Enhanced 2D Proppant- Transport Simulation: The Key To Understanding Proppant Flowback and Post-Frac Productivity

Transcription

1 Enhanced 2D Proppant- Transport Simulation: The Key To Understanding Proppant Flowback and Post-Frac Productivity M. B. Smith, SPE, NSI Technologies; A. Bale, SPE, Statoil; L. K. Britt,* SPE, Amoco Production Co.; B. W. Hainey, SPE, Arco E&P Technology; and H. K. Klein, SPE, Jaycor Summary It has been assumed that along with fluid viscosity and pump rate, gravity dominates final proppant placement in hydraulic fractures. Results here, based on detailed multiphase-flow modeling, show that other factors such as slurry rheology (effect of adding proppant on slurry viscosity), fluid loss and layered fluid loss, and vertical fracture-width variations often are more important than gravity in controlling placement. Abstract The goal of a hydraulic-fracture treatment is to create a large flow area exposed to the formation and connected to the wellbore along a conductive path. The only goal of hydraulic-fracture models is to predict this final proppant placement accurately. Most theoretical, modeling, and experimental efforts in this area have focused historically on understanding and predicting only gravity effects on proppant placement. However, for proppant-laden, viscous fluid or slurry flowing along a fracture, other forces are always more important than gravity, and can easily cause proppant to move upwards, both during pumping and fracture closure. Adifferential-fracture closure occurs when a fracture growing vertically penetrates zones with higher or lower closure stress. After shut-in, higher stress zones close first. This forces any proppant-laden slurry covering these zones (at shut-in) to migrate to low stress zones where fracture width is greater, and can easily lead to upward proppant movement as fracture-closure stress generally decreases with depth. After shut-in of a propped fracture treatment all fluid must leak off into permeable formations penetrated by the fracture. Until closure, viscous fluid continues to transport proppant (possibly upward) toward fluid-loss layers, often corresponding to pay. As proppant is introduced to fluid, the resulting slurry has a higher density and tries to move downward. However, solids also act to increase viscosity, and more viscous slurry prefers the wide middle of a fracture. This serves to keep proppant near the middle of the fracture, often in the pay zone. This paper discusses the combined effect of these forces on proppant placement in a context of post-frac analysis of several field treatments. Analysis used a fracture model including rigorous, numerical, 2D material transport, and the often-unexpected results are compared with supporting evidence from post-frac well performance. In many instances, the combined effect of proppantplacement forces is beneficial, with more proppant placed across the pay than suggested by simple models. In other cases, postshut-in proppant redistribution can (and did) cause catastrophic job failure. *Now with NSI Technologies Copyright 2001 Society of Petroleum Engineers This paper (SPE 69211) was revised for publication from paper SPE prepared for presentation at the 1997 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5 8 October. Original manuscript received for review 24 November Revised manuscript received 21 January Manuscript peer approved 22 August Introduction The goals of a hydraulic-fracture treatment are to increase the flow area exposed to the formation, and then to connect that flow area to the wellbore via a high-permeability path. For propped-fracture treatments, placing a proppant in the fracture creates this conductive path. The quality of proppant is designed to maintain lasting, high permeability under conditions of in-situ stress, temperature, etc. Because the only goal of field operations is to place this permeable proppant in the desired location, results from numerical design and analysis models must represent proppant transport in the fracture accurately. Proppant transport has received its share of attention along with the required analysis/design steps of understanding and predicting fracture geometry and fluid loss. This led immediately to studying effects of gravity on proppant placement. As anyone falling off a ladder can attest, gravity is a major natural force. Because the oil industry normally deals with nearvertical fractures, the influence of gravity on proppant placement and proppant settling is clearly a major concern. Kern et al. 1 conducted laboratory experiments to determine a critical velocity where no additional sand dune formation would occur. This was followed by important work by Novotny, 2 Clark and Quadir, 3 and others. These works concentrated on single particle or Stoke s law -type proppant settling. Stoke s law can be stated as v f d 2 r m f g, (1) where the equation in this form must use consistent units. The actual phenomenon is more complex, of course, and final proppant placement is a function of pump rate and the effects of proppant concentration on slurry viscosity and thus on settling rates. In its simple form, however, this still shows settling as a combined function of gravity and viscosity. More recently, it was understood that proppant-laden slurry was denser than the clean fluid pad pumped to open a fracture. This heavier slurry tends to sink and tries to under-run the lighter pad fluid. This was probably first discussed (in terms of 3D fracture modeling) by Clifton and Wang. 4 This behavior has been proposed as a major influence on proppant placement. 5,6 Clark and Zhu 7 proposed a dimensionless constant which uses consistent units, written as f q h N, (2) c = 12 m ( / 2 / ) 3 r gb where values 1 would indicate a strong possibility for convection, while for values 1 lateral flow would dominate and convection-type settling would be minimal. If confirmed, this could prove a valuable tool for modeling, particularly for cases where a rigorous fluid-flow, proppant-transport solution is not used. While N c is valuable as a screening tool, results and comparisons suggest the problem is more complex than suggested by this dimensionless constant. The additional complexity arises because of variations in fracture width over the fracture height, and effects of proppant on slurry rheology. 50 February 2001 SPE Production & Facilities

2 Other factors were identified that often can dominate gravity effects. These include fluid loss, layered fluid loss, and late-time changes in fracture geometry. Any of these, along with gravity effects, affect proppant placement. All of these can cause significant proppant movement after shut-in. Post-shut-in proppant movement can be either beneficial or terrible. However, in most cases studied, significant post-shut-in proppant movement was predicted, and this must be planned for in the design process. Model Smith and Klein 8 discussed the numerical model used for the following case histories. This model couples a pseudo-3d fracture geometry model of the cell type with a rigorous 2D-multiphase numerical fluid-flow and proppant-transport solution. Mathematical details of this solution are included in Ref. 8. The flow solution is a multiphase, 2D, implicit (in time) solution for proppant transport. This, for example, treats the fluid and multiple types of proppant as separate phases. Should proppant movement be slowed by bridging or slurry dehydration, the fluid phase continues to flow through and past the resulting blockage. Ref. 8 also compares the numerical model to several published physical experiments. Case Histories The following sections discuss combined effects of in-situ stress variations and height growth, fluid loss, gravity, and slurry viscosity on proppant placement. One surprising result is that gravity is generally a minor force for proppant placement. Clear exceptions to this are low fluid-viscosity cases, where traditional single particle or Stoke s law-type settling dominates. Effect of Height Growth on Proppant Placement. A fracture growing vertically generally penetrates zones with higher and/or lower closure stress. After shut-in, higher stress zones close first. This closing forces the proppant-laden slurry adjacent to these layers to flow, often upwards, to lower stress zones where fracture width is greater. This can be devastating to results if breaking into a lower-closure-stress zone causes additional vertical height growth (upward or downward) late in a treatment. After shut-in, slurry in the fracture can continue to migrate in this new direction, stealing proppant from a targeted pay zone. The following describes a case history for this behavior. Late height growth while fracturing an oil well in California caused extensive upward migration of proppant-laden slurry (defying gravity), leaving proppant concentration in the pay too low to be effective. This case study involved a field demonstration of economic recovery of bypassed oil in the fan margin areas of a slope-andbasin clastic reservoir where lateral thinning of individual sand lobes and lateral deterioration of reservoir properties made conventional development uneconomical. Multiple hydraulic-fracture treatments of a high angle (56 ) well obliquely penetrating the Stevens formation in Kern County, California were designed to provide vertical communication between layers and commercialrate capability. The first fracture treatments targeted the very bottom and most productive interval at 13,250 to 13,280 ft. A 300-bbl minifrac was designed to be pumped at 30 bbl/min using a 45-lbm/1000-gal high-temperature borate-crosslinked guar fluid. Due to high treating pressures, only 16 bbl/min could be achieved without exceeding the 10,000-psi maximum surfacetreating-pressure limit. Decline analysis showed a net pressure of approximately 1000 psi, indicating fracture containment in the 30-ft thick pay zone. A contained, 600-ft half-length fracture treatment was designed using a 619-bbl pad. This was followed by 1,086 bbl of slurry carrying 165,000 lbm of 20/40-mesh bauxite at concentrations of 1 to 10 lbm/gal. A three-fold productivity increase was expected for a contained fracture in this 1.0-md permeability reservoir. The main fracture treatment again experienced high treating pressures, allowing a pump rate of only 2 to 11 bbl/min during the pad stage. Like the minifrac, the fracture appeared contained initially. However, as the job progressed, a break back in treating pressure occurred in the slurry stage allowing the remainder of the job to be placed in the formation at rates of 17 to 23 bbl/min. Postfrac simulation of the fracture treatment showed containment initially, but as the volume grew, the fracture broke through the upper confining shale barrier as seen in Fig. 1. Height growth during the slurry stages allowed most of the proppant to move upward and out of the perforated interval as seen in Fig. 2. However, if gravity effects were to dominate post-shutin proppant movement, much of this proppant might still have ended up effectively propping the target interval. Fig. 3 shows upward flow continues as the fracture closes, and even more proppant is lost to the upper part of the fracture. This proppant lost to the upper part of the fracture due to height growth then is sealed off from the perforated interval by the intervening high-stress shale layer. Given a formation embedment of 1.0 lbm/ft 2 for the 20/40-mesh bauxite leaves only a short 100-ft propped fracture with coverage above 2 lbm/ft 2 (effective coverage of 1 lbm/ft 2 ) in communication with the perforated section of the wellbore. Prior to stimulation, the well was produced at a rate of 250 B/D total fluid and 130 BOPD. After fracturing, the well improved only slightly to 280 B/D total fluid and 150 BOPD, significantly less than the threefold increase expected. Unfortunately, no additional fracture diagnostics (other than the pressure behavior) were available to confirm this massive, explosive height growth. However, upward movement of proppant during height growth, and its isolation from the perforated interval by intervening shale, provides a credible explanation for the well s lack of productivity improvement. Effect of Fluid Loss. Another surprising result (though quite simple and plausible after a bit of thought) is the extensive influence of fluid loss on final proppant placement. After shut-in, as the fracture closes, all fluid must flow to permeable, fluid loss, and these zones generally coincide with the pay. If fluid has sufficient viscosity to suspend proppant effectively (that is, minimal Stoke s law-type or single particle proppant settling occurs), then this fluid Fig. 1 Case 1: Fracture geometry vs. time. Fig. 2 Case 1: Proppant distribution at shut-in. February 2001 SPE Production & Facilities 51

3 Fig. 4 Canadian example, minifrac pressure decline. Fig. 3 Case 1: Proppant distribution at fracture closure on proppant. flow naturally convects, or carries, proppant to the pay zone. This effect has quite profound implications with regard to the historical success of fracturing. Despite what we do or do not do, proppant tries to end up covering productive formations! This behavior is discussed with reference to a Canadian gas well. Fracturing-pressure behavior suggested extensive height growth out of the productive zone, and the fracture-model-predicted fracture length based on this height growth is in excellent agreement with the productive fracture length determined from post-frac well test data. However, fracture conductivity indicated from well tests was much greater than predicted. Fracture Design for a Canadian Well. A fracture stimulation was designed to increase productivity of a well in the Pembina field in central Alberta, Canada. The well produces from the Jurassic-age Rock Creek formation at a depth of approximately 7,400 ft. Net permeable pay consists of about 6 ft of reservoir with an average permeability of 1.4 md, porosity of 8%, and average reservoir pressure of 2,800 psi. Given the limited permeable pay, fracture-height growth into nonproductive formation was anticipated. A minifrac test was conducted and treatment was redesigned based on the analysis of the data. Fig. 4 plots pressure vs. square root of time for minifrac pressure decline. Evaluation of this data indicated a fracture-closure pressure of 4,370 psi, fracture fluid efficiency of nearly 61%, and final net treating pressure at shut-in,,p S, of 755 psi. In addition, both the pressure decline (early downward concave character) and the declining net treating pressure during the minifrac indicated significant height growth beyond the perforated permeable reservoir. A geomechanical rock property and stress profile was developed by coupling the minifrac pressure interpretation with interpretation of logs and cores. The resulting calibrated stress profile was used to history match the net treating-pressure history from the minifrac test with a pseudo-3d model as shown in Fig. 5. Fluid leak-off and resulting fracture geometry were characterized and used to redesign the fracture stimulation. The redesigned fracture stimulation consisted of 71,300-lbm 20/40 Ottawa sand pumped in 595 bbl of gelled oil at concentrations from 1 to 10 lbm/gal. Fig. 6 shows the calibrated stress profile used in this analysis and the predicted width and height profile resulting from this stimulation. A maximum fracture width of 0.29 in. and fracture height of nearly 358 ft were developed by the end of the fracture stimulation. In addition, a final propped-fracture half-length of 543 ft was achieved based on the fracture-model prediction. These predicted results were in agreement with data from other wells in the area that indicated hydraulic fractures grow well outside the productive pay. A post-fracture buildup test on this well confirmed fracture length; however, the buildup-derived fracture conductivity was well in excess of that expected from 71,300-lbm 20/40 Ottawa sand distributed over the entire fracture area. One explanation for the higher than anticipated fracture conductivity is the effect of post-fracture recession and proppant redistribution due to fluid flow. Another explanation is that the propped height above the pay increases the effective fracture conductivity as discussed by Cipolla. 9 Either or both explanations are plausible. To investigate the effect of this height growth on proppant placement in a reservoir with limited thickness, coupled fracture-fluid-flow simulations were conducted with the model described. Fig. 5 Net pressure history match, minifrac net pressure behavior. Fig. 6 Canadian example, calibrated stress profile and fracture height, end of minifrac. 52 February 2001 SPE Production & Facilities

4 Fig. 7 Canadian example, proppant distribution at shut-in. Fig. 8 Proppant distribution 70 minutes after shut-in. Post-Fracture Proppant Movement. Fracture stimulation and post-stimulation-fracture recession were simulated. This model showed, as indicated by the treating pressure record, that fractureheight growth continued throughout the pumping period of treatment. This distinctly different height-growth behavior from the previous case is a major reason for the different results. During this time, the fracture grew to a maximum height of 358 ft. Once the pumps were shut down and the fracture began to close, the importance, or dominance, of fluid flow on ultimate placement of proppant in the fracture was realized. Fig. 7 shows a contour plot of proppant concentration for the fracture at the end of pumping, indicating that when the pumps were shut down, proppant was distributed fairly uniformly over the entire fracture area. It further highlights significant upward fracture growth that occurred during the latter part of the fracture stimulation as the highest proppant concentration is found above the perforated interval. However, following the end of the fracture stimulation, while fracture fluid was leaking off and the fracture was closing, significant proppant movement occurred. Fig. 8 shows a contour plot of proppant concentration after 70 minutes of leakoff, post-pump shutdown. Fracture height receded to 195 ft. During this recession, maximum proppant concentration aligned with the permeable interval as fluid leaked off and proppant slurry dehydrated. Similarly, fracture height continued to recede and maximum proppant concentration stayed aligned with the leak-off area until fracture closure on the proppant. Fig. 9 shows a contour plot of proppant concentration at fracture closure. At this time, fracture height had receded and the proppant was being concentrated in and around the permeable pay. Final fracture dimensions at closure resulting from this fracture stimulation include a well propped-fracture height of 165 ft, fracture half-length of 543 ft, and fracture conductivity of approximately 900 md-ft. A post-fracture buildup test was conducted on this well to evaluate fracture dimensions. Analysis of the buildup test indicated a fracture half-length of 558 ft and dimensionless fracture conductivity of 6.2. The fracture half-length derived from the pressure-transient analysis was consistent with the model-predicted fracture half-length. However, fracture conductivity derived from the buildup-test analysis far exceeded the fracture conductivity predicted from conventional 3D fracture modeling, and was somewhat greater than predicted by the numerically coupled fluid-flow-fracture geometry model. Therefore, though proppant-concentration effects caused by fluid flow and height recession nearly triples fracture conductivity over the permeable perforated interval, additional conductivity benefits were derived from the conductive fracture above the productive pay interval. This behavior has been discussed by Cipolla 9 and confirmed for this case through extensive numerical reservoir modeling.* Conclusion. Fluid flow and leak-off are extremely important to final proppant placement in the hydraulic fracture. Further, in the presence of fracture-height growth into nonproductive pay, this example suggests that the operator should design the breaker schedule to allow adequate proppant-carrying capability while the fracture is closing, thus ensuring that this fluid-flow phenomenon can do its work concentrating proppant and maximizing fracture conductivity associated with the permeable and productive reservoir. Effect of Layered Leak-Off. Fluid flow inside a fracture after shut-in tends to carry proppant toward fluid-loss layers. This is often good. However, for cases of highly layered fluid loss, this can cause severe post-shut-in proppant redistribution. For cases where additional additives, such as curable resin-coated (RC) proppant or other proppant-flowback-prevention materials, are used to control flowback, this redistribution can cause failure. This case study involves an unusual application of hydraulic fracturing where simply increasing rate was not the objective. The goal was to modify the vertical-inflow profile to maximize reservoir recovery for the bottom, lower-permeability zones. In addition, the fracture should still contact and provide sand-free production from the main pay without the need for normal sand-control measures. A consolidated, moderate-permeability (50 md) zone (Rannoch-1) at the bottom of a fining-downward sand sequence was perforated and stimulated. The goal was to stimulate the deeper Rannoch-1 while at the same time providing communication with, and formation-sand-free production from, the high-permeability Fig. 9 Proppant distribution at closure. * Hagar, C.J. and Agarwal, R.G., personal communication, Amoco Production Co., 1997 February 2001 SPE Production & Facilities 53

5 Fig. 11 Comparison of measured vs. model-predicted treatingpressure behavior. Fig. 10 Typical log section and fracture geometry, layered fluid-loss case. (1000 md ) layer (Rannoch-3) at the top of the formation. Fig. 10 depicts a typical log section for this formation. Initial treatment of this type was very successful both in stimulating the lower zones and in establishing communication with the weak, high-permeability, main pay. 10 Post-frac productivity Index (PI) was in line with expectations. This first job used 331 bbl of pad followed by 890 bbl of fluid carrying 155,000-lbm 16/20-mesh ceramic proppant; the pad represented 23% of total slurry volume pumped. Unfortunately, no RC proppant was used. While the fracture stimulation achieved all design goals in a theoretical sense, post-frac production was marred by massive proppant-flowback problems that made the well unstable. Later, similar volume treatments using 50 to 80% curable RC, 16/20-mesh and 12/18-mesh ceramic proppant were uniformly successful in achieving reservoir goals without significant proppant flowback. These later wells were stable producers. However, post-frac well tests showed clear indications of turbulent flow, suggesting that near-perforation-fracture conductivity was dominating productivity. Thus, while the treatments were successful, there appeared to be room for additional improvement. Recent Treatment. In an effort to increase productivity, a treatment was designed to achieve an in-situ propped width approximately twice that achieved in earlier jobs. Following a minifrac test, the new design consisted of 133 bbl of pad, followed by 1,219 bbl of fluid carrying 244,000 lbm of 16/20-mesh ceramic proppant at concentrations of 1 to 8 lbm/gal, followed by 564 bbl of fluid carrying 239,000 lbm of RC 12/18-mesh ceramic proppant at concentrations of 9 to 11 lbm/gal. Pad made up less than 5.5% of the treatment volume. Treatment was pumped at 40 bbl/min with no problems. Fig. 11 plots the bottomhole-measured net-pressure behavior against the prefrac-simulator predicted behavior. Clearly more than two-thirds of the treatment was pumped with net pressure increasing on a unit slope, indicative of a good tip screenout (TSO) treatment. Post-frac productivity was also very high, confirming that this aggressive design achieved its reservoir goals. However, despite tailing in with 239,000- lbm RC-proppant (almost 50% of total proppant pumped), postfrac production was marred by massive flowback volumes of noncoated proppant. RC tail-in of about 50% of total proppant, which was successful for several previous wells, failed in this case to control proppant flowback. Post-Shut-In Proppant Movement. This type of behavior is sometimes blamed on convection, density-driven movement of high-concentration slurry toward the bottom of the fracture. For this case, however, perforations are at the bottom of the fracture. Any such downward movement of the final, high-concentration slurry stages would have been helpful only in eliminating proppant flowback. Detailed modeling of proppant redistribution after shutin shows the problem here is upward migration of proppant. This is driven by high fluid loss at the top of the formation. Fig. 12 plots the concentration of Stage 12, the final stage of treatment at 11 lbm/gal. At shut-in time of 60.7 minutes, this stage covers the perforations. However, at later times, as the fracture closes, material in this stage is forced up, away from the perforations. Finally, at fracture closure (210 minutes), the fracture over the bottom half of the perforated interval is filled with proppant that, prior to shutdown, was stored near the bottom of the fracture. This is mostly nonrc proppant. Physically, the following describes what the model shows. After the start of the TSO, fracture width in the low-fluid-loss Rannoch-1 and shale section below the perforations is increasing faster than fluid is being lost. Thus, proppant in this part of the fracture does not dehydrate, but remains stored in the fracture as mobile slurry. The very aggressive nature of this treatment, vs. earlier Rannoch completions, created a very large width below the perforations (and everywhere else, of course), resulting in storing a large proppant volume, mostly or entirely consisting of nonrc proppant, below the perforations. After shut-in, all flow in the fracture is upward due to fluid loss in the high-permeability Rannoch-3 zone. The fracture located in the low-fluid-loss sections below the perforations then begins to close, forcing mobile proppant-laden slurry there to flow up, over the bottom part of the perforations. The end result of this, at fracture closure, is that the bottom part of the perforated interval is not covered by a solid pack of RC proppant. The well is then subject to proppant flowback. In addition, a large volume of nonrc proppant pumped early in the job is stored immediately over (and below) the perforations, and Fig. 12 Layered-fluid-loss case, proppant distribution at shutin and closure. 54 February 2001 SPE Production & Facilities

6 Fig. 14 Gravity effects on proppant-laden fluid. the observed proppant flowback will come with the 16/20-mesh, nonrc proppant. Stage 11 also used RC proppant. Analysis shows this material even further up and away from the perforations. Basically, while late RC stages carried half the proppant, early nonrc stages accounted for most pump time. Thus, most of the width increase in the lower part of the fracture occurred with nonrc proppant being pumped. During closure, this proppant is simply squeezed up, over the bottom half of the perforations. During pumping of the final two RC stages, fluid movement was dominantly upward, thus the bulk of RC proppant was placed high in the fracture, up and away from the critical near-perforation area. Conclusion. When fracturing in nonhomogeneous formations, and particularly with the perforation interval skewed relative to the fracture geometry, careful treatment design is required if RC proppant is to stop proppant-flowback problems successfully. Simply tailing in with RC proppant may not be sufficient in many cases. Gravity & Rheology Effects. Gravity and viscosity effects on proppant transport are intimately connected. For low-viscosity fluids, where single-particle settling dominates, this is seen clearly from Stoke s law. A somewhat more complex link is seen for convection settling. Eq. 2 presented a dimensionless group proposed by Clark and Zhu. 7 This is recast using common units to give N Fig. 13 Gravity effects on injection of heavy fluid. c qm f = h rb (3) For the case discussed below, average fracture width is about 0.28 in. giving a value for N c of approximately 0.2. This is much less than 1, indicating that convection should be a dominant force. For the simple case of a heavy fluid following a light fluid with identical viscosity, convection is a dominant behavior. Fig. 13 plots results from the numerical model for injecting a heavy fluid, specific gravity (SG) of 1.5, behind a lighter fluid, SG of 1.0. Both fluids have 200 cp viscosity. The heavy fluid immediately begins to fall to the bottom of the fracture and runs under the lighter fluid. At the later time, there is actually a circular flow near the leading tip of the Stage 2 fluid; with reverse flow above the Stage 2 fluid. This is classic convection settling. Ref. 8 gives details of this field case. For these simulations, Stage 1 injection rate was 13.5 bbl/min slowed to 8 bbl/min for Stage 2. Injection was through a perforated interval from 11,500 to 11,584 ft. The second model simulation was identical to the first with a 1,666-bbl pad volume at 13.5 bbl/min. This was followed by a Stage 2 fluid volume of 714 bbl at 8 bbl/min with SG of 1.0 and viscosity of 200 cp, carrying a concentration of 8 lbm/gal of 20/40- mesh sand. This sand concentration gives a slurry SG of approximately 1.5, similar to the fluid SG of the first example. Fig. 14 shows that despite this density difference,,h, of 0.5 gm/cm 3, there is essentially no settling. Even at the low rate, proppant-laden slurry simply moves uniformly out through the fracture, with somewhat faster velocity in the fat middle of the fracture. What is the difference in these two cases? The difference between Case 1 (Stage 2 being a heavy, 200 cp, fluid) and Case 2 (Stage 2 carrying an 8-lbm/gal sand concentration) is the effect of solids on slurry rheology. Holditch 11 discusses several relations predicting the effect of proppant on the viscosity of fracturing fluids. The relation used by the numerical model here is closer to the Amoco Relation. 11 This relation predicts an 8- lbm/gal sand concentration to increase the viscosity of the resulting slurry by a factor of approximately three times. In that case, the 8- lbm/gal slurry has a viscosity of approximately 600 cp vs. 200 cp for the pad fluid. If the relation of Ref. 11 was used, the resulting slurry-viscosity increase would be even larger. In either case, the large viscosity increase associated with proppant concentration does not allow convection settling. More viscous slurry prefers the wide, middle of the fracture, and avoids the narrow width near the bottom of the fracture. The viscosity increase is a larger effect than gravity. Thus, while pumping continues, and fluid is forced to flow along the fracture, convection settling of proppant cannot occur. (In real cases, proppant concentration is slowly increased from pad to 8 lbm/gal, and there is even less tendency for convection than seen in this extreme example of 8 lbm/gal immediately following clean pad.) For lower fluid viscosity, Clark s 3 dimensionless constant suggests that convection type proppant movement is more likely. To look at this, the simulation was redone using a 5-cp fluid (giving N c of less than 0.05). Fig. 15 shows results for the fluid-only case, (injecting a Stage 2 of heavy fluid). Behavior in this case exhibits February 2001 SPE Production & Facilities 55

7 Fig. 15 Gravity effects on injection of heavy, low-viscosity fluid. even more pronounced convection, as expected, with the heavier Stage 2 fluid running out to 400 ft in only 17 minutes. If the density difference is created by adding proppant, results (just as with the 200 cp case) are again different. Fig. 16 clearly shows much less convection. As compared to the 200 cp case, however, there is now some downward movement of the proppant laden fluid. Detailed examination of these results shows this to be predominantly Stoke s law behavior or single-particle settling. Conclusions. For many, if not most cases, convection-type proppant settling does not exist. For viscous fluids, viscosity increase associated with proppant addition precludes very viscous slurry from migrating to the narrow, bottom parts of a fracture. For very low-viscosity fluids, viscosity increase would not be so dominant, and convection-type settling might be possible. However, for low-viscosity fluids, single-particle Stoke s law-type settling becomes the dominant proppant-movement mechanism. These results also suggest using typical parallelplate systems for laboratory tests could be misleading if used to predict actual in-situ behavior as opposed to measuring physical parameters of the materials. Conclusions For all cases studied, final proppant placement is quite plausible. In general, however, it is probably not one s first expectation. Such plausible but surprising results often are seen when more rigorous proppant-placement modeling is used. The other general result is that final proppant placement is a complex function of several variables. These include at least four factors. 1. In-situ stress variations and late-time fracture-height growth can have a serious negative effect on proppant placement. 2. Fluid loss and layered fluid loss can cause significant post-shutin proppant movement. This can be either positive or negative, and can easily cause upward proppant movement in defiance of gravity. 3. Gravity and viscosity are major factors in proppant placement. Single-particle settling in a low-viscosity fluid is generally a more important mechanism than convection-type settling. 4. Fluid rheology and the effect of proppant concentration on rheology play a major role in proppant placement. This effect, along with natural vertical-width variations of a hydraulic fracture, precludes significant convection-settling during pumping. Because of the interactions of these various forces, it is generally impossible to recognize, a priori, what will be the dominant force controlling final proppant placement. Possibly the only case where the dominant effect is recognizable in advance would be classic banking treatments using low-viscosity fluids. In such cases, single particle or Stoke s law -type settling will dominate. Fig. 16 Gravity effects on proppant-laden stage of 5 cp fluid. Acknowledgments We would like to thank several organizations for permission to publish this paper. These include Amoco Production Co., Arco Western Energy and Arco E&P Technology, units of Atlantic Richfield Co., and Statoil. Nomenclature b average fracture width, L, in. [cm] d proppant particle diameter, L, in. [cm] F cd fracture conductivity, dimensionless g acceleration of gravity, L/t 2, ft/s 2 h fracture height, L, ft N c convection tendency group, dimensionless q total injection rate, L 3 /t, bbl/min P C fracture closure pressure, m/lt 2, psi v f particle settling velocity, L/t, ft/sec t C time from shut-in to fracture closure, t, min x f fracture half-length, L, ft,h density difference, m/l 3, lbm/ft 3,P S net pressure at shut-in, m/lt 2, psi H fluid density, m/l 3, lbm/ft 3 f fracturing fluid viscosity, m/lt, cp References 1. Kern, L.R., Perkins, T.K., and Wyant, R.E.: The Mechanics of Sand Movement in Fracturing, Trans., AIME (1959) 216, Novotny, E.J.: Proppant Transport, paper SPE 6813 presented at the 1977 SPE Annual Technical Conference and Exhibition, Denver, Colorado, 9 12 October. 3. Clark, P.E. and Quadir, J.A.: Prop Transport In Hydraulic Fractures: A Critical Review of Particle settling Velocity Equations, paper SPE 9866 presented at the 1981 SPE/DOE Low Permeability Symposium, Denver, Colorado, May. 4. Clifton, R.J. and Wang, J-J.: Multiple Fluids, Proppant Transport, and Thermal Effects in Three-Dimensional Simulation of Hydraulic Fracturing, paper SPE presented at the 1988 SPE Annual Technical Conference and Exhibition, Houston, 2 5 October. 5. Cleary, M.P. and Fonseca, A. Jr.: Proppant Convection and Encapsulation in Hydraulic Fracturing: Practical Implications of Computer and Laboratory Simulations, paper SPE presented at the 1992 SPE Annual Technical Conference and Exhibition, Washington, DC, 4 7 October. 6. Chris, W.: GRI Advanced Stimulation Deployment Program: 1995 Annual Report, Report No. GRI-96/ Clark, P.E. and Zhu, Q.: Convective Transport of Propping Agents During Hydraulic Fracturing, paper SPE presented at the 1996 SPE Eastern Regional Meeting, Columbus, Ohio, October. 56 February 2001 SPE Production & Facilities

8 8. Smith, M.B., and Klein, H.H.: Practical Application of Coupling Fully Numerical 2-D Transport Flow Calculations With a Pseudo-3-D Fracture Geometry Simulator, paper SPE presented at the 1995 SPE Annual Technical Conference and Exhibition, Dallas, October. 9. Cipolla, C.L., and Lee, S.J.: The Effect of Excess Propped Fracture Height on Well Productivity, paper SPE presented at the 1987 SPE Production Operations Symposium, Oklahoma City, Oklahoma, 8 10 March. 10. Bale, A., Owren, K., and Smith, M.B.: Propped Fracturing as a Tool for Sand Control and Reservoir Management, paper SPE presented at the 1992 European Petroleum Conference, Cannes, France, November. 11. Holditch, S.A., et al.: The Effect of Viscous Fluid Properties on Excess Friction Pressures Measured During Hydraulic Fracture Treatments, SPEPE, (February 1991); Trans., AIME, 291. SI Metric Conversion Factors bbl E 01 m 3 ft 3.048* E 01 m ft * E 02 m 2 in. 2.54* E 00 cm lbm E 01 kg md E 04 m 2 psi E 00 kpa *Conversion factors are exact. SPEPF Larry K. Britt is with NSI Technologies in Tulsa, Oklahoma. lkbritt@nsitech.com. Formerly with Amoco Production Co. for more than 20 years as a reservoir engineer, he led the Frac Team at Amoco s Tulsa Research Center for 8 years. Britt holds a BS degree in geological engineering from the U. of Missouri at Rolla. An SPE Distinguished Lecturer on hydraulic fracturing in , he also has served on numerous SPE committees. Michael B. Smith is co-founder and President of NSI Technologies in Tulsa, Oklahoma. mbsmith@nsitech.com. He founded NSI after 10 years with Amoco Production Co. working in the areas of rock mechanics and hydraulic fracturing. Smith holds BA, MME, and PhD degrees in mechanical engineering from Rice U. He served as an SPE Distinguished Lecturer on hydraulic fracturing, and most recently was presented the SPE Lester Uren Award for his contributions to fracturing technology. Arthur Bale is a senior staff engineer with Statoil in Stavanger and Bergen. arba@statoil.com. His areas of responsibility include petrophysics, rock mechanics, and hydraulic fracturing. Prior to joining Statoil in 1984, he worked with Amoco in both Norway and the U.S. Bale holds an MSc degree in petroleum engineering from the Norwegian Inst. of Technology in Trondheim. He has authored numerous SPE papers, and served on SPE committees. Henry K. Klein is Division Manager in the Simulation Engineering and Testing Group at Jaycor. hklein@jaycor.com. He has been with Jaycor for more than 20 years and manages projects for industry and government clients. He has developed detailed computer models to predict fracturing in reservoirs and gravel packing and cementing in wells. Klein holds a BS degree in physics from Loyola U. in New Orleans and MS and PhD degrees in physics from the U. of Maryland. He has authored several SPE papers. Biographical information is not available for B.W. Hainey. February 2001 SPE Production & Facilities 57