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Abstract A number of robust predictive methods for establishing sanding thresholds have been developed over the past decade. Having identified when the onset of sanding occurs, recent research efforts have focused on determining the rate at which sand will be produced once these thresholds are exceeded. In this paper a new analytic model for predicting the rate of continuous (steadystate) sand production is described. This sanding rate model is consistent with the threshold prediction model, and utilizes as its basis the nondimensionalized concepts of loading factor (nearwellbore formation permeability, viscosity, density and flow velocity). Interpreted this way, the results of laboratory sand production experiments are used to derive an empirical relationship between loading factor, Reynold’s number and the rate of sand production. A second empirical sand production ‘boost factor’ incorporates the effects of water production. The derived model is compared with field data from a total of six wells from two fields, for a wide range of flowing conditions. The predictions are a good match to the field data, typically overestimating the fieldmeasured data by a factor of less than four. However, as the model is for continuous sanding only, this degree of overprediction is considered acceptable for field application, as it provides some compensation for shortlived transient sand production at rates higher than steadystate values.
SPE/ISRM 78168 New Model for Predicting the Rate of Sand Production S.M Willson (BP America Inc.), Z.A Moschovidis, J.R Cameron (PCM Technical Inc.) & I.D Palmer (BP America Inc.) Copyright 2002, Society of Petroleum Engineers Inc This paper was prepared for presentation at the SPE/ISRM Rock Mechanics Conference held in Irving, Texas, 20-23 October 2002 This paper was selected for presentation by an SPE/ISRM Program Committee following review of information contained in an abstract submitted by the author(s) Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers or International Society of Rock Mechanics and are subject to correction by the author(s) The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, International Society of Rock Mechanics, its officers, or members Papers presented at SPE/ISRM meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited 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, TX 75083-3836, U.S.A., fax 01-972-952-9435 Abstract A number of robust predictive methods for establishing sanding thresholds have been developed over the past decade Having identified when the onset of sanding occurs, recent research efforts have focused on determining the rate at which sand will be produced once these thresholds are exceeded In this paper a new analytic model for predicting the rate of continuous (steady-state) sand production is described This sanding rate model is consistent with the threshold prediction model, and utilizes as its basis the non-dimensionalized concepts of loading factor (near-wellbore formation stress normalized by strength) and Reynold’s number (a function of permeability, viscosity, density and flow velocity) Interpreted this way, the results of laboratory sand production experiments are used to derive an empirical relationship between loading factor, Reynold’s number and the rate of sand production A second empirical sand production ‘boost factor’ incorporates the effects of water production The derived model is compared with field data from a total of six wells from two fields, for a wide range of flowing conditions The predictions are a good match to the field data, typically overestimating the field-measured data by a factor of less than four However, as the model is for continuous sanding only, this degree of overprediction is considered acceptable for field application, as it provides some compensation for short-lived transient sand production at rates higher than steady-state values Introduction Over the past decade considerable research efforts have been expended in developing robust methods for predicting the onset of sand production as a function of rock strength, drawdown and reservoir pressure The most notable contributions to this area of work have been by Shell; References and provide a good overview of this decade of effort In recent years, attention has now focused on establishing methodologies for predicting the rate at which sand is produced once the sanding threshold is exceeded The principal motivation for this work is to determine whether sand production can be managed at surface, or if downhole sand control is needed There are pros and cons to both approaches – both management and exclusion In the sand management scenario, the biggest risk and challenge is being able to reliably estimate the amount and concentration of the produced sand This is important for sizing facilities sand handling capabilities, as well as ensuring that erosion limits for chokes and surface pipework are not exceeded From a HSE perspective, this is especially critical in high rate gas wells, as well as in high rate oil wells, particularly where gas-oil ratios are high From an operating cost perspective, the consequences of severe sand production and choke erosion could be very costly in subsea wells, especially in deepwater On the positive side, the cased and perforated completion option usually employed with sand management does permit avoidance of producing from notably sanding prone intervals through selective or optimized perforating Cased and perforated completions also maintain access to the producing interval to shut-off water or to recomplete in other secondary producing horizons This has allowed significant increases in reserves recovery in a number of fields worldwide The alternative to sand management is sand exclusion When properly implemented, downhole sand control will exclude the bulk of the formation sand from being produced (It is noted, however, that some fines, smaller than the filter media apertures, may still be produced to surface even for successfully installed sand control; this is particularly true of transient fine sand production) The downside of this option is typically a significant increase in up-front well completion cost, and oftentimes, a lower well productivity than a comparable cased and perforated completion Occasionally, sand control completions may also ‘fail’ during the well life, either mechanically, so permitting the influx of formation sand, or suffer degrading inflow performance due to plugging The ability to easily intervene in sand control completions to shut-off water is often difficult, as the preferred completion S.M WILLSON, Z.A MOSCHOVIDIS, J.R CAMERON & I.D PALMER option – typically open-hole gravel packs, screen completions and frac-packs – may allow the water to by-pass the treated interval Therefore, there is often a significant cost benefit – both for capital and operating expenditure – if sand management can be successfully implemented However, to reliably this in a new project development it is necessary to be able to produce a credible prediction of the rate at which the sand might be produced The derivation and validation of such a model is described in the sections following To avoid sand production the largest effective tangential stress (St2 - pw) should be smaller than the effective strength of the formation, U, next to the hole, i.e.: St − pw ≤ U S t1 = 3S − S1 − p w (1 − A) − Ap0 (1) and similarly S t = 3S1 − S − p w (1 − A) − Ap0 (2) where it is assumed that the wellbore pressure is communicated in the formation (i.e during production of a permeable interval); pw is the wellbore pressure, p0 is the reservoir pressure far field and A is a poro-elastic constant given by: A= (1 − 2ν )α (1 − ν ) (3) and α is Biot’s constant given by: α = − C r / Cb (4) where ν is the Poisson’s ratio and Cr and Cb are the grain and bulk rock compressibility, respectively (5) S2 St2 Description of Sand Rate Model Impact of Stress Concentration Effects In the development of sand rate prediction models, it is important that the basic framework is consistent with the sanding threshold models applied in other applications This ensures continuity in approach between predicting the onset of sanding and its severity once it occurs The following formulation has been used for the onset of sanding calculations; i.e the calculation of the critical bottomhole flowing pressure resulting in sand production, CBHFP It is based on a simple apparent strength criterion, together with assumed linear-elastic behavior, applied to a formation element next to a circular hole The hole could be the wellbore (for open hole completion) or a perforation (for cased hole completion) The orientation of the wellbore or the perforation is reflected in the calculation of the principal stresses perpendicular to the hole in terms of suitably transformed in situ principal stresses Given the far field total stresses on a plane perpendicular to the axis of a hole, S1 and S2, (S1 > S2), the tangential stresses on the surface of the hole (see Figure 1) are given by: SPE/ISRM 78168 St1 S1 Figure 1: Tangential stresses at the wall of a hole Solving the inequality for pw and introducing the notation CBHFP (Critical Bottom Hole Flowing Pressure) it follows that: p w ≥ CBHFP = 3S1 − S −U A − p0 (2 − A) (2 − A) (6) The critical drawdown pressure (CDP) is defined as the drawdown from the reservoir pressure to cause failure (and sand production) of the reservoir Using the definition, the bottom hole pressure in the well is: pw = p0 – CDP Introducing this in (6) we find the functional relation between the reservoir pressure, p0, and CDP p0 = [3S1 − S −U + CDP (2 − A)] (7a) [2 p0 − (3S1 − S −U )] 2− A (7b) CDP = In particular the CRP (critical reservoir pressure), defined as the reservoir pressure that would not tolerate any drawdown, is given by (7a) for CDP=0: CRP = (3S1 − S −U ) / Note that S1 and S2 depend linearly on the reservoir pressure po Therefore, (6) should not be used with constant S1 and S2 values for cases where reservoir depletion effects are considered Relation of Effective Formation Strength, U, to Measured Strength In the sanding models employed by BP, the collapse pressure of a so-called thick-walled cylinder test NEW MODEL FOR PREDICTING THE RATE OF SAND PRODUCTION (TWC) is used as the fundamental strength measure for unsupported boreholes and perforations This is consistent with the original methodology described by Veeken et al1 The standard dimensions for the TWC samples used by BP are 1½” OD × ½”ID × 3” long These are slightly larger than the sample dimensions adopted by Shell1 A relationship between the effective in-situ strength of the formation, U, and the TWC strength is necessary since the TWC test does not directly replicate perforation collapse pressures The standard TWC test is performed on specimens where the ratio OD/ID = At in situ conditions, the effective strength would be represented by a TWC strength where OD/ID tends to infinity There is an ID scaling issue too, as perforation tunnels may easily exceed 0.5” diameter when deep penetrating perforating charges are used in low-strength sandstones Scaling relationships to account for these effects have been published by van den Hoek at al2 They found that for Castlegate sandstone, with an OD/ID ratio of infinity, the maximum size effect factor varies between 3.0 and 3.8, depending upon the amount of post-failure softening Comparable internal research by BP investigated the TWC collapse resistance of a number of sandstones having a variety of OD/ID ratios, and different values of ID (see Figure 2) 7500 External Pressure (psi) 7000 1.7 1.6 TWC Strength Factor SPE/ISRM 78168 1.5 Castlegate Saltwash South 1.4 1.3 1.2 1.1 0.9 0.8 10 Figure Scaling Factors for TWC Collapse Pressures, Normalizing by Collapse at Large OD/ID Ratios Concept of a Loading Factor Having defined the appropriate expressions for predicting sanding thresholds (i.e the onset of sanding), it is convenient to non-dimensionalize the stress state acting on a perforation tunnel or borehole by considering the concept of a “Loading Factor”, LF, where, to be consistent with (5), LF is defined as: LF = ( S t − p w ) U 6500 ID = 0.30" 5000 ID = 0.50" 4500 ID = 0.63" 4000 ID = 1.00" 3500 LF = 3000 0.0 2.0 4.0 6.0 8.0 10.0 OD/ID TWC Sample Ratio 12.0 14.0 Figure Increasing TWC Collapse Pressure in Castlegate Sandstone with Different OD/ID Ratios The trend of results for varying OD/ID ratios is presented in Figure 3, which compares the relative strengths of experiments run in large specimens (OD/ID = 14) with those at smaller and standard OD/ID ratios Overall, these laboratory results are in good agreement with the analytical results of van den Hoek at al2 The testing showed that relative to the collapse pressure of the standard specimen, TWCsp, the equivalent formation strength, U, of a specimen with an OD/ID ratio of infinity would be equivalent to: U = × 1.55 × TWCsp = 3.10 × TWCsp (9) where St2 is the maximum tangential total stress acting on the formation or perforation We note that for LF1 the formation is failed and sand is produced To be consistent with the field, i.e with (6), substituting (2) and (8) into (9) it can be shown that LF must also be equal to: 6000 5500 15 TWC Sample OD/ID Ratio (8) Note that in the above, the factor of is introduced to compute the effective (or ‘boosted’) formation strength by virtue of the linear-elastic model assumptions inherent in the derivation of critical bottom hole flowing pressures 3S1 − S − pW − A( p0 − pW ) 3.10 * TWC (10) Impact of Fluid Flow Effects Intuitively, once perforation tunnels have been stressed sufficiently that a mechanically-weakened zone and disaggregated sand grains exist around the perforation tunnels, it is reasonable to assume that these could be produced to the surface with sufficient production flow This is in contrast to the analysis of sanding thresholds, where fluid flow rate has only a negligible effect in rocks with moderate cementation The analytical approach adopted to assess fluid flow effects in the sanding model draws on extensive work undertaken to assess required underbalance surge flow rates for perforation clean-upe.g 3,4 In these previous studies, the removal of shock-damaged and mechanically-weakened debris due to non-Darcy flow or turbulence in the region adjacent to the perforation cavity was correlated with the non-dimensional Reynold’s number, defined by: S.M WILLSON, Z.A MOSCHOVIDIS, J.R CAMERON & I.D PALMER kβρV µ (11) Here, k is the permeability (in mD); β, the non-Darcy flow coefficient (having dimensions of ft-1); V is the velocity of the fluid crossing the lateral surface of the perforation or well (in inches/second); ρ is the density (in lb/ft3); and µ is the viscosity (in cP) Various correlations have been proposed in the literature between β and formation permeability, k, porosity, φ, and/or saturation, Sw In this work, as well as in Tariq3, a correlation of the form β = constant/ke is used The range of the exponent, e, in the literature varies from 1.03 to 1.65 The relation used by Hovem et al4 is used specifically here: β = 2.65 × 10 / k 10 1.2 (12) Therefore, by non-dimensionalizing the fluid flow contribution, variations in formation permeability, fluid flow rate, viscosity, etc., can be easily captured in the analysis Laboratory studies have shown a value of Re > 0.1 is necessary for effective perforation clean-up during underbalanced flow Subsequent discussions will show that similar high values of Reynold’s number are needed for massive sand production rates At Reynold’s numbers less than 0.1, the sand production rate is dominated by the loading factor Sources of Experimental Data An important feature of the prediction model described here is that the sand rate magnitude is established from an empirical interpretation of laboratory sand production tests, rather than relying upon empirically derived relationships from field sanding events; e.g as done in Reference This permits laboratory sanding experiments to be performed on reservoir core to derive field-specific sanding relationships; however, the results presented in this paper have been derived from generic relationships based on earlier sand production experiments Extensive laboratory testing programmes have been undertaken in the past decade, primarily to establish sand production thresholds; e.g References through In these programmes, the effects of fluid flow rate, seepage forces and stress levels have been investigated separately, thus providing ideal input data so that these individual contributions can be properly quantified The TerraTek CEA#11 testing, in particular, investigated the sanding response of formations having unconfined compressive strengths in the range 500 psi to 2000 psi, so making it directly applicable to common field situations where sand production is a concern The results of a typical “stress-to-failure” experiment from the CEA#11 testing programme is shown in Figure In the experiment shown, the flow-rate was kept constant (typically at 50 cc/sec) and the confining pressure increased step-wise (with associated ‘hold’ periods) and the sand production rate SPE/ISRM 78168 monitored until approximately stable and constant sand production rates were observed Short-lived transient sand production is seen each time the stress level is increased, though this decays to a lower continuous sanding level after a period of time The model data used in this study are only those constant sanding rate values observed at the end of each successive period where the confining pressure is held constant In the example shown, the constant sanding rate is seen to increase gradually as the applied confining stress is applied until a catastrophic sanding event is seen at 7000 psi confining stress 1000 8000 Drilled Hole 'Stress to Failure' Test 7000 100 6000 5000 10 4000 3000 2000 Sand Production Rate Confining Pressure 0.1 200 400 600 800 1000 Confining Pressure (psi) R e = 1.31735 × 10 −12 Sand Production Rate (lb/1000 bbls) 1000 1200 Cumulative Flow Through Sample (litres) Figure Typical Result of Stress-to-Failure Sand Production Experiment Using the normalized parameters of Loading Factor and Reynold’s Number, it has been possible to consistently combine results from different sandstones (e.g accounting for strength and permeability variability), as well as factoring in the effects of fluid viscosity and flow rate It is specifically noted here that the model scope is limited to weakly compressible fluids (oils and water) and not to highly compressible gas flows However, the authors see no reason why the methodology cannot be extended further if sufficient calibrating sand production tests were performed For the data available, from the CEA#11 sand production JIP project6,7,8 and from Papamichos9, the empirically-derived surface shown in Figure was fitted to the data This relates the constant sand production rate (in pounds per thousand barrels, pptb) to the Loading Factor and Reynolds Number for those tests flowing oil only To address the impact of water-cut on sand production rate, other sand production experiments that were conducted using two-phase flow were analyzed In this step, the continuous sand production rate at a specified water-cut and stress level was compared with that of a test flowing dry oil only at similar conditions This permitted the derivation of a “water-cut boost factor” to raise the level of sand production from that evaluated from the function pertaining to no water production The form of this correlation is shown in Figure It is recognized that the method used to increase sand NEW MODEL FOR PREDICTING THE RATE OF SAND PRODUCTION production after water-cut is a crude approximation of an effect that is a function of many different physical processes – capillary pressure reduction, increased seepage pressures due to relative permeability effects, fluid viscosity effects, as well as possible mechanical strength reduction post waterbreakthrough However, within the confines of this simple analytical model for predicting sand production rate, the water-cut boost factor shown below is seen as an expedient compromise Definition of Reynold’s Number, Re = f(permeability, flow rate per perforation, viscosity, density, perforation number and size) Definition of Sand Production Rate, SPR = f(LF, Re, watercut) pptb 150 150 100 100 75 75 15 20 10 15 10 5 0 pptb 125 125 50 50 25 0 3.5 LF 2.5 1.5 0.5 0 0.0 0.1 0.1 0.2 0.2 No lds o n y Re 25 50 75 Water-Cut ( %) 20 15 15 Sand Rate f(w) Boost Factor 95 10 10 0 84 86 88 90 Water Cut (%) 1000 90 Water Cut (%) 20 Figure Fitted Surface to Experimental Sand Production Rate in Terms of Loading Factor & Reynold’s Number (Dry Oil Flow Only) 85 100 pptb 25 pptb pptb Definition of the Load Factor, LF = f(in-situ stresses, well trajectory, reservoir pressure, drawdown & depletion, TWC strength) 175 175 pptb SPE/ISRM 78168 92 50 100 Water Cut (%) Figure Field Data From Four Wells Showing Approximately 10Fold Increases in Sanding Rate After Water-Breakthrough 100 10 0.1 20 40 60 80 100 Water Cut % Figure Experimental Data and Analytical Function to Account For Two-Phase Flow Sand Production Rate Increases We have field data from sand producing fields, moreover, which suggests that this boost factor correlation to account for water-cut effects is not unreasonable Figure shows four such example wells where the sand production rate is compared with the measured water-cut These plots are not quite like-with-like comparisons, as in Figure 6, as drawdowns and depletion values are not entirely constant for the data combinations compared Nevertheless, the overall trend of the observed sand production variation with water-cut is not inconsistent with that derived from the experimental data Final Form of Sand Rate Model From the preceding discussions the final form of the sand rate model is thus defined It comprises three basic components: The analytical expressions for the load factor and Reynold’s number can be applied on a foot-by-foot basis using petrophysical wireline data Contributing to the Loading Factor, the rock strength profile is typically derived first using standard predictions of unconfined compressive strength, UCS, and then using a laboratory-derived relationship between measured UCS and TWC strengths Profiles of insitu horizontal stresses can be derived by knowing the overburden pressure, pore pressure, formation Poisson’s ratio and any contribution of tectonic stresses (e.g assessed from leak-off tests, minifrac tests, step-rate tests, or from water injection data) Contributing to the evaluation of the Reynold’s number, formation permeability can be assessed using standard correlations between porosity and permeability evaluated at appropriate net mean stress conditions from routine core analysis Formation fluid properties are typically known From the above, the sanding rate can be evaluated for any combination of drawdown and depletion As the individual contribution per foot (or half-foot, depending on logging data frequency) is assessed, then it is easy to assess the consequences of selective perforating should the highest permeability formations not be perforated 6 S.M WILLSON, Z.A MOSCHOVIDIS, J.R CAMERON & I.D PALMER Field Case History Analyses of Sand Production Rate Prediction The methodology for predicting sanding rates is now applied to two fields in the section following The first field example (two wells) is producing dry oil at modest to high rates (between 2,000 and 20,000 bopd); the second field example (four wells) has historically produced at high rates – initially at up to 38,000 bopd, though with time total production rates have declined to approximately one-half this initial amount as water production has increased to over 90% These two field examples (6 wells in total) therefore provide a quite thorough testing of the model Table provides a summary of formation properties over the perforated intervals analyzed However, as the model takes into account the half-foot-byhalf-foot variability of in-situ properties, the minimum and average values are not necessarily representative of those formation characteristics dictating the overall rate of sand production For the fields analyzed, strength profiles were established by conducting both unconfined and thick-walled cylinder measurements over the whole range of formation quality, so characterizing the extent of strength variability In-situ stresses were determined from using procedures described previously The results of the sand rate prediction analyses are shown in Figures and for Field A wells, and in Figures 10 to 13 for Field B wells Figures and simply compare the observed and predicted sand production rates for dry oil production only Figures 10 to 13 also show the measured water-cut, which in some cases varies significantly over the period analyzed The data presented in Figures through 13 were collected when the specific wells were flowed through a test separator Thus, good measurements were made of oil, water and sand rates, as well as surface flowing pressures from which bottomhole flowing pressures were estimated from nodal analysis Therefore, the data used to validate the sanding models are the best typically available offshore Overall, the prediction model derived from the laboratory sanding experiments is able to reproduce the measured sanding response, though typically over-predicting that measured by a factor of two to four For those wells producing dry oil (Figures and 9) very good agreement is reached The predicted rates of pptb to pptb typically provide an upper limit to that measured For those wells producing water (Figures 10 to 13) the match is still quite acceptable, though there is more scatter in both the measured sanding data and the predictions The principal cause of this is the representation of the produced water in the model If a well is producing with 50% water-cut, the model assumes a 50/50 split in oil and water over the entire perforated interval This maximizes the applied water-production sanding “boost factor” shown in Figure The reality could be quite different, with perhaps the top half of the perforated interval producing dry oil, whereas water coning has caused the lower half to water-out The distribution of the water influx in the SPE/ISRM 78168 wells analyzed is not known, however, and the analysis approach adopted is known to be conservative Figure 14 shows the predicted sand influx distribution for well B / for the following specified producing conditions: 29,690 bpd gross liquid production; 77% water-cut; 592 psi drawdown and 265 psi depletion The overall predicted sand production for the entire perforated interval is 119 lbs/day, equivalent to a sanding rate of pptb Also shown in this figure is the formation permeability distribution This correlates well with porosity and inversely with formation strength (high permeability, low strength) The figure shows a high permeability streak from 9927 ft to 9930 ft TVD.SS is predicted to produce 12 lbs of sand per day, approximately 10% of the overall predicted total Therefore, if sand production rate and erosional constraints were of concern in this well, then it may be prudent to omit perforating this feet long interval It would be possible to make such an assessment in the time available between logging and perforating a well, if the required correlations between strength, porosity and permeability were established beforehand Conclusions The non-dimensionalized approach described to combine and interpret laboratory sand production experimental data can be used as a basis for deriving credible sand production rate prediction methods The “Loading Factor” concept allows the derived sanding rate model to be consistent with existing models for predicting the on-set of sand production The “Reynold’s Number” concept to include fluid flow effects is well documented from perforation clean-up research, and the empirical “sand production boost factor” to account for the effects of water production is corroborated by field evidence Applied to field examples from sand producing wells, the derived analytical model is seen to perform well when compared with the measured data The over-prediction of the continuous sanding rate, by a factor of typically two to four, is seen as acceptable when using these data for sizing facilities sand handling capabilities Acknowledgements We thank BP America Inc for permission to publish this paper The efforts of Dr Joe Hagan in overseeing the work associated with the TWC scaling relationships are specifically acknowledged References Veeken, C.A.M et al: “Sand Production Prediction Review: Developing an Integrated Approach”, paper SPE 22792, presented at the 1991 SPE Annual Technical Conference and Exhibition, Dallas, 6-9 October van den Hoek et al: “A New Concept of Sand Production Prediction: Theory and Laboratory Experiments”, SPE Drilling & Completion, Vol 15, No 4, December 2000, pp 261-273 SPE/ISRM 78168 Tariq,S.M “New, Generalized Criteria for Determining the Level of Underbalance for Obtaining Clean Perforations”, paper SPE 20636, presented at the 1990 SPE Annual Technical Conference and Exhibition, New Orleans, 23-26 September Hovem,K., Jøransen,H., Espedal,A., & Willson,S.M “An Investigation of Critical Parameters for Optimum Perforation Clean-Up”, paper SPE 30084, presented at the European Formation Damage Conference, The Hague, The Netherlands, 15-16 May 1995 Papamichos,E & Malmanger,E.M “A Sand Erosion Model for Volumetric Sand Predictions in a North Sea Reservoir”, paper SPE 54007, presented at the 1999 SPE Latin American and Caribbean Petroleum Engineering Conference, Caracas, Venezuela, 21-23 April Halleck,P.M., “An Experimental Investigation of Sand Production: CEA Project #11 Final Report”, prepared by TerraTek, Inc., June 1991 Willson,S.M “CEA 11, Phase II, An Experimental Investigation of Phenomena Affecting Sand Production in LowStrength Sandstones,” Final Report, Vol 1, Summary of Results, prepared by TerraTek, Inc., August 1993 Willson,S.M “CEA 11, Phase III, An Experimental Investigation of Phenomena Affecting Sand Production in LowStrength Sandstones,” Final Report, Vol 1, Summary of Results, prepared by TerraTek, Inc., April 1995 Papamichos,E., “A Volumetric Sand Production Experiment,” Pacific Rocks 2000, Girard, Liebman, Breeds & Doe (eds) 2000 Balkema, Rotterdam, ISBN 90 5809 155 Table Summary of In-Situ Properties For Wells Analyzed Field/Well A/1 A/2 B/1 B/2 B/3 B/4 Perf’d Interval (TVD.SS) & Well Deviation 9365 ft to 9788 ft 43º deviation 8949 ft to 9440 ft 39º deviation 9761 ft to 9958 ft 0º deviation 9253 ft to 9291 ft 58º deviation 9686 ft to 9725 ft 13º deviation 9426 ft to 9527 ft 35º deviation Property Perm (mD) UCS (psi) TWC (psi) Overburden (psi) 9714 Initial Reservoir Pressure (psi) 4825 Initial Horizontal Stress (psi) 7570 Average Minimum Maximum Average Minimum Maximum Average Minimum Maximum Average Minimum Maximum Average Minimum Maximum Average Minimum Maximum 112 10 353 98 10 640 219 20 1048 675 35 2044 450 40 1133 601 21 3761 2481 902 4820 3302 2955 160 4972 1647 9325 4658 7320 3281 1442 7365 4913 8810 4224 7780 1592 967 5146 4025 8230 4055 6174 2544 1923 6512 5675 8658 4180 7110 2456 493 6366 2874 8456 4121 6975 Avg Measured Sand Rate (pptb) Predicted Rate (pptb) 6.0 5.0 4.0 pptb NEW MODEL FOR PREDICTING THE RATE OF SAND PRODUCTION 3.0 2.0 1.0 0.0 2000 4000 6000 8000 10000 12000 14000 16000 Q (bpd) Figure Predicted vs Measured Sand Production Rate – Field A, Well 18000 20000 S.M WILLSON, Z.A MOSCHOVIDIS, J.R CAMERON & I.D PALMER Avg Measured Sand Rate (pptb) SPE/ISRM 78168 Predicted Rate (pptb) 14.0 12.0 8.0 6.0 4.0 2.0 0.0 2000 4000 6000 8000 10000 12000 14000 Oil Rate(bpd) Figure Predicted vs Measured Sand Production Rate – Field A, Well Predicted Rate (pptb) WaterCut (%) 30 100 27 90 24 80 21 70 18 60 15 50 12 40 30 20 10 29000 30000 31000 32000 33000 34000 35000 36000 38000 37000 Tot Liquids (bbd) Figure 10 Predicted vs Measured Sand Production Rate – Field B, Well Predicted (pptb) WaterCut (%) 25 100 23 95 20 90 18 85 15 80 13 75 10 70 65 60 55 19000 20000 21000 22000 23000 24000 25000 26000 50 27000 Tot Liquids (bpd) Figure 11 Predicted vs Measured Sand Production Rate – Field B, Well WC (%) Sand Rate (pptb) Sand Production (pptb) WC (%) Sand Production (pptb) Sand Rate (pptb) pptb 10.0 SPE/ISRM 78168 NEW MODEL FOR PREDICTING THE RATE OF SAND PRODUCTION Predicted Rate (pptb) WaterCut (%) 20 100 16 90 12 80 70 60 WC (%) Sand Rate (pptb) Sand Production (pptb) 50 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000 21000 22000 Tot Liquids (bpd) Figure 12 Predicted vs Measured Sand Production Rate – Field B, Well Predicted Rate (pptb) WaterCut (%) 100 90 16 14 80 70 12 60 10 50 40 30 20 10 12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 WC (%) Sand Rate (pptb) Sand Production (pptb) 20 18 32000 Tot Liquids (bpd) 10000.00 Formation Permeability (mD) 4.5 Formation Permeability (mD) Sand Production Rate (lbs/ft) 1000.00 3.5 100.00 2.5 10.00 1.5 1.00 0.5 0.10 9750 9775 9800 9825 9850 9875 9900 9925 9950 9975 Sand Production Rate Rate Per Half-Foot Interval (lbs/day) Figure 13 Predicted vs Measured Sand Production Rate – Field B, Well 10000 Depth (feet TVD.SS) Figure 14 Predicted Distribution of Sand Production For Well B / For Specified Producing Conditions