Correlation of Pore Volume Compressibility with Porosityin One of the Iranian Southern Carbonate Reservoirs

Akhoundzadeh, Hamid; Moghadasi, Jamshid ١; Habibnia, Bahram١

* Corresponding author: Hamid Akhoundzadeh,Petroleum University of Technology (PUT), Abadan, Iran,

E-mail: hamid.akhoundzadeh@gmail.comPhone number: ٠٩١٢٤٤٦٨١٠٧

١ Petroleum University of Technology, Abadan, Iran

Abstract

Pore volume compressibility is one of the most important parametersthat must be considered in reservoir calculations. Due to the time-consuming and expensive procedure of laboratory measurements, anaccurate estimation of pore volume compressibility is necessary forprecise simulation of the reservoir behavior.In the present study, porevolume compressibility data of one of the Iranian southern carbonatereservoirs has been used. A total of fifteen samples from three wellswere selected for laboratory measurements. Petrographical analysis wasconducted for determination of rock type and pore structure of thesamples, then the effects of pressure and porosity on porecompressibility was investigated. The result of this study has shown thatpore volume compressibility of the selected samples, which almost werepure limestone, has good correlations with porosity and pressure. Thena new formula for pore volume compressibility versus porosity haspresented and has compared with published correlations.

Keywords: Pore Volume Compressibility – Porosity – Correlation -Effective Pressure - Carbonate reservoir

Introduction

During depletion of fluids from the reservoir rocks, the internal porepressure decreases and therefore, the effective pressure (differencebetween overburden and internal pore pressure) increases. Thisincrease causes the changes in the grain, pore, and bulk-volume of therock. These volume changes tend to reduce the pore space andtherefore, the porosity of the rock.

The engineering parameter quantifying this volumetric variation iscompressibility, which is the fractional change in the volume of the rockper unit change in pressure.

Pore volume compressibility is one of the most important and effectiveparameters of mechanical, seismic and reservoir properties ofhydrocarbon reservoirs.

Knowledge of the compressibility of reservoir rocks is essential for abetter understanding of rock mechanics and aids in the solution ofnumerous oil wells drilling and production problems (Von Gonten andChoudhary, ١٩٦٩).

An accurate estimation of pore volume compressibility of reservoirrocks is essential for compaction evaluation, reservoir drivedetermination, reserve estimates, reservoir pressure maintenance,casing collapse analyses and production forecasting. This information isthen used in modeling the reservoir and calculating the economic valueof the project. Thus, obtaining credible indications of this value isinvaluable (Wolfe et al., ٢٠٠٥).

Due to its importance in reservoir engineering analysis, pore volumecompressibility must routinely measure in the laboratory.

Pore volume compressibility of a reservoir rock is not a constantbut varies with compacting pressure, porosity and temperature. Rocktype and pore structures of the samples have effect in porecompressibility.

Several authors have attempted to correlate the porecompressibility with various parameters including the porosity.

For many years, the petroleum industry has relied on Hall’s (١٩٥٣)correlation, for estimating pore volume compressibility. Based on the

measurement on seven consolidated limestone and five consolidatedsandstone samples, Hall obtained a relationship of compressibilitywith porosity of rock (Figure ١).

Newman (١٩٧٣) has presented a more comprehensive porevolume compressibility data based on ٢٥٦ samples, ١٩٧ weresandstones from ٢٩ sandstone reservoirs, and ٥٩ were limestonesfrom ١١ limestone reservoirs.

His data show little or no correlation between pore volumecompressibility and initial sample porosity. The data showconsiderable disagreement with Hall's correlation.

Based on extensive measurements of Newman (١٩٧٣), Horne(١٩٩٠) obtained trends of pore volume compressibility versus initialporosity for consolidated limestones, consolidated sandstones andunconsolidated sandstones(Figure ٢).

Jalalh (٢٠٠٦) provide new correlation for pore volumecompressibility versus porosity based on the rock compressibility dataavailable in the literature and his laboratory measurements.

The main objective of this work is to evaluate and discuss therelationship between pore volume compressibility with pressure andporosity based on experimental compressibility measurement of somecarbonate sample in Iranian reservoir rock in a wide-range value andvaried types of porosity. Finally, a new general formula for pore volumecompressibility versus porosity is presented and obtained results iscompared with the published correlations.

Test Procedure

Compressibility tests were performed under a hydrostatic load byusing CMS-٣٠٠ equipment, while the stress has changed at ٤ or ٥risingintervals. The net stress variation was between ٠ to ٦٠٠٠ psi, whichis compatible with Middle East reservoirs. As the effective confiningpressure was increased, the changes in rock pore volume weremeasured and pore volume compressibilities were calculated at eachcorresponding pressure intervals.

This measurement is agreed with other published measurements of porecompressibility.

Compaction data determined under hydrostatic loading can becorrected to into uniaxialcompactions, which is much morerepresentatives for reservoir conditions,if the Poisson ratio of the rock isknown or can be estimated accurately, by using the theoretical formulaas described by Teeuw (١٩٧١).A correction factor of ٠.٦٢ specific for acase study was used in conversion from hydrostatic to uniaxial condition.However, the accurate correction factor must be determined from thefield samples under study.

For example, figure ٣shows the measured values of pore volumecompressibility for the limestone sample taken from a depth of ٣٦٢٠ feet,and had an initial porosity of ١٣.١%.

Method Description

In the present work for classification of carbonate rocks according todepositional texture, Dunham Classification is used.Dunham (١٩٦٢)proposed a widely used classification that categorizes carbonate rocksaccording to the amount and texture of grains and mud.Furthermore, forpresenting type of porosity, Choquette and Pray (١٩٧٠) classification willbe applied.

In this study, rock typing and detecting pore type is done based on thinsection studies. Comprehensive thin-section analysis was performed toobtain rock type, mineralogy, and pore types.

The pore volume compressibility values are pressure dependent. Tocorrelate pore compressibility with porosity and compare samples thathad been obtained from various depths, which means the samples weresubjected to various effective stresses under reservoir conditions, acommon effective pressure base of ١٠٠ percent of the lithostaticpressure was used. This value was selected as the most probableaverage effective stress the sample would encounter during reservoirdepletion(Jalalh, ٢٠٠٦b). For this purpose, the overburden pressure isassumed to be ١ psi per foot of depth and pore pressure is assumed tobe ٠.٥ psi per foot and pressure difference between overburden and

internal pore pressure is referred to as the effective overburdenpressure.

The values obtained at this pressure can be plotted against the porosityand we can analyze the effects of the porosity and other factors incompressibility of various samples, which acquire from a different depth.

For presents a correlation between variables, we used statisticalprograms for regression analysis by using the least square method.

Field Description

Compressibility measurement data used in this study werefifteensamples taking from Middle Cretaceous BangestanGroup, whichacquired from three wells in one of the Iranian southern carbonatereservoirs.

The Middle Cretaceous carbonates in the Persian Gulf region are amongthe most productive oil-bearing stratigraphic intervals in the world,containing numerous giant fields.

Table ١ show the characteristics of the various rock samples used in thisstudy for pore volume compressibility analysis.As shown in table ١, allsamples are pure limestone and are composed of more than ٩٠%calcite.According to the Dunham classification, samples are grain-dominate and almost all of them are grainstoneorpackstone tograinstone.

Although samples have a wide range of porosity, but they have sameporosity type; Vuggy and microfracture which illustrate in figure ٤ are thedominant porosity type in these samples.Figure ٥ shows the frequencyof above properties in well A-٣.

The results for evaluation of pore volume compressibility versus effectivestress are presented in figure ٦.

Results and Discussion

The compaction of rock causes changes in the structure of thepores and grain shapes, and reduces the pore volumes.

As has seen in the above figure, pore compressibility is a function ofeffective pressure and it increases as effective pressure decreases.Apower function in the form of Y = aX usually shows the best fit forcompressibility and the net confining pressure relationship.

For instance, figure ٧ illustrate power function of pore compressibilityversus effective pressure for two samples.

Thus, the compressibility data of each sample can be expressed interms of two fit parameter Aand B, which are defined to the followingequation:

(١)

Table ٢ summarizes the best-fit compressibility parameters A and B forall samples.

The value of pore compressibility is dependent on the texture, type andvalue of porosity. Insomuch in the investigated formation, the samplesalmost have same rock type and near porosity type (as mentionedearlier), it can be represented, in this reservoir pore compressibilitydependonly the value of porosity and it increases as porosity decreases.

This fact can be seen in figure ٦ which pore volume compressibilitycurves move down by increasing the initial porosity. This is clear to seethat the pore volume compressibility of our limestone samples increasewith decreasing porosity.

In figure ٨ through ١٠, porosity value was classified in the three groupsand pore compressibility of each group is illustrated on it. It can be seengraph of the sample with near porosity value is close to each other.

The values of pore volume compressibility obtained at the reservoircondition (effective pressure) plotted against the initial porosity. Infigures ١١ and ١٢the presented data are compared with widely used Halland Horne’s correlation curves.

Both figure ١١ and ١٢ displays clearly poor agreement with Hall andHorne correlation. Therefore, the correlation formulas that are availablein the literature (i.e., Hall’s and Horne’s correlations) cannot be appliedto estimate the compressibility of these reservoir rocks.

The above discussion supports the necessity for laboratorycompressibility measurements in evaluating rock compressibility andestablishing the new rock compressibility correlation for a givenreservoir.

For this purpose, an attempted has been made to find a simple andaccurate formula, which gives more precise pore volume compressibilityvalues with considering all of the measured compressibility data in theinvestigated field.For sophisticated analysis, the data has transferredinto one of the professional fitting regression programs.

In this program, XY data can be modeled using a toolbox of linearregression models, nonlinear regression models, interpolation, orsplines.Over ٣٠ models are built-in, but custom regression models mayalso be defined by the user. Full-featured graphing capability allowsthorough examination of the curve fit. The process of finding the best fitcan be automated by letting the program compare my data to eachmodel to choose the best curve.

Every possible regression model has examined for the input data set.The best-fitting result is the Reciprocal Logarithm Model (equation ٢).This model gives the correlation coefficient (R) = ٠.٩٣٢.

(٢)

Therefore the new limestone compressibility correlation is (where∅ ≥٠.٠٣):

(٣)

Figure ١٣ presents newly obtained pore volume compressibilitycorrelation versus porosity in the investigated reservoir.

In addition, figure ١٤ demonstrate graphical comparisons of the Hall’sand Horne’s correlation curves to new correlation curve. It can be seengoodness fit data of new fitting curve.

Conclusions

١. Pore volume compressibility of reservoir rock is highly pressuredependent and it increases as effective pressure decreases.

٢. For investigated samples, there is a power model correlationbetween pore volume compressibility and effective pressure.

٣. The value of pore compressibility is dependent on the texture, typeand value of porosity. Insomuch in the investigated formation, thesamples almost have same rock type and near porosity type, it canbe represented in this reservoir pore compressibility depends onlythe value of porosity and it increases as porosity decreases.

٤. It was found that the pore volume compressibility values reportedin this study are in poor agreement with the publishedcompressibility-porosity correlations (Hall’s and Horne’scorrelations) and these correlations cannot be used for estimatepore volume compressibility of studied reservoir rocks. Therefore,the laboratory compressibility measurement is necessary forevaluation of pore compressibility for a given reservoir.

٥. Base on laboratory compressibility measurement of studiedlimestone samples, a new correlation of pore volumecompressibility with porosity was presented for one of the Iraniancarbonate reservoirs.

Acknowledgements:The authors would like to thank the National Iranian ExplorationManagement Company (Exploration Directorate) for their supports.

References

١. Choqutee, P. W., and Pray, L. C., ١٩٧٠, Geological Nomenclatureand Classification of Porosity in Sedimentary Carbonates: Bull.AAPG, ٥٤, ٢٥٠-٢٠٧.

٢. Dunham, R. J., ١٩٦٢, Classification of Carbonate Rocks Accordingto Their Depositional Texture, AAPG Memoir I, ١٢١-١٠٨.

٣. Hall, H. N., ١٩٥٣, Compressibility of Reservoir Rocks, PetroleumTransactions ofthe AIME, ١٩٨: ٣١١-٣٠٩.

٤. Horne, N.R., ١٩٩٠, Modern Well Test Analysis A Computer-AidedApproach, Petroway Inc.

٥. Jalalh, A.A., ٢٠٠٦b, Compressibility Measurements of PorousRocks: Part II. New Relationships, Acta Geophysica, ٥٤, ٤, ٣٩٩-٤١٢.

٦. Newman, G. H., ١٩٧٣, Pore Volume Compressibility ofConsolidated, Friable, and Unconsolidated Reservoir Rocks underHydrostatic Loading, SPE Journal of Petroleum Technology, (٢)٢٥:١٣٤-١٢٩.

٧. Teeuw, D., ١٩٧١, Prediction of Formation Compaction fromLaboratory Compressibility Data, SPE Journal, (٣)١١: ٢٧١-٢٦٣.

٨. Von Gonten, W.D. and Choudhary, B. K., ١٩٦٩, The Effect ofPressure and Temperature on Pore Volume Compressibility, FallMeeting of the Society of Petroleum Engineers of AIME (٤٤thAnnual).

٩. Wolfe, C., Russell, C., Luise, N. Chhajlani, R., ٢٠٠٥, Log BasedPore Volume Compressibility Prediction_A Deepwater GoM CaseStudy, SPE ٩٥٥٤٥.

Table ١: summarizes of data in the presented carbonate reservoir in southern ofIran.

Table ٢: Best fit compressibility parameters of the samples.

WellNo.

Sample#

Grain density(gr/cm3)

Porosity(%)

Effective stress(psi)

Compressibility(1/psi × 10^-6)

13H 2.72 20.7 5851 4.61

39H 2.7 13.1 5939 6.44

56H 2.71 8.3 5980 7.38

67H 2.71 10.9 5998 6.09

93H 2.73 15.2 6042 5.42

3H 2.71 17 5594 5.52

21H 2.71 20.4 5629 5.6

25H 2.71 17.3 5635 5.58

50H 2.71 7.4 5677 9.27

59H 2.72 8.6 5693 9.19

20H 2.71 18.4 6402 4.35

56H 2.71 14 6466 5.52

78H 2.71 11.7 6524 2.61

92H 2.71 6.9 6578 10.39

98H 2.71 8.2 6598 7.32

A-1

A-2

A-3

WellNo.

Sample#

Porosity(%)

Fit parameterA

Fit parameterB

Correlationcoefficient

13H 20.7 550.72 -0.546 0.915

39H 13.1 4203.4 -0.759 0.999

56H 8.3 173915 -1.169 0.978

67H 10.9 317730 -1.262 0.979

93H 15.2 1014.3 -0.603 0.953

3H 17 1819.8 -0.679 0.999

21H 20.4 1025.1 -0.61 0.998

25H 17.3 1265.4 -0.635 0.998

50H 7.4 32529 -0.953 0.996

59H 8.6 27283 -0.931 0.989

20H 18.4 7611.1 -0.861 0.952

56H 14 2267.5 -0.705 0.999

78H 11.7 62749 -1.16 945

92H 6.9 152799 -1.118 0.988

98H 8.2 107112 -1.117 0.988

A-1

A-2

A-3

Figure ١: Hall’s correlations forpore volume compressibility versusporosity (Hall, ١٩٥٣).

Figure ٢: Horne’s correlation forpore volume compressibility versusporosity (Horne, ١٩٩٠).

Figure ٣: Pore volume compressibility of a limestone sample measured by CMS-٣٠٠ from southern of Iran.

Figure ١: Hall’s correlations forpore volume compressibility versusporosity (Hall, ١٩٥٣).

Figure ٢: Horne’s correlation forpore volume compressibility versusporosity (Horne, ١٩٩٠).

Figure ٣: Pore volume compressibility of a limestone sample measured by CMS-٣٠٠ from southern of Iran.

Figure ١: Hall’s correlations forpore volume compressibility versusporosity (Hall, ١٩٥٣).

Figure ٢: Horne’s correlation forpore volume compressibility versusporosity (Horne, ١٩٩٠).

Figure ٣: Pore volume compressibility of a limestone sample measured by CMS-٣٠٠ from southern of Iran.

Figure ٤: Vuggy (left) and microfracture (right) as a dominate porosity in theinvestigated reservoir.

Figure ٥: Geological and petrophysical properties of the samples in well A-٣.

Figure ٦: Groups of compressibility values of the samples versus effectivepressure.

Figure ٧: Power function of pore volume compressibility versus effective pressurein two samples.

Figure ٦: Groups of compressibility values of the samples versus effectivepressure.

Figure ٧: Power function of pore volume compressibility versus effective pressurein two samples.

Figure ٦: Groups of compressibility values of the samples versus effectivepressure.

Figure ٧: Power function of pore volume compressibility versus effective pressurein two samples.

Figure ٨: Pore volume compressibility versus effective pressure for porosity range١٠-٥%.

Figure ٩: Pore volume compressibility versus effective pressure for porosity range١٥-١٠%.

Figure ١٠: Pore volume compressibility versus effective pressure for porosityrange ٢٠-١٥%.

Figure ٨: Pore volume compressibility versus effective pressure for porosity range١٠-٥%.

Figure ٩: Pore volume compressibility versus effective pressure for porosity range١٥-١٠%.

Figure ١٠: Pore volume compressibility versus effective pressure for porosityrange ٢٠-١٥%.

Figure ٨: Pore volume compressibility versus effective pressure for porosity range١٠-٥%.

Figure ٩: Pore volume compressibility versus effective pressure for porosity range١٥-١٠%.

Figure ١٠: Pore volume compressibility versus effective pressure for porosityrange ٢٠-١٥%.

Figure ١١: Pore volume compressibility of studied limestone samples versusinitial porosity, compared with Hall’s correlation curve.

Figure ١٢: Pore volume compressibility of studied limestone sample versus initialporosity, compared with Horne’s correlation curve.

Figure ١١: Pore volume compressibility of studied limestone samples versusinitial porosity, compared with Hall’s correlation curve.

Figure ١٢: Pore volume compressibility of studied limestone sample versus initialporosity, compared with Horne’s correlation curve.

Figure ١١: Pore volume compressibility of studied limestone samples versusinitial porosity, compared with Hall’s correlation curve.

Figure ١٢: Pore volume compressibility of studied limestone sample versus initialporosity, compared with Horne’s correlation curve.

Figure ١٣: New correlation of pore volume compressibility for studied limestonerock samples with porosity.

Figure ١٤: graphical comparisons of the Hall’s and Horne’s correlation curves tomy new correlation curve.

= . + . ( )Correlation Coefficient:

٠.٩٣٢٣

Figure ١٣: New correlation of pore volume compressibility for studied limestonerock samples with porosity.

Figure ١٤: graphical comparisons of the Hall’s and Horne’s correlation curves tomy new correlation curve.

= . + . ( )Correlation Coefficient:

٠.٩٣٢٣

Figure ١٣: New correlation of pore volume compressibility for studied limestonerock samples with porosity.

Figure ١٤: graphical comparisons of the Hall’s and Horne’s correlation curves tomy new correlation curve.

= . + . ( )Correlation Coefficient:

٠.٩٣٢٣