A simple analysis of oil-induced fracturing in sedimentary rocks

A simple analysis of oil-induced fracturing in sedimentary rocks Ismail Ozkaya Geology Department, Kuwait University, AI-Kuwait, Kuwait

Received 18 September 1987; accepted 14 December 1987 Geometric form of kerogen patches control oil-induced fracturing in impermeable source rocks. Thin elongate kerogen flakes cause lateral fracturing. Kerogen has to occur in spherical or cylindrical forms to induce vertical fractures. If length to width ratio of kerogen flakes is sufficiently large, then lateral fractures are definitely initiated during oil generation in impermeable source rock. Oil and rock compressibilities, and lateral to vertical stress ratio are decisive factors in vertical fracturing in impermeable rocks. Lateral to vertical stress ratio is generally higher than the maximum for oil-induced vertical fracturing in tectonically relaxed sedimentary basins. Oil generation cannot initiate vertical fractures, except when the lateral to vertical stress ratio is reduced below critical level either by tectonic tension or erosion of overburden. When the source rock is permeable, then the rate of oil seepage from kerogen into the surrounding rock is crucial in fracture initiation. Oil-induced fractures cannot form unless permeability, and hence rate of oil seepage from kerogen into the surrounding rock, is non-existent or negligible. Most source rocks have some permeability. Therefore, oil-induced fracture initiation should be a rare phenomenon. Keywords: fracture; oil-induced; primary migration

Oh, is related to effective vertical stress, Ov as follows:

Introduction Microfractures in source rocks are a likely means of primary oil migration. Microfractures may be caused by tectonic disturbances such as lateral tension or differential uplift and burial. Pore fluid pressures may aid fracturing by reducing effective stresses. Several authors have also suggested that oil generation may induce fracturing in source rocks (Tissot and Pelet, 1971; Momper, 1978; du Rouchet, 1981). The aim of this paper is to evaluate conditions of oil-induced fracture initiation. Below, the assumptions which are incorporated in the analysis are summarized. Oil source bed is linearly elastic and isotropic. It is progressively buried under continuous sedimentation. The basin of sedimentation is tectonically relaxed. Maximum principle stress Sv, is vertical and equals overburden weight. Total least lateral stress Sh is related to Sv as follows:

Sh=kSv

(1)

where k is the lateral to vertical stress ratio which ranges between 0.6 and 0.9 within depths of oil generation, depending on particular basin conditions (Breckels and van Eekelen, 1982). Total stress, S and effective stress, o are related as follows (Hubbert and Willis, 1957):

s=a+ew

(2)

where Pw is pore fluid pressure. Effective lateral stress,

Oh=k' Ov

(3)

where k' is the effective lateral to vertical stress ratio, although k' depends on basin conditions, in general, it increases with depth from a minimum of 0.3 up to 0.9 (Breckels and van Eekelen, 1982). Source bed enters oil window with continuing burial and part of the kerogen in isolated cavities is converted to oil. Fraction of organic matter convertible to oil, la is large so that in the final stage of oil generation, kerogen concentrations turn into rock cavities that are filled with oil and gas. Oil is less dense than solid kerogen, hence there is a certain volume expansion associated with oil generation under constant pressure. The fraction of volume expansion, ~ is -0.1-0.2 (Goff, 1983). We will first evaluate the internal oil pressure within isolated kerogen flakes enclosed in impermeable source rocks, and then examine tangential stress distribution at boundaries of oil-filled cavities. The conditions for oil induced tensional fracturing will then be evaluated.

Oil pressure within oil-filled cavities in sedimentary rocks Kerogen flakes are isolated and confined within an impermeable rock. Oil pressure within a kerogen flake will rise up to the overburden pressure upon oil generation plus an additional pressure increment. The

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Oil-induced fracturing in sedimentary rocks: Ismail Ozkaya additional pressure increment, ~ P is caused by density reduction during conversion of kerogen into oil:

Po=Sv+~P ~ P can kerogen constant elaVk~. constant

be approximated as follows. When part of is converted to oil, volume expansion under pressure A V' equals EVoiI which in turn equals Pressure increment AP' to keep volume is:

A P ' = e A V' / Vker= El.lI6o

A P= A P'-(1/13o) (2 Ar/r)

(6)

Radial strain in a circular opening of radius r is related to internal fluid pressure /~p as follows (Jaeger and Cook, 1976):

~p=2GAr/r

(7)

Equating (6) and (7), excess pressure/~ P is obtained as follows:

A P= Gel,t/(1 + BoG)

Sh

(5)

where 13o is oil-compressibility. One can imagine that upon oil generation, oil pressure first rises up by A P ' with no volume change. Subsequently, the volume of the kerogen expands. Oil pressure gradually declines by volume expansion while pressure within the rock increases by volume contraction until the pressure equilibrium is reestablished. Consider a kerogen body with a circular cross section of radius r, and width ~ l , and average volume Vk~r=~r2Al. At the final stage, excess oil pressure ~ P is:

(8)

For G=104 MPa (van Eekelen, 1982), and oil compressibility, 13o=10-2 MPa (Nghiem et al. 1984), e=0.1 and la=0.4 (Goff 1983), the value of A P is - 4 MPa. Vertical stress at 3000 m depth Sv equals 67.7 MPa. Oil pressure within isolated cavities is - 7 1 MPa at 3000 m depth. Relative contribution of A P to total oil pressure is small in comparison to Sv. Stress distribution around oil-filled cavities

Stress distribution around kerogen concentrations depend on their geometric form. Only tangential stress, St at the boundary of a cavity is needed to evaluate conditions of tensional fracturing. St is given for eliptical, cylindrical and spherical cavities in the following section. Consider an oil-filled cavity with an elliptical cross section in the plane of principle and least stresses. Width of the ellipse is w and height is h. Vertical stress is S,, and lateral stress is Sh. Sv and Sh are related by Equation (1). Oil pressure within the cavity, Po, is given by Equation (4). Tangential stress at points A and B on the boundary (Figure 1) due to Sv and Sh are given by (Jaeger and Cook, 1976): O,A'=Sv (1 +2w/h)-Sh

(9)

orB' =Sh (1 +2h/w)-S,

(9b)

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sv I

(4)

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t .t t Figure 1.0il-filled elliptical cavity underground. StA and StB are tangential stresses on the boundary at the point A and B respectively.

Tangential stress at A and B due to internal pressure P,, are: OtA"= Po (1-2w/h) and orb "= Po (1-2h/w)

(lO) (10b)

Total tangential stress at A and B can be found by superimposing Equations (9) and (10): StA = Sv (1 + 2w/h)- Sh + P,, (1-2w/h) and StB = Sh ( 1 + 2h/w) - S,, + Po (1-2h/w)

(11) (lib)

If the oil-cavity is circular (h=w), then StA and StB become: StA = 3Sv - Sh - Po

(12)

StB= 3Sh -- Sv- Po

(12b)

Stress distribution about a spherical cavity related to unidirectional stress, Sv is given in the literature (Obert and Duval, 1967). Using their results and superposition principle, tangential stress orb at the apex of a spherical cavity can be obtained for the following case. The sphere is subject to vertical stress Sv, lateral least and intermediate stresses, Sh and internal fluid pressure, Po. The result is dependent upon Poisson's ratio, v. For v=0.2:

StB= 2Sh-O.5Sv-O.5 Po

(13)

Effect o f plastic yielding Stress concentration about cavities may be considerably lowered by plastic yielding. For example, if there is plastic yielding, tangential stress at the boundary of a spherical cavity related to external pressure P is (Obert and Duvall, 1967): o,=2hP

(14)

For h=0.4,o t equals 0.8P. If there is no plastic yielding, ot = 1.5P.

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Oil-induced fracturing in sedimentary rocks: Ismail Ozkaya Effect of pore fluid pressure and poroelasticity The oil-source rock is assumed to be non-porous and impermeable in the preceding analysis. In case the oil-source rock has some porosity and permeability, then total stresses must be replaced by effective stresses because only effective stress can be tensile and cause fracturing. If oil within cavities is sealed off and does not flow into the source rock, effective tangential stresses at point A and B in Figure 1, become:

OtA=StA--Pw OtB=StB--ew

(15)

(16)

(17)

Where Ao is poroelastic constant given by:

Ao=~(1-2v)/(1-v)

Consider again an oil-filled cavity with an elliptical cross section (Figure 1). A lateral fracture forms at A if the effective stress StA is tensile and greater than the tensile strength of the rock, T: (19)

Substituting Po from Equation (4) and Sh from Equation (1), and rearranging terms the condition for lateral fracturing becomes: (20)

The excess oil pressure A P causes lateral fracturing when w/h ratio is sufficiently large. In other words, no matter how small A P is, it should cause lateral fracturing when the kerogen occurs as thin elongate flakes. For example, at 3000 m depth, Sv=67.7 MPa, k=0.75 and A P - 5 Mpa. For T=10 Mpa, w/h > 40 for lateral fracturing. In other words if a kerogen flake is 0.1 mm thick then its width must be more than 4 mm for lateral fracturing. When the source rock is slightly porous and permeable, but there is no oil seepage from kerogen lamina into the walls, then the condition for lateral fracturing is analogous to Equation (20):

oP(2w/h-1)>ov(2-k')+ T

Po>3Sh-Sv+T

(22)

(23)

Condition (23) is analogous to the well known criterion for hydraulic fracturing in boreholes with circular cross section (Hubbert and Willis, 1957). Substituting Po from Equation (4) and Sh from Equation (1), in Equation (22) and rearranging terms, the condition for vertical fracturing becomes:

S~(k-2h(1-k)/w)+ AP(1-2h/w) < - T

(24)

A P is - 5 Mpa as shown earlier. Tensile strength of rocks varies between 5 and 10 MPa (Closmann and Bradley, 1979). Assuming AP(1-2h/w)nearly equals T, then the condition for vertical fracturing simplifies to the following:

(21)

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Height to width ratio of oil-filled cavities must be greater than a minimum for vertical fracturing. The minimum is determined by the lateral to vertical stress ratio, k. For k=0.5:

h/w > 1/2

Condition for lateral fracture initiation

AP(2w/h-1) > S~ ( 2 - k ) + T

Po(2h/w- 1) > Sh(1 +2h/w)-Sv+ T

2h/w>k/(1-k)

(18)

0~is Biot's constant which equals ( 1 - Kr/Kb), Kr being matrix and Kb bulk rock compressibility. Ao varies between 0 and 1.

Po (2w/h- 1) > S~ (1 +2w/h)--Sh+ T

A vertical fracture is initiated at B (Figure 1) if the following condition is satisfied:

For a circular cross section:

where P'=Po-Pw. If the oil-source rock is porous and permeable, and there is some oil seepage from oil-filled cavities into the walls, then, poroelastic effect must be taken into consideration. Minimum effective tangential stress at the boundary of a circular hole with outward radial fluid flow is (Haimson and Fairhurst, 1967): OtB=3Oh--Ov--P ' (2-Ao)

Condition for vertical fracture initiation

(15b)

If the cavity has a circular cross section, the minimum tangential effective stress is:

OtB=3Sh-Sv-P'

If there is oil seepage into the host rock, then the excess pressure A P is dissipated and oil ceases to play any role in lateral fracturing.

(26)

For a cavity with circular cross section (w=h): k < 2/3

(27)

Lateral fracturing requires thin elongate kerogen flakes, whereas vertical fracturing requires cylindrical or spherical kerogen concentrations. A vertical fracture initiates at the apex of a spherical oil-filled cavity when the following condition from Equation (13) is satisfied:

2Sh-O.5Sv-O.5Po < - T

(28)

with Sh--kSv, Po=Sv+AP, this reduces to: AP>2(Ov(1-2k)+ T)

(29)

Neglecting T, and A P: k < 1/2

(30)

A comparison shows that stress concentration at the apex is less for a spherical cavity than a cylindrical cavity, and hence a smaller value of k is required for vertical fracturing. The condition (30) is even more difficult to meet than (27). Empirical formulae of Breckels and van Eekelen (1982), which relate lateral stress Sh to depth show that k--0.75 at a depth of 3000

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Oil-induced fracturing in sedimentary rocks: Ismail Ozkaya m. In general, k is greater than 2~ at oil generation Conclusion

depths. Vertical fractures are unlikely to form by oil generation. Moreover, plastic yielding Equation (14) may considerably lower tangential stress especially in case of rocks with small yield coefficient, h. This renders oil-induced vertical fracturing even more difficult. When the oil-source rock has pore fluid pressure, Pw but the oil in cavities is sealed off by solid organic matter around the walls of an oil-filled cavity, and cannot penetrate into the source rock, then, the condition for vertical fracturing from Equation (16) is: P ' > 3Oh--Or+ T

(31)

P' equals Ov+ A P. Thus criterion for vertical fracturing is: A P > (3k'-2)o~+ T

(32)

Assuming A P nearly equals T, (32) simplifies to:

k' < 2/3

(33)

This is analogous to Equation (27). Let us now include poroelastic effect on vertical fracturing. The condition for fracturing at the apex of a circular oil-filled cavity can be derived from Equation (17) as follows: P ' > (3Oh--O~+ T)/(2-Ao)

(34)

Replacing P' by ov+AP, Oh from Equation (3), the criterion for vertical fracturing at the boundary of a circular oil-cavity becomes: ( 3 k ' - 3 +Ao)Ov+ T AP >

(35) 2-Ao

Assuming A P ( 2 - A o ) is nearly equal to T, Equation (35) simplifies: k ' < 1-Ao/3

(36)

Although condition (36) is much more relaxed than (30), the underlying assumption that Po>=Sv may no longer hold if the source rock is permeable to oil. Oil seepage into the source rock from oil-cavity must cause oil pressure to decline by volume expansion if the cavity fails to close. Equation (7) shows that relative reduction of radius, Ar/r of cylindrical opening subject to pressure p equals p/2G. Assuming p equals Sv, the relative closure Ar/r at a depth of 3000 m is merely 0.03%. It can be concluded that there is only a negligible closure of cylindrical or spherical cavities following oil drainage. Hence, oil pressure depends only on rate of oil generation and rate of oil seepage out of an oil-cavity into the surrounding rock, which in turn depends on permeability of the rock. The minimum value of oil pressure is Pw+Pc. When oil pressure drops down to Pw+Pc, there is no fluid movement and no poroelastic stress, and P' in Equation (16b) is zero. In such a case oil plays no role in fracturing.

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In the case of isotropic and impermeable source rocks in which kerogen is concentrated in isolated bodies, the geometric form of kerogen concentrations plays an important role in deciding whether lateral or vertical fracture are initiated. Lateral fractures are almost certain to form if kerogen occurs as thin and elongate flakes, and if the surrounding permeability is zero. Kerogen forms with nearly equal width to height ratio are needed for vertical fractures. Vertical to lateral stress ratio, k, and oil compressibility 130 are a decisive factor in formation of vertical fractures in impermeable source rocks. In most cases, lateral to vertical stress ratio, k is more than the maximum for fracturing, hence vertical fractures are unlikely to form, except when k drops below the critical value (Condition 30) either by tectonic tension or erosion of overburden. In the case of slightly permeable rocks, fractures can only form if oil seepage from kerogen bodies into the source rock is non-existent or extremely small. When the rate of oil seepage is greater than the rate of oil generation, and oil pressure within kerogen cavities drops down to pore fluid pressure plus capillary pressure, oil ceases to play any role in fracturing. Most source rocks have some permeability. Hence, fractures may rarely be initiated by oil generation. Microfractures which aid primary oil migration most probably form by other means which are not genetically related to oil generation. Oil generation, however, may facilitate initiation and fluid expulsion out of the source rocks by contributing to the pore fluid pressure and reducing the effective stresses.

Nomenclature Ao G h k k' Po Pw r S Sh S~ v w St T 0¢ 130 la o oh Ov ot

Poroelastic constant Rock rigidity (MPa) Height of an elliptical cavity (cm) Total lateral to vertical stress ratio Effective lateral to vertical stress ratio Oil pressure (MPa) Pore fluid pressure (MPa) Radius of a cylindrical cavity Total stress (MPa) Total lateral stress (MPa) Total vertical stress (MPa) Poisson's ratio Width of an elliptical cavity (cm) Total tangential stress (MPa) Tensile strength (MPa) Biot's constant Oil compressibility (MPa -j) Fraction of oil volume expansion Fraction of organic matter convertible to oil Effective stress (MPa) Effective lateral stress (MPa) Effective vertical stress (MPa) Tangential stress (MPa)

Acknowledgement This work is a product of an ongoing research project which is jointly supported by Kuwait University and Kuwait Foundation for Advancement of Science (KFAS).

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Oil-induced fracturing in sedimentary rocks: Ismail (~zkaya References Breckels, I.M. and van Eekelen, H.A.M. (1982) Relationship Between Horizontal Stress and Depth in Sedimentary Basins J. Petrol. Technol. (September), 2191-2199 Closmann, P.J. and Bradley, W.B. (1979) The Effect of Temperature on Tensile and Compressive Strengths and Young's Modulus of Oil Shale Soc. Petrol. Eng. J. (October), 301-312 du Rochet, J. (1981) Stress Fields, a Key to Oil Migration Bull. Am. Assoc. Petrol. Geol. 65, 74-85 Goff, J.C. (1983) Hydrocarbon Generation and Migration from Jurassic Source Rocks in the E. Shewtland Basin and Viking Graben of the Northern North Sea J. Geol. Soc., London 140, 445-474 Haimson, B. and Fairhurst, C. (1967) Initiation and Extension of Hydraulic Fractures in Rocks Soc. Petrol. Eng. J. (September), 310-318 Hubbert, K. and Willis, D.G. (1957) Mechanics of Hydraulic Fracturing AIMEPetroL Trans. 210, 153-163

Jaeger, J.C. and Cook, N.G.W. (1976) Fundamentals of Rock Mechanics, Chapman and Hall, London Momper, J.A. (1978) Oil migration Limitations Suggested by Geological and Geochemical Considerations. In: Physical and Chemical Constraints on Petroleum Migration. (Eds W. H. Roberts and R. Cordell.) Am. Assoc. Petrol GeoL Course Note 8, B1-B60 Nghiem, L.X., Forsyth Jr. P.A. and Behie, A. (1984) A Fully Implicit Fracture Model J. Petrol TechnoL (July), 1191-1198 Obert, L. and Duvall, W.I. (1967) Rock Mechanics and the Design of Structures. John Wiley and Sons Inc., London Tissot, B. and Pelet, R. (1971) Nouvelles Donnes sur les Mecanismes de Genese et de Migration du Petrole: Simulation Mathematique a la Prospection Proc. 8th World Pet, Cong. 2, 35-46 van Eekelen, H.A.M. (1982) Hydraulic Fracture Geometry: Fracture Containment in Layered Formations Soc. Petrol, Eng. J. (June), 341-349

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