Elastic properties effect on the petrophysical

Elastic properties effect on the petrophysical characteristics Case study

for the Lower Safa Reservoir in Qasr filed North Western Desert,

Egypt.

Ali E.Farag a, Elshayeb H. b , Abu-Hashish MF c, and Harby Hane d

a British University, Cairo, Egypt b&c Geology Department, Menoufiya University, Egypt

d Schlumberger Company

dAuthor for correspondence, email: [email protected]

ABSTRACT

A set of relationships between the static elastic constants (elastic wave velocities in the rocks along

with its densities), dynamic elastic properties (sonic logs), and petrophysical parameters were utilized to

calculate the in-situ mechanical properties of the rock. These relations applied to Safa Members of the

Qasr_4 well belonging to the Qasr oil field, which located in the Shushan basin of the western desert, Egypt.

This member is belonging to Khatatba Formation, which is consisting mainly of Sandstone and Shale

interbeds and considered as a hydrocarbon bearing horizon. The proposed member was studied

geomechanically by the aid of petrophysical and geomechanical parameters for the purposes to estimates

the relationship between the elastic properties and rock strength, which enhancing drilling; to specify a

local independent moduli equation in the Qasr field, and to geomechanically predict this relationship with

the absence of core chips. The relation between the static and dynamic Young's modulus was utilized to

predict porosity as when the difference between static and dynamic is high, it indicates unconsolidated

formation, and hence, the porosity will be high. However, when the variation is small, it indicates that

formation is well consolidated, and porosity will decrease.

KEYWORDS: Qasr field, Safa Members, the elastic properties on the petrophysical characteristics

INTRODUCTION

The rock mechanics defined as the theoretical and practical response of a rock due to the external

stresses, whether it is natural or human-made. Its broadly applied by civil and mining engineers as well as,

it has been useful for many aspects in the petroleum industry, especially in drilling, production, and

Wutan Huatan Jisuan Jishu

Volume XVI, Issue X, OCT/2020

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reservoir engineering. Most drilling-related failures are caused by unstable boreholes, whether these are

caused by lost circulation due to wellbore instability, or stuck pipe. The brittleness is a vital rock mechanical

property that characterizes the ability of a rock to fracture under the small value of deformation or strain

(Neuendorf et al. 2011). A typical brittle rock tends to fail at peak stress and easily forms cracks under

indentation and strikes. It usually has a more excellent ratio of compressive to tensile strength, higher

internal friction angle, more magnificent Young’s modulus, and lower Poisson’s ratio than a typical ductile

rock (Hucka and Das 1974). To recognize the effect of the borehole stress concentration on the borehole

sonic logging, a detailed analysis of the propagation of waves in a three-dimensional borehole model need

to be conducted. The elasticity of the formation around a borehole is described by the stiffness tensor that

is governed by the constitutive relation between the stress field applied around a borehole and the elasticity

of rock with micro-cracks embedded in the matrix. However, there is a lack of wave propagation simulation

in all previous studies on this subject so that, the present study is focused on this concept to apply it on the

Lower Safa Members in Qasr oil field, which is belonging to the Northwestern desert, Egypt (Figure. 1).

GENERAL GEOLOGY

Western Desert Egypt from south to North splits into four tectonic units (Figure.2) namely: stable

and unstable shelves, hinge zone, and miogeosyncline (Schlumberger, 1984). QASR fields are a gas field

which is located in the unstable shelf. It is characterized by the Northward thickening of the sedimentary

successions ranging in age from Palaeozoic to Recent and characterized by its prolific feature due to the

high organic richness and proper trapping geometry (Al Shaarawy, 1994). The area that forms the scope of

this study located in the Shoushan Basin, North Western Desert, Egypt. (Figure. 1). Shoushan Basin is the

most productive basin in the North-Western Desert of Egypt and has attracted the notice of numerous

researchers, authors, and oil companies. The Shoushan Basin contains sediments of Jurassic and younger

ages. The presence of possible source rocks in the Shoushan Basin occurs in the Jurassic, Cretaceous, and

Palaeozoic rock units (Ghanem et al. 1999; El-Nady et al. 2003; Al Sharhan & Abd El-Gawad 2008 and

Shalaby et al. 2011&2013).



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Figure1: The location map of the study area showing different basins and sub-basins within the

Western Desert (A) and spatial distribution of studied wells in the Qasr oil field (B).

Figure 2: The Western Desert Tectonic Units (Schlumberger, 1984).

B

A



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METHODOLOGY

Vertical stress has been calculated from density using extrapolated methods; Por pressure and Fracture

gradient have been computed using Eaton sonic method then validated by using different calibration tools

(Mud weight, RFT points and Leak off test results). Elastic properties (Bulk, Shear moduli Young’s

modulus and Poisson ratios and Biot coefficient) calculated from wireline logging data, then Rock strength

(UCS, Tensile strength, friction angle, and Cohesion) has been calculated by using the elastic properties

derived from log measurements. The workflow has been conducted by using the Techlog, a Schlumberger

software.

• Vertical stress:

The result from the combined weight of the formation matrix plus the fluids in the pore space, overlying

the formation of interest. This combined weight is mentioned to as the bulk density Density is

extrapolated up to mud line using the following equation,

Equation 1: The vertical stress using Extrapolation methods.

ρ extrapolated = ρ mudline + Aₒ x (TVD – Air Gap – Water Depth) α

where ρ mudline is the density at the sea floor or ground level

Aₒ and α are fitting parameters

is the exponent coefficient

• Pore Pressure Estimation:

The pore pressure and fracture gradients were estimated using the empirical equation of Eaton (1975),

which is consequent from compressional slowness:

Equation 2: The pore pressure calculation using compressional slowness Eaton (1975).

𝑃𝑝𝑔 = 𝑂𝐵𝐺 − (𝑂𝐵𝐺 − 𝑃𝑛𝑔)(∆𝑡𝑛 ∆𝑡⁄ )3

where 𝑃𝑝𝑔 is a formation pressure gradient

𝑂𝐵𝐺 is the overburden stress gradient.

𝑃𝑛𝑔 is the normal hydrostatic pore pressure gradient.



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∆𝑡𝑛 is the compressional slowness in shale.

∆𝑡 is the transit time in shale.

• Fracture gradient:

Fracture gradient calculated from pore pressure and vertical stress.

Equation 3: The fracture gradient calculation using Eaton (1975).

𝐹𝐺 = 𝐾 ∗ (𝜎𝑣 – α𝑃𝑃) + α𝑃𝑃

where FG = Fracture Gradient (ppg)

PP = Pore Pressure Gradient (ppg)

𝜎𝑣 = Overburden Gradient (ppg)

α = Poisson's Ratio (dimensionless)

K is the stress ratio (unitless)

• Poisson’s ratio and Young’s modulus

Thomas Young defined the elastic properties of a solid undergoing tension or compression in one

direction, Young’s modulus is the ability of a material to withstand changes in length when under

lengthwise tension or compression, Young’s modulus is corresponding to the longitudinal stress

divided by the strain. 𝑌𝑜𝑢𝑛𝑔’𝑠 𝑀𝑜𝑑𝑢𝑙𝑢𝑠 =𝑆𝑡𝑟𝑒𝑠𝑠

𝑆𝑡𝑟𝑎𝑖n

Equation 4: The 𝑌𝑜𝑢𝑛𝑔’𝑠 𝑀𝑜𝑑𝑢𝑙𝑢𝑠 modified Morales algorithm

𝐾𝑠𝑡𝑎

𝐸𝑠𝑡𝑎

3(1 + 2𝑣𝑠𝑡𝑎)

Where: Ksta is the Bulk modulus

𝐺𝑠𝑡𝑎𝐸𝑠𝑡𝑎

2(1+𝑣𝑠𝑡𝑎)

where: 𝐺𝑠𝑡𝑎 is the shear modulus

Poisson’s Ratio is an elastic constant that measuring the compressibility of material perpendicular

to the applied stress, or the ratio of latitudinal to longitudinal strains, Poisson’s ratio used to convert

the effective vertical stress component into an effective horizontal stress component



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(Alkhathami,2007).

• Uniaxial Compressive Strength (UCS)

Uniaxial Compressive strength (UCS) is the amount of compressive force per unit area in a single

direction (zero confinement) required to induce failure. 𝑈𝐶𝑆 (𝑀𝑃𝑎) =𝑃

𝐴.

where P is Compressive Load at Failure (kN)

A is cross-section all area (mm) of the rock sample

Equation 5: The UCS calculation using Young’s Modulus

UCS= 4.242*static Young’s Modulus.

Several researchers have introduced many equations for the determination of rock strength via

simple physical properties. Utilizing such properties, rock strength may be determined in an easy

quick and inexpensive manner during field investigations in the study area the relationship between

total porosity and Uniaxial compressive strength showing the plotted results using negative linear

regression determining (Figure.3)

The best-fitting equation is (R2 = -0.850), Equation 6: 𝑈𝐶𝑆 = −121637.6 ∗ 𝑃𝑂𝑅 + 244460.

This can be clarified that when UCS increases, the porosity will decrease.



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Figure3: Relationship Between Total Porosity and UCS in QASR_4.

(Figure.4) Shows the plotted results, using negative linear regression determining the relationship

between effective porosity and Uniaxial compressive strength. The best-fitting equation will be:

(R2=-0.870), Equation (7) UCS = − 121452.8 ∗ PHIEND + 22442.44



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.

Figure.4: Relationship Between Effective Porosity and UCS in QASR_4.

• Tensile Stress and Porosity:

Tensile stress known by force per unit cross-sectional area which mandatory to pull a substance

apart, if the hydrostatic pressure of the fluid in the wellbore roots the maximum tensile stress

induced in the vicinity of the wellbore to exceed the tensile strength of the formation, This is the

fundamental mechanism employed in hydraulic fracturing; however, unintentional tensile failure

may occur during drilling, If too heavy a mud is used the critical wellbore pressure will be

exceeded causing tensile failure which may result in lost circulation, Tensile failure also occurs in

injection wells if the injection pressure is too high. (R.A. Farquhar (Heriot-Watt University) |

B.G.D. Smart (Heriot-Watt University) | B.R. Crawford (Heriot-Watt University).

TSTR = K * UCS

where K = Facies and zone based factor, default: 0.1.



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TSTR: Tensile stress

In the study area relations Between Total Porosity and Tensile stress shows that when porosity

increase Tensile stress decrease the best fitting equation will be (R2 = -0.846), the

Equation(8): 𝑇𝐸𝑁𝑆𝐼𝐿 𝑆𝑇𝑅𝐸𝑆𝑆 = −16257.54 ∗ 𝑝𝑜𝑟𝑜𝑠𝑖𝑡𝑦 + 2837.679 . (Figure. 5), this is

matching with the previous relation between UCS and Porosity. porosity sandstone increases with

bigger grain size, which might make possible lower strength Grain size distribution can also

influence rock strength as great arrangement and packing of grains and hence extra contact points

between grains.

Figure 5: Relationship Between Total Porosity and Tensile stress in QASR_4.

The uniaxial compressive strength is obtained by setting = 0, in the equation gives:

Equation(9) Σ 𝐶 = 𝜎 𝐶𝑖 𝑆𝑎 Hoek and, the tensile strength are Equation(10) 𝜎𝑇 = −𝜎𝑆𝑐𝑖

𝑀𝐵. Hoek sci

is the UCS of the intact rock material and, MB and S are material constants, where s = 1 for intact

rock. Hoek-Brown failure. (Figure.6) Shows the plotted results, using negative linear regression



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determining the relationship between effective porosity and TENSIL STRESS. The best-fitting

equation is (R2 = -0.857), Equation(11):

𝑇𝐸𝑁𝑆𝐼𝐿 𝑆𝑇𝑅𝐸𝑆𝑆 = − 13074.6 ∗ 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑝𝑜𝑟𝑜𝑠𝑖𝑡𝑦 + 2293.056.

The two key elastic factors are Poisson’s Ratio and Young’s Modulus Measurement, which are

generally used in rock failure models. It is the quantity of the stiffness of the rock material, i.e. the

sample resistance against the compressive stress (load). Elastic constants are estimated from the

stress versus lateral and axial strains measured in conjunction with the triaxial compressive testing

(Al-Awad,2002). The effective stress is described as the total stress minus the pore pressure

(Alkhathami,2007) The purpose of theory is to calculate fracture dimensions based on the linear

elasticity, Young’s modulus is described as “the ratio of stress to strain for uniaxial stress”

(Howard and Fast. 1970). The modulus of a material is a measure of the stiffness of the material,

If the modulus is large, the material is stiff, The relation in (figure.9) between Poisson's ratio and

porosity it's showing that the relationship is reversed and the best fitting Equation(12) is (R2 = -

0.846):𝑃𝑅𝑆 𝑇𝐴 = − 2.000564 ∗ 𝑃𝐻𝐼𝐸_𝑁𝐷 + 0.2661489.

The relation between the static and dynamic Young's modulus was utilized to predict porosity as when

the difference between static and dynamic is high, it indicates unconsolidated formation, and hence, the

porosity will be high. However, when the variation is small, it indicates that formation is well consolidated,

and hence, porosity will be low. (figure 8).



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Figure 6: Relationship Between Effective Porosity and Tensile stress in QASR_4.

The relation in (Figure.7) between Young's modulus and porosity relation is reversed, and the best

fitting equation is (R2 = -0.846), Equation(13) 𝑌𝑀𝐸_𝑆𝑇𝐴_𝐽𝐹𝐶 = − 40.3294 ∗ 𝑃𝐻𝐼𝑇_𝑁𝐷 +

6.795265.



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Figure 7: Relationship YM and Porosity in QASR_4



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Figure 8: Relationship static YM, Dynamic YM, and Porosity in Qasr _4



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Figure 9: Relationship poison’s ratio and Porosity in QASR_4.

• Effected Porosity and Stress

Understanding rock properties and how they react under various types of stress is significant to

the development of a geomechanical model before drilling which will enhance drilling ability and

decrease NPT (Nun productive time) After rocks are loaded previous a certain point, when the

load on the rock almost isotropic (σ1 ≅ σ2 ≅ σ3), the rock will begin to compact and drop in

volume, mainly due to a decrease in porosity, This technique is known as shear-improved

compaction as when the effect happens at lower mean stress the shear stress will increases Moos,

D. and Chang, C. 1998



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Figure 10: Relationship SHMAX and Porosity in QASR_4.

Effective stress is vital as it’s known from extensive laboratory experiments (and from

equations) these features as well as velocity, porosity, resistivity, density, and strength are affecting

on the effective stress and will vary with effective stress, it is possible to calculate the effective

stress from measurements of physical properties like velocity or resistivity. Castillo, D.A., and

Zoback, M.D., 1995. The cross plot on the study area between porosity and maximum, minimum

stress in the (figure 10,11) showing when stress increase effective porosity will decrease porosity,

it is showing that the relationship is reversed and The best fitting Equation (14) is (R2 = -0.863)

with SHmax,

𝑆𝐻𝑀𝐴𝑋_𝑃𝐻𝑆 = − 103764.1 ∗ 𝑃𝐻𝐼𝐸_𝑁𝐷 + 16485.53. and is (R2 = -0.845) with

SHmin Equation(15) 𝑃𝐻𝐼𝐸𝑁𝐷 = − 9.857056𝑒 − 06 ∗ 𝑆𝐻𝑀𝐼𝑁𝑃𝐻𝑆 + 0.1479852.

The relation between geomechanically and petrophysical properties in Qasr_4 Lower Safa

Members are represented in (figure.12), strength is launching to landing with increased water



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saturation. This contains rock tensile strength, UCSare, and compressive strength [Hawkins and

McConnell, 1992] [Priest and Selvakumar, 1982], depending on rock texture, fluid chemistry, and

mineralogy. A large percentage of the strength drop occurs after only a minor gain in water

saturation or moisture amount in the dry state [Mellor, 1971; West, 1994]. Moreover, growth in

moisture content has a small effect on rock strength and its elastic properties;

Figure 11: Relationship SHMIN and Porosity in QASR_4.

• Velocity and Rock Property Relationships

Borehole acoustic logging data provide an important way to interpret formation elasticity (Sinha

and Kostek, 1995). Monopole and cross-dipole measurements are widely used for determining the

formation of P-wave velocity and S-wave anisotropy (Sinha and Kostek, 1995; Sinha and Kostek,

1996; Tang et al., 1999; Tang et al., 2002; Winkler et al., 1998). Most unfractured reservoir rocks,

such as sands, sandstones, and carbonates, show very little intrinsic anisotropy in an unstressed



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state (Wang,Z,Wang.R,Wang.F,Qiu,h,Li,T,2015). However, the stress-induced anisotropy, which

is caused by the opening or closing of the complaint and crack-like parts of the pore space due to

tectonic stresses, significantly affects the elasticity of rocks. Drilling a borehole in a formation

strongly alters the local stress distribution. (Winkler 1998) experimentally measured the azimuthal

P-wave velocity (VP) variation around a borehole that was subjected to a uniaxial stress loading

and showed that the borehole stress concentration has a strong impact on the velocity

measurements. The velocity variation with applied stresses is accounted for through the use of the

third-order elastic constants, on the study area (figure 13) showing the effect of UCS to VP when

UCS increase VP increase and it's showing the affecting of presence of shale volume on VP and

UCS when shale volume increase both UCS and VP will decrease however VPVS will increase as

(figure 14), The best fitting equation is (R2 = 0.729), equation:

Equation (16) VP = + 0.08249725 * UCS_YME + 3754.526 . The second approach (Tang and

Cheng, 2004; Tang et al., 1999) uses an empirical stress-velocity coupling relation to estimating

the variation of shear elastic constants (C44 and C55) as a function of stress. It is useful to

understand how the velocities are affected by rock properties such as bulk density and porosity

(Figure 15) shows the relationship between Vp porosity, color-coded by volume of max stress. It

is observed that when porosity increase and Vp decrease as the stress will decrease, which can be

used as a quick estimation for stress and direction.



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Figure12: Geomechanical and petrophysical properties in Qasr_4.



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Figure 13: Relation between UCS and Vp in Qasr_4.

Figure 14: Relation between UCS and VpVS in Qasr_4.



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Figure 15: Relation between porosity and Vp in Qasr_4.

(Figure 16 and figure 17) Showing the relationship between vpvs and Acoustic impedance

colored by SW and Vshale in QASR field from this figures we can determine where there is clean

sand , sand with shale and shale as well as in (figure16) showing that when VPVS more than “1.6”

shale will be more and clean sand when vpvs less than “1.6” and acoustic impedance less than

“3.75 g.f/cm3.s” and this is matching with (figure 17) which colored by SW in the same area where

we said we have clean sand it has low SW. An interpretation of the P-wave velocity measured

from borehole sonic logging needs to consider the effect of borehole stress concentration which

results from varying stress-induced anisotropy in the formation around a borehole and deviation

of the wave path of the refracted P-wave from a straight wave path along borehole axis direction

it's showing in (figure 18) that relation between UCS, TSTR, and YME with Rock Physics is

extreme relationship.



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Figure16: Relation between Acoustic impedance and Vpvs colored shale volume in Qasr_4.

Figure17: Relation between Acoustic impedance and VPVS colored SW in Qasr_4.



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Figure18: Rock properties and Rock physics in Qasr_4.

• Mechanical Earth Model

Mechanical Earth Model (MEM) is a numerical representation of the state of stress and

rock mechanical properties for an exact stratigraphic section in a field , Several oilfield

projects are challenging since of geomechanical difficulties arising from overpressure,

wellbore instabilities, reservoir compaction, causing failure, sanding, surface subsidence,



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fault Minimizing the risk of problems related to geomechanical properties requires

considerate the geomechanics of well building and field. Building MEM can drastically

decrease time and cost of field development, Some applications of MEM which have been

applied in oil industry like Estimate of pore pressure and fracture gradient to design casing

program which reduces the cost of materials and rig time, Risk decrease of stuck pipe

incidents because of wellbore instability that may cause lost BHAs and subsequently

increasing NPT(Non productive time) for freeing pipe, performing additional wiper trips

and hole cleaning and side tracking.1( Meisam Afsari (NIOC) The study aims to predict

the data which is needed to predict MEM as in figure 19.



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Figure 19: Result of wellbore stability predicted from MEM QASR_4 profiles showing safe mud window,

kick zone, shear failure zone, tensile failure limit, and mud loss region concerning the actual mud weight

used while drilling.



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CONCLUSION AND DISCUSSION

This study allows to estimate rock physics and build MEM to all the field as a result of there is no

enough data to build MEM in all wells as per figure 19.

Estimation of rock physics needs more core data analysis to confirm this equation in the Qasr field.

This study helps to know the wellbore stability and drilling without any failure to avoid

consequences are mostly due to drilling-related failures, which are caused by unstable boreholes,

whether these are caused by lost circulation, wellbore instability, or stuck pipe. These consequently

lead to NPT.

These correlations offer the opportunity to reduce the costs for exploration by minimizing the

amount of core data required to calibrate rock properties calculated from costly wireline logs.

Correlations of the physical properties allow us to estimate UCS in wells with no core.

The relation between static and dynamic Young’s modulus help to predict porosity when the

variation between static and dynamic is higher; it indicated unconsolidated formation, and the

porosity will be high; however, when the difference is smaller, it indicates that formation is well

consolidated and porosity is less.

The variation between static and dynamic Young’s modulus can help to evaluate ROP in realtime,

which can lead to a decrease in drilling time more data needed to build this relationship.

Relation between UCS and porosity help us to predict fluid movement direction in the field, when

there will be a deformation in the reservoir there will be a possibility for fluid movement and

productivity which can be traced it by making models to all the field as the permeability is

depending on porosity, need more study to all the field and another field to confirm this estimation.



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From petrophysical parameters, we can estimate Geomechanical properties

(UCS,TSTR,YM,PR and stresses) for the formation. We are using Regression analysis in Qasr

field.

Those established relationships of the elastic properties can be used in drilling, while the planning,

execution and evaluation phases, are to enhance the drilling performance and to understand the

nature of the rock, to avoid the wellbore instability.



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Meisam Afsari (NIOC) | Mohammadreza Ghafoori (University of Calgary/ Petroleum University of

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LIST OF FIGURES

Figure1: The location map of the study area showing different basins and sub-basins within the

Western Desert (A) and spatial distribution of studied wells in the Qasr oil field (B).

Figure 2: The Western Desert Tectonic Units (Schlumberger, 1984).

Figure3: Relationship Between Total Porosity and UCS in QASR_4.

Figure.4: Relationship Between Effective Porosity and UCS in QASR_4.

Figure 5: Relationship Between Total Porosity and Tensile stress in QASR_4.

Figure 6: Relationship Between Effective Porosity and Tensile stress in QASR_4.

Figure 7: Relationship YM and Porosity in QASR_4

Figure 8: Relationship static YM, Dynamic YM, and Porosity in Qasr _4

Figure 9: Relationship poison’s ratio and Porosity in QASR_4.

Figure 10: Relationship SHMAX and Porosity in QASR_4.

Figure 11: Relationship SHMIN and Porosity in QASR_4.

Figure12: Geomechanical and petrophysical properties in Qasr_4.

Figure 13: Relation between UCS and Vp in Qasr_4.

Figure 14: Relation between UCS and VpVS in Qasr_4.

Figure 15: Relation between porosity and Vp in Qasr_4.

Figure16: Relation between Acoustic impedance and Vpvs colored shale volume in Qasr_4.

Figure17: Relation between Acoustic impedance and VPVS colored SW in Qasr_4.

Figure18: Rock properties and Rock physics in Qasr_4.

Figure 19: Result of wellbore stability predicted from MEM QASR_4 profiles showing safe mud

window, kick zone, shear failure zone, tensile failure limit, and mud loss region concerning the

actual mud weight used while drilling.



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