Copyright 2003, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Denver, Colorado, U.S.A., 5 – 8 October 2003. This paper was selected for presentation by an SPE 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 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, its officers, or members. Papers presented at SPE 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 Sand prediction at BP has been developed by dividing it into three parts: (1) onset, (2) transient sanding, (3) steady-state sanding. For example, as drawdown is increased in a well in a sand-prone formation, significant sanding begins at some point (the onset), and this is followed by a transient sand burst, which may last hours or days or months. The sanding eventually declines to a background level (steady-state), in the range 1–100 pptb. We have made recent step-changes in (2) and (3), and we now have a tool that can predict sanding onset, and volumes during any stage of a well’s production history, or even injection history.

The onset of sanding is predicted using a stress-based model. This model is conservative, based on a benchmarking study of field applications. One application predicts sanding in water injectors during shut-in, and recommends not using sand control. Another application explains delayed sanding in an HPHT gas reservoir, in terms of restraining forces due to capillary cohesion (i.e., the damp sand effect at the beach). The transient sanding model is a fully-coupled finite element (FE) model. The model has successfully predicted sand volumes in laboratory and field tests. With this model, we can judge whether we can manage the produced sand, from both production and injection wells. Finally, we have applied this to predict whether a well will kill itself after a blowout, due to sand in the wellbore increasing the hydrostatic pressure.

The steady-state model is an empirical model that is based upon extensive tests of sanding from cores in the laboratory. The model has been applied to predict sanding in an offshore field, and this has led to the conclusion that sand rates can be managed at surface, without sand control: a huge economic advantage. Finally, we present a case history where we use all three models to make an integrated prediction of onset,

∗ now at Higgs Technologies, Houston

transient, and steady-state sanding, and find quite good agreement with field observations. In summary, the new three- fold strategy of sand prediction at BP has significantly increased our capability to predict sanding in production or injection wells. This quantum leap is invaluable to help decide if we can manage the sand at surface (or if downhole sand control is required); to decide if we can defer sand control until a later date (possibly increasing production as well as saving completion costs); to decide how much sand will be produced if we increase the drawdown in a sand-prone well; and even decide if we need sand control in water injectors. Introduction Sand prediction at BP has progressed in three stages: (1) onset, (2) transient sanding, (3) steady-state sanding. As drawdown is increased in a well in a sand-prone formation, significant sanding begins at some point (the onset). Alternatively, the trigger may be an increase in depletion. This is followed by a transient sand burst, which may last hours or days or months. The sanding eventually declines to a background level (steady-state), in the range 1–100 pptb. Figure 1 is a summary of the three stages. Figure 1. Strategy of sand prediction as a function of time, from onset through transient to steady-state Recent step-changes have been made in the transient and steady-state stages, and we now have models that can predict sanding onset, and volumes during any stage of a well’s production history, if it is an oil well. For a gas well, we can predict the transient sand volume, but not the steady-state sand rate. In this latter case, the fundamental methodology is

SPE 84499

Predicting and Managing Sand Production: A New Strategy Ian Palmer (BP*), Hans Vaziri (BP), Stephen Willson (BP), Zissis Moschovidis (PCM), John Cameron (PCM), Ion Ispas (BP)

transientvolume

steady statesand rate

onset of sandingquantum leaps in two areasto complement prediction

of failure onset

2 SPE 84499

established, but to date the necessary calibrating laboratory data have yet to be collected. We have even been able to apply the new strategy to predict onset and transient sanding in an injection well, after such a well has been shut in.

However, the modeling has some limitations. We are not yet able to obtain the profile of the transient sand event at the surface (i.e., sand volume vs. time). For example, if the drawdown is suddenly increased, we can compute the total volume of sand influx into the well, but not the rate of influx or the total time it takes. Clearly this depends on the rate of sand uptake by the incoming fluid (e.g., factors like drag force, velocity and viscosity, and whether the fluid is oil or gas). The sanding profile at surface also depends upon the velocity and slippage of sand particles relative to the fluid flow up the well. Although this part of the model is still being developed, we are able to present some crude modeling to illustrate the results.

The main driver of this work has been to decide if a well can be completed without sand control. If we can reliably predict the volume and concentration of sand, we can decide if sand can be handled at surface, and better design the facilities for handling sand. The potential advantages of no sand control are cheaper well installation, higher production rate, and ability to shutoff water. Another driver is to be able to assess whether an increase in drawdown can boost a well’s flow rate, without excessive sand produced. A third aspect is to be able to evaluate whether a cased/perforated completion can be used initially, and to defer a sand control option until later, with cost and flow rate and environmental advantages.1 In summary, there is often a substantial cost benefit – both for capital and operating expenditure – if sand management can be deployed successfully.

Below, we summarize the modeling used in each of the three stages, so the overall strategy is clear, and we present new applications. We conclude with some implications about sand management.

Note: when we speak of sand production, this may be equated with solids production, as the modeling in this paper applies equally well to carbonates or other formations. Onset of sanding Model summary The onset of sanding is predicted using a stress-based model of shear failure around a perforation or an open hole wellbore. Essentials of the BP sand onset model are: • Predicts shear failure around a perforation or an open hole

(but this may not predict when sand actually enters a well) • Predicts the onset of sand production in cased and

perforated and open hole completions using a combination of empirical and analytical relationships.

• The essential inputs to the model are thick-walled cylinder tests (TWC) obtained from cores tested in the laboratory, and unconfined compressive strength (UCS) predicted from logs (gamma-ray, density and dipole sonic).

• The TWC collapse strength corresponds to the point of significant sanding (equivalent to development of many shear bands that eventually coalesce).

• Analysis is performed at the weakest point of the UCS log.

The UCS log is calibrated to the measured TWC. • Sand production is assumed to occur once the maximum

value of the effective tangential stress around the perforation exceeds the apparent UCS (i.e., the perforation fails at the same cavity loading as occurs in the TWC test). No consideration is given to sand transport by drag forces.

• The BP model can account for different orientations of the well or perforations.

The criterion for sanding is:2

AAP

ACBHFP r

y

−−

−

−−<

223 31 σσσ

(1)

where CBHFP is the critical bottomhole flowing pressure, Pr is the current average reservoir pressure, σ1 and σ3 are the total principal major and minor stresses, A is a poroelastic constant which is a function of the Poissons ratio and formation compressibility, and σy is the formation strength near the opening:

TWCy ×= 1.3σ (2) where TWC is strength as determined in the thick-walled cylinder test. The factor 3.1 includes the scale transformation from TWC laboratory sample (OD:ID = 3) to field (OD:ID = infinity).

Note that σ1 and σ3 may depend linearly on the reservoir pressure Pr . Therefore, Equation (1) should not be used with constant σ1 and σ3 values for cases where reservoir depletion effects are considered.

While there is some support for advancing the notion that sand failure and sand production can be considered to be essentially the same event, a number of field cases have shown that failed sand can remain in a stable state until fluid and flow conditions reach a certain level to produce the disaggregated sand.

Figure 2 shows a typical CBHFP (oblique line sloping up to the left). CBHFP is approximately 300 psi at the start of field development. As the reservoir depletes, CBHFP gets higher. The critical drawdown pressure (CDP) at the start of production (~4,500 psi) is shown as the maximum drawdown arrow. With depletion, this drawdown arrow becomes smaller as it moves to the left. When the reservoir is depleted to around 1,700 psi, any drawdown at all will lead to sanding.

=

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Max D

rawdow

n

Figure 2. Sand prediction using shear failure model for cased and perforated vertical well

SPE 84499 3

Benchmarking of onset model Sanding onsets have been predicted in seven field cases, which are summarized in Table 1. Sanding has been observed in five out of seven cases. These are a variety of field cases: four are gas reservoirs, the minimum UCS ranges from 250 to 3053 psi, and two of the cases can be classed as HPHT. We can use this data set to compare sanding prediction with actual observation (see Figure 3).

Figure 3: Comparison between CBHFP predicted and that observed in the field Two of these cases are open hole: Immortelle and Mahogany. Note: two cases in Table 1 have a negative ratio of predicted/observed CBHFP. This is because the predicted CBHFP is negative, i.e., no sanding is expected, even if the reservoir pressure is drawn all the way down to zero. Our conclusions from Figure 3 are: • Five of the seven predictions have predicted/observed

CBHFP ≥1 meaning the BP model is conservative (i.e., the field were able to go to lower BHFP than predicted, without sand). Being conservative is acceptable, as there is a safety factor in-built to the prediction.

• Only one prediction is definitely too optimistic. This is a field in North Sea, which was predicted to be safe (negative CBHFP), but sanding occurred (we have not found an explanation for this).

• One other case has negative predicted/observed CBHFP, but no sand has been observed yet, so we don’t know if the model is conservative or not.

• Three out of seven of the predictions use 3 σ1 - σ3 in Equation (1). This means keeping σ3 as the far-field stress instead of resetting it to σ1 (i.e., this does not double-dip effect of stress concentration around wellbore). This is the preferred method of application, but it makes the model prediction even more conservative (i.e., CBHFP is larger).

The main conclusion is that the BP prediction is generally conservative. That is, sanding occurs at lower BHFP than predicted. And it can be very conservative, for example: • actual CBHFP = 4,500 vs. 16,000 psi predicted at

Tuscaloosa (largest discrepancy of the 5 conservative wells)2

• actual CBHFP = 3,500 vs. 7,000 psi predicted in a GOM Shelf well (only one well)

The conservatism of the BP model, which predicts shear failure of the formation, may be explained by: • residual cohesion holding sand grains together (i.e., due to

connate water, or interlocking grains)

• stress reduction due to arching at the tip of the perforations A comprehensive study of benchmarking for open hole horizontal wells has not been done yet (the exception being the two cases in Table 1). Nevertheless, recent predictions for three open hole wells in the North Sea indicated no sand, and for the first 6-12 months of well life this was the case.

The cased perforated results of Table 1, and the success of BP sand prediction for open hole wells, means the BP onset sanding prediction is viable, although conservative (in all but one case). Furthermore, the predictions in four out of seven cases from Figure 3 give: • CBHFP (pred) = (1 2) × CBHFP (obs) • CBHFP (obs) = (0.5 1) × CBHFP (pred) and this can be useful as a quick rule-of-thumb. Delayed Sanding One class of problems where the BP sand prediction model has not been well validated is in HPHT wells. As discussed by Vaziri et al.,2 the shear-failure model is overly conservative in predicting the onset of sanding. This is emphasized by Figure 4, which shows, for five wells in Tuscaloosa, the CBHFP predicted by the BP model, and by a service company model (the two segmented lines agree fairly well). But the field observations are shown by the blue squares, where sanding has not yet occurred. Thus the model predicts sanding much too early. This may be due to the fact that for a given rock strength, failure is hastened in high stress systems. The early failure of rock makes the difference between sand failure and sand production more pronounced.

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Min

imum

Bot

tom

hole

Flo

win

g P

ress

ure

(psi

)

Shear Fail Model-BPRealityShear Fail Model- 3rd Party

Figure 4: Comparison of the predicted critical BHFP against observed minimum BHP Do tensile failure models do any better? We illustrate this by making predictions using the ARCO model3, under conditions of turbulent flow. The field data indicate that very high flow rates had prevailed throughout most of the production phase; average rates in the order of 500 MSCFD/ft had been recorded. In fact, the flow rate through some of the higher permeability zones was probably several times higher than this. Following Vaziri, et al.,2 the turbulent flow-corrected results are shown in Figure 5. The reduction of CDP due to turbulence is generally 25-50%, and we have used 25%. Using 50% would make the discrepancy with observation (blue dots in Figure 5) worse. The interpretation is that the tensile failure

predicted / observed CBHFP

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CB

HFP

ratio

lower limit: no sand, asgrains held together by capillary forces

lower limit: no sand…still consistent with BP model

over-optimistic prediction: not consistent with BP model

conservative predictions:BP model predicts sanding too early.This is safety factor

1 / 7 cases BP model is over-optimistic….not good

4 SPE 84499

model is also conservative, but not as much as the BP shear failure model.

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sure

(psi

)

Tensile Fail ModelRealityRegression Model

Figure 5: Comparison of the predicted critical drawdown pressure against observed maximum drawdown pressure For comparison, we include results of a fully-coupled numerical model, ENHANS, in the form of a simplified regression formula. This accounts for the sand failure (disaggregation from intact to granular state) but does not assume sand production until the disaggregated sand undergoes a liquefied state, that is, a state of zero effective stress among the sand particles. In this state, sand is assumed to have reached a mobile state and is thus producible. Again following Vaziri, et al.,2 we have plotted the results of the regression formula in Figure 5 (red line).

The regression formula shows CDP values that all fall above the maximum drawdown values observed, suggesting that most of the wells could have been drawn down further before sanding would occur. The prediction agrees with the observation, in the sense that both indicate no sanding yet. The regression formula can also calculate the volume of sand for any drawdown level, in excess of that shown for the onset of sanding, and hence allow an engineer to assess the risks associated with adopting a more aggressive drawdown strategy.

In summary: for this HPHT field case, the usual shear-failure models (e.g., BP) and the tensile failure models (e.g., ARCO), both predict sanding onset that is too early (i.e., both models are conservative). The numerical-based model, ENHANS, lies on the other side of the data, suggesting these wells could have been drawn down even more before sanding. Note that sanding did eventually occur in several of these wells, coincident with water influx, and this is discussed below under “Water-induced sanding”. Transient sanding volumes

The transient sanding model is a fully-coupled FE model called ENHANS. The model has successfully predicted sand volumes in a large-block test, in a drawdown-induced transient in the field that lasted a few months (and increased flow rate by > 50%), and in a choked-back well that was opened up until the well stabilized at a higher flow rate. With this model, we can judge whether we can manage the sand, and we can even predict the increase in well productivity, due to porosity

increases in the formation. Finally, we now have a means to predict whether a well will kill itself after a blowout, due to a sand in the wellbore increasing the hydrostatic pressure. Essentials of the model are:2 • Predicts tensile failure around a perforation or an open hole

(i.e., does predict when sand will enter a well) • Fully coupled stress and fluid flow finite element analysis.

It allows time-dependent simulation of applied boundary conditions.

• Any element that develops a liquefied state is assumed to have failed. The element is smeared (not removed) and given properties of a liquefied zone (e.g., high perm, loss of cementation, reduced moduli).

• The volume of sanding can be rigorously determined. As such the model can be used not only to predict the onset of sanding but also the severity of sanding.

• The model computes the improvement in wellbore skin with sanding, so can easily be converted to an increase in well PI.

• Key parameters are the real and projected cohesion. • The model has shown good agreement when compared

with volume of sanding in weak sands (laboratory and two field cases).

Water-induced sanding As described by Vaziri, et al.,4 failed and disaggregated sand can be held together remarkably well by tiny capillary cohesion forces, due only to connate water, when water saturation is low (i.e., a sand-castle made with damp sand). But when water saturation increases with water influx, this capillary cohesion is extinguished, and sand will enter the well and be produced (i.e., sand-castle collapses as tide comes in). The numerical, fully-coupled FE model ENHANS has been able to model this effect, and Figure 6 shows a typical result. There is very little sand production before water influx. But when this occurs, the sand production increases dramatically, by a factor of ~5, if the capillary cohesion goes away completely. In short, this explains why in many wells, sand production accompanies water influx.

Influence of capillary adhesion after water production

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-3500-3000-2500-2000-1500-1000-5000Drawdown (psi)

Volu

me

(ft^3

per

1.5

m o

f pay

leng

th)

Cprw = 0.3 psi

Cprw = 5 psi

Cprw = 0.7 psi

Base case properties:Cip = 350, Cir = 15, Cpp = 145, Cpr = 7, Ctp = 10, Ctr = 1.5, Cppw = 135

water production

Figure 6: Influence of the capillary cohesion force within the failed zone on the volume of sand after water production

SPE 84499 5

Illustrative modeling of water injection wells - onset and transient sanding In a weak reservoir that is to be water-flooded, an important question is whether the water injectors need sand control. That is, what is the likelihood of sand influx into a well during injector shutdown? If water injectors can be completed without sand control (i.e., just casing and perforations), the advantages are substantial as the completion: • allows zonal isolation; • avoids inevitable screen or gravel-pack plugging, and

injectivity loss (it is very difficult to clean or replace a screen economically);and

• the total cost savings can be tens of millions of dollars, or more

Figure 7: Multizone injector with potential cross flow from zone B to zone A According to Santarelli, et al.,5 cross flow-induced sand can fall into the rathole, or be carried into perforations of another zone, where the sand can completely fill the perforationss (a downhole TV failed to see plugged perforations in one case). This perforation plugging by sand is the cause of injectivity loss (not fines plugging). There is a simple field test for cross flow sanding: if the injectivity index (II) decreases after each shutdown then cross flow sanding is occurring. The II can be measured using programs to calculate BHP from WHP.

There are two sources of sanding in an injector during shutdown: (a) fluidization of the formation due to water hammer (not evaluated here), (b) cross flow-induced sanding, which itself has two origins: • pressure differential caused by diffusivity difference

between two pay zones. • pressure differential between two pay zones, due to sealing

fault or pinch-out (Figure 7). From some typical reservoir modeling we have done, the

first source of cross flow sanding leads to typical “drawdowns” that are small, <50 psi. However, the second source leads to typical drawdowns that can be much larger, 100-500 psi. Thus the latter will dominate over the former.

To understand the sanding potential, one approach is to calculate sand onset for cross flow scenarios caused by potential sealing faults or pinch-outs, and to estimate sand volumes for the same scenarios. This two-pronged approach provides a stronger basis from which to decide whether injectors need sand control. As Figure 7 reveals, a pressure differential may exist within a multi-zone injector, and at

shutdown this will lead to cross flow, which may bring in sand. The illustrative cross flow scenarios we consider are those for which Pb - Pa = 100, 200, 300, 400, 500 psi. At shutdown, these are the effective drawdowns that can bring in sand.

Figure 8. Onset of cross flow sanding, for different UCSmin values, and different Pa values. Pb lies in the range 5,000-5,400 psi. Cross flow is from zone B to zone A. The BP model is used to predict cross flow sanding, based on a typical log profile of UCS in zone B (calibrated to laboratory measurements of TWC), and the results are shown in Figure 8. The plot shows the minimum allowable pressure in zone A, to avoid cross flow sanding from zone B to zone A. The results are virtually the same whether Pb is elevated to 5000 or to 5400 psi. In short, if the minimum UCS ~500 psi, Pa would have to fall to ~3,500 psi to get any cross flow sanding, even if Pb were elevated to 5,400 psi by a sealing fault.

In the worst case scenario, Pb rises to 5400 psi (e.g., due to a sealing fault) and Pa stays at about 5,000 psi (expected situation). From Figure 8, the BP model predicts no cross flow sanding unless min UCS <200 psi. Minimum UCS refers to minimum UCS in zone B, as determined from a sonic log, from where the cross flow enters the well. In a case that all UCS (sonic log) > 500 psi, there should be no cross flow-induced sanding, and there would be quite a large margin of safety.

This cross flow sanding prediction is based on a horizontal perforation (i.e., the weakest perforation), and therefore should be applicable to wells deviated from the vertical, if perforations are not oriented. However if sanding did occur in a highly deviated well, the sand may not fall into the rathole, and this could exacerbate injectivity loss. Predicting sand volumes during cross flow The BP model only addresses the onset of significant sanding, and it cannot predict the transient volume of sand caused by a change in drawdown. But estimates of volumes would be invaluable to quantify the risk of sanding, and below we illustrate how we have done this using the transient sanding model ENHANS. Morita et al.6 have done similar modeling of sand production in injection wells.

In multi-zone injectors, the volume of sand induced by injector shutdown depends on the “drawdown” between zone B and zone A (see Figure 7). We assume 500 psi worst case, since these injectors may lead to potential “drawdowns” of

sealing fault or pinchoutcauses Pb > Pa

Pa

Pb

I P1 P2

result is Pb – Pa may

be up to 500 psi

Does this produce sand via crossflow

after shutdown?

sealing fault or pinchoutcauses Pb > Pa

Pa

Pb

I P1 P2

result is Pb – Pa may

be up to 500 psi

Does this produce sand via crossflow

after shutdown?

Min Allowable Pressure in Zone A, to Avoid Crossflow Sanding

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the difference between the 2 curves is in the noise

if UCS < 200 psi,predict sanding due to crossflow

Predictionbased onBP model

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the difference between the 2 curves is in the noise

if UCS < 200 psi,predict sanding due to crossflow

Predictionbased onBP model

6 SPE 84499

100-500 psi between pay zone B and pay zone A. Then using the ENHANS numerical model, we estimate a sand volume of 1.6 – 4 bbl (the uncertainty lies in the bilinear Coulomb plot of strength vs. stress). This volume of sand would fill up 6-16 ft of 8-inch rathole. We can classify this worst-case situation as a P10 case. The volume ranges are plotted in Figures 9 and 10.

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Figure 9: Summary of sand volume risk after cross flow: water injector

The other component of cross flow sanding, due to

diffusivity differences between zones A and B in Figure 7, leads to smaller sand volumes because typical “drawdowns” are lower (<50 psi) and substantially smaller than the previous values of 100-500 psi. Sand volumes are predicted in the range 0.5-1.0 bbl. We may regard this result as a P90 calculation of sand volume, since it is likely to occur whether or not there is any cross flow sanding due to a pressure differential between zones A and B in a multi-zone injector. That is, single-zone injectors will likely be subject to this component of transient sanding, and so the P90 result applies to them. Obviously, the risk of sanding for single-zone injectors is lower.

A P50 result is obtained by assuming a “drawdown” of 150 psi in the multi-zone injector case (recall the range of pressure differential between zones A and B is 100-500 psi). This leads to a prediction of sand volumes in the range 1.2-3.3 bbl.

We can summarize the risk of sand volumes in water injectors by showing the P10, P50, and P90 results in Figures 9 and 10. Figure 9 shows the sand volume risk, while Figure 10 shows the rathole filling risk. Clearly, a deeper rathole would be an advantage.

For gas injectors, the sand volumes in Figures 9 and 10 will be reduced by typically 5 times, that is, gas injectors are much safer than water injectors because capillary cohesion can hold disaggregated sand grains together. Note: There are caveats in the calculations we have made of sand volumes: • The volume estimate only applies to the first shutdown.

Later shutdowns are also expected to produce some sand, but in diminishing volumes.

• The calculations are for instantaneous shutdown. For slower shutdown, sand volumes can be substantially less.

Nevertheless, these sand volume calculations illustrate how a potentially powerful tool can help us decide whether to install sand control in water injectors.

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Figure 10. Summary of rathole filling risk after cross flow: water injector

The profile of transient sanding versus time If the drawdown in a well is suddenly increased, we can compute the total volume of sand influx into the well, but not the rate of influx, or the total time it takes. Clearly this depends on the rate of sand uptake by the incoming fluid (e.g., factors like drag force, fluid velocity and viscosity, and whether the fluid is oil or gas). The sanding profile at surface also depends upon the velocity and slippage of sand particles relative to the fluid flow up the well. Although this part of the model is still being developed, we can do some crude modeling to illustrate the results.

Assuming a single sudden increase in drawdown, there are two steps: • Calculate the maximum percentage by volume of sand that

is picked up by the fluid as it enters the well (one way is a “drag force” approach). This gives the time-profile of sand entering the well. For example, the sand influx will be constant, if flow rate is constant (and other fluid parameters), and if only one sudden drawdown increase has occurred that causes disaggregation of a large volume of sand. That is, we assume the failure of the formation takes much less time than the sand grain uptake by the flowing fluid.

• Calculate the dispersion of the sand as it moves with the fluid up the well. This is complex, and involves slip of sand grains through the fluid, which is a function of grain size, fluid viscosity, velocity, well deviation, etc. If the sand event at the sand face is small (i.e., an impulse), the result at surface is a rapid onset of sanding followed by a gradual decline (i.e., a transient decay response). If the sanding event is large at the sand face, the surface signal may be: flat with time, if the dispersion is small; gradually increasing with time, followed by a decline, if

dispersion is large. Dispersion can be calculated by modeling the flow of fluid and sand grains up the wellbore. To make things simple, we assume here no dispersion, so that the time profile of the sand at surface is the same as that at the sand face. Then the problem reduces to the first bullet above. We first compute the drag force, from the fluid properties and the sand size. Then we use a correlation we have developed for uptake of sand (% by volume) as a function of drag force. From the flow rate, we can calculate how long the uptake of sand ensues, until the total disaggregated sand volume at the sand face has influxed into the well.

SPE 84499 7

Application to well blowout We consider here an illustrative vertical gas well, cased and perforated, with pay zone at approximately 10,000 ft depth, and producing ~ 10 MMcfd. Suppose the original reservoir pressure was over-pressured, and approximately 7,500 psi. In a typical situation, flow rate is maintained by gradually increasing the drawdown as the reservoir depletes.

The finite element code ENHANS was used to predict the likelihood of sanding under a scenario in which the drawdown reached 650 psi when the reservoir had depleted by 3,200 psi (i.e., total drawdown defined as depletion + drawdown was 3,850 psi). One of the key parameters in the modeling is the in-situ sand cementation. This is actually the cohesion due to the sum of mechanical cement and capillary cohesion due to connate water. We assumed the capillary cohesion to be 4 psi and the mechanical bonding to be 16 psi. Using a lower total cementation would result in sanding at much lower total drawdown. For reference, a total cementation of 20 psi is equivalent to a UCS of approx 60 psi (this is very weak sand).

In the simulation, we modeled both depletion and drawdown. The scheme used to vary these with time was arbitrary, but based on limited parametric runs we did not see an appreciable influence of this. At the time of sanding, it is reasonable to assume that all the mechanical cementation has been destroyed due to a depletion of >3,000 psi. And evidently the capillary cohesion due to connate water is not sufficient to hold the sand grains together.

Figure 11 shows the sanding prediction. Another key parameter that affects the sand volume is the state of the sand behind the casing after the sand event. We assume that sand production leads to a “cavity” (which could be a zone of disaggregated sand with much higher porosity than the formation sand). This results in a stable condition. The much higher permeability in this zone creates a sharp drop in the pressure gradient, which leads to stability when the well is put back on line (i.e., no more sand).

In Figure 11, the X-axis represents the total drawdown (depletion + drawdown). The left hand Y-axis shows the drawdown (light blue line). The yellow line shows the volume of sand produced in bbls. Sanding is predicted at a drawdown of around 610 psi. At this point the mechanical cementation started to break down and was totally destroyed by the time the drawdown reached about 650 psi (note that there is still 4 psi of capillary cohesion). The sanding level escalates rapidly as cementation erodes away and culminates in about 12 bbls of sand. A brief shutdown is modeled after the drawdown has reached 650 psi, and during this time, sand continues to be produced and goes up from about 12 to 13 bbls. After this, the well was beaned back up to a drawdown of 650 psi, and then the drawdown was increased more rapidly, up to 970 psi (see blue line in Figure 11). During this period, sanding increases but only by a small amount. This shows that if a cavity-like sand state develops around the well, sanding will not be re-triggered. For completeness, the pink line represents the shear-failed or plastic zone: this is the zone that has been impacted by the

Figure 11. Sand volume and failure zones, assuming creation of a cavity-like geometry

total loss of cementation. The dark blue line shows the radius of the zone experiencing sand production (tensile failure), the so-called cavity zone. The yellow line in Figure 11 shows cumulative sand increasing with drawdown, and reaching ~13 bbl at the end. We can now predict whether the well would have killed itself. We do this by first calculating the drag force acting on a typical sand grain,7 and then comparing it with the results of Figure 12.

y = 14.373x - 0.2952

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Figure 12. Correlation between sand-carrying capacity of fluid, and drag force on a sand grain For the well of Figure 11, producing ~10 MMcfd, the drag force is high, and the sand-carrying capacity is at the upper limit of the plot in Figure 12 (i.e., 60% of sand by volume in the well). About 12 bbl of sand would occupy a sand column of only 426 ft in this 10,000 ft well. The extra hydrostatic pressure due to this column of sand is only 316 psi. When added to the gas column in the rest of the well (727 psi), we get a total hydrostatic pressure of 1,043 psi. This could not kill the well, since the BHP just inside the well is 3,700 psi (depleted reservoir pressure minus drawdown). We estimate that >100 bbl of sand would be needed to kill the well. Note however, we have not investigated possible well self-kill by bridging of sand in tubing, or by flow surging which can increase friction pressure and thereby increase BHP.

Note that if the sand-carrying capacity were 30% instead of 60%, the height of sand column would be twice as high, but

8 SPE 84499

the hydrostatic pressure due to the sand column would be almost the same (this is true only if both sand columns do not exceed the well height).

The important point is that we now have a tool to calculate transient sand volume during a well blowout, and to estimate whether the well will kill itself by hydrostatic pressure increase. Steady-state sanding The steady-state model is an empirical model that is based upon extensive tests of sanding from cores in the laboratory (Willson, et al.8). A non-dimensionalized approach is used to combine and interpret laboratory sand production experimental data. This includes a “Loading Factor” concept that allows the derived sanding rate model to be consistent with existing models for predicting the onset of sand production. A “Reynold’s Number” concept includes fluid flow effects, and is well documented from perforation clean-up research. Lastly, an empirical “water boost factor”, which accounts for the effects of water production, is corroborated by field evidence.

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Figure 13. Predicted Distribution of Sand Production For Well B/1 For Specified Producing Conditions Then we have: Sanding rate = f (Loading factor, Reynolds number, Water boost factor) When applied to field examples from sand producing wells, the new model is seen to perform well when compared with the measured data.

The model has been applied to predict continuous sanding in an offshore field,8 and has led to the conclusion that sand rates can be managed at surface, without sand control. This is a huge economic advantage. Figure 13 shows the predicted sand influx versus depth for well B/1 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 4 pptb. Also shown in Figure 13 is the formation permeability distribution. This correlates well with porosity and inversely with formation strength (high permeability, low strength). The figure shows that 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 3-foot long interval.

Integrated sand prediction Background An example from the field, described previously by Vaziri, et al.2, is reexamined here to demonstrate how all three phases of sand prediction can be integrated (onset, transient, and steady-state) in a deviated well. The well is referred to as A/3 of Field A for the purpose of this paper.

This unconsolidated sand reservoir produced sand from early times: well A/3 has been online since September 1999. In early 2001 the well was producing at 9,000-10,000 bopd (no water), when a decision was made to try to increase the flow rate by either gravel packing the well, or just opening the choke. Near the end of April 2001, the choke was opened, and a prolonged transient sand burst occurred, lasting about 3 months (see Figure 15). The flow rate increased to ~15,000 bopd, which is a prime example of how to increase a well’s productivity by deliberately producing sand (see also Palmer, et al.9).

A comprehensive data gathering and logging program was performed for Field A, as also described previously by Willson, et al.8. The in-situ stresses were estimated from logs (e.g. sonic logs, density log, etc) and were calibrated to measured stresses from leak-off tests. The following is a summary of all the data needed to make the various sand predictions: • Sanding event data (pptb, choke size, flow rates, BHFP) • UCS log and TWC log (estimated from logs and calibrated

to measurements in the laboratory) • Cohesion log (estimated from logs) • In situ stresses (overburden, horizontal stresses, reservoir

pressure) • Drawdown pressure changes with time • Permeability log • Fluid viscosity • Completion information (shots per foot and perforation

diameter Onset of sanding prediction The in situ strength of the reservoir was estimated from sonic logs and given in terms of UCS (unconfined compressive strength). Clean sands (GR < 40 API units) have lower strength than shaly intervals, and the weakest interval has UCS ~ 2000 psi.

Figure 14 shows the results of our onset prediction, for the deviated A/3 well, producing at a rate of 15,000 bopd through a cased-and-perforated completion (CHC). These results apply to the transient event that began in late April 2001 as shown in Figure 15. The CBHFP (Critical Bottom Hole Flowing Pressure) is the lower limit of the BHP to avoid sand production.

SPE 84499 9

Figure 14. Sanding onset prediction for deviated A/3 well We notice in Figure 14 that the BHP of the well is lower than the CBHFP at a depth 15604.76 ft MD (indicated by the horizontal arrow), and therefore the formation there is expected to fail next to the wellbore. This is viewed as an indication of loose sand, which could be produced to the surface (i.e., sand production). This agrees with actual sand production, which occurred during the transient event (Figure 15). Several other intervals are also very close to failure, where the actual BHP is only slightly higher than the CBHFP. This plot shows that the well is prone to produce sand, especially as the reservoir is depleted further. Before the transient event, flow rate was lower: 9,000-10,000 bopd. Drawdown was lower by 140 psi, and actual BHP was higher by 140 psi. Figure 14 predicts that at the weakest point (15604.76 ft MD) there would still be sanding. Thus the prediction of onset of sanding agrees with that observed, both before and during the transient sanding event of April 2001. Transient sand volume prediction Figure 15 shows the sanding event in the field due to a change in choke size designed to increase oil production from ~10600 B/D to 15,000 B/D, initiated on April 17, 2001. The sand rate is measured by a strap-on sand detector. As discussed by Vaziri, et al.,2 the BHP changes in steps, as portrayed in Figure 16, and these have been computed from WHP values using a model for oil/gas flowing up a wellbore. The corresponding drawdown changes can be found by adding in depletion changes (0.8 psi/day). It turns out the maximum drawdown increase of 103 psi occurs on 3 June, at the time of maximum in Figure 16. To predict the volume of transient sand, the parametric transient equation was applied to every foot of the perforated interval, using the cohesion derived from the wireline logs.2 Although we did not have any cores to perform direct strength measurements in this well, several

A/3 Sand Cleanout April-July 01

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Figure 15. Sand rate in pptb (second from top) and oil flowrate (top curve) during transient sanding event uniaxial strength and TWC (thick wall cylinder ) tests were available in the field and were used to calibrate the strength obtained from logs. The clean sand intervals (GR <40), occupying 312 ft of sand formation (compared with 647 ft of perforations), were assumed to produce the sand. Since sand had been produced before this transient event, we assumed the perforations had been washed out; i.e., the transient sand

Figure 16. Change in BHP with time during transient sand event volume is predicted for an open hole well, not a cased/perforated well. Note that the sand volume is predicted in ft3 in the model, and converted to lbs using 120 lb/ft3, corresponding to a porosity of 30%.

The drawdown profile derived from Figure 16 is based on nine individual calculations in Figure 15, with straight-line interpolations between these nine values. The straight-line interpolations were then broken up into many small steps, and for each small drawdown step, a corresponding cumulative sand volume was predicted. This gives a profile of cumulative sand vs. time at the formation face. If we assume that the sand is carried into the well and up to the surface very quickly compared with the time between drawdown steps, this is also the profile of cumulative sand vs. time at the surface. This is probably a good approximation, since the transient sand event lasts a relatively long time (~ 3 months). The inferred profile of cumulative sand vs. time at the surface is presented in Figure 17. This is the prediction.

In Figure 17 is also shown the observed cumulative sand vs. time, obtained by integrating under the sand rate curve in Figure 15 (see also Vaziri, et al.2). The prediction agrees rather well with that observed, given the many uncertainties.

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10 SPE 84499

The prediction at 100 days is 47.6 bbl of cumulative sand, compared with 50.6 bbl observed.

The initial portion of the match is not very good, perhaps because sand is not carried out of the well as quickly as assumed in the model (we assumed an exit that was very rapid). In addition, at late times, the sand prediction levels off because drawdowns are no longer increasing (i.e., they are lower than the maximum drawdown on 3 June). According to the ENHANS model, this situation will not result in extra sanding. However, it seems possible that delays when the sand exits the well could also explain this discrepancy. Overall though, it is clear that the prediction matches remarkably well the actual transient sanding, especially given the many uncertainties in the prediction.

The prediction in Figure 17 is cumulative sand vs. time, and this could be differentiated to find a profile of sand rate vs. time. The best fit to the predicted cumulative sand vs. time is a polynomial, as shown in Figure 17. If we differentiate this, we obtain a sand rate curve that falls below the first large peak in Figure 15 (pink curve), but then agrees pretty well with the observed sand rate out to 70 days, before falling off too rapidly. This is an area of future development: to extend the ENHANS model by adding a model for sand transport from the sand face to wellhead (including sand pickup at the sand face, and slippage of sand grains through the carrying fluid in the wellbore).

y = -0.016x3 - 2.0381x2 + 593.16x + 6887.7R2 = 0.9216

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Figure 17: Observed profile of cumulative sand versus time at surface, compared with that predicted by transient sanding model ENHANS Steady-state sanding prediction Finally, to assess the rate of steady-state sand production, the BP model was applied to the production conditions after the transient sand event of Figure 15. Since the well has been producing sand for a significant time, it is expected that the perforations will be washed-out and the completion will behave as an open hole completion. The model has been discussed in detail elsewhere.8 The steady-state sanding rate predicted by the model is 2.13 pptb (or 32 lbs/day). This is compared with observation in Figure 18, where the observed sand rate after the transient event lies between 1 and 8 pptb, as judged by the interval after 3 July 01 in Figure 15. Although the observed range does bracket the prediction, it appears the prediction is on the low side. However, it is possible that the observed range has not

yet reached its true steady-state, and that agreement will improve over time. But this is not supported by a verbal report made in October 2001, that sand production was in the range of 7-20 pptb. We should not take the latter range too seriously, without examining the sand detector records, to see whether there may have been other new transient sanding events that occurred.

Note that for a cased and perforated completion, our model predicts 5.19 pptb (or 78 lbs/day), which matches better the data of Figure 18. However, we do not think that this rate is applicable for extended periods of sand production, because the perforations will wash out.

In summary, in this one example, we have shown how the BP suite of sanding models can predict the onset of sanding, the volume of sand in a transient event, and the steady-state level of sanding after the transient event. This new integrated strategy is a powerful tool for helping to decide on the need for, and timing of, sand control installations.

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Figure 18. Observed profile of cumulative sand versus time, including steady-state prediction

How this helps in sand management: 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

SPE 84499 11

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 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 do 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.

These cost implications were the principal motivation for developing the sand prediction tools described in this paper. In totality, they comprise over 20 man-years of R&D effort expended over the past 15 years. In particular, the development and application of these technologies has undergone a significant advance following the mergers between BP, Amoco and ARCO. This is because each company was actively focusing on different aspects of the sanding problem.

These inter-related and complementary efforts have now evolved into a powerful suite of tools that enable realistic predictions to be made of sanding potential, rates, and volumes throughout the life of a well. Conclusions In summary, the new three-fold strategy of sand prediction at BP has increased tremendously our ability to predict sanding in production or injection wells. This quantum leap is invaluable to help decide if we can manage the sand at surface (or if downhole sand control is required); to decide if we can defer sand control until a later date (possibly increasing production as well as saving completion costs); to decide how much sand will be produced if we increase the drawdown in a sand-prone well; and even decide if we need sand control in water injectors. • The standard BP prediction of sanding onset is generally

conservative. That is, sanding occurs at lower BHFP than predicted. In four out of seven cases CBHFP (obs) = (0.5 1) × CBHFP (pred)

and this could be used as a quick rule-of-thumb. • In one HPHT field case the BP shear-failure model is very

conservative. The ARCO tensile-failure model is also conservative, but not as much as the BP model. On the other hand, the ENHANS coupled model actually suggests these wells could have been drawn down even more before sanding (disaggregated sand grains held together by capillary cohesion due to connate water in pendular rings).

• In this same field case, sand finally comes in with water influx, and this is modeled by the removal of capillary cohesion forces.

• We have illustrated a tool to calculate transient sand volume during a well blowout, and to estimate whether the well will kill itself by hydrostatic pressure increase.

• To understand the sanding potential in water injector wells, one approach is to calculate the onset of significant sanding for various cross flow scenarios caused by potential sealing faults or pinch-outs, and to estimate transient sand volumes for the same scenarios. We have illustrated the risk of transient sanding by showing P10, P50, and P90 results for sand volumes produced, and for rathole filling with sand. Clearly, a deeper rathole would be an advantage.

• For gas injectors, the sand volumes will be reduced by typically 5 times, i.e., gas injectors are much safer than water injectors because capillary cohesion can hold disaggregated sand grains together.

• The new steady-state model has been applied to predict continuous sanding in an offshore field, and has led to the conclusion that sand rates can be managed at surface, without sand control. This is a huge economic advantage.

• In one illustrative example, we have shown how the BP suite of sanding models can predict the onset of sanding, the volume of sand in a transient event, and the steady-state level of sanding after the transient event. The prediction of sanding onset agrees with that observed, both before and during a large transient sanding event in April 2001. During the transient sanding event, the predicted profile of cumulative sand vs. time at the surface agrees rather well with that observed, given the many uncertainties. After the transient event, the range of sand rates observed does bracket the prediction, but it appears the prediction is on the low side.

Development of the sand prediction tools described in this

paper comprised over 20 man-years of R&D effort expended over the past 15 years. In particular, the development and application of these technologies has undergone a significant advance following the mergers between BP, Amoco and ARCO. This is because each company was actively focusing on different aspects of the sanding problem. These inter-related and complementary efforts have now evolved into a powerful suite of tools that enable realistic predictions to be made of sanding potential, rates, and volumes throughout the life of a well. Aknowledgments: We thank Marie Morkved, Yogi Patel, and Mike Kutas for assistance with field data. We thank Xu Li for contributing to the calculations behind Figure 12. We are grateful to BP for permission to publish this paper.

12 SPE 84499

Nomenclature: A a poroelastic constant (a function of the Poissons

ratio and formation compressibility) BHFP bottomhole flowing pressure BHP bottomhole pressure CDP critical drawdown pressure at the start of

production CBHFP critical bottomhole flowing pressure CHC cased hole completion Pr current average reservoir pressure TWC thick-walled cylinder strength UCS unconfined compressive strength WHP well head pressure Greek σ1 and σ3 total principal major and minor stresses σy the formation strength near the opening References: 1. Ispas, I., Bray, R.A., Palmer, I.D., and Higgs, N.G.:

“Prediction and Evaluation of Sanding and Casing Deformation in a GOM Shelf Well”, SPE/ISRM 78236 presented at the SPE/ISRM Rock Mechanics Conference, Irving, Texas, October 20-23, 2002.

2. Vaziri, H., Xiao, Y., and Palmer, I.D.: “Assessment of several sand prediction models with particular reference to HPHT wells”, SPE/ISRM 78235 presented at the, SPE/ISRM Rock Mechanics Conference, Irving, TX, October 20-23, 2002.

3. Weingarten, J.S. and Perkins, T.K.: “Prediction of Sand Production in Gas Wells: Methods and Gulf of Mexico Case Studies”, SPE 24797 presented at the 67th Annual SPE Technical Conference and Exhibition, Washington DC, October 4-7, 1992.

4. Vaziri, H., Barree, R., Xiao, Y., Palmer, I., and Kutas, M.: “What is the Magic of Water in Producing Sand?”, SPE 77683 presented at the SPE Annual Technical Conference and Exhibition., San Antonio, TX, September 29 – October 2, 2002.

5. Santarelli, F.J., Skomedal, E., Markestad, P., Berge H.I., Nasvig, H.: “Sand Production on Water Injectors: Just How Bad Can It Get?”, SPE 47329 presented at the SPE/ISRM Eurock 98, Trondheim, Norway, July 8-10, 1998.

6. Morita, N., Davis, E., and Whitebay, L. “Guidelines for Solving Sand Problems in Water Injection Wells”, SPE 39436, pres. at SPE Intl. Symp. Formation Damage Control, Lafayette, LA, Feb 18-19, 1998.

7. Tronvoll, J., Santarelli, F.J., Sanfilippo, F., and Dusseault, M.B.: “Sand Production Management for Seabed Separation Systems”, Report prep. for CoSWaSS Consortium, Dec 1998.

8. Willson, S.M., Moschovidis, Z.A., Cameron, J.R., and Palmer, I.D.: “New Model for Predicting the Rate of Sand Production”, SPE/ISRM 78168, presented at the, SPE/ISRM Rock Mechanics Conference, Irving, TX, October 20-23, 2002.

9. Palmer, I.D., McLennan, J.D., and Vaziri, H.H. “Cavity-Like Completions in Weak Sands”, SPE 58719, presented at the International Symposium on Formation Damage Control, Lafayette, Louisiana, February 23-24, 1999.

SPE 84499 13

Table 1: Field cases used to benchmark model for onset of sanding

initialfield gas/oil TVD Po UCSmin 3Sv-Sh? HPHT? sand CBHFP ratio

observed? pred/observed

field 1 gas 22000 15800 2000 yes yes no 3.72 lower limitfield 2 gas 15000 15000 3053 yes yes yes 1.94field 3 oil 9400 4100 2000 no no no -1.45 lower limitfield 4 oil 10050 4910 250 no no yes 1.83field 5 gas 13150 5750 1000 no no yes 0.93field 6 gas 17000 14500 800 no no yes 1.33field 7 oil 8315 3400 1900 yes no yes -0.456