RS_05A

◆Appendix: Evolution of Hydraulic Fracturing Design and Evaluation K. G. Nolte, Schlumberger Dowell Overview This Appendix to Chapter 5 reviews the evolution of hydraulic fracturing design and evaluation methods. Complementary reviews are the application of fracturing by Smith and Hannah (1996) and fracturing fluids by Jennings (1996). This review of design and evaluation considers three generations of fracturing: damage bypass, massive treatments and tip-screenout (TSO) treatments. The first two generations of fracturing and their links to practices are emphasized because these contributions are not likely well known by the current generation of engineers. The review focuses on propped fracturing and does not explicitly consider acid fracturing. Although the principles governing the mechanics of both are essentially the same, the fluid chemistry for obtaining fracture conductivity is quite different (see Chapter 7). These principles have their roots in civil and mechanical engineering, more specifically in the general area of applied mechanics: solid mechanics for the rock deformation and fluid mechanics for the flow within the fracture and porous media. For the porous media aspects, fracturing evaluation has benefited greatly from the reservoir engineering practices discussed in Chapters 2 and 12. This review reflects the author’s perspective and bias in interpreting the impact of past contributions, and therefore parts of this review should be anticipated to raise objections from others with an extensive knowledge of fracturing. In addition to this volume, the Society of Petroleum Engineers (SPE) Monograph Recent Advances in Hydraulic Fracturing (Gidley et al., 1989) provides balanced, detailed coverage of the diverse areas of fracturing from the perspectives of more than 30 fracturing specialists. This review concludes with speculation concerning a future generation, in which fracture design and reservoir engineering merge into fracturing for Reservoir Stimulation reservoir management (i.e., control of both the vertical and horizontal flow profiles within the reservoir). Similar speculation in a 1985 lecture suggested that development of the technical foundation for the TSO generation would quickly bring higher permeability formations into consideration as typical fracturing candidates (i.e., “moderate k (2×)” on Appendix Fig. 1a, with 2× indicating a target for folds of increase [FOI] in the production rate, in contrast to 10× for tight gas and massive treatments). However, the advent of this generation was considerably delayed because of two factors that have generally dominated technical considerations during the history of fracturing. These dominating factors are hydrocarbon prices and resistance to trying something new until established practices fail to allow the economic development of a prospect. The cycles of fracturing activity in Appendix Fig. 1a clearly reflect the timing of the first two fracturing generations. Appendix Fig. 1b identifies economic drivers for corresponding cycles in the U.S. rig count. The first surge of activity resulted when rotary drilling was introduced, which enabled the development of deeper reserves. Fracturing activity followed this trend soon after its commercialization in 1949 because it was found to be an effective, low-cost means of mitigating the resulting drilling mud damage to reservoir sections (i.e., the damage bypass generation). Both drilling and fracturing activities began a long-term decline after 1955 because of degrading prices caused by imported oil and regulated gas prices. Similarly, both activities began a rapid increase at about 1979 as prices increased because the Organization of Petroleum Exporting Countries (OPEC) reduced its oil supplies and a natural gas shortage developed in the United States. The gas shortage, and its 10-fold-plus increase in price, encouraged the development of tight gas reserves and an associated demand for massive fracturing treatments to develop the tight reserves. The failure of past fracturing practices for A5-1 (a) Mode rate k (2×) High c onduc tivity Un T de ight rst ga an s( eq ding 10×) uip , m me ate nt ria ls, Rem ove dam age Treatments 4000 0 1950 1955 1971 Year ? 1981 15.1 Up Up 9. 9% /y ea r %/y ear 4500 OPEC overextends 4000 Prices fall U.S. gas prices regulated Middle East discoveries 3500 3000 U.S. production peaks OPEC develops 2500 price authority Do wn 2000 6. 1% /ye 1500 ar 1000 Rotary displaces 500 cable tool drilling 0 1940 1950 1960 1970 1980 1985 forcast flat .5%/yea Down 25 The beginning r Annual average rotary rig count (b) 1990 2000 Year Appendix Figure 1. (a) Trends in fracturing activity treatments per month (courtesy of K. G. Nolte and M. B. Smith, 1985–1986 SPE Distinguished Lecture). (b) U.S. drilling rig activity shows five major trends (updated from Oil & Gas Journal, 1985). large treatments spurred a significant research and development effort that beneficially impacted every aspect of fracturing and essentially developed the fracture design and evaluation framework presented in this volume. The industry’s rapid contraction during the early 1980s resulted again from OPEC, but this time because of OPEC’s failure to maintain artificially high prices. The TSO treatment for creating the very wide propped fractures required for high permeability evolved during this time. This technique allowed the development of a troublesome soft-chalk reservoir in the North Sea by fracturing. However, the significant potential of the TSO generation did not materialize until about 10 years later, when its application was required on a relatively large scale to achieve viable economics for two highpermeability applications: bypassing deep damage in the Prudhoe Bay field and its coupling with gravel A5-2 packing to achieve low-skin completions for a significant venture in the Gulf of Mexico. The potential for a future reservoir management generation was demonstrated in 1994 for the Norwegian Gullfaks field. The potential is to use TSO treatments and indirect vertical fracturing for increased reserves recovery, formation solids control and water management. However, the unique benefits and favorable economics for this different approach to reservoir “plumbing” were slow to materialize because of the industry’s comfort with deviated drilling and more traditional completions. Another observation from this historical perspective is the 1985 forecast of a flat drilling level (Appendix Fig. 1b). However, activity continued to decrease rapidly, to less than one-half of the forecast, and subsequently declined by another one-half. Stable activity levels within the petroleum industry are not seen in the historical cycles and remain the product of wishful thinking. The concept of hydraulic fracturing within the petroleum industry was developed during the last half of the 1940s within Stanolind (now BP Amoco; e.g., Clark, 1949; Farris, 1953; Howard and Fast’s Hydraulic Fracturing Monograph, 1970) by building on the industry’s experience with injection techniques that had experienced increased injectivity by fracturing: acidizing (Grebe and Stoesser, 1935), squeeze cementing and brine injection wells. A reissued patent was granted (Farris, 1953, resulting from an initial filing in 1948) that was comprehensive in scope and covered many recognized practices and products: proppant, gelled oil, breakers, fluidloss additives, continuous mixing, pad-acid fracturing, emulsified acids and the use of packers for fracturing multiple zones. Several aspects of the patent that later became important included the implication that fractures were horizontal and the use of a “lowpenetrating” fluid or with viscosity > 30 cp. The first experimental treatments were performed in 1947 on four carbonate zones in the Houghton field in Kansas (Howard and Fast, 1970). The zones had been previously acidized and were isolated by a cup-type straddle packer as each was treated with 1000 gal of napalm-thickened gasoline followed by 2000 gal of gasoline as a breaker. These unpropped Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation R. In the following review. the orientation consideration is expanded to also cover the state of stress in more general terms.. Activity rapidly expanded to about 3000 treatments per month by 1955 (Appendix Fig. It consisted of 23 bbl of gelled lease crude. An inherent advantage of propped fracturing. a vertical fracture). Fast.. but adds the consideration of producing from bottomwater or an upper gas cap. the treatments used river water and sand. 1997). comm. The water was outside the definition of a nonpenetrating fluid within the patent’s specified filtrate rate through filter paper or viscosity greater than 30 cp. FOI prediction and fracture conductivity in production enhancement.. is that a fracture opens the complete section and retains a conductive path into the zone. but also the fluid pressure required to propagate a fracture that has operational importance. and TSO treatments have been routinely performed in Prudhoe Bay oil columns only 50 ft thick and above very mobile water (Martins et al. The technology for this fracturing generation is summarized in the Howard and Fast (1970) Monograph. The complete opening overcomes the diversion consideration for matrix treatments (see Chapter 19). Key to the favorable settlement for Stanolind was its welldocumented demonstration of a horizontal fracture in the Pine Island field (see fig. R. However.000 treatments were performed during the 17-year period of the patent (C. comm. As implied by the name. Halliburton originally obtained an exclusive license from Stanolind and commercialized fracturing in 1949. A subsequent treatment of the Woodbine sand in the East Texas field was highly successful. 1a). 7-1 in Howard and Fast.treatments did not increase production and led to the incorrect belief for some time that fracturing had no benefit over acidizing for carbonate formations. Fast. 1997). the precision of fracturing improved significantly. Fracture orientation and in-situ stress The application of mechanics to fracturing was catalyzed by the horizontal orientation of fractures implied in the Stanolind patent and the desire of several operators to avoid paying the nominal patent royalty of $25–$125. The first generation: damage bypass Applications of first-generation fracturing were primarily small treatments to bypass near-wellbore drilling fluid damage to formations with permeability in the millidarcy range. Other note- Reservoir Stimulation worthy design and evaluation methods from this generation are fracture orientation (horizontal or vertical). water production can be significant. pers. 1970). comm. which provided the historical preference for matrix treatment in higher permeability applications. 160 lbm of 16-mesh sand at 0. water or “river” fracturing became popular in lower permeability areas such as the San Juan basin (C. vertical fracture growth into surrounding formation A5-3 . The breadth of this volume is shown by its comprehensive consideration of candidate selection (see Chapter 1) and optimal design based on economic return (see Chapters 5 and 10). 1992b). the fracture preferentially aligns itself perpendicular to the direction of minimum stress because this orientation provides the lowest level of power to propagate the fracture. The preference for a horizontal fracture requires a vertical minimum stress direction. R. The fracture orientation debate eventually led to a lawsuit that was settled before the trial ended. large amounts of produced water are generally not a problem. The central issue in the orientation debate was the direction of the minimum stress. hence. Fast. The pressure required to extend a fracture must exceed the stress acting to close the fracture. Before a universal license was granted to other service companies. the royalty benefits were more than nominal to Stanolind because about 500. The stress state defines not only the fracture orientation. in-situ stress and fracture width models. relative to matrix treatment for damage removal. pers. based on volume (C..15 ppa and 24 bbl of breaker (Farris. Therefore. For higher permeability formations.e. as is now known to be the general case for typical fracturing conditions. pers. The settlement accepted the patent and nominal royalty payments and stipulated that other service companies receive a license to practice fracturing. For lower permeability formations. 1997). 1953). However. The stress at any point in the various rock layers intersected by the fracture is defined by its magnitude in three principal and perpendicular directions. the fracture plane orientation is generally vertical (i. The minimum stress direction is generally horizontal. Significant research activity was conducted to show that fractures can be vertical.. If the converse were the general case. Harrison et al. dimension in this relation. after removing the fluid-loss volume. or smaller and finite. 1 provides the current basis for using mechanical properties logs to infer horizontal stress. The first paper to be considered is by Harrison et al. Another assumption for Appendix Eq. Nolte and M. there is one problem with this 1954 conclusion concerning horizontal stress.σ h = Ko σ v . Using Poisson’s ratio ν of 1⁄4.’s 1954 paper does not discuss fluid loss. 1 is correct for the effective stress σ′ but not for the total stress σ that governs fracture propagation: σ′ = σ – p. Volume balance for fracture placement (equation from Harrington et al.. they can be appropriately averaged over the length. Harrison et al. Appendix Eq. the material balance in reservoir terminology) is an essential part of fracture design and fracture simulation code. fracturing pressures are generally lower than this value and therefore fractures are not horizontal. Harrison et al. 1 provides the horizontal stress response to maintain the horizontal dimensions of a unit cube constant under the application of vertical stress. 2. which also has a role in transferring the vertical stress into horizontal stress as explicitly shown by Appendix Eq. by twice the product of the L= Vi 2hf (w + CL √8t ) η= 2hf wL Vi Fluid loss CL √ t Proppant layers and stress acting to crush proppant or to close etched channels from acid fracturing. However. 2. The half-length is then obtained by simply dividing the remaining volume. These models are discussed in the next section and Chapter 6. Therefore. As shown schematically on the left side of Appendix Fig. The crushing stress is the minimum stress minus the bottomhole flowing pressure in the fracture. Some of the important points in the paper are that the overburden stress (vertical stress σv) is about 1 psi per foot of depth. Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation . They used the fracture length for the characteristic. Selecting the height. based on the premise that the circumference of the earth does not change as sediments are buried to the depths of petroleum reservoirs and hence the horizontal components of strain are zero during this process. Appendix Eq. Smith. This framework has become the basis for predicting fracture width and fracturing pressure response (see Chapters 5. The role of volume balance (or equivalently. where p is the pore pressure. also reported the Sneddon and Elliott (1946) width relation for an infinitely extending pressurized slit contained in an infinitely extending elastic material. is termed the PKN model. (However. If the latter two dimensions are not constant along the fracture length. Selecting the length for the characteristic dimension resulted in what is now commonly termed the KGD model. B. The general case of higher stress in shales than in reservoir rocks was a necessary condition for the successful application of fracturing because fractures follow the path of least stress. height hf and width w. 1984–1985 SPE Distinguished Lecture). Appendix Eq. A5-4 Harrison et al. 3-51). considered a width relation because of its role in fracture design to determine the fluid volume required for a desired fracture extent. each unit of fluid injected Vi is either stored in the fracture to create fracture volume or lost to the formation as fluid loss. The orientation debate resulted in three papers that will remain significant well into the future.) The stored volume is the product of twice the fracture half-length L. (1) where Ko = ν/(1 – ν) = 1⁄3 for ν = 1⁄4 (see Eq. Harrison et al. as is the case for a very long fracture. G. 1973) (adapted courtesy of K. (1954). fractures would prefer to propagate in shales and not in reservoir zones. and an inference from elasticity that the minimum horizontal stress is Geometry hf 2L Proppant (% area = η) w Pad Volume Appendix Figure 2. (1954) correctly postulated that shales have higher horizontal stresses and limit the vertical fracture height. 1 is uniaxial compaction. 6 and 9). with Poisson’s ratio obtained from a relation based on the shear and compressional sonic wave speeds (see Chapter 4). concluded that the horizontal stress is about one-third of the vertical stress and therefore fractures are vertical. . 2) with minimal creep and sediments with higher clay content. This extreme difference in the assumptions for Appendix Eqs..2) because of the difference in horizontal stress resulting for layers with different values of Young’s modulus (stiffness). For this case the horizontal stress is much less than the vertical stress except in the extreme geopressure case of pore pressure approaching overburden..g. Additional considerations for horizontal stress outlined by Prats (1981) include the role of long-term creep. both clay content and Poisson’s ratio produce the same effect on horizontal stress. but by an active state of failure along discrete boundaries (e. They also used simple sandbox experiments to demonstrate normal and thrust faulting and to define the state of stress for these conditions (see Sidebar 3A). within Appendix Eq. 1) inferred from sonic velocities. 1986b) (see Sidebar 6L). More of the tectonic action and higher levels of stress are supported by the stiffer layers. the ratio of stored to total volume is termed the fluid efficiency η and directly affects the proppant additional schedule (Harrington et al.. This effect is well known for salt layers that readily creep and can collapse casing by transferring most of the larger overburden stress into horizontal stress. thereby enabling the horizontal stress to increase toward the larger vertical stress governed by the weight of the overburden. the stress is not governed by the behavior of the intact rock matrix. 2 to microdarcy-permeability sandstones). Reservoir Stimulation Hubbert and Willis also provided an important set of postulates: the rock stresses within the earth are defined by rock failure from tectonic action and the earth is in a continuous state of incipient faulting. For the latter experiments. The fluid-loss volume depends on the fluid-loss surface area. 2 to accurately predict the horizontal stress in tectonically relaxed sandstone formations ranging from microdarcy to darcy permeability. The role of stress relaxation is an important mechanism for providing favorable stress differences between relatively clean sands governed by friction (i. as shown on the right side of Appendix Fig. The second paper to be discussed from the orientation era is by Hubbert and Willis (1957). Creep deformation allows relaxation of the stress difference between the overburden and horizontal stresses. Nolte. The implication of the correlation is that clay-rich A5-5 . 1 is defined by the internal friction angle (ϕ = 30° for sand) and is 1 ⁄3 for the minimum stress during normal faulting and 3 for the maximum stress during thrust faulting. The clay structure is prone to creep that relaxes the in-situ stress differences and increases the horizontal stress for a clay-rich formation. They showed that Ko. The accuracy obtained for microdarcypermeability sands is subsequently explained. The lessons from this paper extend beyond fracturing and into the area of structural geology. (2) where Ko = 1⁄3 with ϕ = 30°. the clay supports some of the intergranular stresses. The author has found Appendix Eq. 1. by sand grains within fault boundaries. However. or a height-length product. 1 and 2 is often overlooked because of the similar value of Ko = ~1⁄3 obtained in the case of a tectonically relaxed region and Poisson’s ratio near 1⁄4. 2. From this perspective.e. there is a positive correlation of clay content (creep-induced stress) to larger Poisson’s ratios (and elastic stress. Appendix Eq. the role of elasticity becomes important in thrusting areas (see Section 3-5. Furthermore. which explains the application of Appendix Eq. Because clay content also increases Poisson’s ratio. as the formations approach the unconsolidated sand in the sandbox experiments. For the normal faulting case and correctly including pore pressure in Appendix Eq.average height and the average width. Hence. This work provides simple and insightful experiments to define the state of in-situ stress and demonstrate a fracture’s preference to propagate in the plane with minimum stress resistance. In the latter case.e. the “formation” was gelatin within a plastic bottle preferentially stressed to create various planes of minimal stress. Both the extreme geopressure case and an active thrust faulting regime can lead to either vertical or horizontal fractures. For the thrust faulting case. This insightful conclusion about the role of failure is at the other extreme of the behavior spectrum from the elastic assumptions that Poisson’s ratio (Appendix Eq. 1973. the total minimum horizontal stress becomes σ h = ( σ v + 2 p) 3 . the larger horizontal stress (i. 1) governs the horizontal stress and that failure has no effect on the stress. which causes all stresses and pore pressure to converge to the overburden stress. for the two horizontal directions) is greater than the overburden and the smaller horizontal stress is equal to or greater than the overburden. The accuracy at the high range is not surprising. from Appendix Eq. or equivalently the horizontal stress. His use of the thermal stress analogy facilitates understanding the poroelastic concept because thermal stresses are generally more readily understood than pore stresses by engineers.5 1. The pore pressure increase provides up to a 1900-psi horizontal and poroelasticity stress increase that extends the fracturing pressure beyond the operational limit. When the rock is constrained.. from fracturing fluid filtrate or water injection) and decreasing stress within the region of decreasing pore pressure (e. as in a reservoir. 1981).0 13. 1 or 2. the rock will expand in the same manner as if the temperature is increased.000 50 8000 Crosslinked gel 40 Injection Step rate Linear gel 6000 30 4000 20 Injection Step rate Minifracture Propped fracture 2000 Injection rate (bbl/min) Bottomhole pressure. without a crosslinked-fluid filtrate (or filter cake) to effectively insulate the formation (as in the thermal analogy) from the increasing injection pressure. The time line for the figure begins with two injection sequences for a linear-gel fluid and shows the pressure increasing to about 7500 psi and reaching the pressure limit for the operation. A5-6 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation . 1997b).) Lubinski presented poroelasticity within the context of its analogy to thermoelasticity. The first two injections. This is apparent from the thermal analogy—as the area of expansion increases the induced stresses also increase. as in the Stanolind patent.g.. BHP (psi) Linear gel 10 BHP Injection rate 0 0 0. Appendix Fig. The long-term impact of Lubinski’s paper is that the importance of poroelasticity increases as routine fracturing applications continue their evolution to higher permeability formations. The correlation of clay and Poisson’s ratio links the conclusions of Hubbert and Willis and Prats that horizontal stress is governed primarily by nonelastic effects and the general correlation between the actual stress and elastic/sonic-based stress profiles. leading to the shut-in for the 10. which is consistent with the general requirement to calibrate elastic-based stress profiles to higher levels of stress (e. During the early part of the third injection period.. Nolte and Smith.0 Time (hr) Appendix Figure 3.5 0 14.8). when the pore pressure is lowered.5-darcy oil formation. For poroelasticity. The analogy provides that when pore pressure is increased in an unrestrained volume of rock. (Poroelasticity could increase horizontal stress and lead to horizontal fractures.0 13. crosslinked fluid reaches the formation and the pressure drops quickly to about 5600 psi (the native fracturing pressure) and remains essentially constant during the remainder of the injection. a localized region of pore pressure change will induce stress changes: increasing stress within the region of increasing pore pressure (e.0 2. Conversely.. the rock will contract as if the temperature is lowered.g.formations can also have horizontal stresses greater than those predicted by either Appendix Eq. The third significant paper from this period is by Lubinski (1954). High-permeability frac and pack treatment (Gulrajani et al. the area of significant transient change in pore pressure increases as the permeability increases (see Section 3-5. resulted in pore pressure increases of significant magnitude and extent within the formation. 3 shows an example of significant poroelasticity for a frac and pack treatment in a 1. He was a Stanolind researcher who introduced the role that poroelasticity can have in generating larger stresses during fracturing. production).g. without fluid-loss control. 4 compares the Khristianovich and Zheltov analytical results for width and pressure to the corresponding parameters from the Warpinski field results. Their formulation was equivalent to the length becoming the characteristic.g. and particularly the accompanying appendix by R. D. the stress increase will not cause the horizontal stress to exceed the overburden (i. Appendix Fig.. generally deeper formations). 1993) and to isolate the fluid path from all but the primary opening within the multitude of cracks (process zone) forming ahead of the fracture (see Chapters 3 and 6). beyond the reach of fracturing fluid and filling with pore fluid. Width models The first rigorous coupling of fluid flow and the elastic response of the formation was reported by Khristianovich and Zheltov (1955). This decrease occurs because of the rapid closure and cessation of fluid loss (that activated the pressure drop). The field data show the width at the fluid front is well established (i.e. The pressure drop supported by the cake and filtrate is about 1300 psi.e.. which is the same reason that surface pressure decreases at the cessation of injection and loss of pipe friction. The fluid lag’s clamping effect provides the natural means to lower the potentially Reservoir Stimulation large tip-region stresses to a level that can be accommodated by the in-situ condition. For the analytical results. However. negative net pressure and acts as a clamp at the fracture tip. However. The presence of the lag region has been demonstrated by field experiments at a depth of 1400 ft at the U. This observation indicates that the insulating effect remained effective from the prior injection of crosslinked fluid. has a large. which is extremely small in comparison with commercialscale fractures.. This low-pressure region. filtrate resistance into A5-7 . as the example shows. The extent of the region. 1997). generally greater than 5% of the maximum width at the wellbore) and that fluid enters only a well-established channel behind the complexity of the process zone. the paper also identified the role for a fluid lag region at the fracture tip. These aspects of the lag region provide great simplification and increased predictablility for applying commercial-scale hydraulic fracturing processes.second injection. for any pore pressure condition in a relaxed area. provides the current framework for fluid loss.. Department of Energy (DOE) Nevada Test Site (Warpinski. For a normally pressured and tectonically relaxed area. They used a twodimensional (2D) formulation based on a complex variable analysis. Carter. The cakes have the consistency of silicon rubber and functionally provide an analogous sealing affect for subsequent tests. Also noteworthy of the experimental results is that tests 4 through 7 with water and test 9 with gel show similar behavior when test 4. dimension and provides the initial “K” for the KGD width model discussed later and in Chapter 6. see SCR Geomechanics Group. 3. Also. as was found for the case shown in Appendix Fig. The paper identifies the three factors controlling fluid loss: filter-cake accumulation. cause horizontal fracturing). The width profiles clearly show the clamping action at the tip. This increase is about one-third of the native stress. 1985). is ignored. the maximum increase in horizontal stress before substantial fracture extension is about onethird of the native horizontal stress (Nolte. during the two subsequent injections the insulating effect of the crosslinked fluid’s internal cake and filtrate allows fracture extension within essentially the native stress state. The last injection for the proppant treatment is also of interest because of the absence of a poroelastic effect during the initial linear-gel injection. as reflected by the rapid pressure decrease after the third injection. The practical importance of the lag region cannot be overemphasized.S. In addition to being the first paper to provide the coupling of fluid flow and rock interaction that is the embodiment of the hydraulic fracturing process. or smaller. A paper by Howard and Fast (1957).e. and the field data appear to be represented by a ϑ0 valve of about π/8 for the analytical cases. Tests 10 and 11 were with a gelled fluid and clearly show progressively different behavior from the preceding tests because of the altered tip behavior resulting from prior gel injections and the residual gel filter cakes that fill the fracture aperture after closure. poroelasticity can significantly increase the fracturing pressure and extend it beyond operational limits for high-permeability reservoirs. decreasing values of the complex variable angle ϑ0 toward the right side of the figure correspond to relatively smaller lag regions and larger differences between the minimum stress and pressure in the lag region (i. adjusts to the degree required to essentially eliminate the role of the rock’s fracture resistance or toughness (e. which had a relatively low injection rate. 5-17 and Chapters 6 and 8).9 0.2 0.15 0.25 0 0. Also of significance was presentation of the Carter area equation.0 Normalized distance from well.4 0. wo and po are the wellbore values of width and pressure. 6-19) that is proportional to the fluid-loss coefficient (loss volume) divided by the width (stored volume) and hence also related directly to the fluid efficiency Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation .2 ϑ0 = 3π 16 0 0.” This difficulty was soon overcome by developing a table for the more complicated terms in the equation using a dimensionless variable (see Eq.8 0.5 0.1 0 0.7 ϑ0 = π 8 w/wo w/wo 0.1 0 Normalized distance from tip.5 0 0.0 1. This equation.4 0. x/L 1.6 0.5 0.0 Test 4 5 6 7 9 10 11 0.3 0. respectively.4 0.7 0.0.4 0. All three factors are governed by the relation 1/√t (where t is time) for porous flow in one dimension.1 0.2 0.2 0.2 ϑ0 = π 16 ϑ0 = 3π 8 0.4 0. x is the distance from the well. the reservoir and displacement of the reservoir fluid (see Fig.10 0.9 1. Comparison of Warpinski (1985) field data (left) and Khristianovich and Zheltov (1955) analysis (right).6 0.6 0.6 1.05 0 0 Normalized distance from tip. which is now an American Petroleum Institute (API) Recommended Practice.4 ϑ0 = π 4 0. The authors also provided the means to determine the coefficient for all three factors using analytical expressions for the filtrate and reservoir contributions and to conduct and analyze the filtercake experiment.1 0.2 0.5 0.6 0. which is solved by Laplace transformation.3 0.2 0. provided the first rigorous inclusion of fluid loss into the fracturing problem (see Chapter 6).8 1. (L – x)/L Normalized distance from well. (L – x)/L 0 0.20 0. The coefficient for this relation was termed the fluid-loss coefficient CL. based on the assumption of a spatial and temporal constant fracture width.3 0.6 p/po 0.4 ϑ0 = π 16 0.8 ϑ0 = 3π 16 0. Equation 6-18.0 0.8 ϑ0 = π 8 ϑ0 = 3π 8 p/po 0. is in terms of exponential and complementary error functions and is not “engineer friendly.3 Width at fluid arrival ϑ0 = π 4 0.0 Test 4 5 6 7 9 10 0.8 0. x/L Appendix Figure 4. with area defined as the product of the A5-8 height and tip-to-tip length. e. For example. 4-17 and 4-18 of the Howard and Fast Monograph). Nomographs for the complete equation were also developed (e. as discussed in the following. 2. the stored compression in the rock acts in the same fashion as compressible fluids in a wellbore after well shut-in. Reservoir response to a fracture Until the advent of numerical simulators. for the first time. Eventually a simple and approximate expression (Harrington et al. .. Their initials coupled with those of the authors of the latter paper form the name of the KGD (or KZGD) width model. 1973) for the Carter equation provided the basis for fracture design into the 1980s. The magnitude of the fracture afterflow is large compared with the wellbore storage case. (1954) and Khristianovich and Zheltov (1955). both turbulent fluid flow and nonNewtonian fluids (power law model) and provided validating experiments for radial geometry and the role of rock toughness. the average width was first determined from either the KGD or PKN model.g.. . as discussed later for Appendix Eq. can be significantly greater than the FOI measure because fracturing also bypasses near-wellbore damage. They considered. which does not account for the effects of fluid loss and local rates of width change (storage change). figs.e.” These statements anticipated two of the important enablers for the second generation of fracturing: the use of pressure in an manner analogous to well test characterization of a reservoir and employment of a calibration treatment to improve the subsequent proppant treatment (see Chapters 5.. material balance). (1962) considered the combined effects of fracture stimulation and damage bypass. Recognition of the role of conductivity was important because the idealized assumption of infinite conduc- A5-9 . 1991). 9 and 10). In 1961 Perkins and Kern published their paper on fracture width models. fluid flow continues toward the tip until either proppant bridges the tip or fluid loss reduces the fracture width and stored compression to the extent that the fracture length begins to recede toward the wellbore (Nolte. The approximate expression is based on the relation at the top of Appendix Fig. After fracture shut-in.η illustrated in Appendix Fig. The observation of both the wellhead and bottomhole pressure during fracturing operations is necessary to a complete understanding and possible improvement of this process. Craft et al. whereas during the first generation a typical FOI target was about 2. Perkins and Kern also discussed fracture afterflow that affects the final proppant distribution within the fracture. For these applications. Papers considering finite-conductive fractures began to appear in 1958 and are summarized in chapter 10 of the Howard and Fast (1970) Monograph. The increase in production. and if the inherent tectonic stresses are known. it should be possible to determine the type of fracture induced. Reservoir Stimulation The one shortcoming acknowledged by Perkins and Kern was not rigorously accounting for the flow rate change in the fracture required by continuity (i. relative to the case before fracturing. . including the long aspect ratio fracture (length significantly greater than height) and radial model (tip-to-tip length about equal to height) as described in Section 6-2. The initial letters of the last names of the authors of these two papers form the name of the PKN model. The enhanced stimulation benefit increases as the magnitude of the damage increases. This assumption was later addressed by Nordgren (1972). as previously considered by Harrison et al. Also of historical interest is that most of this work was performed on analog computers with electrical circuits representing the reservoir and fracture components. The remaining paper of historic importance for width modeling is by Geertsma and de Klerk (1969). They used the Carter area equation to include fluid loss within the short-aspect fracture.. relative to zero skin effect.2. most fluid injected is lost during pumping) for a long-aspect fracture and Newtonian fluid (see Section 6-2. who provided closed-form equations for the bounding cases of negligible fluid loss and negligible fracture storage (i. After pumping stops. They assumed that the volumetric flow rate was constant along the fracture’s length. removing a skin effect of about 25 increases production by about a factor of 4. 2.2). Another 1957 paper was by Godbey and Hodges (1958) and provided the following prophetic phrases: “By obtaining the actual pressure on the formation during a fracture treatment. production models for a fracture did not consider transient flow effects and were based on the FOI relative to the reservoir’s radial flow response with no damage (skin effect = 0). 4. 26 could be a practical target for high-permeability reservoirs. Incorrectly considering a fracture to be a permeability increase can lead to incorrect conclusions concerning reservoir recovery and waterflood sweep.. 1991.13 re ln 0. The boundary and conductivity effects are summarized in the set of pseudosteady-state curves shown in Appendix Fig.5x f 0.5 1 rw′ = 0. this value is about an order of magnitude lower than the optimum case for the long transient period of a very low permeability reservoir. with the vertical axis reflecting the FOI as J/Jo and the horizontal axis reflecting dimensionless conductivity based on the drainage radius. CfD = kf w/kxf = π/2α). This concept is illustrated in Appendix Fig. provided by the fracture. Prats’ proppant optimization condition at CfD = 1. Prats (1961) used mathematical analyses to conduct a comprehensive consideration of finite-conductivity fractures with the assumption of steady-state flow (i. although proppant volume is generally not a realistic criterion because proppant cost is only part of the investment for a fracture treatment (e. rw′/xf tivity. provides a powerful tool for efficiently calculating the FOI. 1987).9 0. A5-10 1..1 CfD = CfD = 0. 1986.3 4 0.. The first is that a fracture is equivalent to enlarging the wellbore and not increasing the formation’s global permeability. Prats also introduced the concept of an effective (or apparent) wellbore radius rw′. He introduced a dimensionless conductivity α that is essentially the inverse of the dimensionless fracture conductivity commonly used for transient analyses (i. The McGuire and Sikora curves were the primary reservoir tool for fracture design and evaluation until the late 1970s. where kf is the fracture permeability. would not offset the operational cost for the additional proppant. The effective wellbore radius.(J/Jo) ( 7.7 0.. coupled with the radial flow equation.g.01 0.1 2 0 102 103 104 Relative conductivity. however.2 0. Treatment optimization Optimizing a fracture treatment is an essential part of maximizing its benefit (see Chapters 5 and 10).e.6 0. 105 kfw k 106 40 √A Appendix Figure 5. constant-pressure boundaries). Another insight is the generally favorable economics for an effectively designed and executed fracture.8 0. rw′ = 0. The effective radius allows describing the fracture response in terms of an enlarged wellbore radius within the radial flow equation. A fracture Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation . adapted from Cinco-Ley and Samaniego-V. The curves reflect different ratios of the fracture length relative to the drainage radius re. Effective wellbore radius versus dimensionless fracture conductivity (Nolte and Economides.2 1. McGuire and Sikora (1960) presented a significant study of the production increase in a bounded reservoir for a fracture with a finite conductivity kf w for the proppant pack. by achieving the infinite-acting case.472 rw ) 14 L/re = 1 12 10 8 0. cannot result from an economics-based optimized treatment. CfD Appendix Figure 6. For this reason Prats’ (1961) optimization consideration is of historic importance.0 Effective wellbore radius.4 6 0. 1981b). Veatch.0 k fw kx f 10 100 Dimensionless fracture conductivity. 1981b). Prats also considered fracture face damage (or skin effect) and provided an optimized treatment based on a fixed amount of proppant. with no pressure loss in the proppant pack.e. The incremental production increase. or negative skin effect. Meng and Brown. 6 for pseudoradial flow (adapted from Cinco-Ley and Samaniego-V. McGuire and Sikora (1960) curves for folds of increase (J/Jo) in a bounded reservoir of area A (acres).5 0.28 k fw k CfD = 30 1 0.. Additional lessons are also provided by the apparentwellbore concept. 5. 1 0. typically of tight gas. 6. This condition did not change until the mid-1970s brought natural gas shortages and higher gas prices to the United States. However the FOI = 10 target required about an order-of-magnitude increase in the volume and cost for a typical treatment and was hence termed massive hydraulic fracturing.. the production rate can be increased economically only by providing more conductivity kf w. For this part of Appendix Fig. The figure indicates that as CfD increases beyond 10. incurring proppant costs without an effective increase in production rate). the design and evaluation tools for most of the next two decades had been established by the contributions discussed. reports of successful field development (e.. Reservoir Stimulation Transition between the first and second generations By 1961. 6 for the roles of conductivity kf w (achieved by proppant cost) and fracture penetration (achieved by fluid and other additive costs. as discussed later. 1977) encouraged continued interest in tight gas development. These conditions stretched the so-called mature technology in almost every conceivable way and resulted in a bumpy journey because of the proportionally large economic penalty when a treatment failed to meet expectations. increasing conductivity within the limits of achievable fracture width and efficiently extending a fracture when the pressure reaches the formation capacity.g. Also affecting technical development was the degrading economics for lower quality reserves as oil import-export increased and fracturing activity decreased (Appendix Fig. see Chapter 7). increasing both fracture length and conductivity to maintain a constant CfD achieves the most efficient conversion of length into an effective wellbore radius. As CfD progressively decreases. that generally exceeded the performance limits for fracturing fluid systems.treatment is equivalent to excavating a very large diameter borehole (e. However. However. Higher prices produced the incentive to develop extensive regions of tight gas reserves with fractures targeting the FOI = 10 range of the McGuire and Sikora curves (Appendix Fig. with an obvious constraint from the available fracture width developed during the treatment. As permeability increases. with FOI relative to an undamaged wellbore. 5).g. with the obvious absence of an effect from length. Before this period. the effective radius is constrained only by length and is termed the length-limited case. The practical limits for the length-limited case are reaching the drainage radius. the ability to increase conductivity becomes the constraint. This conversion is the basis for effectively fracturing low-permeability formations. a log-log unit slope is approached that relates rw′ to kf w/k. and the extremities of the fracture cannot provide a production benefit. This constraint was significantly extended by the third fracturing generation of TSO treatments.e. This new target introduced higher temperature reservoirs. Incremental development of these tools slowed because fracturing was considered a mature technology. and proportionally decreases CfD. typical fracturing targets were oil reservoirs with an FOI of about 2. hundreds of feet in most cases) and therefore is an extremely cost-effective way to provide an equivalent excavation.2. The most important optimization lesson is found in Appendix Fig. His procedure formed proppant packs from a slurry composed of polymer-based fluids by using a cell with rock faces that allowed fluid loss and the subsequent application of closure stress. the effective wellbore radius approaches one-half of the fracture length and there are diminishing returns for additional increases in conductivity (i... Realistic estimate of conductivity Cooke (1975) reported realistic experiments for characterizing the conductivity of proppant packs. Fast et al. the conductivity-limited case is reached. 1). the wellbore drawdown completely dissipates within the fracture before reaching the tip. The Cooke cell is now a standard apparatus for a fracturing fluid laboratory A5-11 . The figure indicates that as CfD decreases below 1. When the unit slope is reached. For the conductivity-limited condition. near a value of 0. which is discussed toward the end of this Appendix. and residue-free viscoelastic surfactant systems. Equally important. Nolte. chapter 3 of Gidley et al. This relation indicates a polymer concentration increase of 20 or greater for typical treatments at that time (e. Cooke’s pioneering work had obvious effects on proppant schedules for treatments and laboratory testing procedures. the use of type curves began to decrease accordingly. the work initiated substantial product development activities. 6) and type curves. partly explains the difficult transition to massive treatments.. Height growth and proppant transport Simonson et al. they identified and provided comprehensive descrip- Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation ..(see Chapter 8). Cinco-Ley and Samaniego-V. the closure period prolongs the time for proppant fall and maintains the channel flow to reduce the effective viscosity. Appendix Fig. (1981b) provided several advancements for understanding and quantifying the transient behavior of a reservoir fracture system. beginning with Cooke’s work on bauxite for high crushing stress. improved breaker chemistry and breaker encapsulation. (3) for a typical proppant pack porosity of 0.65.3. In addition to advancing the effective wellbore concept (e. coupled with the prior discussion on conductivity and effective wellbore radius. complementing the postulate by Harrison et al..g. large reductions of polymer concentration for crosslinked fluids. Transient reservoir response The FOI consideration for fracture production was found to be completely inadequate for the substantial period of transient flow that occurs in tight formations (see Section 12-2). 1989). These include improved proppants.33 and proppant specific gravity (s.e. foams and emulsions.g. which is the essential ingredient for the fracturing pressure decline analysis (e. For non-Newtonian fluids.. (1954) concerning the role of stress for height confinement. which significantly increases the polymer concentration remaining within the proppant pack porosity after fracture closure. Novotny also provided a brief analysis of the volume balance during closure. The concentration factor for the polymer and other additives remaining in the fracture relative to the original concentration can be expressed as CF = 44 / ppa . This unexpected discovery of a significant reduction in retained permeability.2). higher shear rate and lower viscosity). The analysis considered a three-layer case for two symmetric barriers (i. By the mid-1980s. These results were unexpected because prior testing procedures did not use fracturing fluids or stress levels for deeper gas reserves. as general access to computers increased. access to computers was generally outside the reach of most engineers. The first tool for finite-conductivity transient flow was type curves provided by Agarwal et al. The relation depends on the average concentration <ppa> defined as the total pounds of proppant divided by the total gallons of polymer-based fluid. Novotny (1977) outlined a comprehensive basis for proppant transport calculations and in particular identified the important roles of channel shear rate and fracture closure in determining the ultimate placement of proppant (see Section 6-5. The three-layer case provided insight into how to adapt more general relations to any number of layers (e.e. Cooke also provided a simple mass-balance relation for this important consideration. This sum is generally dominated by the channel flow and is much greater than that for a particle in stagnant fluid (i. Although these curves were developed from numerical simulators. These relations led to the calculations employed in pseudo-three-dimensional (P3D) fracture simulators (see Section 6-3. (1979). In addition. the effective viscosity for sedimentation is determined from the vectoral sum of the shear rate in the channel and that caused by proppant fall (as for stagnant fluid). The evolution of fracturing fluid chemistry was reviewed by Jennings (1996). Both effects produce more proppant fall.g. The primary difference resulted because the rock acts as a polymer screen at moderate and smaller permeability levels.g. Nolte and Smith. two barriers extending A5-12 infinitely above and below the pay section with each barrier having the same magnitude of stress). as discussed in Chapter 7. Type curves were also used for optimizing treatment design. (1978) presented the mechanics governing fracture growth into a layer with higher stress..) of 2. <ppa> of 1 to 2 lbm). The experiments showed that the retained pack permeability could be very small. These and similar type curves became the standard evaluation tool to assess production from a fracture treatment. 1981..g.. 1979) that is used for calibration treatments (see Section 9-5). Dobkins (1981) presented improved cased hole logging procedures for inferring the fracture height that were also used by Rosepiler to qualitatively validate his novel use of mechanical property logs. was paramount for bridging the gap between fracture design and subsequent evaluation based on production or well tests. The manuscripts for this comprehensive volume. Reservoir Stimulation These advancements and insight from Bennett et al.000 treatments that did not provide commercial wells resulted in a significant investment for fracturing research.g. which led to overly optimistic estimates of conductivity and proportionally pessimistic estimates of length. the bilinear period can last on the order of a year or more for a long fracture (>2500 ft from the well). 2 and Chapter 4). fracturing was considered in a framework similar to that used for reservoir characterization. Roberts. The coupling of these two factors produced incorrect and negative assessments for many early attempts to establish massive fracturing as a viable means of developing tight gas formations. 1989). During bilinear flow the stabilized pressure drawdown progresses along the fracture length.. Another contribution to incorrect interpretations was ignoring Cooke’s (1975) report of very low retained-pack permeability. wireline logs for the formation parameters and geophysics for the macroview. The reservoir framework consists of pressure transient analysis for the flow characteristics. • Pressure transient analysis (PTA): Nolte and Smith (1981) introduced the role of pumping pressures by A5-13 . only five years after the 1979 SPE annual meeting provided the first meaningful number of papers from this research effort. by the slope of a plot of pressure versus the quarter-root of time. The second generation: massive fracturing As indicated in the preceding section. They indicated relatively short fracture lengths that were assumed to be treatment placement failures and led to the common and contradicting result: how can 1 million lbm of sand be contained in a fracture length of only 100 ft? Much longer propped lengths were later substantiated by production data after the bilinear period had ended (e. for the first time in its 30-year history. independent of length and hence most reliably. One result of this effort is the SPE Monograph Recent Advances in Hydraulic Fracturing (Gidley et al.. were completed in 1984. They also identified another important aspect of bilinear flow that occurs because of the transient flow condition within the proppant pack: the fracture conductivity can be characterized.tions for the distinctive transient regimes resulting from a finite-conductivity fracture (see Section 12-2). values of fracture half-length xf > 5000 ft. generally the first to occur during production or a well test. the bumpy road to successful massive fracturing also included massive penalties because the cost of a fracture treatment could become equivalent to the well cost. Therefore. During this period. 1981). a meaningful evaluation for fracture length cannot be obtained until the bilinear period ends and the transient response progresses toward pseudoradial flow (potentially several years). Well test interpretations misinformed instead of informed. For permeability in the range of 10 µd. (1986) for layered formations provide a solid foundation for the reservoir response to fracturing. with more than 30 contributors. it is not possible to determine the length of the fracture from a well test or production data because the total length has not had time to effectively experience the wellbore drawdown. The key was that. the length can be determined only from long-term production data. An obvious implication in this case is that a standard well test cannot be used to determine fracture length. The combined effect of many companies experiencing $500. The bilinear flow regime. The papers presented at this meeting were significant also because they presented a key that enabled the reliable application of massive fracturing and rapid progression of the treatment size record from 2 million lbm in 1979 to more than 7 million lbm by 1986. The 1979 papers include the following (a different reference year indicates the publication date): • Logging: Rosepiler (1979) introduced application of the long-spaced sonic tool to infer stress in different layers (see prior discussion of stress concerning Appendix Eq. Recognition of these consequences for bilinear flow also explains the difficult transition to the successful application of massive treatments. the pressure is independent of the fracture parameters and depends on the reservoir response to the fluid lost during the treatment.using a log-log plot as a diagnostic tool (similar to PTA practice) for fracture growth characteristics. Nolte (1979) introduced the role of pressure during the postinjection closing period to quantify fluid loss and predict fracture width and length by using a specialized time function in a manner analogous to the Horner plot. are similar to the reservoir response for an injection test with a pressure increase (pumping) and subsequent falloff (closing). Appendix Fig. enable characterizing the stored and lost components of the volume-balance equation shown in Appendix Fig. 1982). The last storage relation. 2. Pressure from bottomhole bomb Bottomhole pressure. and the closure data are governed by the fluid loss. 1 dVf 1 1 = = Vf dp f pnet p f − pc (4) 1 1 dw = for constant h and L. where k is the permeability. respectively. provides an analog of the reservoir pressure and reflects the height-averaged minimum stress for the pay zone (see Sidebar 9A). for constant lateral dimensions. After closure. closing and the after-closure period. h is the reservoir thickness. The respective reservoir and fracturing equivalents are kh/µ → w2h/µ (transmissibility). The last expression for storage contains an inverse proportionality to the net fracture pressure pnet. and E is the formation’s elastic modulus. The closure pressure is the datum for the net pressure that constrains the A5-14 width prediction. 1982). Fracturing pressure: analog of reservoir response An important component of fracturing pressure analysis is the closure pressure. and µ is the appropriate fluid viscosity. 7. Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation . w is the width. The data in Appendix Fig. The combination of these two papers provided a foundation for the common use of the calibration treatment and pressure-history matching for defining design parameters (see Chapter 9). ct is the total system compressibility. The result is a significant storage capacity considering typical conditions with more than 1000 bbl for fracture volume and only hundreds of pounds per square inch for net pressure. This can be written in terms of the fracture volume Vf. The fundamental analogy between reservoir and fracturing behavior results because a diffusion-type process governs both behaviors. where φ is the porosity. The fracture width is proportional to the net pressure. fluid pressure pf and closure pressure pc. as discussed later. compressed to contain the fracture’s volume. the role of pressure simulation for quantifying geometry (including height growth) and the role of calibrated stress profiles obtained from mechanical property logs. These two conditions. 7 illustrates the fracturing pressure for three distinct phases: pumping. A companion paper in 1980 showed the synergistic benefit when these individual considerations are unified for tight gas exploitation (Veatch and Crowell. w dpnet pnet (5) This equation implies that the elastic formation. • Geophysics: Smith (1979) introduced the role of mapping fracture trajectories by using surface tiltmeters and borehole passive seismic techniques to improve reservoir recovery by the correct placement of infill wells (see Section 12-1). one of the first recordings of bottomhole pressure during a treatment. and φct → h/(wE) ∝ 1/pnet (storage capacity of the reservoir). Bottomhole fracturing pressure (Nolte. pw (psi) Inferred pressure 9000 Fracture treatment Pressure decline Fracture Transient reservoir closing pressure near wellbore 8000 7000 6000 Fracture closes on proppant at well Net fracture pressure pnet = pw – pc Closure pressure pc = horizontal rock stress Reservoir pressure 5000 38 40 42 44 46 48 50 56 58 Clock time (hr) Appendix Figure 7. is important for a TSO. produces a system compressibility analogous to an equal volume of perfect gas at a pressure equal to the fracture’s net pressure. The injection pressure is governed by the evolving fracture geometry. For these reasons. 1986). acid fracturing (e... Techniques to determine the closure pressure are discussed in Section 3-6 and the Appendix to Chapter 9. 1973).. or more precisely P2D models.. Treatment design and evaluation The primary fracture evaluation advance from the massive treatment generation is the calibration treatment performed before the proppant treatment to define placement parameters.. 1994). and the farfield elastic coupling between width and pressure produces local parameters that have a general dependence on the pressure everywhere within the fracture’s unknown boundaries. Gulrajani et al.. 1997a) and a basis for rationally judging and selecting the model complexity appropriate for the specific application. see Section 12-1). available data and simulation resources. P3D models. Gulrajani and Romero. The calibrated TSO treatment. height and width by employing passive seismic measurements and tiltmeters in observation Reservoir Stimulation wells (Warpinski et al. 1982).. (1984). Settari and Cleary.g. Because of nonuniqueness in the reservoir response and the basing of reservoir models on overly idealized modeling assumptions for a fracture. The importance of these measurements for fracture design and evaluation cannot be overemphasized. Combining the calibration treatment and the purpose-designed TSO treatment produced the primary treatment innovation of the second generation..Fracture simulators Describing a hydraulic fracture produces a significantly more complex role for the diffusive process than the reservoir case because the basic parameter groups change continuously with time. Nolte and Economides. An equally important advance was the parallel evolution of process-controlled mixing and blending equipment for reliable execution of more demanding treatment schedules and progressively more complex chemistry that requires precise proportioning (see Chapters 7 and 11). The convergence of modeling assumptions failed for several reasons.g.. 1987). Mapping constraints on all three fracture dimensions provide a unique. 1996. objective test of the geometry model assumptions (e.. Another reason was the failure to achieve a dominant industry opinion on either the technique or procedures for a specific technique to define closure pressure (e. Gulrajani et al. Nolte... The two most common means were relaxing the lateral coupling in the long direction of the fracture (as for the PKN model) to allow a cellular representation and vertical height growth of the cells (e.g. 1995). Smith and Klein. Fracture mapping and model validation An important achievement was the definition of fracture length. evolved to include automated proppant scheduling and the temperature-exposure history for polymer and additive scheduling (e.g. The first was fundamental to the pressure-matching process and results because of the multitude of opportunities for nonuniqueness.g. 2) provide a long-awaited benchmark for validating fracture models. Meng and Brown. 1997b) and rigorous 2D slurry flow (e. 1996. became the key to the third fracturing generation (discussed later) and essentially removed width as a constraint for the conductivity required to successfully fracture A5-15 . Nolte. Like the first generation’s failure to find a consensus for width models (e. 1991. Independent measurements for each component of the fracture volume (Appendix Fig.g.g. 1982) or prescribing the boundary and width profiles by elliptical segments and a lumped dependence on the governing parameters (e. developed by Smith et al. 1991). Veatch 1986. Originally restricted to in-office use.g. The modeling difficulties led to widespread use of simulators based on P3D assumptions that partially circumvent the far-field elastic-coupling condition. Perkins. fracture simulators that rigorously and robustly couple these parameters in a general manner (see Section 6-3) have not progressed at the same rate as reservoir simulators. Plahn et al. the reservoir response cannot generally provide an effective constraint on the achieved fracture length (Elbel and Ayoub...g. with a nonlinearity for the equivalent permeability. economic optimization for treatment design (e.g. pressurehistory matching could not resolve the second generation’s conflicting adaptations of the P3D framework (see Chapter 6). automated pressure-history matching (e. This state of affairs allowed selecting a closure pressure procedure to validate particular modeling assumptions and therefore justify relatively arbitrary and ad hoc modeling assumptions. Mack and Elbel. 1997). these models merged with on-site fracture monitoring systems to provide treatment evaluation and simulation in realtime mode. the equation predicts 1900 lbm/1000 gal crosslinked fluid (in reality. The marginal success of the treatment is readily understood by considering Appendix Eq. The capacity (Nolte. 1a. or approximately 80.1 ppa. However. pnet (psi) very high permeability formations. The subsequent fluid loss also leaves proppant behind to further enhance slurry dehydration and proppant bridging.The following paragraphs link several aspects of the massive and TSO generations by using the information available from the diagnostic log-log plot for fracturing in Appendix Fig. The sand was disposed of with 900. 8. The cited reference has an unsurprising theme of the negative effects of excesses of pressure. Type Approximate log-log slope value Interpretation I 1 ⁄8 to 1⁄4 Restricted height and unrestricted expansion II 0 Height growth through pinch point. it was one of the first 2 million lbm treatments and hence functioned better as a “sand-disposal” treatment than a gas-stimulation treatment. III-b II III-a I IV Inefficient extension for pnet ≥ formation capacity pfc log time or volume Appendix Figure 8. 1982). The data are from two massive treatments in tight gas formations. 1982) defines the pressure limit for efficient fracture extension and is analogous to the pressure-capacity rating for a pressure vessel. when the net pressure reaches the mechanism’s initiation pressure. the size and viscosity for this treatment provided an ideal test condition of how a formation responds to fluid pressure and an excellent illustration for the concept of formation Variable injection rate 2000 Proppant begins II I * 1000 II I 500 40 III-a Proppant begins II x [5 MPa] 60 III-b IV III-a 100 200 400 600 1000 Time (min) Idealized Data log pnet Transition between the second and third generations Field Data Net pressure. Three mechanisms for a formation can define its pressure capacity before “rupture” accelerates fluid loss from the formation’s pay zone. 1977).000 lbm of polymer. which was designed by this author. Appendix Table 1 lists the interpretations for various slopes exhibited in the figure by the net pressure during fracturing. However. as indicated by Appendix Fig. Log-log diagnostic plot for fracturing (Nolte. The treatment related to the lower curve was not particularly successful. the first microdarcy-permeability field development (Fast et al. 3.. The mechanisims are Appendix Table 1. fissure opening or T-shaped fracture III-a 1 Restricted tip extension (two active wings) III-b 2 Restricted extension (one active wing) IV Negative Unrestricted height growth A5-16 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation . The top curve is a treatment in the Wattenberg field.000 gal of crosslinked fluid containing 90 lbm/1000 gal of polymer. capacity. This capability and timing produced the overly optimistic prediction in 1985 for the beginning of the TSO generation. Slopes of fracturing pressures and their interpretation in Appendix Fig. or zero log-log slope. provided insight for developing the TSO treatment that enables successfully fracturing darcyscale oil formations. polymer and viscosity. The behavior shown by the lower treatment curve. Each mechanism is defined by the in-situ stress state and results in a constant injection pressure condition. a solid) remaining in the proppant pack porosity after the treatment. For the treatment average of 2. 8. indicating unrestricted vertical growth through a lower stress zone after the barrier was penetrated.000 gal of fluid and 600. 8.. This value provides one of the largest formation capacities ever reported.• opening the natural fissures in the formation. illustrates the fissure-opening mechanism with the Type II zero slope occurring at a net pressure of 1700 psi. a Type III-a slope for a fracture screenout occurs because slurry dehydration forms frictional proppant bridges that stop additional extension (i. with decreasing pressure. The upper curve on Appendix Fig.. the pressure became constant for a short period at 1200 psi with a Type II slope that probably resulted from opening natural fissures to define a second. After a significant increase in pressure. 1982). model simulations indicated that Reservoir Stimulation the required penetration could be obtained by not exceeding the formation capacity.000 lbm of sand with an average concentration of 2 ppa. After the penetration is arrested. this was the first field successfully developed in the massive treatment generation (Fast et al.000 gal and 900. The Wattenberg treatment consisted of 300. similar to the previous example. which could have resulted from one wing of the fracture being blocked to flow near the well because of slurry dehydration from the fissure fluid loss. governed by the difference in the horizontal stress for the barrier and pay zone • initiating a horizontal fracture component when the pressure increases to exceed the level of the overburden stress. The wellbore region experiences the largest pressure and is most prone to adverse fluid-loss effects from exceeding a capacity limit. the very high polymer concentration formed a thick polymer filter cake at the fracture tip that probably restricted further horizontal extension. the major portion of the fluid injected is stored by increasing width (see Appendix Eq. Subsequently the slope increased to an approximately 2:1 slope indicated as Type III-b. During the preceding 6-hr period of significant vertical growth. and continued injection was stored by increasing width indicated by the Type III-a unit slope. Thus. including • Type I indicating extension with restricted height growth • Type II defining this formation’s lowest pressure capacity at 1000 psi for the penetration of a stress barrier • Type IV. Returning to Appendix Fig. the extremities of the fracture were restricted either by proppant or polymer cake. most likely because the proppant bridged vertically in the width pinch point formed by the penetrated stress barrier and restricted additional height growth. After the treatment defined the formation capacity. Almost immediately after proppant entered the fracture the pressure increased. governed by the difference in the horizontal stresses • extending the height through a vertical stress barrier and into a lower stress (and most likely permeable) zone. after the period of constant pressure and enhanced fluid loss. A5-17 . However. all future treatments for the field can generally be effectively designed on the basis of only one bottomhole pressure recording and its detailed analysis (see Section 9-4). The Type IV condition continued until proppant was introduced. As a result. As a result.e. higher capacity. Therefore. 8. The amount of width increase is proportional to the net pressure increase. 4) and the net pressure develops the unit slope characteristic of storage. for the Wattenberg treatment. the treatment was successful because a polymer-emulsion fluid with low proppant pack damage was used. conditions in this formation are favorable for propagating a massive fracture. the horizontal growth was retarded. 8 is for the aforementioned sand-disposal treatment in the Cotton Valley formation of East Texas. 1997). and it provided incentive to continue the development of massive treatment technology. This latter slope for a storage mechanism indicates that about one-half of the fracture area had become restricted to flow. An important observation for the pressure capacity is that it depends on the in-situ stress state and therefore does not change for the formation in other well locations unless there are significant local tectonic effects. A subsequent treatment designed using 150. The fissure opening is preceded by restricted height growth and unrestricted extension (Type I slope) that provide the most efficient mode of fracture extension. the treatment provided an opportunity to observe a large range of fracturing behavior with five types of interpretive slopes occurring. The lower curve on Appendix Fig. As previously discussed. a generally undesired screenout for a tight formation requiring fracture length over conductivity). not by coincidence.000 lbm of sand (an average of 6 ppa) became the prototype for the remaining development of the field (Nolte. 5 and 6.1). The conductivity increase also translates into a 100-fold increase of the target permeability for fracturing.. extensive contraction of activity in general. as detailed in the discussion following Appendix Eqs. 1985. Smith et al. 1a was slowed not only by the unanticipated. In addition. The patent’s goal was increased width to enable placing larger size proppant in the fracture. but also by two prevailing mind sets: high-permeability formations cannot be successfully fracture stimulated and why fracture a commercial well? Additional field proof for the benefits of a TSO treatment came from two successful programs: a significant improvement over conventional fracture treatments for the Ravenspurn gas field in the southern North Sea (Martins et al. several of its developments are reviewed here. the observation that proppant bridging could restrict height growth was developed for treatments to mitigate height growth (Nolte.3 and 12-3. Reimers and Clausen.Subsequent treatments were improved after understanding the formation’s pressure behavior as in the Wattenberg case and for this area after understanding the implications of Appendix Eq. as implied by Appendix Figs. 8 for the sand-disposal treatment: a purpose-designed TSO treatment. An effective and relatively impermeable bridge can be formed within the pinch point to retard height growth by mixing a range of coarse and fine sand for the first sand stage after the pad fluid. beyond the reach of matrix treatments) facilitated sidestepping the mind set of not applying Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation . with successful placement of progressively larger propped width increases.. The ability to significantly increase the width after screenout results from the large storage capacity of a fracture. 2 million lbm of proppant could be placed. Additional discussion on the fracture completion in Valhall field and the TSO treatment is in the “Reservoir and Water Management by Indirect Fracturing” section. A5-18 The third generation: tip-screenout treatments A proper historical perspective of this third generation requires perspective from the next generations. The increases for width and conductivity also mitigate nondarcy (or turbulent) flow effects in the fracture for high-rate wells. The resulting treatment design was based on the behavior on the log-log plot in Appendix Fig. with the bridging material consisting of petroleum coke particles (approximately neutral density to ensure transport to the extremities). 1991. Smith et al.. This design.e. However. 4 and 5. 1972). 1982). Another component for the successful fracturing of high permeability was the continued development of synthetic proppants that can produce a cost-effective 10-fold increase in permeability relative to sand for higher closure stresses (see Chapter 7). and the net pressure increase indicated that this occurred by doubling the width after the screenout initiated. a similar concept for a TSO was disclosed in a 1970 patent (Graham et al. however. they observed that after the initial screenout occurred. particularly gas wells (see Sections 10-7. For the disposal treatment. 1992a). Fracturing was considered for this formation because other completion techniques would not sustain production because of chalk flow. 3 for concentrating polymer. As a historical note.. Coupling this increase in permeability with the similar increase for propped width achieved by a TSO treatment in a moderate. Deep damage Fracturing in Prudhoe Bay was particularly successful because deep formation damage induced by prior production (i. became the tool that enabled the development of this formation.to low-modulus formation provides about a 100-fold increase in conductivity over a conventional sand fracture. A more comprehensive presentation and reference are by Smith and Hannah (1996). (1984) later sought a means to significantly increase fracture width for the development of a chalk formation within the Valhall field in the Norwegian sector of the North Sea. 1992b) and high-permeability applications in the Prudhoe Bay field (Hannah and Walker. The additional width was required because laboratory tests indicated the likelihood of substantial proppant embedment into the soft formation that would lead to the loss of effective propped width. the anticipated growth rate shown on Appendix Fig. Martins et al. designed and successfully placed a TSO treatment in which proppant reached the tip and bridged to increase the width by a factor of 2 during continued slurry injection after the purpose-designed TSO occurred. Demonstration of the ability to routinely place a successful TSO treatment opened the door for effective fracture stimulation of higher permeability formations. 9) acts as an excellent external gravel pack for reducing the pressure drop through the perforated region. Frac and pack The frac and pack completion consists of a TSO treatment before a conventional gravel pack.. The threefold-plus increase in production rate.fracturing to high permeability. notably offshore Indonesia. Another significant aspect of the Prudhoe Bay application is that the fractures were routinely placed in a relatively small oil zone above a rising water zone without entering the water zone (Martins et al. frac and pack treatments were applied on a limited basis around the world. by eliminating the skin effect. For a well-designed and executed frac and pack.g. The reservoir section had a multidarcy-permeability upper zone that graded downward to a permeability of about 100 md. i. An important feature of a frac and pack is reduction of the inherent flow restriction around and through the perforations. an edge-water drive would encroach through the high-permeability zone and turn a prolific oil well into an even higher water producer. this technique was tried at various times but without sustained success. This precise fracturing was achieved by coupling an initial detailed fracture modeling study with a calibration treatment before each proppant treatment. The standard completion was to perforate and gravel pack the upper zone. Gulrajani et al. potentially superior alternative to matrix treatments in high-permeability formations.g.. Casing External gravel pack connecting all perforations with propped fracture Packed-back fracture Appendix Figure 9. Successfully packed-back TSO treatment. West Africa. A5-19 . The first successful application began because of economic considerations and therefore overcame the mind set of not fracturing a commercial well. resulted from more than just adding a TSO treatment to the procedure. the skin effect ranged between 7 and 30.. 1997b). if the formation is pushed apart 2 in. Smith and Hannah. The incremental production from only one year of the fracturing program would have ranked as the 10th largest producing field in the United States (e. 1992a). A significant field development was not meeting production expectations because standard gravel-packed completions could not consistently achieve a low skin effect. which demonstrated that fracturing is a viable. The ring results from the large TSO Reservoir Stimulation fracture width that mechanically must continue around the wellbore. The large propped width from a TSO treatment was a necessary ingredient for successful frac and pack applications.. As for other applications of TSO treatments. The skin effect was 10 after the first frac and pack treatment and progressively decreased to near zero from improvements in the treatment design and the use of larger size proppant (Hannah et al. the initiating screenout at the tip is progressively packed back to the well to completely pack the resulting ring. The frac and pack boom was in the Gulf of Mexico.e. 1994b). The prototype example for this application was in the Norwegian Gullfaks field (Bale et al. Prior to the TSO treatment era. During the early 1990s. as discussed later. technology transfer resulted in a wider geographical distribution for this sand control technique (e. Reservoir and water management by indirect fracturing Another application of TSO treatments is reservoir management. The ring of proppant around the casing (Appendix Fig. without including similar results achieved by another operator in the other half of the field. over the large surface area of the fracture. 1996).. 1994). the rock around the wellbore must be displaced accordingly. An important observation is that the same analysis procedures and design models introduced for the massive treatments of tight gas formations in the late 1970s were transferred directly to frac and pack treatments in soft formations.. The continuing success of the initial frac and packs started a rapid conversion to this completion. However. In addition to continued use offshore Indonesia.. with the frac and pack becoming the preferred Gulf of Mexico sand control completion. 1994a. on-site redesign after a calibration treatment became a standard frac and pack practice. When this zone was put on production.e. The combination with a successful packed-back TSO achieves an external gravel pack of stable proppant (i. This method couples the proppant ring around the casing from a TSO treatment and proppant with effective flowback control (e. (1994a) also placed a TSO-IVFC in a lower competent part of the formation. This completion enabled chalk-free production from both the upper and lower zones (Smith et al. 1997). Screenless sand control Another apparent role of the IVFC is to eliminate the need for a screen in many sand-control environments by selecting and perforating only competent sections within or near the unconsolidated sections of the formation. Therefore.... The zone selection method can potentially be enhanced by a sonic log application. This indirect access to the primary producing zone has come to be known as an indirect vertical fracture completion (IVFC) and is illustrated in Appendix Fig.A solution was found from the pioneering work of the Valhall TSO treatment discussed for Appendix Fig. The primary objective was for controlling chalk production from the primary producing zone above where the TSO treatment was placed. chalk filled the tubing and led to casing collapse. This application takes advantage of the generally considered negative effect of near-wellbore refracted and relatively slower waves caused by the wellbore mechanical damage that routinely occurs in weak or highly stressed formations (Hornby. 9). 1993). a TSO-IVFC becomes a solids control and reservoir management application (see Section 5-1.g. Indirect vertical fracture for reservoir management (Bale et al. The upper chalk zone was very soft with high porosity and composed of almost as much oil as chalk. Perforation and completion considerations are addressed in Section 11-3.g. A second method of achieving a screenless sandcontrol completion is applied without strategically placed perforations (e. but more importantly it enables economic development of significant behind-pipe reserves that do not warrant the mobilization and operational costs for a rig on an offshore production platform. which is caused by the wellbore stress concentration within the in-situ stress field. 1994a). The technique of perforating and fracturing only from competent sections and producing from incompetent sections is a robust method for controlling the production of formation material and increasing recovery from the lower permeability zones by fracture stimulation. Malone et al.. curable-resin-coated proppant or both). The screenless completion obviously eliminates the cost of the screen and related tools. the layers with a minimal near-well change in wave speed relative to the far-field speed are the more competent candidate zones for perforating and applying a TSO-IVFC to achieve screenless formation-material-controlled production. 8 to reservoir and water management with the intermediate development of the TSO-IVFC for solids control in the Valhall field. The zone was produced by placing the TSO treatment in the more competent zone below and extending the fracture height into the bottom of the very high porosity formation. This application completes the link between the sand-disposal thight gas treatment in Appendix Fig. In addition to providing sand control and managing reservoir depletion.. However. The Gullfaks adaptation by Bale et al. 1984). an external formationmaterial screen as illustrated by Appendix Fig.. This application in the early 1980s was for more than mitigating proppant embedment.5. the negative effect becomes a positive effect because the change in the wave speed for the refracted wave is a direct indication of the state of rock failure around the well.2). as generally required for a standard gravel-pack completion. for screenless completions. Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation . fibers. 8. A5-20 from the lower sections by fracture stimulation and a significant increase in drawdown. From this perspective. it was a water management treatment because it delayed water breakthrough and greatly increased reserves recovery High permeability Propped fracture Low or moderate permeability Appendix Figure 10. 10. Cased hole logging and logging while drilling can be used to identify IVFC target locations for connection to bypassed reserves and management for their exploitation. The general benefit for a horizontal well. Achieving full potential for horizontal wells and laterals The preceding discussion of the IVFC is in the context of single. from correctly placed perforated sections. the analysis and design tools have evolved for considering the role of fractures in NODAL analysis for reservoir. essentially vertical wells. The potential for innovative strategies to drain a reservoir increases several fold by adding consideration of horizontal and lateral wells. The long-term radial response following fracture closure was developed and presented in a pair of papers: Gu et al. an extended reach well cannot drain what it is not connected to nor can it efficiently drain what it is isolated from by wellbore damage. through a NODAL analysis. An attractive aspect of the use of fracturing for testing is that the fracture enhances the likelihood that all the zones are open and captured by the test. They considered the role of the permeable fracture plane on the reservoir’s 3D flow pattern and how tailoring the distribution of conductivity can advantageously affect this flow pattern (e. Staged fracturing. (1993) from the application perspective and Abousleiman et al. labeled “transient reservoir pressure near wellbore. Therefore. 1981b) and is the same flow regime used for standard well testing. Cinco-Ley and Samaniego-V. is magnified by the fracture adding a large vertical permeability component (see Chapters 11 and 12). Fracturing for well testing The after-closure portion of Appendix Fig.2). (1994b) for the Gullfaks application. Optimal reservoir plumbing From a broader viewpoint. Extended optimization requires additional considerations for designing the plumbing system provided by the fracture in the reservoir and also within the fracture itself. can be specified by correctly placed perforations within a cemented casing and an effective fracture design and execution. Simply stated. as demonstrated by the first fracturing generation’s rate of 100 treatments per day in 1955.. This potential for a fracture is ensured by the well-known result that the long-term reservoir response is pseudoradial flow (e.. These highly deviated wellbores are typically placed without cemented casing because of economic considerations and therefore do not generally reach their full potential because they lack an effective technique to remove wellbore damage. Another attraction of fracturing or injection testing is that the wellbore is generally filled with water that provides minimal wellbore storage and formation volume factor effects. This blurring of past distinctions provides prospects for additional innovations and the advent of a fourth fracturing generation. This is an important consideration for layered formations and particularly thinly layered zones that can be missed by open perforations. formation material and water management. (1994) from the theoretical perspective. the IVFC and strategically placed perforations provide the means to extend optimized plumbing into the reservoir. see Section 5-1. 7.. The outline for these considerations was defined by Bale et al. They recognized that the radial A5-21 . is generally practiced only for the surface facilities and within the wellbore.g.” shows the return of the fracturing pressure to the reservoir pressure and demonstrates the well testing potential for any injection above fracturing pressure. The addition of a vertical fracture allows efficient drainage of all isolated sections that the propped fracture reaches. Optimized plumbing. The location of the fracture. or plumbing source. particularly with vertical variations of permeability.A future generation: fracturing and reservoir engineering merger? The previous discussion of the TSO generation clearly shows the blurring of what can be controlled on the inside and outside of the casing and of what have been the traditional roles of a fracture design engineer and a reservoir engineer. reducing the conductivity as the fracture approaches the high-permeability upper zone to delay water production while increasing the conductivity in the lower permeability zone and applying a large drawdown to accelerate production from this zone. enables highly effective damage bypass. The solution Reservoir Stimulation of using cemented casing for effective treatment diversion tends to be overlooked because of an apparent failure to appreciate lifecycle economics or the effectiveness of good cementing techniques (see Chapter 11).g. g. Reservoir characterization from a calibration testing sequence to define fracturing parameters provides the ingredients essential for on-site. Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation . economics-based treatment optimization.response from fracture injection met the assumptions for a slug (or equivalently an impulse) test and that they could directly apply this developed area of reservoir technology.. These applications from the reservoir behavior of fracturing complement the 1979 adoption of reservoir methodologies and achieve a direct merging of fracturing into the classic realm of reservoir testing and characterization (see Chapters 2 and 12). Quan- A5-22 tifying spurt loss is particularly important for highpermeability formations and is not practically attainable by any other means than after-closure analysis. fracture length and hence the fluid-loss coefficient. and the division of fluid loss between normal wall diffusion and tip spurt). Another well-known flow regime for a fracture is pseudolinear flow. Consideration of this regime by Nolte et al. and a method to quantify reservoir parameters during the closure period is presented in Section 2-8. Incorporating the analysis of this after-closure flow regime was the last link of the fracturing–pressure analysis chain between the beginning of injection and returning to reservoir pressure. (1997) indicated that the reservoir “memory” of the fracturing event can validate several aspects for analysis of a calibration treatment (e. The after-closure analyses are presented in Section 9-6. closure time and hence the critical closure pressure.