indicates an increasingly elongated or highly complex region. Figure 11 gives the sample histogram results of the rock.

Each of those features is averaged by weighing its individual parameter by the pore size to avoid insignificant number of small pores with specific geometry dominating few larger pores (Anselmetti et.al., 1998):

(10)

Table 5 describes the summary of average features that calculated from the histograms, resistivity dispersion and their transport properties. Resistivity dispersion is defined as the difference between resistivity at characteristic frequency (fc) and at 200 KHz. A characteristic frequency is a frequency border between the electrode polarization and the samples reading.

It appears that parameter of gamma, circularity, pore aspect ratio and pore orientation do not have a good correlation with resistivity dispersion (Figures 12). On the other side, crossplot of resistivity dispersion with pore radius distribution shows a good correlation in positive gradient trendline (Figure 13). It indicates that electrical dispersion is not influenced by the pore shape except the pore size and the electrical polarization occurs at the interface or the boundary between grain and pore fluid. The bigger pore radius causes higher resistivity dispersion. The similar result is shown by Abousrafa et.al (2009) who observes the resistivity and formation factor only affected by pore throat radius. The two outliers point (red diamond) occurs due to high initial saturation level in carbonate cores sample of number 347 and 368. Thus, the fluid saturation prefers to fill in large structure rather than small structure because of the difference of their water surface tension and capillary properties. The relationship of saturation level with resistivity dispersion gives an exponential relationship (Figure 14). The higher the water saturation, the lower the resistivity dispersion will be.

Since the electrical dispersion has a good correlation to the pore radius distribution, we can expect the same result in porosity. Figure 15 shows a good dependency of porosity on the electrical resistivity dispersion occurring at low water saturation. The three point outlier corresponds to the small pore radius (Sample P33) and to relatively high initial water saturation (Sample 347 and 368).

The scenario of water saturation start from the brine water introduces into medium, it begins to make thin layer on the pore wall (Figure 16a). This process continues until the water covers the pore wall and makes thick layer (Figure 16b-c). Most of the pore throats are now covered by water with the air bubbles trapping inside (Figure 16d). Vacuum process is used to suck the air bubbles until the pores completely saturated (Figure 16e). Removing the brine water is initiated from the center of pore space whereas it is the weakness part of water molecule bonding (Figure 16f). The desaturation continues until both sides of pore walls are separated (Figure 16g). The thick water layers now become thinner (Figure 16h-i). At the end of drying, the thin layer is slowly discontinuous and makes water-salt film coats the pore wall (Figure 16j).

Referring to the previous process it can be concluded that the rate of saturation and desaturation depends on its pore size distribution. The larger the pores radius, the longer the time is needed to saturate. When both sides of pore walls are completely covered by fluid, the volumetric conductivity effect will be more dominant than the surface conductivity (see Figure 8).

Because of the dispersion and the surface conductivity have similar analogy to the capacitor, the smaller the pores radius, the easier the dispersion vanishes. The large structure of pore geometry tends to have more dispersion as well as thin pore-water surface and needs more time to fill the whole pore space. On the other way around, a small structure gives less contribution to the electrical dispersion due to the simple saturation process.

Figure 17 presents the pore radius distribution effect on electrical dispersion for sandstone samples (P19, P03, P45 and P33). At the time water saturation achieves less than 15%, the dispersion on small pores of Sample P33 will vanish. The pore radius size of Sample P33 is mostly less than 30 mm, whereas small portion of macropore with maximum pore radius is around 65 mm, which does not seem to give significant contribution to the dispersion unless the saturation could be reduced to less than 10%. Although the macropore has a size bigger than 70 mm or approximately twice bigger than micropore very little, it contributes very significant dispersion. This can be observed in Sample P19, P03 and P45. Furthermore, small pore radii may block the anion because the double layers touch each other, while the ion motion is undisturbed for the larger pore radii. The presence of clay minerals throughout the rock partially blocks ionic solution. Negative charges on clay minerals tend to capture the electrolyte cations and the anion move to the other way. Under the influence of electric field, the cations easily pass the cationic cloud and resulting in the accumulation of ionic charges.

Evaluation on carbonate rocks (347, 368 and 9056) reveal similar trend of resistivity dispersion (Figure 18). When the water saturation achieves 13%, the dispersion of Sample 9056 starts to vanish, whereas for other samples it starts moving out when the water saturation reach more than 17%. The small pores on Sample 9056 have one order higher resistivity than the rest. This may occur due to the electrical path is difficult to pass through the medium.

## 4. Dielectric and Conductivity Model

Model developed here is addressed to modify electro diffusion D-Model of Lima and Sharma (1992) for shaly media. Their model presented for low salinity and did not account partial saturation effect. Electrical double layer (EDL) may present as long as the solid-grain contact with the pore-fluid. Therefore, the model will be developed should be accounted the partial saturation. EDL plays more in low water saturation and on the other way around, the bulk volume conductivity are dominant.

Evaluating Maxwell equations and their constitutive relationship subjected time dependence of harmonic sinusoidal field obtained

(11)

Rewrite the electrical properties of composite conductive minerals having dispersed spherical particles deduced from Wegner's theory as

(12)

whereas f, , , are porosity, total electrical conductivity, fluid and solid grain respectively. Each of conductivities is a complex function.

The present of clay-coated sand grain replacing with

(13)

In this case and refer to solid clay and non-conducting mineral. For most sandstone detrital minerals (Lima and Sharma, 1990); p is volume fraction of clay shell equal to with a and b as the radius of core and of composite sphere; is effective complex conductivity of grain and it is associated with double layer effect. This depends on particle dimension, salinity and surface charge density. The complex conductivity of solid clay is given by

(14)

Y is the complex number given by

(15)

The variable represents relaxation time for the double layer around the charged particle. Evaluation of Equation (14) and (15) in complex notation and due to dielectric properties depend on frequency in power-law at all level of saturation, it is modified the dielectric dependent power-law frequency with exponent of q and get the result as

(16)

where

(17)

(18)

(19)

where q is the constant that depend on level of saturation. Substituting complex notation of conductivity into Equation (13) and represent the result in Wagner's composite model is obtained

(20)

As a result is implied from Garrrouch (2001), approximation can be made to simplify Equation (14) by assuming clay-sand grain permittivity is much greater than the water fluid permittivity () and fluid conductivity () is much greater than clay-sand grain conductivity (). Using those two approximations, the composite clay-sand grain conductivity expressed as

(21)

Separating imaginary and real conductivity by multiplying its denominator with complex conjugate it is obtained

Re (22)

Im (23)

The real result is dedicated for conductivity meanwhile the imaginary part is dielectric permittivity model. Figure 19 displays the previous model and its modification for shaly sandstone reservoir. Figure 20 gives the result of original Lima-Sharma's, modified D-model and experimental data which is tested for sample P03. Exponent of q and C are two constants dependent to water saturation level. These parameters are estimated through curve fitting. Figure 21 provides the comparison between dielectric permittivity data and its estimation with coefficient correlation is 0.96.

The surface conductivity rises when there is a contact between clay mineral with the water. It must be agree the condition which is allowed the surface conductivity vanish when the saturation is increased. Thus, it is proposed a modification of Archie's model to include interfacing properties in calculating effective conductivity as follows:

(24)

where Sw, m, n, N, sq are water saturation, cementation factor, saturation exponent, coated-water volume factor and spherical grain clay-sand conductivity (Equation 22). The coated-water volume factor refers to the amount of the water coated the solid grain. If water saturation is equal to one, the model turns into Archie's formula. Figure 22 presents the effective conductivity as a function of water saturation.

The plotting of effective conductivity to frequency with different water saturation based on Equation (24) appears similar trend with the experimental data as tested in sample P45 (Figure 23). The curve fitting should be made in order to fit with the data to obtain parameter of N. The effect of electrode polarization at low frequency less than characteristic frequency must be removed prior optimization process. The parameter used are p=0.94, d1=1.2x1018/m2, sw=10.03 S/m, ew=6.78x10-10 F/m, D1=0.315x10-8 m2/s, τm=2.315x10-5 s, f=0.254, N=0.0001. Cementation factor (m) is 1.887 for sample containing 10% shale (Catagay et.al, 1994) and saturation exponent (n) is 1.8 for wet shaly sandstone (Abdassah et.al, 1998).

## 5. Conclusion

The pore radius distribution and saturation correlate to electrical resistivity dispersion. The larger structure of pore geometry, the more dispersion will be. It is because the thin pore-water surface need more time to fill the whole pore space. The simple process of saturation in small structure gives small electrical resistivity dispersion. Furthermore, the electrical resistivity dispersion can be a new alternative tool to estimate porosity of the reservoir rock.

The confining pressure effect on resistivity only contributes at low water saturation. The resistivity gives small changes during pressurize reflects that pore geometry relatively undisturbed. To detect pore changes due to pressure it is better to use imaginary resistivity rather than real resistivity.

In high water salinity, electrical dispersion presents only in low water saturation degree and leaves with water saturation increment. It is the condition where the pore wall completely covered by the water. This reflects volumetric conductivity is now more dominant than surface conductivity.

New electrical dispersion for high water salinity has been developed based on modified D-model. The new model of dielectric permittivity may communicate with the prior Lima-Sharma's model. Modification of effective conductivity of Archie's model has been provided to account surface conductivity. The model is dependent on water saturation and frequency.

## 7. Appendices

## Appendix-A

Pressure Test Result

1. Sample P33

2. Sample P19

3. Sample P03

4. Sample P45

5. Sample BR-1

6. Sample 368

7. Sample 158

8. Sample 347

9. Sample 9056

## Appendix-B

Results of Resistivity Measurement

1. Sample P33

2. Sample P19

3. Sample P03

4. Sample P45

5. Sample BR-1

6. Sample 368

7. Sample 158

8. Sample 347

9. Sample 9056

## Appendix-C

Pore Geometries Histogram and Binary Pictures

1. Sample P33

2. Sample P19

3. Sample P03

4. Sample P45

5. Sample BR-1

6. Sample 368

7. Sample 158

8. Sample 347

9. Sample 9056