SPE 9064 SPE Society of PetroIeu"n EngIneers of AIME

FUNDAMENTALS OF FRACTURING

by Gene Daniel and Jerry White, Dowell

©Copyright 1980, American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. This paper was presented at the SPE Cotton Valley Symposium, held in Tyler, Texas, May 21,1980. The material is subject to correction by the author. Permission to copy is restricted to an abstract of not more than 300 words. Write: 6200 N. Central Expwy., Dallas, Texas 75206.

ABSTRACT

The basic theory of massive hydraulic fracturing as it relates to rock mechanics and rock properties will be reviewed with particular emphasis on the Cotton Valley Formation. The assumptions and basic concepts in frac geometry and orientation will be discussed. The parameters required for design will be identified and their effect delineated. Although this paper will be geared for a general understanding of fracturing, recent findings in rock mechanics and key areas requiring further definition will be presented.

I NTRODUCTI ON

The hydraulic fracturing of reservoirs to stimulate oil and gas production revolutionized the petroleum industry. The fracturing of reservoirs greatly increases the economic lives of some wells. This is particulary true for tight. gas sands, or in cases where portions of the reservoir may be depleted and will not flow adequately without stimulation.

The hydraulic fracturing of wells has developed into a highly sophisticated technique over the past thirty years. The initial treatments have evolved from sma 11 jobs usi ng a few thousand pounds of sand to highly technical .computer designed treatments that sometimes incorporate one million pounds of sand. While fracturing was growing in popularity, so was the need for more efficient frac fluids, different types of sand, special additives, sophisticated pump­ing equipment and the use of technically engineered treatments. Whil e techn; ques and equi pment are con­stantly changing and being upgraded, there are still questions to be answered and significant improvements to be made. There is often a gap between theory and practical field application. These theories must be applied and tested in a usable form at the operations 1 evel.

It is the intent of this paper to review the basics of fr acturi ng and to provi de a better understandi ng of day to day operations.

PRINCIPLES

Increased emphasis has been put on the study of rock mechanics in recent years. This study has great importance, especially in tight gas sands. It is as­sumed that formation rock is isotropic, homogeneous and e 1 ast i c, and is generally defi ned by two con­stants, Young's Modulus and Poisson's Ratio. Al­though these assumptions are never completely true, their simplification is necessary to handle the complexities that arise.

Formation rock is under three principle stresses. The bas i c premi se of rock fa il ure is that it occurs perpendicular to the least principle stress. In re­laxed areas with normal faulting, the principle stress is vertical with a value of approximately 1 psi/ft. In this instance, the fracture will be vertical with the intermediate and least principle stresses in horizontal directions, as shown in figure 1. Th i sis normally the case in the Gu 1 f Coast, Mi d-Cont i nent and West Texas areas, as supported by frac gradients less than one.

The relationship between the vertical maximum matrix stress (cr v) and the horizontal matrix stresses, where the horizontal stresses are equal is given by:

OJ = °L = (-H-)Ov 1-lJ

where 1.1 is Poisson's Ratio. For petroleum reservoirs,Poisson's Ratio ranges from 0.15 to 0.35. This gives a horizontal matrix stress of 18 to 55% of the vertical matrix stress.

Hydraulic fracturing is basically a process of rup­turing the formation rock. In order to rupture the rock, the matrix stress, pore pressure and tensile strength of the rock must be overcome. The total stress(S) is composed of matrix stress plus pore pressure. Since the tensile strength of rock is low and highly variable, it is frequently ignored. In this instance, the least horizontal total stress or frac gradient (FG) would be:

2 FUNDAMENTALS OF FRACTURING SPE 9064

For example let: Smax = 1 psi/ft. (2.11 x 104PaLM) Po = 0.46 psi/ft. (0.97 x 10~Pa/M)

= 0.2 then, SL = FG = 0.6 psi/ft. (1.26 x 104Pa/M)

Based on the frac gradient from this equation, an increase in either Poi sson' s Ratio or pore pressure will cause a subsequent increase in the frac gradi­ent. When the frac gradient is known, equation 1 can be used to estimate pore (reservoir) pressures or re­lative variations in rock properties. Although equa­tion 1 can be used to estimate the frac gradient, normally it is available from acid and fracturing treatments. It is achieved by dividing the sum of, instant shut-in pressure (Pisi) and hydrostatic pressure (Ph), by depth.

(2) FG = fisi~ Depth

The three principle stresses are generally unequal. The magnitude of the differences in the intermediate and least stresses will determine the preferred com­pass direction (azimuth) of the fracture. They will also determine the potential for secondary fractures, perpendicular to the matn fracture, which might occur during a fracturing treatment. If there is a large difference between the intermediate and least stres­ses, a preferred azimuth will be more likely, while the chances of secondary fractures wi 11 be 1 ess pro­bable. The converse is true when there is small dif­ferences between the i ntermedi ate and 1 east stres­ses.

In practical terms2, the intermediate stress is given by:

(3) °1 = 3°L - Pb - Po + to

where Pb = breakdown pressure Po = pore pressure to = tensile strength

The value for the breakdown pressure has the greatest uncertainty because the number and orientation' of perforations may greatly affect it. 3 However, larger breakdown pressures, due to perforations, will lead to conservative or low values for the intermediate stress.

The least horizontal stress is assumed to be ap­proximately equal to the instant shut-in pressure:

(4) °L = Pisi

The instant shut-in pressure can be higher than the least stress by about 200 psi (1.4 x 106Pa). How­ever, it should be sufficient for practical compari­sons.

Equations 3 and 4 provide a powerful tool to reflect downhole stresses, which can provide insight into the day to day fracturing process. However, these values for the most part are not being used.

Rosepiler recently performed a comprehensive study of the Rri nci p 1 e stresses in the Cotton Valley Forma­tion. 2 The 1ithostatic gradient, (total maximum

vert i ca 1 stress), from dens ity logs, was found to be approximately 1.07 psi/ft. (2.26 x 1Q4Pa/M). The average of Poisson's Ratio from acoustic logs were, 0.16 for sands and 0.29 for shales. The least stress measurements taken from instant shut-in pressures compared favorably with the calculated values. Using breakdown pressures and equat i on 3, Rosepil er found that the. intermediate horizontal stress' was usually greater than the least horizontal stress. This implies additional tectonic forces are present. The least stress, represented by instant shut-in pressures, ranged from 5594 psi to 7190 psi for sands. The intermediate stress was generally 1.2 times the least stress, although they were very near equal in 5 cases. The intermediate stress ranged form 5618 psi to 9191 psi in sands.

One use of stress data is to predict the probability of secondary fractures. Nolte4 presented the fol­lowing relationship to predict the opening of second­ary fractures.

P = ~Id-1-j,I

Pis the pressure that must be exceeded to create secondary fractures. Rosepil er2 has provi ded data which suggests the pressure needed to open secondary fractures in the Cotton Valley would range from 500 psi to 2000 psi. Pressures in this range can be reached, particularly in long fractures. Nolte4 has presented a basis for interpreting fracturing pressure, which includes the effects of secondary fractures. His method could become a,valuable aid in understanding fracturing, since it combines theory and practical applications that can be tested and analyzed in the field.

The effect of fracture azimuth on optimum field de­velopment of stimulated low permeability reservoirs can be very pronounced, as shown by Smith. 5 Using a reservoir simulator, he found a variation in azimuth of approximately 45° could decrease 30 year product i on by as much as 18%. I n East Texas and North Louisiana, limited data suggests a northeast by southwest direction for fracture azimuth, but the azimuth will tend to parallel faults in the area. In a relative manner, consistency from well to well of a high ratio of least and intermediate horizontal stresses may i ndi cate the probabil ity of the same fracture azimuth.

Although several aspects of rock mechanics are un­clear, industry is making a concentrated effort in this area. The greatest clarification may come from refinements in field results.

APPLICABILITY TO FRACTURING

The key to successful hydraulic fracturing is based on hori zonta 1 format i on permeabil ity, fracture con­ductivity and fracture penetration (length), as a function of the effective drainage area. This as­sumes that there is an economical quantity of hydrocarbons in the reservoir and enough poros ity, saturation, productive interval and reservoir con­tinuity and pressure exists.

Permeability is often poorly defined and commonly overstated. In tight gas sands, this can lead to poorly designed frac jobs. The most rel iable per-

SPE 9064 G. F. DANIELS AND J. L. WHITE 3

meability values are obtained through pressure build­up or decline analysis and matching of production histories. Using permeability values that are based on core analyses can result in values that are too high.6 Permeabil ity measured under confining pres­sures provide more realistic numbers. 6•7 Routine perms on clean Cotton Valley sands should be reduced by a factor of about 16. For shale.Y CV sands, the factor would be close to 60. Joneso gives a method to estimate actual CV perms based on perms from routine core-analysis.

The production curve (PI) shown in figure 2, has been used for years to relate the effect of formation per­meabil i ty, fr acture conduct i vity, spaci ng and pene­tration to fracturing effectiveness. Several assump­tions exist that limit a quantitative analysis using the PI, but relative comparisons are useful. A re­servoir simulator is the best way to obtain quanti­tative and economic analysis, particularly for low permeability reservoirs (O.Olmd and less). The op­timum frac length will be discussed later in the paper.

FRACTURING DESIGN

The basic assumption in fracturing design is the cre­ation of vertical fractures and that there are two rectangular, opposing in-line wings. These wings have dimensions of height, length (one wing) and width as shown in figure 3. How these dimensions are achieved is a more complex matter.

Presently, there is no ~ethod available to accurately predict gross fracture height, and this value must be defined for computer design. The uncertainty in fracture height is generally considered the greatest limitation in frac design. In de~ign, the net height determines the area over which fluid loss will occur and normally exceeds the pay interval.

Although there is no quantitative method to determine gross fracture height, lithological barriers are gen­erally agreed to contain frac height. 8 These bar­riers occur as a result of in situ stress differ­ences which are qualitatively related to elastic pro­pertries of the formation (e.g., Young's Modulus and Poi sson' s Ratio). Shale and low permeabil ity zones are generally considered potential barriers due to their high Poisson's Ratio which allows for higher horizontal stresses (EQ. 1). The barriers are deter­mi ned based on logs and are 1 ater confi rmed, after the frac job, by: 1) temperature surveys; 2) gamma ray analysis using radioactive sand, radial differ­ential temperature logs and noise 10gs.9, 10 Tem­perature surveys and gamma ray logs have proven ef­fective. The gamma ray logs are most effective when radioactive sand is run throughout all the propping agent. These methods wi 11 i dent i fy the fr ac hei ght near the we1lbore. The question still remains as to the frac height away from the wel1bore.

The thickness required to constitute a barrier has long been a topic of lively discussions. A shale zone of only 6 to 8 feet (1.8 to 3.5m) has been re­ported as an effective barrier for frac contain­ment.10 Many Cotton Valley operators feel the minimum shale thickness should be from 10 (3.0m) to 30 feet (9.8m) to contain fracture height. Usually the greater the thickness of the barrier. the more effectively it functions in frac containment. Huff tIl reported that an 80 foot (26.2m) shale

section in the Cotton Valley failed to contain a fracture. The uncertainties of barrier containment are not only a function of poorly defined stresses and the effect of zone thickness, but the effect of pump rate, fluid viscosity and frac length in ex­ceedi ng thi s pressure or stress 1 imit must also be considered. The latter effects Gould explain the widely varying opinions. Nolte's4 method of ana­lyzing fracturing pressures could be a valuable tool to establish the effects of rate, viscosity and frac­ture length on frac height.

Frac barriers may be time dependent i.e., as the Pw increases with time, barrier penetration may occur and this rate of penetration may be slower than the rate in the pay zone. With time, the barrier will be completely penetrated. Nolte points out that rate is only one factor in frac height and that treating volume or time can result in pressure great enough to penetrate barriers.

Hufftll has proposed that rate can be used to con­trol frac height growth in the Cotton Valley Forma­tion. His relationship was establ ished for a pump rate range of 8 BPM to 15 BPM as H = 24eO•164Q.

This translates to 11 feet of height/BPM at 8 BPM and 18 feet of height/BPM at 15 BPM Although many East Texas CV operators use somewhere between 8 feet/BPM to 15 feet/BPM as a rule of thumb for fracture height, several operators feel rates from 15 to 25 BPM have little effect on height.

Some operators design the frac job based on what they would like the height to be (e.g., net height) rather than reality. In any event, use of correct fr ac height and containment of height to the pay interval can have a dramatic effect on economic optimization.

Fracture width is computed by one of two basic mod­els. One model developed originally by Perkins and Kern,12 is where the fracture cross section, paral­lel to its height is elliptical. The example at the right of figure 4 illustrates this fracture shape. The elliptical width is more realistic than the sec­ond model. The equation for model 1 has the form,

W = 4(1- /.1 2) liPH E

where ~ P = friction pressure loss in the fracture.

In order for the width to increase. the friction pressure in the fracture must increase as the job proceeds. If this model is val id, bottom-hole pres­sure shOUld increase with time. Indeed, a pressure rise during treatment has been observed in some tight reservoirs by Nolte. 4 However. one limitation for the Perkin and Kern model is the difficulty in com­puting sand transport without assuming consistent fracture width along its height.

The second model for frac width was orl~inallY devel­oped by Khristianovich and Zheltov. It has a constant width along the height, as shown to the left of figure 4. The equation for model 2 is similar to the one in mode 1 I, except fr acture 1 ength of one wing replaces the height.

w = 4(1- /.1 2) APL E

4 FUNDAMENTALS OF FRACTURING SPE 9064

In model 2, the width can increase without an in­crease in fracture friction pressure. Computation of pressure with model 2 shows the pressure to de­crease during early stages of the treatment and then reaching a constant value that is still higher than the minimum horizontal stress. Model 2 will general­ly give wider fractures and shorter lengths than mod­ell. Model 2 simplifies computing prop transport.

Fracture width will tend to increase with greater pump rates, higher fluid viscosity and lower Young's Modulus. In model 2, the width will increase with length. The fracture width only needs to be wide en­ough to accept the desired size and quantity of proppants wh~n effective transport is maintained. Any width beyond this amount is wasted and reduces the fracture length.

The des i gned hydr au1 ic fr acture 1 ength is computed, based on the width and fluid loss equations, assuming a constant fracture height. The fracture length will increase with narrower widths, greater fluid loss ef­ficiency and a higher Young's Modulus. The PI curve in figure 2 can be used as a guide to desirable frac length. For economic analysis, a reservoir simulator should be used.

An example of present value, as a function of frac length on a typical Cotton Valley evaluation is shown in figures 5 and 6 for 320 acre (1.3 x 106m2) and 640 (2.5 x 106m2) spacing respectively. The opti­mum length for 320 acre spacing is between 1500 feet (457m) and 2000 feet (610m). For 640 acre (2.5 x 106m2) spacing, the op-timum length is over 2000 feet (610m). Holditch14 found similar results for tight gas reservoi rs with opt imum 1 engths of 1500 feet (457m) to 1800 feet (610m). Most people agree a 320 acre (1.3 x 106m2) or less spacing will be required for the effective drainage of the gas in p1 ace.

If a critical fracturing pressure exists, as suggest­ed by Nolte,4 there may be a practical operational limit on fracture length.

There is a general trend among operators to under­design fracture length. This becomes even more cri­tical when the actual lengths from reservoir simula­tor studies are significantly less than the designed length. For example, Holditch found that on the average the actual length from history matching was 70 percent of the designed length.

The topics of fluid loss, fluid selection, prop selection and prop transport are very important aspects of the design procedure. They will be dis­cussed in detail in a companion paper16 •

1.

2.

3.

CONCLUSIONS

The fracturing breakdown pressure and instant shut-in pressure reflect down-hole stress values which are generally not used. These values coupled with down-hole fracturing pressures should be used to gain a better understanding of the day to day fracturing operations.

Gross and net fracture heights remain the great­est uncertainties in fracturing design.

In tight gas sands, an accurate permeability is required to optimize fracture length.

4. From an optimum, economical standpoint, there is trend fracturing treatments.

REFERENCES

fracture length to underdes i gn

1. Howard, G. C. and Fast, C. R.: Hydraulic Fracturing, Society of Petroleum Engineers of AIME, New York (1970).

2. Rosepiler, M. J.: "Determination of Principle Stresses and Confinement of Hydraulic Fractures in Cotton Valley", paper SPE 8405 presented at SPE 54th Annual Fall Meeting, Las Vegas, September 23-26, 1979.

3. Daneshy, A. A.: "Experimental Investigation of Hydraulic Fracturing Thru Perforations", J. Pet. Tech. (Oct., 1973).

4. Nolte, K. G.: "Interpretation of Fracturing Pressures", paper SPE 8297 presented at SPE 54th Annual Fall Meeting, Las Vegas, Sept. 23-26, 1979.

5. Smith, M. B.: "Effect of Fracture Azimuth on Product i on wi th app 1 i cat i on to the Wattenber g Gas Field", paper SPE 8,298 presented at SPE 54th Annual Fall Meeting, Las Vegas, Sept. 23-26, 1979.

6. Jones, F. O. and Owens, W. W.: "A Laboratory Study of Low Permeabil ity Gas Sands", paper SPE 7551 presented at SPE-AIME Symposium on Low Permeabil ity Reservoi rs, Denver, May 20-22, 1979.

7. Strict1and, F. G. and Feves, M. L.: "Microstructural Damage in Cotton Valley Format i on Cores", paper SPE 8303 presented at SPE 54th Annual Fall Meeting, Las Vegas, Sept. 23-26, 1979.

8. Simpson, T. A. and Abou-Sayed, A. S.: "Containment of Massive Hydraulic Fractures", Soc. Pet. Eng. J., (Feb. 78) 27-32.

9. Dobk ins, T. A.: "Methods to Better Determi ne Hydrau1 ic Fracture Height", paper SOE 8403 presented at SPE 54th Annual Fall Meeting, Las Vegas, Sept. 23-26, 1979.

10.

11.

12.

Pearce, R. M.: "Evaluation Treatments Using Tracer and Surveys", paper SPE 7910 presented Symposium on Low-Permeability

·Denver, May 20-22, 1979.

of Fracture Temperature at SPE-AIME Reservoirs,

Hufft, H. F.: "The Evolution of a Fracturing Technique for the Cotton Valley", paper SPE 6868 presented at SPE 52nd Annual Fall Meeting, Denvei, Oct. 9-12, 1977.

Perkins, T. K. and Kern, L. R.: "Widths of Hydraul ic Fractures", J. Pet. Tech. (Sept., 1961).

SPE 9064 G. F. DANIELS AND J. L. WHITE

13. Kristianovic, S. A. and Zheltov, Y. P.: "Formation of Vertical Fractures by Means of Highly Viscious Liquid", Proc. Fourth World Pet. Cong., Rome (1955).

14. Holditch, S. A., Jenning, J. W., and Neuse, S. H.: "The Optimization of Well Spacing and Fr acture Length in Low Permeabil ity Reservoi rs" , paper SPE 7496 presented at SPE 53rd Annual Fall Meeting, Houston, Oct. 1-3, 1978.

15. Holditch, S. A. and Lee, W. J.: "Fracture Evaluation with Pressure Transient Tests in Low Permeability Gas Reservoirs, Part II: Field Examples", paper SPE 7930 presented at SPE-AIME Sympos i urn of Low-Permeabi 1 ity Reservoi rs, Denver, May 20-22, 1979.

16. Daniel, E. F. and White, J. L.: "Design of MHF Treatments in the Cotton Va 11 ey", paper SPE 9065 to be presented at the 1980 Cotton Valley Symposium, Tyler, Texas, May 21, 1980.

E

FG

Pisi

Q

S

W

NOMENCLATURE

Young's Modulus

Fracturing Gradient

Frature Height

Gross Fracture Height

Net Fracture Height

Permeability

Length

Pressure

Breakdown Pressure for Fracturing

Hydrostatic Pressure

Instant Shut-in Pressure

Pore or Reservoir Pressure

Pump Rate

Total Stress

Width

Matric Stress

Poisson's Ratio

5

FUNDAMENTALS OF FRACTURING

(T Z=MAXIMUM STRESS (T A =LEAST STRESS (Ta=INTERMEDIATE STRESS

ORIENTATION OF FRACTURE EXPECTED BY , APPLYING INTERNAL PRESSURE EQUAL TO

OR GREATER THAN LEAST STRESS

IDEALIZED STRESS DISTRIBUTION., TECTONICALl Y RelAXED FORMATION

Fig. 1 - Idealized stress distribution; tectonically relaxed formation.

14

12

10

I-- VERTIcAL IFRA~TURES ~::: I-- 1 00%

90% 80% 70% 60% Z 50% 0

I--

~ ~

8

6

4

~ ~ ;:;;'-1-"" L.-

~ ~I-"" ~ ~ ~ r--

JI!!!. ~ 2 ~

o 0,1 0,3 0.6 1 3 6 10

KfW ~ 40 K S

40%

30', 20',

10',

30 60 100

i= oC(

'" .... """ Z

""" CI..

Fig. 2 - Estimated production increase after fracturing (vertical fractures).

(a) VERTICAL

(h) NEAR-VERTICAL

Fig. 3 - Fracture orientation.

OVERBURDEN OVERBURDEN

UNDERBURDEN UNIlERBUROEN

Fig. 4 - Possible fracture geometry.

250

:z 200

~ 150 > :: z 100 0

;;;; 50

~ ""

·50

·100

.150 0

PRESENT VALUE VS FRACTURE LENGTH COTTON VALLEY • 320 ACRE SPACING

PERM 0.0022 md POROSITY 5% HEIGHT 360 FEET INITIAL GAS PRICE 1229/MCF

ESCALATEO AT 2S,!; TO A MAXIMUM OF 16 OOIMCF

~ INTEREST RATE IIR)

~ DISCOUNT IR

~OISCOUNT IR

r·",,""' " 1000 2000 2500

FRACTURE LENGTH

Fig. 5 - Present value vs. fracture length, Cotton Valley - 320 acre spacing.

300

250

200 .... :z

~ 150

> :: 100

;;;; => ....

50 .. ""

·50

·100

-1 50 0

PRESENT VALUE VS FRACTURE LENGTH COTTON VALLEY 640 ACRE SPACING

0" DISCOUNT

INTEREST RATE (lR)

PERMEABILITY 0.0022 md

POROSITY S" HEIGHT 360 FEET

INITIAL GAS PRICE 52.29/MCF

ESCALATED AT 25'1> TO A

MAXIMUM Of SO.OO/MCF

10\ DISCOUNT

y::::::::

1000 1500 2000 2500 fRACTURE LENGTH

II

II

IR

Fig. 6 - Present value vs. fracture length, Cotton Valley - 640 acre spacing.