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Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, Texas 75083-3836 U.S.A., fax 01-972-952-9435. Abstract The search for practical engineering tools to better manage water injectors has been ongoing for many years. Simple analytical solutions have proven inadequate, and most reser- voir simulators do not explicitly model water injectors. This paper proposes a methodology of using detailed and coupled fracture and reservoir modeling to ensure proper injection start-up procedures, and managing injection rates to avoid out- of-zone injection. This is combined with simple rate-pressure data to understand injection behavior, and from that control the process. Introduction Water injection, in particular produced water injection, in most cases creates a fracture. As is well established [1], temperature effects are important, because the cold injection fluid reduces the temperature of the near well formations, leading to a reduced minimum in situ stress. If the fracture remains within the cooled region, the reduced stress may be a significant factor in reducing fracture height growth, or in other words, for the confinement of the fracture to a given formation. As a result, simulations of water injection need to take fracturing and the temperature effects on fracturing into account. In this paper we briefly review some elementary aspects of the response of a fractured injector. We proceed to show field examples of fracture growth, with particular emphasize on its episodic nature. Next, we describe a new model for the simulation of water injection, which includes thermal effects and plugging due to dirty injection water. The main part of the paper is a discussion of some simulations, focusing in particular on how the rate schedule of injection start-up may be used to influence the height growth of the fracture. This is of central relevance for many field cases, where it may be imperative to constrain fracture height growth, e.g. to avoid growing into a thief zone. In terms of reserve recovery, this is crucial. If the fracture grows into high permeability layers, those layers begin to ac- cept more injection. This causes preferential cooling in those zones, reducing closure stress there. The fracture then migrates there, further increasing injection into that zone, causing more cooling, etc., etc. Ultimately, this causes early water break- through and lost reserves! Basic injector performance With modern data acquisition systems, extensive datasets are normally available for all or many of the injectors in a field. Hence it is important to find an effective way of screening the data, in order to single out the features for further study. A plot of large amounts of data in a pressure versus rate plot may be an effective method, in particular if color coding is used to separate different time intervals. Before showing real data, we briefly recap the main features of injector response in the pressure versus rate domain. Fig. 1 schematically shows the response of an injector working both in the matrix and fracture regimes. The full line describes an initial situation, in which the injector injects into matrix up to a given pressure where the fracture opens, and an increased injectivity results. The dashed line shows the change resulting from a stress reduction due to reservoir cooling. To a first approximation the slopes of the matrix and fracture injection lines are unchanged, but the intercept takes place at a lower pressure due to the reduced reservoir stress. The dash-dot lines show the effect of pressure build-up around the injector. This affects both the matrix injection and the fracture injection. Note how the intercept occurs at a lower injection rate. This is because the matrix injection responds directly to the pressure, while the initiation of fracture injection responds to the changes in the leakoff stress, which is general smaller. Fig. 2 shows the effects of changing the injector’s choke. The curved full lines correspond to various choke settings, while the straight lines represent two different values of injectivity. If, for a fixed choke setting, the injectivity changes for some reason, the response will stay on the fixed choke line. Thus, the path in the p-q plot is fully determined by the choke setting, and in itself cannot say anything about the mechanism leading to the change in injectivity. SPE 110329 Better Reservoir Management Through Improved Water -Injection Methods With Data Analysis and Detailed Fracture/Reservoir Modeling Håvard Jøranson, SPE, Statoil; Henry H. Klein, SPE, H.K. Technologies; Arne M. Raaen, SPE, Statoil; and Michael B. Smith, SPE, NSI 2 SPE 110329 Analysis of injector data In this section we will show some field examples of injector response, focusing on effects of reservoir pressure build-up around the injection well and on fracture growth incidents. Reservoir Pressure Build-Up Effects Although a steady injection is aimed for, an injector will in practice be shut in and reopened at irregular intervals during normal operation. It is generally attempted to close and reopen an injector in a controlled manner, with a constant choke closing/opening rate, but in certain situations a fast shut-in may be necessary. Depending on the cause for the shut-in, the length of the shut-in interval may vary from a few hours or less up to several days. As a result, data from the daily ope- ration of an injector may give information on local reservoir pressure build-up. The basics of the influence of reservoir pressure build-up around injectors were discussed in conjunction with Fig. 1. Fig. 3 shows a field example of pressure versus rate data for a period of about two weeks. Prior to the period, the injector was shut in for several days. This example demonstrates that the simple principles outlined above are relevant for field data: The 3 main groupings of data (emphasized by the pairs of solid lines in the figure) result from injection being shut-in for various periods of time. The data indicated by the rightmost solid lines (red data points) is for the start-up after several days of shut-in, while the leftmost data is a controlled shut- down after some days of injection at full rate. The middle data are from the start-up after a shorter shut-in period. Note how the intercept of the matrix and fracture lines occur at lower flow rate for the pressured-up cases, in accord- ance with Fig. 1. The vertical separation of the matrix injection lines is an indication of the change in near well pressure, while the vertical separation of the fracture lines is a response to the change in in situ stress seen by the fracture. Hence, plots like Fig. 3 may be a quick method to determine the reservoir stress path (Δσ h /Δp). However, much caution is necessary, since temperature effects etc. may strongly in- fluence the situation. Also, the measured stress path is relevant for the situation around the injector, and not necessarily for the field itself. The data in Fig. 3 are particularly easy to interpret, since the typical time for pressure build-up is long compared to the time used for starting and stopping the injector. If the time constants are more similar, the trends during start-up and shut- down will deviate from straight lines. Fracture growth episodes As shown in Fig. 2 any pressure-rate change at constant choke appears as a line with negative slope in the pressure versus rate (p-q) plot. When reservoir pressure build-up around the injection well is significant, such negative slope changes will occur after any choke change. When the choke opening is increased, the initial response is to move up-right along an injectivity line. Increased injection rate may then locally increase reservoir pressure/stress, causing the negative slope, constant choke event (up-left). Similarly, closing (reducing) the choke would first cause a reduced pressure/rate, a movement down-left along the injectivity line. Reduced injection rate then results in a reduction in near wellbore reservoir pressure that might then cause a negative p-q slope constant-choke event (down-right). Sometimes, however, similar behavior is observed even if the choke has been constant for a long time. In such cases, a “negative slope event” is a signal of a change in injectivity not related to reservoir pressure build-up. Often, one will see that the increase in injectivity is only temporary, and in such cases the “negative slope events” stand out clearly from the main injector response. Fig. 4 shows an example with several events that can not be related to reservoir pressure build-up around the injection well. The plot quickly identifies some events that may be can- didates for further investigation. Fig. 5 shows pressure and rate versus time for one of the incidents in Fig. 4. The rate increases significantly over a few hours, while the injection pressure drops correspondingly. We emphasize that the choke was kept constant prior to, during and after the incident. Then, the situation is more or less re- stored over a few hours. We interpret this as a fracture growth incident, which exposes fresh formation, possibly in a lower pressure regime. Then injectivity reduces as the faces of the new part of the fracture gradually plug, or reservoir pressure builds up around the recently exposed fracture. During the life of the injector, many such incidents occur, indicating episodic fracture growth. The size of the episodes may be very significant, as demonstrated in Fig. 5, or much less pronounced, as seen in Fig. 6. This response is an indica- tion of repeated small fracture growth incidents, resulting in a net increase in injectivity. A New Simulator Clearly, as seen in the injection/time histories above, water injection is complex. As opposed to “simple” hydraulic frac- turing, changes in reservoir pressure/temperature have a strong impact on fracturing and injectivity. Thus, the problem be- comes highly “coupled”. Injection can alter the injection and the fracture geometry, fluid loss from the fracture, reservoir pressure/temperature/stress changes, etc. must all be consi- dered simultaneously. This complex behavior also forces the use of “Fully” 3D, planar fracture geometry simulations. Since the exact path of fracture growth cannot be predicted with any reasonable cer- tainty (except maybe for very simple, single layer cases), sim- pler “2D”/“Pseudo 3D” fracture growth models are not appli- cable. The numerical model (using a combination of finite ele- ment/finite difference techniques) employed in the data analy- sis here implicitly couples a planar, “Fully” 3-D, gridded frac- ture propagation model to a 3-D single phase, multi-compo- nent, variable temperature reservoir simulator. The coupled model includes thermal and pore pressure modification of stress, “filter cake” build-up and plugging on the fracture face inhibiting leakoff. The simulator was used to study the long term injection (> 1 year) on fracture evolution and water placement in the reservoir and to identify the importance of the each of the phenomena of permeability contrasts (vertical and horizontal), stress contrasts, plugging, and injection rate. The details of the model for fluid flow in the fracture and fracture propagation are presented in [2], and the details of the SPE 110329 3 coupled fracture-reservoir model are presented in [3]. An overview is included in Appendix A. In standard fracture models leakoff is determined analyti- cally using the standard “Carter” leak-off coefficients. In the present model fluid loss from the fracture face is directly computed from flow into the reservoir. Finally, as discussed in more detail below, a fluid “filter cake” effect was used to simulate the effects of water quality on fracture growth for injection above fracturing pressure. This C W , i.e., filter cake, effect was based on laboratory core data for a formation similar in character to the zones studied here. Some example results Discussions below present results demonstrating the role of thermally induced waterflood fracturing in vertical sweep con- formance of injection wells. In highly variable reservoir qual- ity sands, injection water tends to be injected into the best zones. This promotes cooling, and the resulting thermally induced fracturing further enhances injection into these zones. This phenomenon has been thoroughly discussed previously [4,5], and typical field experience is early water breakthrough in the high permeability layers, leaving the other zones poorly swept with poor reserve recovery. While the example simulations below use data from actual cases, the discussion is meant to be general. The reservoir se- quence is shown in Fig. 7. Injection water has a downhole temperature of 25 °C, and initial reservoir temperature is 80 °C. The reservoir rock is quite “soft”, a Young’s modulus of, 2–6 GPa (about 0.3–0.9×10 6 psi). Since thermally induced stress changes are related to the modulus (and the coefficient of thermal expansion) TE T Δ∝Δ α σ it might be expected that cooling effects are not significant. However, for injection above fracturing pressure, the low modulus also leads to low net pressure (i.e., the injection pres- sure above fracture closure pressure), and thus, relatively small stress changes might be important. Only detailed, rigorous simulations can address such questions. The “pre-injection” in situ stresses are additional important data, and the stress profile in the figure is based on differential depletion measured prior to the start of injection. Initially, all sands and shales in this reservoir have similar horizontal stress. With depletion in the sands, a stress contrast between sand/shale layers develops. Reservoir Goals For the example well in the figure, the injection goal is to achieve maximum injection into the zones from 2482–2507 m. Ideally, some fracture growth upwards would provide injection and sweep into the zones from 2450 to 2482 m. However, fracture growth into the high permeability zone with its base at 2445 m must be avoided. Effects of Injection Rate All simulations use a constant injection rate in each step. We first study the effect of rate, and want to find the maximum in- jection rate that can be injected into the sands between 2482– 2507 m. Ideally we would like to see some fracture growth to sweep the sands above, but fracture growth into the extremely high permeability sand with base at 2445 m must be avoided. Table 1 shows the injection history for the well during the first 2 months of injection. Fig. 8 shows the fracture geometry after this injection. What is seen is that the well is fractured, but there is no need to extend the fracture more than what is needed to bypass the plugged near wellbore area, i.e. there seems little risk of fracture growth out-of-zone from this lim- ited interval at this limited rate. The simulations assume very dirty water is injected. The “C W ” of the model represents the lab data shown in Fig. 9, where the sea water in this case had a particle (fines) content of 0.00375. That is, 0.375 % by volume of the fluid was solid particles. Injection water samples from the field have been tak- en in a few wells. They show a particle content typically much less than 1/10 of the lab data. In actual fact, the lab tests do NOT show a physical filter cake, rather the apparent “C W ” effect is caused by formation damage a short distance into the formation. Presumably this damage is related to the volume of particulates, just as a physical filter cake is related to the thickness of the filter cake (i.e., to the volume of fines). In that case, C W is related to the particle concentration fluidfines cakecake W 2 μ C pk C Δ ∝ where C fines is the volume fraction of particles. Thus, if the actual particle concentration is 1/10 (0.000375), then C W is increased by a factor of √10. When simulating the dirtier water, the need for bigger frac- tures is enhanced. The simulations should therefore represent a conservative view on the effect of fracture growth. Simula- tions with no particles in the water show no fracture is created. Naturally, there would be substantial benefit from in- creased injection rate. Fig. 10 shows the results of an injection period of 200 days at 4000 m 3 /D. As seen, even this rate can be injected without undesired height growth. To demonstrate that “any rate” can be injected into this moderately permeable sand, a simulation with 9000 m 3 /D was run for an injection period of 200 days. Fig. 11 shows a frac- ture half-length of about 120 m, but almost no height growth outside the perforated interval. Thus, a different problem, we need to perforate the sands higher up to achieve vertical sweep, but we still must avoid in- jection into the extremely high permeability sand at the top. Simulations were then run to determine if a fracture starting from the next sand up (2468–79 m) would sustain injection without frac growth into the high permeability sand at the top. The width profile after 200 days at 1500 m 3 /D is shown in Fig. 12. The fracture has grown down into the lower, more permeable sand, but still injects into newly perforated sand and the sand above. There is no risk of fracturing into the extremely permeable sand at the top. The figure also shows the leakoff contours, showing most of the leakoff at the tip and dominated by the permeability. However, while the highest rates of injection are, of course, into the higher permeability zone, overall this injection scenario slightly favors the poorer quality rock as seen in Fig. 13. This appears to be a reasonable possible injection plan, and further investigation of higher rates would be required. 4 SPE 110329 Taking this one step further, i.e. perforating the next sand up and injecting at 2000 m 3 /D will result in a fracture growing into the top sand after 5–6 days. The width profile after 100 days of injection is shown in Fig. 14. Due to cooling effects, the fracture is migrating near totally into the overlying zone. Since fracture propagation is strongly affected by injection (increased reservoir pressure around the well and formation cooling) it should be possible to control fracture height growth. That is, cooling the formation by injecting at a low rate will reduce stress; rate can then be gradually increased. In this way one could force a fracture to be contained. Simula- tions were conducted to design such an injection scheme for this example case. Assuming the same perforation interval as the case above (where undesired, upward height growth occurred), injection start-up used a relatively low rate of 1000 m 3 /D for 50 days, 1500 m 3 /D for 50 days and finally 2000 m 3 /D. The evolution of the fracture is pictured in Fig. 15. In the first picture (after about 1 day), contours show the essentially instant response to injection pressure. Fracture clo- sure pressure has increased by about 35 bar (at the wellbore) – with no apparent cooling (stress reduction) effects yet appear- ing. Then after about 1 week (second picture), one sees a re- gion of “0” stress change near the wellbore. The poro- and thermal effects cancel. Finally, the third picture shows the stress change after about 50 days. This shows a stress reduc- tion of about 15 bar in the injection zone. Note, however, that the stress reduction in the shale at 2454 m is even greater (−35 bar). Basically, the thermal effects are slower/larger in the shale since the cooling is only by conduction (no convec- tion from fluid flow through the rock). However, there is NO poro-effect. Thus, the overall effect (for this case) is a greater stress reduction in the shale than in the sand. Thus, eventually fracture height growth may occur. However, even though “breakthrough” may occur, the large fracture area open in the deeper, lower permeability zones would continue to allow those zones to dominate injectivity long after “breakthrough”. For even better height confinement (for this case), a lower initial rate would be required in order to let the formation cooling move out into the formation faster than the fracture length growth. This would then further reduce injection pres- sure, and totally prevent any fracture height growth into the shale. At that point, the shale cool down, stress reduction would depend solely on vertical heat conduction, further de- laying shale stress reduction and subsequent height growth. The final picture shows the fluid loss (inflow into the for- mation) distribution at the end of 200 days. Fracture growth downward has contacted the lower sand, and upward height growth is nearing the overlying, high permeability zone. The major difference between upward/downward growth is that the upper shale is slightly thicker, thus cooling by conduction takes additional time. While not plotted here, eventually after a year, the fracture did penetrate the high permeability zone. However, even for months after “‘breakthrough”, the deeper, lower permeability zones still dominated injectivity. Conclusions • As expected, and discussed many times in the literature, reservoir cooling has a strong effect on fracturing. Even for this low modulus formation, there is a strong tendency to keep fractures well confined. However, even where shale barriers exist, eventually cooling via conduction may reduce the stress in the shale and allow vertical fracture migration. • Start-up procedures can be used to reduce or delay un- wanted height growth. However, the exact procedure or injection pattern will depend on the specific conditions of permeability, fluid/formation temperatures, etc. In gene- ral, however, cooling of shale layers via conduction will eventually cause stress reduction and fracture height growth may resume. • Quite “dirty” water can be injected as long as fractures are allowed to grow with no danger of fracturing into “forbid- den” zones. • The combination of detailed injection data, a simple “p-q” plot, and rigorous coupled model (simultaneously considering injection, fracture growth, temperature, pore pressure, etc.) can provide a powerful engineering tool for management of water injectors. Nomenclature A = Area A p = Poroelastic constant A T = Thermoelastic constant B = Biot coefficient C = Concentration C t = Compressibility E = Young’s modulus K = Stiffness matrix T = Temperature V = Volume k = permeability p = Pressure q = Flow rate w = width α T = Coefficient of thermal expansion φ = Displacement potential σ = stress μ = Viscosity ν = Poisson's number References 1. Perkins, T.K. and Gonzalez, J.A., The effect of thermoelastic stresses on injection well fracturing. Soc. Petr. Eng. J., 25, 78– 88, 1985. 2. M. B. Smith, A. B. Bale, L. K. Britt, H. H. Klein, E. Siebrits, and X. Dang, “Layered Modulus Effects on Fracture Propagation, Proppant Placement, and Fracture Modeling,”. SPE 71654, presented at the 2001 SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana, 30 September–3 October 2001. 3. Michael B. Smith, Michael Bose, Henry H. Klein, Brent R. Ozenne, Ron S. Vandersypen, “High-Permeability Fracturing: "Carter" Fluid Loss or Not”, SPE 86550 presented at the SPE International Symposium and Exhibition on Formation Damage Control held in Lafayette, Louisiana, 18–20 February 2004. SPE 110329 5 4. Clifford, P.J., “Simulation of Waterflood Fracture Growth with Coupled Fluid Flow, Temperature and Rock Elasticity,” presented at the 2 nd joint IMA/SPE European Conference on the Mathematics of Oil Recovery, Cambridge, 25–27 July 1989. 5. Clifford, P.J., Berry, P.J., Hongren, G., “Modeling the Vertical Confinement of Injection-Well Thermal Fractures”, SPEPE, 6(6), 377–383, 1991. 6. E. J. L. Konig, “Fractured Water Injection Wells – Analytic Modelling of Fracture Propagation,” SPE 14684 (Unsolicited), 1985. Appendix A The fracture evolution is determined by volume conservation of the fluid, () x zpl V qq qq t ∂ +Δ + = + ∂ (A-1) where V is the local fracture volume = wA y , w is the fracture width, A y is the area of the fracture face, x q and z q are the volumetric flow rates along the length and height of the fracture respectively. These flow rates are functions of the pressure gradient, the (non-Newtonian) viscosity, and the width. p q is the pump rate and l q is the leakoff rate at the fracture face p . The fracture width is related to the pressure through the fracture stiffness, [ ] [ ] [ ] Kw p σ =− (A-2) K is the stiffness matrix, pre-calculated using the finite element method for varying layer moduli or analytically for uniform modulus using a boundary integral approach. p is the pressure and is the stress. In the standard fracture models the leakoff is determined using the standard “Carter” leak-off coefficients. In the present model the fluid loss from the fracture face is directly from flow into the reservoir. The leak-off rate is () y filtrate reservoir fracture l filtrate l Ak p p q L μ − =− (A-3) where f iltrate k is the permeability inside the fracture-reservoir face, and can include relative permeability effects;. f iltrate μ is the viscosity of the fluid inside the fracture-reservoir face, and it can include non-Newtonian and temperature effects. reservoir p is the pressure at the reservoir face, and f racture p is the pressure at the fracture face. l L is a length that includes gel and solids filtercake buildup on the fracture face, the distance of the invaded zone of the leak-off fluid, and the compressibility of the reservoir fluid The volume conservation in the reservoir is given by 0 y x z t k k k pp p p C tx x y y z z μμμ ⎛⎞ ⎛⎞ ⎛⎞ ∂∂ ∂ ∂ ∂ ∂ ∂ +− +− +− = ⎜⎟ ⎜⎟ ⎜⎟ ∂∂ ∂ ∂ ∂ ∂ ∂ ⎝⎠ ⎝⎠ ⎝⎠ (A-4) t C is the compressibility of the reservoir fluid; x k , y k , z k are the permeabilities in the three space dimentions; is the fluid viscosity. Equations (A-1)–(A-4) are solved simultaneously for the fracture width and the pressure in the fracture and reservoir. Equations for the conservation of energy are solved to provide the temperature in the fracture and reservoir. As the injected fluid leaks off from the fracture the reservoir pore pressure increases and the temperature increases or decreases depending on the relative injected and reservoir temperatures. The pressure and temperature changes have a direct effect on the stresses confining the fracture. Following Konig [6] the poro-thermo stress change is 1 ij p ij T ij ij E Ap AT vx x σ ϕδ δ ∂ ∂ Δ= +Δ +Δ +∂∂ (A-5) is the displacement potential which is a solution to the Poisson Equation 2 11 pT Ap AT EE ν ν φ ++ ⎛⎞ ⎛⎞ ∇=−Δ −Δ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ (A-6) Δp is the pressure change from the initial reservoir pressure, and ΔT is the temperature change from the original reservoir temperature. p A is the poro-elastic constant defined as 12 1 p A B ν ν − = − (A-7) where B is Biot’s constant. T A is the thermo-elastic constant defined as 1 T T E A α ν = − (A-8) where T α is the thermal expansion coefficient. Equations (A-5) and (A-6) are solved to give the change in local fracture confining stress. The updated stresses are used in Equation (A-2) to give the fracture response to the stress changes. 6 SPE 110329 Figure 1 – Basic injector response. The full (black) line shows the transition from matrix to fracture injection at the level indicated by the dotted gray line. The dashed (blue) line shows the effect of cooling. Similarly, the dash-dot line (red) shows how reservoir pressure increases around the injector changes both matrix and fracture injectivity. Note how the crossing moves towards lower rate, as discussed in the text. Figure 2 –Basic injector response. The dashed (blue) lines correspond to two different injectivities, while the solid (black) lines apply for different choke settings. If injectivity changes with constant choke, the response will move along the choke curves, as illustrated by the thick (red) line segments. Figure 3 – Field example of reservoir pressure build-up around an injector. The data points are colour coded with rainbow colors, with early data being red and late date being blue. The solid black lines indicate the matrix and fracture injection regimes for three different levels of pressure build-up around the injector, as dicussed in the text. Figure 4 – Field example of fracture growth incidents. Most of the data points gather around the fracture injection “line”, but there are several “negative slope events” corresponding to temporary increase in injectivity. One of the events is shown in more detail in Fig. 5. SPE 110329 7 Figure 5 – Flow rate (upper) and pressure (lower) versus time for one of the fracture growth incidents in Fig. 4. Figure 6 – Field example of a series of smaller fracture growth incidents, leading to a net increase in injectivity. Note, however, how the injectivity decreases following each event. Heidrun A49 Lower Tilje Injection_LastSP TVD (m) 240024202440246024802500 ShalesandSilt GR API 0200100 RHOB g/cm3 1.95 2.952.45 Pcl (Bar) 300 400 E (MMpsi) 0.0 1.6 K Ic 02000 S Heidrun A49 Lower Tilje Injection_LastSP TVD (m) 240024202440246024802500 ShalesandSilt GR API 0200100 RHOB g/cm3 1.95 2.952.45 Pcl (Bar) 300 400 E (MMpsi) 0.0 1.6 K Ic 02000 S Drag logs onto graphs as desired Figure 7 – Geologic layering for example simulations 8 SPE 110329 Table 1 – Actual Startup Injection Rate History Injection - (m 3 /D) Time - (Days) 950 4 1250 9 1550 4 0 21 2000 7 Fracture Penetration (m) 10 20 30 64145.82 min 2470 m TVD 2480 2490 2500 2510 Stress (Bar) 350 375 sandsandsandShale 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500 Width - Total in Figure 8 – Fracture Geometry After Startup Injection 10 20 30 40 50 60 70 20 40 60 80 Pore Volumes Injected Start Dirty Water 5 micron particles Solids Fraction 0.00375 Consta nt Flowrate Variable Δ p 5101520 20 40 60 80 √ Time (min) Loss Volume (cc/cm ) 2 C = 0.0164 X Slope = 0.065 ft/ √ min W Figure 9 – “C W ” for “Dirty” Injection Water Fracture Penetration (m) 20 40 60 80 274305.16 min 2460 2480 m TVD 2500 2520 2540 Stress (Bar) 320 360 400 sandsandShalesand 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500 Width - Total in Figure 10 – 4000 m 3 /D Figure 11 – 9000 m 3 /D SPE 110329 9 Fracture Penetration (m) 20 40 273328.97 min 2460 m TVD 2480 2500 Stress (Bar) 320 360 sandsandsandShale 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 Width - Total in Fracture Geometry after 200 Days Fracture Penetration (m) 20 40 273328.97 min 2460 m TVD 2480 2500 Stress (Bar) 320 360 sandsandsandShale 0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000 Leakoff M3/Day Injection Distribution after 200 Days Figure 12 – Injection of 1500 m 3 /D into “middle” zone (2468– 79m) 00.20.40.60.8 Fraction "kh" Fraction Injection 2456-63m 2468-79m 2482-89m 2489- 2507m Shale Shale Figure 13 – Cumulative Injection Distribution (1500 m 3 /D for 200 Days) Figure 14 – Injection into “Top” Zone at 2000 m 3 /D. The fracture penetrates into the overlying, “forbidden” high permeability zone in < 1 week. 10 SPE 110329 Fracture Penetration (m) 10 20 30 40 50 60 70 80 1494.05 min 2400 m TVD 2410 2420 2430 2440 2450 2460 2470 2480 Stress (Bar) 320 360 sandsand (50.000) (40.000) (30.000) (20.000) (10.000) 0.000 10.000 20.000 30.000 40.000 50.000 Stress Change Bar Fracture Penetration (m) 10 20 30 40 50 60 70 80 10134.05 min 2400 m TVD 2410 2420 2430 2440 2450 2460 2470 2480 Stress (Bar) 320 360 sandsand (50.000) (40.000) (30.000) (20.000) (10.000) 0.000 10.000 20.000 30.000 40.000 50.000 Stress Change Bar Fracture Penetration (m) 10 20 30 40 50 60 70 80 70614.05 min 2400 m TVD 2410 2420 2430 2440 2450 2460 2470 2480 Stress (Bar) 320 360 sandsand (50.000) (40.000) (30.000) (20.000) (10.000) 0.000 10.000 20.000 30.000 40.000 50.000 Stress Change Bar Fracture Penetration (m) 10 20 30 40 50 60 70 80 305647.00 min 2400 m TVD 2410 2420 2430 2440 2450 2460 2470 2480 Stress (Bar) 338 360 382 sandsand 0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 Leakoff M3/Day Figure 15 – Effect of Injection Start-Up on Fracturing . Introduction Water injection, in particular produced water injection, in most cases creates a fracture. As is well established [1], temperature effects are important, because the cold injection. of thermally induced waterflood fracturing in vertical sweep con- formance of injection wells. In highly variable reservoir qual- ity sands, injection water tends to be injected into the best. better manage water injectors has been ongoing for many years. Simple analytical solutions have proven inadequate, and most reser- voir simulators do not explicitly model water injectors. This