Determination of Swirr from MICP, Electrical Resistivity Measurements and NMR Logs

Geophysics Department Faculty of Science Ain Shams University

Determination of S ^w

^irr

from MICP, Electrical Resistivity Measurements and NMR Logs

Prepared by

Anas M. ElGendy

Under the Supervision of

Prof. Dr. Add El-Moktader M. El-Sayed

January 26, 2016

Acknowledgment

I cannot express enough thanks to my Supervisor Prof. Dr. Add El-Moktader M. El-Sayed My completion of this project could not have been accomplished without his support.

To my caring, loving, and supportive Mother: my deepest gratitude. Your encouragement when the times got rough are much appreciated and duly noted. My heartfelt thanks.

Content

 Abstract

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¹

 Introduction

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³

 Units

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 C H A P T E R 1 Calculation of Irreducible Water Saturation Swirr from NMR Logs (In Tight Gas Sand) o Preface....……….……….……….…………. o Problems of SwirrCalculation from NMR Logs in Tight Gas Sands...……….……….……….……….……..… o Novel Model of Estimating Swirrfrom NMR Logs……….…………..13

o SDR Model...……….……….……….…..… o Case studies...……….……….……….…….  C H A P T E R 2 Calculation of Irreducible Water Saturation from Capillary Pressure and Electrical Resistivity Measurements o Petrophysical Parameter……….…… o Experimental Tests……….………27

 Porous Plate Method……….………..27

 Impedance Measurements Method………..28

 Description of Electrical Resistivity Measurement Methodology………..……… o Tests Results……….……….………..33

o Discussion………..……….………..36

 Conclusion

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 Reference

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List of Figure

 Fig.1.1 Statistical graph of the T2 cutoff for 36 core samples in tight sandstones.

 ^Fig.1.2 Comparison of the shape of the T2 spectrum for four different conditions.

 ^Fig.1.3 Comparison of the T2 spectra in gas-bearing formations.

 ^Fig.1.4 Relationship between the core porosity and the permeability intight reservoirs in four wells.

 ^Fig.1.5 Relationship between T2lm calculated from field NMR logs and from NMR experimental measurement.

 ^Fig.1.6 Relationship of T2lm obtained from laboratory NMR experimental measurements under two different conditions.

 ^Fig.1.7 Calculation of irreducible water saturation from field NMR logs in tight gas sands and watersaturated layers and the comparison with the core analysis results.

 ^Fig.1.8

o Fig1.8a Comparison cross plots of Swirr, and core analyzed results o Fig1.8b Comparison cross plots of Swirr, Swi_20.75 ms, and core

analyzed results.

o Fig1.8c Comparison cross plots of Swirr, Swi_33 ms and core analyzed results.

 ^Fig.2.1 Typical electrical resistivity trends for non-conductive and saturated mineral rocks as modeled with Equation 2.

 ^Fig.2.2 Schematic of the capillary versus saturation cell (after Core Lab Instruments, 2000).

 ^Fig.2.3 Sketch of the electrical resistivity measurement setup.

 Fig.2.4 Equivalent two-electrode circuit and the effect of blocking electrodes.

 ^Fig.2.5 Effect of electrode polarization on impedance measurement. a) Varying electrode Lgap for constant rock resistivity �_�= 1 Ωm; b) Varying rock resistivity for constant electrode gap Lgap = 10-6 m

 ^{Fig.2.6 _} Effect of type of electrode on the measurement of the impedance on Berea sandstone core specimen 22. a) Al foil electrodes; b) Silver-based paint electrodes. Electrode polarization controls the impedance measurement with the Al foil electrodes.

 ^Fig.2.7 Capillary pressure-brine saturation curves for all eight Berea sandstone core specimens.

 ^Fig.2.8 Pore size distribution for all eight Berea sandstone core specimens.

 ^Fig.2.9 Electrical resistivity versus brine saturation for all eight Berea sandstone core specimens.

 ^Fig.2.10 Capillary pressure and resistivity index versus brine saturation in Berea sandstone core specimens.

 ^Fig.2.11 Capillary pressure and resistivity index versus brine saturation in twelve Quartz (very fine-grained) sandstone core specimens.

 ^Fig.2.12 Capillary pressure and resistivity index versus brine saturation in ten Limestone core specimens.

 ^Fig.2.13 Effect of percolation on the capillary pressure and electrical resistivity measurements.

 ^Fig.2.14 Effect of brine saturation the saturation exponent in Berea sandstone specimens.

 ^Fig.2.15 Effect of brine saturation the saturation exponent in Berea sandstone specimens.

 ^Fig.2.16 Effect of brine saturation the saturation exponent in Berea sandstone specimens.

 ^Fig.2.17 Calculated tortuosity versus degree of saturation in Berea sandstone specimens.

Figures from 1.1 to 1.8 shows the calculation which made by:

Liang Xiao • Zhi-Qiang Mao • Yan Jin

Published online: 3 November 2011_Springer-Verlag 2011

Figures from 2.1 to 2.8 shows the calculation which made by:

A.M. Attia, D. Fratta and Z. Bassiouni

Published online: Wiley Online Library 2008

List of Equations

 Equation.1.1 Timur model; found that rock permeability is proportional to porosity, and inversely proportional to Swirr.

 Equation.1.2 Timur model with respect to the difference of geologic settings in fields or regions.

 Equation.1.3 SDR model; proposed by Schlumberger—Doll Research Center to estimate permeability from NMR logs directly.

 Equation.1.4 Derivative expression of the algebraic transformations in

“Equation.1.3” and substituting it into “Equation.1.2”.

 Equation.1.5 Shows that once the values of C2, m and n have been calibrated by NMR experimental data set, Swirr can be estimated from NMR logs.

 Equation.1.6 The values of C2, m and n in (Eq.1.5) are calibrated and Swirr

calculation equation, with the data set listed in Table 1.

 Equation.2.1 The electrical resistivity of a formation ρ

 Equation.2.2 The effect of surface conductance.

 Equation.2.3 Archie (1942) proposes semi-empirical relationship.

 Equation.2.4 Function of the percolation porosity φ^o that is the minimum porosity that connects the pores in a rock formation.

 Equation.2.5 Archie (1942) expresses the resistivity index IR.

 Equation.2.6 Tiab and Donaldson (1996), Tortuosity Function.

 Equation.2.7 The electrical impedance for the equivalent circuit Zeq.

 Equation.2.8 The theoretical electrical resistivity of the plateau.

List of Tables

 Table.1.1 36 core samples were drilled for NMR experimental measurement in Xujiahe formation.

Form Liang Xiao • Zhi-Qiang Mao • Yan Jin, Paper Published online: 3 November 2011_Springer-Verlag 2011

 Table.2.1 Geometric properties of tested Berea sandstone specimens.

 Table.2.2 Summary of porosity, tortuosity, ionic length, formation resistivity factor, cementation factor, and water saturation exponent for all tested Berea sandstone core specimens (Attia, 2005).

 ^Table.2.3 Summary of porosity, quartz flour content, formation resistivity factor, and water saturation exponents for all tested Quartz sandstone core specimens (after Attia, 2005).

From A.M. Atti, D. Fratta and Z. Bassiouni Paper Published online: Wiley Online Library 2008

Abstract

Irreducible water saturation value is an indication of total volume of oil and water producible from a reservoir. It also influences the production rate from that reservoir. Irreducible water saturation (sometimes called critical water saturation) defines the maximum water saturation that a formation with a given permeability and porosity can retain without producing water. This water, although present, is held in place by capillary forces and will not flow.

Critical water saturations are usually determined through special core analysis.

The critical water value should be compared to the reservoir's in-place water saturation calculated from downhole electric logs. If the in-place water saturation does not exceed the critical value, then the well will produce only hydrocarbons. These saturation comparisons are particularly important in low permeability reservoirs, where critical water saturation can exceed 60% while still producing only hydrocarbons.

It is difficult to calculate irreducible water saturation Swirr from nuclear magnetic resonance (NMR) logs in tight gas sands due to the effect of diffusion relaxation on the NMR T2 spectrum at present. By combining with classical Timur and Schlumberger—Doll Research SDR models, a novel model of calculating Swirr is derived. The advantage of this novel model is that Swirr can be calculated without a T2 cutoff, and all input information can be acquired from NMR logs accurately. With the calibration of 36 core samples, which were drilled from Xujiahe Formation in Bao-jie region of Triassic, Sichuan basin, southwest China, the values of these statistic model parameters are defined. Field examples of tight gas sands show that the proposed model is reliable. The Swirr calculated with the proposed model match well with core

analyzed results both in tight gas formations and water-saturated layers, the absolute error is in the range of ±4%. The calculated results by using 20.75 ms as the T2 cutoff are accurate in water-saturated layers but are overestimated in gas-bearing intervals. Defining 33 ms as the T2 cutoff is unusable both in gas- bearing and water layers.

Irreducible Water Saturation from Capillary Pressure and Electrical Resistivity Measurements, the results of capillary pressure and electrical resistivity measurements for three kinds of core specimens: Berea sandstone, Quartz and Limestone. Experimental data of resistivity index, formation resistivity factor, tortuosity, capillary pressure, and water saturation exponent in the air/brine system for these cores are reported. The electrical resistivities data are evaluated using the modified Archie’s law. Capillary pressure and electrical resistivity versus brine saturation results show the existence of two irreducible water saturations corresponding to two different physical phenomena. The two values of irreducible brine saturations yield upper and lower limits that can be used to estimate the production capacity of po rous media. The detailed analysis of the data has also shown a change in the value of the saturation exponent. This change would be also be observed at the irreducible brine saturation as obtained with capillary pressure data.

Introduction

In the upstream oil and gas industry, new ideas and solutions have been developed as a result of computerization, technology and building on the knowledge of prior discoveries and amassed data, especially with regard to residual oil, irreducible water saturation and the overall process of fluid displacement in porous media. Before the previous century (in the 1800's) injecting water in an oil field was outlawed in the United States. However, subsequent to the success of an accidental water-flood, the industry gradually accepted this technology. In the mid 1900's, the preponderance of evidence indicating the benefits of water-flooding, encouraged petroleum technologists to study the displacement process theoretically and in the laboratory. Detailed laboratory analyses and mathematical derivations were developed to explain and predict the performance of a water-flood. It has been well documented that the immiscible displacement process of oil by water behaves in a non-uniform, channel-like fashion. However, in order to develop mathematical models such as the "Buckley-Leverett Frontal Advance Theory", the concept of an oil bank and flood front were defined. It had been stated by the first generation of water - flood scientists and engineers that such mathematical models are an extreme simplification, and should advancements in computation occur, then more accurate estimates of water-flood performance could be performed3. In addition to the simplifications, assumptions have been made for the purpose of generating "conservative" results. In spite of these simplifications and conservative bias, previous interpretations have resulted in a reasonably accurate solution that represents a first-order or second-order approximation.

The industry is now challenged to producing additional reserves beyond the first and second approximation. In order to do this, simplifications and

conservative practices that have been ingrained in our industry must be refined.

With advances in technology and computerization such approximations no longer are warranted or necessary and in some cases have been misleading. The intrinsic assumptions, as they relate to residual oil, irreducible water saturations and immiscible displacement processes are defined below:

 For a given rock type the irreducible water saturation is considered constant above the "transition zone."

 2Irreducible water saturation is considered the lowest water saturation measured from a core sample using centrifuge or core- flood techniques.

Many permeability calculation models based on log analysis require knowledge of the irreducible water saturation. In a reservoir at initial conditions, above the water contact, the irreducible saturation is equal to the actual or initial saturation, as found from conventional water saturation calculations. However in transition zones, water zones, and depleted zones, irreducible is less than the actual saturation. So we need to find irreducible saturation in these zones some other way.

Swirr is equivalent to the minimum water saturation found from capillary pressure curves determined from special core analysis. Typical capillary pressure curve relationships are shown below.

Oil production based on reserves in place in the Ashtart oilfield required the precise knowledge of the main reservoir parameters including porosity, permeability and irreducible water saturation. The reservoir series is comprised of Nummulitid but heterogeneous limestones of the El Garia Formation, the petrofacies texture, geometry and petrophysical parameters of which were

apprehended using seismic profiles; gamma-ray and sonic lateral logs, as well as cores and cuttings taken in drillwells. The evaluation of residual oil saturation, multiphase flow and oil production techniques from the Ashtart reservoir also depend on variations and zoning of the irreducible water saturation. Estimation of the initial water saturation and hence variations in the capillary pressure in the reservoir, required compilations of porosity data measured on cores, supplemented by additional but computed porosities based on acoustic log diagrams. Furthermore, Gamma Ray, Sonic log, and well to well correlations tied to core results and well cuttings, help recognize the layered lithologies within the El Garia flat lying but stratified, Ypresian in origin reservoir rocks. Abundant permeability and porosity values compiled in the light of seismic sequence and Gamma Ray and Sonic log details, were integrated in an empirical approach using the Leverett J function, to model the irreducible water saturation depending on the capillary pressure distribution in the whole reservoir. Variations of this principal hydraulic parameter in a wide range (Swirr: 12 to 40%) compared to the preceding lithostratigraphic, petrographical and petrophysical results help recognize four main rock pore types in the commercial Ashtart reservoir. These vary from (a zone with a rock pore type showing an irreducible water saturation as low as 12%, and a fairly good reservoir character in the lower third part of the lithologic column which is thought to channelize a multiphase fluid flow in the global oilfield, to those zones built-up of rock pore types with higher initial water saturation amounts which in certain cases tend to indicate zones of degraded reservoir. Our study suggests that diagenesis prevalently controls porosity, due to operative dissolutions of the Nummulitid tests/bioclasts, and cementation; moreover, diagenesis exerts effects on permeability by interconnecting intergranular and intratest pore spaces. In contrast, microfracturing enhances permeability of the

reservoir. This is notably the case in the fairly permeable central zone in the Ashtart reservoir with excellent petrophysical parameters, but which were found to degrade gradually towards its peripheries.

Capillary pressure is an important property used in the evaluation of pore fluid distributions, particularly in the transition zone between wetting and non- wetting phases (water to oil or gas in reservoir formations). This property is important in the evaluation of oil recovery processes. Also it can be used either to calculate oil reserves or to simulate reservoir behavior using computer modeling techniques. The capillary pressure curves also provide data on the irreducible water saturation of a reservoir rock and the entry pressure of the reservoir rock. Capillary pressure curves are difficult to measure in the field.

However, some of the parameters controlling the development of capillary pressure curves may be evaluated from electrical resistivity measurements.

Therefore geophysical techniques can be used to estimate the electrical resistivity and the needed petrophysical properties related to wettability, interfacial tension, fluid saturation history, pore size distribution and pore geometry. This paper presents experimental results obtained from porous plate and two electrode resistivity measurements. The electrical resistivities versus brine saturation data for all cores are evaluated using the modified Archie’s law.

The results of cementation factor, saturation exponent and tortuosity are related to the capillary pressure and electrical resistivity measurements.

C H A P T E R 1

Calculation of Irreducible Water Saturation Sw^irr from NMR Logs in Tight Gas Sand

1 Preface

Tight gas reservoirs always display characteristics of micropore body, small pore throat radius and poor pore connectivity. The proportion of micropore space is large, which leads to irreducible water saturation Swirr being higher than that of conventional formations, thus resulting in low resistivity contrast between gasbearing formations and water-saturated intervals. It is difficult to distinguish tight gas formations from water-saturated layers. To improve the reliability of tight gas reservoirs evaluation, it is necessary to obtain information on Swirr and nuclear magnetic resonance (NMR) logs have a unique advantage in this aspect. Although Swirr can be calculated from NMR T2 distribution after a T2 cutoff is defined in conventional reservoirs, it is of great difficulty to calculate Swirr from NMR logs even if the T2 cutoff has been obtained in low-permeability oil-bearing formations and tight gas sands. NMR T2 spectrum is distorted due to the contribution of bulk relaxation of light oil and diffuse relaxation of natural gas. In gas-bearing intervals, the T2 spectrum of natural gas is overlapped with that of irreducible water. Parts of the T2 spectrum of natural gas are considered to be that of irreducible water and the calculated Swirr from NMR logs will be overestimated. To remove the effect of bulk relaxation of light oil and diffuse relaxation of natural gas on the NMR T2

distribution, the best way is to estimate Swirr from NMR logs without a T2 cutoff. In

this study, by means of transforming Timur and Schlumberger—Doll Research (SDR) models, a novel model of calculating Swirr from NMR logs is derived.

2 Problems of Swirr Calculation from NMR Logs in Tight Gas Sands

The common method of calculating Swirr from NMR logs is to define a T2 cutoff, which segregates NMR T2 distribution into two volumes. Swirr is defined as the ratio of the accumulation of T2 distribution for T2 relaxation time being lower than T2

cutoff to the sum area of T2 distribution.

2.1 Problems of Calculating Swirr from NMR Logs by Using a Defined T2 Cutoff In practical applications, there are two problems of calculating Swirr by using a T2

cutoff:

1 An appropriate T2 cutoff determination is difficult, and there is not an optimum method to acquire T2 cutoff from NMR T2 distribution at present. A default T2 cutoff of 33 ms has been proposed for clastic reservoirs and 92 ms for carbonate reservoirs.

However, in practical applications, defining 33 ms as a T2 cutoff is not always accurate in clastic reservoirs, especially, in tight gas sands.(Fig.1.1) shows the statistical graph of the T2 cutoff from 36 core plugs, which were drilled from tight gas sands in Xujiahe formation in Bao-jie region of Triassic, Sichuan basin, southwest China. It illustrates that the statistic T2 cutoff for NMR experimental data set is not 33 ms or other fixed value but is lower than 33 ms, the main distribution ranges from 17 to 24 ms, the weighted average is 20.75 ms.

3~10 10~17 17~24 24~31 31~38 38~45 45~52 >52 T2 cutoff (ms)

Figur.1.1 _ Statistical graph of the T2 cutoff for 36 core samples in tight sandstones

2 Swirr cannot be estimated in field formation evaluation even if the value of T2

cutoff has be obtained accurately from core samples because the core data set is obtained from laboratory NMR measurements with fully water saturation.

For tight hydrocarbon sands, if the pore space is occupied by light oil or natural gas, the shape of the T2 spectrum will be distorted due to the contribution of bulk relaxation of light oil and diffusion relaxation of natural gas.

2.2 Effects of Hydrocarbon on the NMR T2 Spectrum

To illustrate the effect of bulk relaxation of hydrocarbon on the NMR T2 spectrum, kerosene and transformer oil were selected to simulate different viscosity oil, 11 sandstone plug samples were chosen for NMR experimental measurement under

% 0 10 % 20 % 30 % 40 % 50 %

four saturated conditions: fully saturated with water, irreducible water saturation (the pore volume contains irreducible water and air through centrifuge), hydrocarbon- bearing condition (the pore space consists of irreducible water and hydrocarbon by kerosene or transformer oil drainage) and residual oil saturation from the drainage of the samples at hydrocarbon-bearing conditions with brine. Residual oil condition was used to simulate the flushed zone of hydrocarbon formation in field NMR logs.

The comparison of NMR T2 distribution for two core samples is displayed in Figure.1.2, Figure.1.2a shows the comparison of T2 distribution under four conditions for conventional core samples, with the transformer oil used. Fig. 2b is for low-permeability sandstone core samples with the same condition as in Fig. 2a, with kerosene used as the oil. The black dotted lines in these two figures are the trough of bimodal NMR T2 distribution with residual oil saturation, which is always considered to be T2 cutoff in field NMR logs, and the black solid lines mean T2 cutoff acquired from laboratory NMR measurements under fully water-saturated condition.

Figur.1.2 _ Comparison of the shape of the T2 spectrum for four different conditions: 1- irreducible water saturation; 2-fully brine-saturated; 3-residual oil saturation; 4-oil-bearing condition; 5-bulk relaxation of transformer oil; 6-bulk relaxation of kerosene.

As shown in Figure.1.2a two core samples have the same porosity, whereas permeability of the core sample shown in Figure.1.2a is higher. Figure.1.2b illustrates that for core plug with conventional porosity and permeability, when the pore space is occupied by transformer oil, the NMR T2 spectrum under residual oil- saturated condition will be distorted only a little, because for rocks with good pore structure, the T2 distribution with fully water saturation is wide, and the T2 spectrum reflecting the bulk relaxation of transformer oil overlaps with that of movable water.

The T2 cutoff acquired from above two different conditions is almost the same. It can be concluded that the T2 cutoff acquired from laboratory NMR measurements with fully water-saturated condition can be used in field reservoir evaluation directly for conventional rocks or formations. However, for a low-permeability sandstone core sample Figure.1.2b, the T2 spectrum is narrow, when the pore space is occupied by non-wetting phase kerosene, the T2 distribution with residual oil saturation will be wider than that with fully water saturation, and the NMR spectrum with long T2

relaxation time reflects the bulk relaxation of kerosene. T2 cutoffs obtained from these two different saturated conditions are discrepant. If the T2 cutoff obtained from fully water-saturated laboratory NMR measurements is used for formation evaluation directly, the Swirr calculated from field NMR logs will deviate.

2.3 Effects of Natural Gas on the Field NMR T2 Spectrum

Figure.1.2b has demonstrated that calculating Swirr from field NMR logs by using a T2 cutoff, which is acquired from NMR experimental measurement, is improper in low-permeability sands. The T2 cutoff is also usable in tight gas sands because of the effect of diffusion relaxation of natural gas. At present, core NMR experimental

Figure.1.3 _Comparison of the T2

spectra in gas-bearing formations. The indication by and is the same as in

Figure.1.2b Field NMR T2 spectrum in gas-bearing intervals corresponding to the same depth of the core sample

measurements under the gas-bearing condition cannot be carried out due to the limitation of experimental apparatus. To illustrate the effect of natural gas on the NMR T2 spectrum, the comparison of NMR T2 distribution obtained from experimental measurement and from field NMR logs is displayed in Fig. 3. Figure 3 illustrates that when the pore space is occupied by natural gas, the morphology of the T2 spectrum is distorted. The T2 spectrum moves to the left, and the signal of natural gas overlays with that of irreducible water, which makes the amplitude of the left peak increase and that of the right peak decrease. If the T2 cutoff acquired from the NMR experimental data set is used for Swirr calculation directly, the Swirr will be overestimated. To estimate Swirr in tight gas sands accurately, the best way is to propose a novel model to calculate Swirr from NMR logs without T2 cutoff.

3. Novel Model of Estimating Swirr from NMR Logs

3.1 Timur Model

Based on the analysis of 155 core samples originated from three different types of fields in North America, Timur found that rock permeability is proportional to porosity, and inversely proportional to Swirr, that is to say, for rocks with high porosity and low Swirr, which will contain high permeability, vice versa. Based on the regression statistics, Timur established a relationship of connecting permeability with porosity and Swirr. It was named as Timur model and expressed as follows

^Eq.1.1

Where; K is the rock permeability in units of 10^-3 lm², u is the rock porosity, and Swirr is the irreducible water saturation, their units being fractions.

In Timur model, the rock permeability can be estimated once the values of u and Swirr have been defined. On the contrary, Swirr can be derived with the values of K and u.

Meanwhile, in the view of the difference of geologic settings in fields or regions, Timur thought the relationship among rock porosity, permeability and Swirr should be different. The differences among them could be displayed by different values of parameters in Timur model. A common formula was written as

Eq.2.2

Where; a, b and c are statistic model parameters. For different kinds of fields or formations, different values will be defined to acquire permeability from porosity and Swirr, their values should be calibrated by core samples.

Figure.1.2 displays the relationship among rock porosity, permeability and Swirr. After the values of a, b and c have been calibrated, Swirr can be calculated once the input parameters of porosity and permeability are acquired. Porosity can be estimated by integrating NMR with conventional logs. The calculation of permeability is a challenge in tight gas sands due to the generally poor correlation between porosity and permeability Figure.1.4. To obtain accurate Swirr, Eq.1.2 should be transformed to avoid requiring permeability but to obtain information from NMR logs.

Fig.1.4 _Relationship between the core porosity and the permeability in tight reservoirs in four wells

X2_well A X2_well B X2_well C X2_well D X4_well B X4_well C X4_well D X6_well B X6_well D

3 SDR Model

An SDR model has been proposed by Schlumberger—Doll Research Center to estimate permeability from NMR logs directly and is written as

Eq.1.3

Where; T2lm is the logarithmic mean of the NMR T2 spectrum in ms, C1, m1 and n1

are the statistical model parameters that can be acquired from core samples experimental results.

Carrying out some algebraic transformations in Eq.1.3 and substituting it into Eq.1.2, a derivative expression can be written as following:

Eq.1.4

Where; all the variables are the same meaning as in Eq.2, 3. Once the parameters are defined as following:

(Eq.1.4) can be rewritten as:

Eq.1.5

(Eq.1.5) shows that once the values of C2, m and n have been calibrated by NMR experimental data set, Swirr can be estimated from NMR logs.

4 Case studies

With the model proposed above, the gas-bearing interval and water-saturated layer in a well with field NMR logs in Xujiahe formation are processed. 36 core samples were drilled for NMR experimental measurement in this region, the NMR experiment data set being listed in Tabel.1.1.

With the data set listed in Table 1, the values of C2, m and n in Eq. (5) are calibrated and Swirr calculation equation can be expressed as Eq.1.6.

^Eq.1.6

In Eq.1.6, the value of m is -0.08326, and n is calibrated as 0.24518.

Eq.1.6 demonstrates that there is a good correlation between Swirr, porosity and T2lm. By using this relationship, accurate Swirr can be obtained from field NMR logs once the input parameters of u and T2lm are obtained precisely.

In practical applications, porosity can be estimated precisely in tight gas sands by integrating NMR with conventional logs, whereas T2lm could be decreased in gas- bearing formations because of the effect of diffusion relaxation. Eq.1.6 is calibrated by using fully water-saturated core experimental measurements. In order to extend this model to field applications, T2lm should be corrected. To obtain accurate T2lm in Eq.1.6, a relationship is established to correct field NMR T2lm to laboratory simulation condition, as is shown in Eq.1.6.

Table. 1 36 core samples were drilled for NMR experimental measurement in Xujiahe formation

Table.1.1 _ 36 core samples were drilled for NMR experimental measurement in Xujiahe formation

Figure.1.5 _ Relationship between T2lm calculated from field NMR logs and from NMR experimental measurement

Figure.1.5 displays a good relationship of T2lm under two conditions. This correlation is caused by the internal relations of three types of relaxation mechanis ms, which are bulk relaxation, surface relaxation and diffusion relaxation. The experimental results of 11 core samples mentioned above can be used to verify this correlation further (Eq.1.6).

Figure.1.7 shows a field example of calculating Swirr from field NMR logs by using the model proposed in this study. Track (e) in Fig. 7 is the comparison of T2lm calibrated from field NMR logs by using the relationship displayed in (Fig.1.5)

(T2lm) and analyzed from core samples (core_T2lm). Track (f) in (Fig.1.7) displays the comparison of the reservoir porosity calculated by integrating the interval transit time with NMR logs (total_porosity) and acquired from core plugs (core_porosity).

Ch.1 Fig.6 _Relationship of T2lm obtained from laboratory NMR experimental measurements under two different conditions.

Preferable consistency in these two tracks demonstrates the accuracy of the used input parameters in (Eq.1.6). Track (g) in (Fig.1.7) displays the comparison of Swirr

derived by three different methods, with Swirr calculated by using the proposed model in this study, Swi_20.75 ms calculated by using 20.75 as a T2 cutoff and Core Swirr analyzing irreducible water saturation from core samples. The drill stem testing

data displayed in the right of Fig.1.7 illustrates that Swirr matches very well with that of core samples (core_ Swirr) in gas-bearing formation, whereas the irreducible water saturation calculated by using 20.75 ms as a T2 cutoff is higher. Track (h) in (Fig.1.7) compares Swirr estimated from the proposed model with that alculated by using 33 ms as a T2 cutoff (Swi_33 ms), and the result demonstrates that the latter is not reliable. These two comparisons mean that the T2 cutoff obtained from laboratory NMR measurements with full water saturation is inapplicable in gas-bearing formations. In water-saturated

Figure.1.7 _Calculation of irreducible water saturation from field NMR logs in tight gas sands and water saturated layers and the comparison with the core analysis results .

Fig.1.8a

Fig.1.8b

Fig.1.8c

Figure 1.8 Comparison cross plots of Swirr, Swi_20.75 ms, Swi_33 ms and core analyzed results (core_Swirr) for 36 core sample layers, Swirr calculated from the proposed model and by using 20.75 ms as a T2 cutoff almost overlap with each other.

They all match well with the core analyzed results, whereas Swirr calculated by using 33 ms as a T2 cutoff is still overestimated. This is because the formation condition is similar to the experimental simulation condition and T2 cutoff can be used in water- bearing formations directly. The derived method is applicative not only in gas - bearing formations but also in water-saturated layers.

Figure 1.7 displays the comparison cross plots of Swirr, Swi_20.75 ms, Swi_33 ms and core analyzed irreducible water saturation. Figure 8a illustrates that the majority of calculated Swirr is close to core_ Swi, and the absolute errors between them are lower than 4%, which meets the requirements of tight gas sands evaluation. However, the calculated irreducible water saturations by using 20.75 and 33 ms as the T2 cutoff are all overestimated (Fig.8b, c).

C H A P T E R 2

Calculation of Irreducible Water Saturation from Capillary Pressure and Electrical Resistivity Measurement

1 Petrophysical Parameter

Petrophysical parameters relate different types of flows: hydraulic, electrical, thermal, chemical, etc. As all types of flows follow similar laws, the parameter that may control one usually controls another (Wang and Anderson, 1992; Mitchell, 1993; Santamarina and Fratta, 2003). For these reasons, geophysical techniques that measure properties related to electrical flow are successfully used to evaluate hydraulic flow parameters. However, the interpretation of the results may be misleading as there are inherent physical differences on the different types of flows and these discrepancies cannot be ignored. Conduction of electricity through porous media occurs by mainly two mechanisms: movement of ions through the bulk saturating electrolyte and by surface conduction of clay minerals. In the case of porous media with coarse grains, tube-like porous and percolating phases, the electrical resistivity of a formation ρf can be modeled as:

Eq.2.1

Where; ρmineral is the resistivity of the rock mineral, ρpore liquid is the electrical resistivity of the pore fluid, ρ^pore gas is the resistivity of the pore gas, φ is the porosity.

Sr is the degree of pore liquid saturation. In most oil-bearing formation rocks, the rock mineral and pore gas are insulators.

One of the drawbacks of this formulation is that Equation1 fails to model the surface conduction in a formation. The effect of surface conductance in a formation can be estimated by adding a surface conduction term to ch.2 eq.1 (Klein and Santamarina, 2003; Santamarina et al., 2001). Then, the resistivity of the formation becomes:

‘

Eq.2.2

Where; Θ is the surface conduction, γmin is the mineral unit weight, is the acceleration of gravity, and Ss is the specific surface of the formation mineral. Figure 1 shows the effect of porosity and surface conduction on different saturated rock formations. This figure is based in (Eq.2.2), which in spite of its limitations yields boundaries to the evaluation of the different parameters. The proper interpretation of this figure provides a solid base for the analysis of geophysical studies. Furthermore, the electrical resistivity of a porous medium is also related to the micro-structural properties, including porosity, pore geometry and surface morphology of the mineral grains lining the pores. Archie (1942) proposes the following semi-empirical relationship:

Eq.2.3

Where; a, m, and nare experimental determined factors. The factor a varies between 0.5 and 2.5. The factor m is also known as the cementation factor and it varies between 1.3 and 2.5 for most rocks. The cementation factor is 1.3 for unconsolidated, clean glass beads, 2 for sandstone formation, and around 5 for carbonates (Telford et al., 1990; Mavko et al., 1998).

Fig.2.1 _ Typical electrical resistivity trends for non-conductive and saturated mineral rocks as modeled with Equation 2 (surface conduction Θ = 1.4⋅10-9 S).

The factor n is known as the water saturation exponent and it has been related to several petrophysical parameters. Typically, its value is around 2 in water-wet formations and it is assumed constant for clean, sandy like formations (Archie, 1942;

Mavko et al., 1998). Lewis et al. (1988), Longeron et al. (1989a, b), Donaldson and Siddiqui (1989), and Moss et al. (2000) found that the saturation exponent n increases to values as high as ten in oil wet formations. Furthermore, Diederix (1982), Anderson (1986), Longeron et al. (1989a, b), and Worthington and Pallat (1992)

found that the saturation exponent is not always constant over the whole saturation range in disagreement with the early work by Archie (1942). The formation resistivity factor FR, is the ratio between the resistivity, ρo, of the rock at 100%

saturated with conducting brine to the resistivity ρ^pore liquid of this brine. This ratio depends on the lithological characteristics of the rock formation and the effective porosity. The formation resistivity factor is sometimes expressed as function of the percolation porosity φ^o that is the minimum porosity that connects the pores in a rock formation:

Eq.2.4

The resistivity index IR is expressed by Archie (1942) as:

Eq.2.5

Swanson (1985) found that the resistivity-saturation plot shows a change in the slope at a saturation point where the corresponding capillary pressure curve indicate a transition from macroporosity to microporosity. Finally, tortuosity is defined as the ratio of the ionic path Li over the distance between the Electrodes �_�. Alternatively, according to Tiab and Donaldson (1996), tortuosity is defined as:

Where �_��� and � _{ℎ� �} are porosities that correspond to the porosity of the trapped fluid that does not contribute to electrical conduction and to the porosity of the fluid that contributes to the conduction. In addition, Attia (2005) found that the tortuosity factor is affected by porosity, cementation factor and degree of brine saturation.

2 Experimental Tests

Here I want to presents petrophysical properties of eight Berea sandstone, twelve Quartz and ten Limestone rock specimens. The experimental results were obtained using 5% NaCl brine solutions. The petrophysical properties of the specimens are tabulated in Tables 1 through 4. During the experimental testing program the following petrophysical parameters were determined for each specimen: pore size distribution, saturation versus capillary pressure curves, and electrical resistivity versus saturation curves. These data are obtained using two measurement techniques: – porous plate – impedance measurement methods. These two methodologies permit the evaluation of process of de-saturation of rock cores and the behavior of the water saturation exponent n. The description of testing procedure is as follows.

2.1 Porous Plate Method

The porous plate method was used to measure the capillary pressure-saturation curves for different types of core specimens (Berea sandstone, Quartz and

Limestone) with 5% NaCl brine solution. The procedure has several steps, including:

– Porous plate saturation: the procedure indicated in the manual “Soil Moisture Capillary Pressure Cell” manual (Core Lab Instruments, 2000) is used to fully saturate the porous stone saturation.

– Core specimen preparation: the core specimens are measured, cleaned, dried, weighed, and saturated with the NaCl brine solution. After the saturation process is completed the core specimens are re-weighed to determine the porosity-φ (Table1).

– Testing procedure: with the core specimen placed on top of the porous plate, the air-brine capillary pressure procedure is ready to begin (Fig.2.2). A certain air pressure pa is applied to the top of the core specimen and the water within the core specimen is allowed to drain through the porous stone. The capillary pressure pc is equal to the difference between the air pressure and the water pressure. When equilibrium is achieved, the air pressure and the top of the cell are removed. Then the core specimen is weighed and the degree saturation is calculated at the applied capillary pressure Pc. The specimen is returned to the cell and the procedure is repeated for higher values of the capillary pressure Pc. The capillary pressure versus saturation curve is obtained and then used to estimate the pore size distribution.

2.2 Impedance Measurements Method

An impedance analyzer Hewlett Packard 4279A LCZ meter is used to measure the electrical resistivity of the Berea sandstone (Berea as example) ore specimens

Fig.2.2 _ Schematic of the capillary versus saturation cell (after Core Lab Instruments, 2000).

under varying degrees of brine saturation. The LCZ meter is capable of measuring inductance, capacitance, dissipation, quality factor, impedance magnitude, and phase angle in equivalent parallel and series circuits (Hewlett Packard, 1984). These measurements cover a frequency range from 100 Hz to 20 kHz. The HP 4297A model is controlled by a personal computer via an HP-IB card and the Agilent VEE Pro software. The card and the software allow the digitalization of the data for the analysis and interpretation of the measurement results. Fig.2.3 presents a sketch of the testing setup, measurement system, and data collection system. The measurements include impedance magnitude and phase angle from 100 Hz to 20 kHz in steps of 100 Hz. The impedance analyzer is equipped with four coaxial BNC connectors and with an HP 16047A Test Feature. This feature combines the high and low voltage and current terminals and permits two terminal measurements of the electrical properties of the specimens. The two-terminal measurement method is a simple procedure to implement, however it has some drawbacks over competitive methods (i.e., four-electrode method – see for example Santamarina et al., 2001).

One of the biggest drawbacks is the problem of electrode polarization. This

phenomenon is explained next. The measurement of the electrical resistivity of rock specimens involves the analysis of an equivalent electrical circuit where the rock core specimen is in series with the electrodes and the required peripheral electronics.

The rock electrode interface feels the movement of ions on the rock specimen, and the movement of electrons on the electronic circuit. At the interface, where the use blocking electrodes is common (i.e., electrodes that do not experience oxidationreduction), ions accumulate at the interface causing electrode polarization.

The phenomenon of electrode polarization may be modeled by adding a thin air-gap Lgap at the interface between the electrode and the rock (Klein and Santamarina, 1997). Consider a parallel plate capacitor with a specimen of thickness LR and cross sectional area A (Fig.2.4) The rock can be represented as a resistor and a capacitor in parallel, with effective electric resistivity ρR (Ωm) and dielectric permittivity εR

(F/m). Then, the electrical impedance for the equivalent circuit Zeq is:

Eq.2.7

Where Cgap= ε^oA/Lgap is the capacitance at the blocking electrode _� = �_��_�/�, and �_� = ε_��/�_� are the resistance and capacitance of the core specimen, and A is the cross sectional area of the capacitor. The results presented in Figure 5 show that

Fig.2.3 _ Sketch of the electrical resistivity measurement setup.

Fig.2.4 _ Equivalent two-electrode

circuit and the effect of blocking electrodes.

Fig.2.5 _Effect of electrode polarization on impedance measurement. a) Varying electrode Lgap for constant rock resistivity �_�= 1 Ωm; b) Varying rock resistivity for constant electrode gap Lgap

= 10-6 m (�_�= 0.0285 m, A= 6.4⋅10-4 m, � = 8.85⋅10-12 F/m and �_� = 20� ).

the effects of electrode polarization become negligible with smaller separation gap Lgap (Fig.2.5a) and that the transition frequency is smaller with the greater rock resistivity �_� (Fig.2.5a – Santamarina et al., 2001). Therefore, electrode polarization effects are not expected in high-frequency laboratory measurements.

However, due to specifications of the HP Impedance Analyzer, the range of measurement extend the low frequency range, where electrode polarization dominates the impedance measurement unless the deportation gap Lgap is very small or the resistivity of the measured material is high. Two different types of electrodes are used in these measurements: Al foil and silver-based paint. The Al foil may act as a blocking electrode if low rate of chemical reaction occurs. However the problem with the Al foil electrodes is that separation gap Lgap is about the same order of magnitude as the sandstone grain size (D50 ≈0.1 mm) and this separation gap may change for different specimen and the applied normal pressure. The silver paint electrodes have been used in the past (see for example Longeron et al., 1989a). The advantage of this type of electrodes is that they reduce the separation gap.

Furthermore, the gap remains constant throughout the testing series and it does not depend on the normal pressure. Figure 6 shows the measured impedance on Berea sandstone core specimen 22 using the Al foil electrodes and silver-based paint for different saturation Sr. It is clear that the Al foil electrode measurements are controlled by the effect of electrode polarization (Fig.2.6a) while the silver-based paint electrode measurement removes most of the effect of electrode polarization in the impedance response (Fig.2.6b). Furthermore, the transition frequency is smaller when the resistivity of the specimen is greater, as observed by comparing side-by- side the two set of results. In light of these observations the silver-based paint electrodes are selected for the electrical resistivity measurements.

2.3 Description of Electrical Resistivity Measurement Methodology

The core specimens are cleaned, dried in the oven, painted on each side, evacuated, and then saturated with 5% NaCl brine solution (ρpore liquid = 0.161 Ωm) by applying vacuum for 12 hours to the submerged specimens. The specimens are then removed and their surfaces are dried with tissue paper. This action renders the specimen saturated-surface dry. Then the specimens are weighed to determine the degree of saturation and placed in the cell to measure the impedance. After each measurement, the specimen is placed in a covered container to stabilize its moisture content till the next set of measurement. This technique reduces the instability of the capillary pressure when the measurements are taken.

3 Tests Results

A set of different petrophysical properties are collected including capillary pressure curves (Fig.2.7), pore size distribution (Fig.2.8), and electrical resistivity versus degree of saturation (Fig. 9) for eight Berea sandstone core specimens. Figure 7 shows that all specimens have similar capillary pressure saturation curves except for the Berea sandstone core specimen 21. All the other core specimens show that the irreducible water saturation is nearly 0.33, while specimen 21 shows it to be 0.23.

This specimen is also the only one that shows no layering (Tabel.2.1). Furthermore, the pore size distribution also shows a marked difference in the characteristics of specimen 21 (Fig.2.8). The average parameters for the Berea sandstone, Quartz (very fine grained) and Limestone specimens are summarized in Tables 2, 3 and 4 respectively.

Fig.2.6 _ Effect of type of electrode on the measurement of the impedance on Berea sandstone core specimen 22. a) Al foil electrodes; b) Silver-based paint electrodes. Electrode polarization controls the impedance measurement with the Al foil electrodes.

Fig.2.7 _ Capillary pressure-brine saturation curves for all eight Berea sandstone core specimens

Table.2.2 _ Summary of porosity, tortuosity, ionic length, formation resistivity factor, cementation factor, and water saturation exponent for all tested Berea sandstone core specimens (Attia, 2005)

Table.2.3 _ Summary of porosity, quartz flour content, formation resistivity factor, and water saturation exponents for all tested Quartz sandstone core specimens (after Attia, 2005)

Table.2.3 Summary of porosity, tortuosity factor, formation resistivity factor, and water saturation exponents for all tested Limestone core specimens

Ch.2 Table.4 _ Summary of porosity, tortuosity factor, formation resistivity factor, and water saturation exponents for all tested Limestone core specimens

4 Discussion

The electrical resistivity and capillary pressure curves for the Berea sandstone, Quartz, and Limestone cores show similar behavior: as the brine saturation decreases, the values of the petrophysical parameters increase. However, the point of irreducible brine saturation in the capillary pressure curve differs from the point where there is a break in the electrical conductivity path. This difference is due to the different nature of the two processes. The capillary pressure versus saturation curve is obtained by applying gas pressure to the brine phase until the air percolates through the porous matrix. This percolation point is the irreducible brine saturation.

It is “irreducible” only in the sense that the air pressure cannot “push” the brine out beyond this point. Nevertheless, at the irreducible brine saturation point, the electrolyte paths are still active and there are no sudden changes in the electrical conduction behavior. The change in the electrical conduction only occurs at a lower degree of saturation, when the conduction paths are broken and the resistivity rapidly increases. The observations presented in Figures 10 through 12 can be clearly explained with the help of Figure 13. This figure shows the process of evacuation (drying) using the porous stone method. As the capillary pressure (air pressure) increases, it pushes the brine out of the porous medium decreasing the saturation and increasing the electrical resistivity of the medium (Figs.2.13a-c). This process continues until the air paths between the top and bottom of the specimen are continuous (Fig. 13d). At this point, the irreducible water saturation in the “capillary pressure sense” is reached. A further increase in the capillary pressure cannot remove anymore brine and the electrical resistivity should remain constant (Fig. 13e).

However, if the medium is allowed to dry due to evaporation the electrical resistivity would still slowly increase because the ionic paths will be strangled as the brine saturation decreases. This process continues until all the ionic paths are broken and

electrical resistivity reaches its final plateau. From Equation 2.1, the theoretical electrical resistivity of the plateau is approximately equal to:

Eq.2.8

The irreducible brine saturation obtained with either method cannot be directly used to evaluate the production potential of a reservoir. They can only be considered as upper and lower limits of the irreducible brine saturation. These two measured levels of brine saturation yield an indication of the percolation phenomena. The true value of the irreducible water saturation will depend on the production method and the affinity of the mineral to the fluid. One common parameter used in the evaluation of the production potential of a formation is the saturation exponent. The saturation exponent in the measured core specimens is not constant for different degree of saturations as indicated by Archie (1942) even for clean Berea sandstone (Anderson, 1986). Figures 14a, 15a and 16a show that average saturation coefficient changes from 1.60 to 2.70, 2.00 to 3.50 and 2.09 to 3.84 for Berea sandstone, Quartz, and Limestone core specimens respectively, when the degree of saturation drops below a certain value. The break in the slope of log(IR) versus log(Sr) occurs at the point that coincides with the capillary pressure-based irreducible brine saturation (see Figs.

14b, 15b and 16b) and it does help in the evaluation of the electrical resistivity-based irreducible saturation that provides the higher bound in the production potential of the formation.

Fig.2.8 _ Pore size distribution for all eight Berea sandstone core specimens.

Fig.2.9 _ Electrical resistivity versus brine

saturation for all eight Berea sandstone core

specimens.

The change in slope seems to indicate the beginning of the process that produces the rupture of electrolyte paths in the porous media. At degrees of saturation higher than the point of sudden change in the saturation exponent, the increase of electrical resistivity seems to occurs only due to the decrease in the cross sectional area of continuous electrolyte paths. Then a change in the behavior seems to occur at the point of capillary pressure-based irreducible brine saturation where the brine phase still percolates at a minimum through the surface of the porous. At this point the isolating non-wetting phase zone starts to become dominant over the conductive wetting phase.

Finally, the evaluation of tortuosity versus brine saturation is presented in Figure 17. The tortuosity is here calculated by modifying Equation 6 to include the effect of saturation:

Eq.2.9

where _��� is the irreducible water in the electrical resistivity sense. This new equation assumes that the trapped porosity does not contribute to the electrical conductivity and the tortuosity reaches infinite value when all the brine in the channel is removed (Fig.2.17a). The normal-normal plot (Fig.2.17a) clearly shows the value of lower value of the irreducible water saturation, while it does not present a clear break in the log-log plot (Fig.2.17b). The tortuosity provides an indication of the twisting of ionic path and it appears as it only changes at a slowly rate and it does not suddenly alter the conduction paths until the last brine percolation path is broken.

Fig.2.10 _ Capillary pressure and resistivity index versus brine saturation in Berea sandstone core specimens. Two irreducible water saturations are identified: one for capillary pressure and another one for the electrical properties.

Fig.2.11 _ Capillary pressure and resistivity index versus brine saturation in twelve Quartz (very fine- grained) sandstone core specimens. Two irreducible water saturations are identified: one for capillary pressure and another one for the electrical properties.

Fig.2.12 _ Capillary pressure and resistivity index versus brine saturation in ten Limestone core specimens.

Two irreducible water saturations are identified: one for capillary pressure and another one for the electrical properties.

References

Fig.2.13 _ Effect of percolation on the capillary pressure and electrical resistivity measurements.

Fig.2.14 _ Effect of brine saturation the saturation exponent in Berea sandstone specimens. a) Log-log plot of the resistivity index versus brine saturation. b) Saturation exponent versus porosity.

Fig.2.15 _ Effect of brine saturation the saturation exponent in Berea sandstone specimens. a) Log-log plot of the resistivity index versus brine saturation. b) Saturation exponent versus porosity.

‘

Fig.2.16 _ Effect of brine saturation the saturation exponent in Berea sandstone specimens. a) Log-log plot of the resistivity index versus brine saturation. b) Saturation exponent versus porosity.

Fig.2.17 _ Calculated tortuosity versus degree of saturation in Berea sandstone specimens. a) Normal-normal plot.(b) Log-log plot.