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.
Trang 1Copyright 2002, Society of Petroleum Engineers Inc
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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 (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 1 and 2 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
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.)
Trang 2option – 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 The derivation and validation of such a
model is described in the sections following
Description of Sand Rate Model
1 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
bottom-hole 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:
0 1
2
1 3 S S p ( 1 A ) Ap
and similarly
0 2
1
2 3 S S p ( 1 A ) Ap
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:
) 1
(
) 2
1
(
ν
α
ν
−
−
=
and α is Biot’s constant given by:
b
r C
C /
1 −
=
where ν is the Poisson’s ratio and Cr and Cb are the grain and
bulk rock compressibility, respectively
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.:
U p
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:
) 2 ( )
2 (
3
0 2
1
A
A p A
U S S CBHFP
pw
−
−
−
−
−
=
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
Introducing this in (6) we find the functional relation between the reservoir pressure, p0, and CDP
)]
2 ( 3
[ 2
1
2 1
)]
3 ( 2 [ 2
1
2 1
p A
−
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 = ( 3 S1 − S2− U ) / 2 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
S 1
S 2
S t1
S t2
S 1
S 2
S t1
St2
Trang 3(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 = 3 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)
Figure 2 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 = 2 × 1.55 × TWCsp = 3.10 × TWCsp (8)
Note that in the above, the factor of 2 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
Figure 3 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:
U p S
where St2 is the maximum tangential total stress acting on the formation or perforation We note that for LF<1 the formation
is not failed, while for LF>1 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:
TWC
p p A p S S
* 10 3
) (
2
2 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:
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
OD/ID TWC Sample Ratio
ID = 0.30"
ID = 0.50"
ID = 0.63"
ID = 1.00"
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7
TWC Sample OD/ID Ratio
Saltwash South
Trang 4βρV 10
31735
.
1
e
k
−
×
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
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:
2 1
10/
10
65
.
=
Therefore, by non-dimensionalizing the fluid flow
contribution, variations in formation permeability, fluid flow
rate, viscosity, etc., can be easily captured in the analysis
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 5 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 6 through 9 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 4 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
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
Figure 4 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 5 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 6
It is recognized that the method used to increase sand
0.1 1 10 100 1000
0 200 400 600 800 1000 1200 Cumulative Flow Through Sample (litres)
0 1000 2000 3000 4000 5000 6000 7000 8000
Sand Production Rate Confining Pressure
Drilled Hole 'Stress to Failure' Test
Trang 5production 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
water-breakthrough 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
Figure 5 Fitted Surface to Experimental Sand Production Rate in
Terms of Loading Factor & Reynold’s Number (Dry Oil Flow Only)
Figure 6 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 7 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:
Definition of the Load Factor, LF = f(in-situ stresses, well
trajectory, reservoir pressure, drawdown & depletion, TWC strength)
Definition of Reynold’s Number, R e = f(permeability, flow rate per perforation, viscosity, density, perforation number and size)
Definition of Sand Production Rate, SPR = f(LF, Re, water-cut)
Figure 7 Field Data From Four Wells Showing Approximately 10-Fold Increases in Sanding Rate After Water-Breakthrough
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 in-situ 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
0 5
1 0
1 5
Water-Cut ( %)
0 5
1 0
1 5
2 0
Water Cut (%)
0 5
1 0
1 5
2 0
Water Cut (%)
0 5
1 0
1 5
2 0
Water Cut (%)
0 0.05 0.1 0.15 0.2 0.25
Reynolds No.
0 0.5 1 1.5 2 2.5
3
3.5
4
LF
0.1
1
10
100
1000
Water Cut %
0.1
1
10
100
1000
Water Cut %
Trang 6Field 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 1 provides a summary of
formation properties over the perforated intervals analyzed
However, as the model takes into account the
half-foot-by-half-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 8 and 9 for Field A wells, and in Figures 10 to 13
for Field B wells Figures 8 and 9 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 8 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 8 and 9) very good agreement is
reached The predicted rates of 3 pptb to 4 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 6 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
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 / 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 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 3 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
1 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
2 The “Loading Factor” concept allows the derived sanding rate model to be consistent with existing models for predicting the on-set of sand production
3 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
4 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
1 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
2 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
Trang 73 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
4 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
5 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
6 Halleck,P.M., “An Experimental Investigation of Sand Production: CEA Project #11 Final Report”, prepared by TerraTek, Inc., June 1991
7 Willson,S.M “CEA 11, Phase II, An Experimental Investigation of Phenomena Affecting Sand Production in Low-Strength Sandstones,” Final Report, Vol 1, Summary of Results, prepared by TerraTek, Inc., August 1993
8 Willson,S.M “CEA 11, Phase III, An Experimental Investigation of Phenomena Affecting Sand Production in Low-Strength Sandstones,” Final Report, Vol 1, Summary of Results, prepared by TerraTek, Inc., April 1995
9 Papamichos,E., “A Volumetric Sand Production Experiment,”
2000 Balkema, Rotterdam, ISBN 90 5809 155 4
Table 1 Summary of In-Situ Properties For Wells Analyzed
(TVD.SS) &
Well Deviation
(psi)
Initial Reservoir Pressure (psi)
Initial Horizontal Stress (psi)
43º deviation
Average Minimum Maximum
112
10
353
2481
A / 2
8949 ft to
9440 ft 39º deviation
Average Minimum Maximum
98
10
640
2955
160
4972
1647
9325 4658 7320
0º deviation
Average Minimum Maximum
219
20
1048
3281
B / 2
9253 ft to
9291 ft 58º deviation
Average Minimum Maximum
675
35
2044
1592
967
5146
4025
8230 4055 6174
B / 3
9686 ft to
9725 ft 13º deviation
Average Minimum Maximum
450
40
1133
2544
1923
6512
5675
8658 4180 7110
B / 4
9426 ft to
9527 ft 35º deviation
Average Minimum Maximum
601
21
3761
2456
493
6366
2874
8456 4121 6975
Figure 8 Predicted vs Measured Sand Production Rate – Field A, Well 1
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Q (bpd)
Avg Measured Sand Rate (pptb) Predicted Rate (pptb)
Trang 8Figure 9 Predicted vs Measured Sand Production Rate – Field A, Well 2
Figure 10 Predicted vs Measured Sand Production Rate – Field B, Well 1
Figure 11 Predicted vs Measured Sand Production Rate – Field B, Well 2
0.0 2.0 4.0 6.0 8.0 10.0
12.0
14.0
Oil Rate(bpd)
Avg Measured Sand Rate (pptb) Predicted Rate (pptb)
0 3 6 9 12 15 18 21 24 27 30
29000 30000 31000 32000 33000 34000 35000 36000 37000 38000
Tot Liquids (bbd)
0 10 20 30 40 50 60 70 80 90 100
0 3 5 8 10 13 15 18 20 23 25
Tot Liquids (bpd)
50 55 60 65 70 75 80 85 90 95 100
Trang 9Figure 12 Predicted vs Measured Sand Production Rate – Field B, Well 3
Figure 13 Predicted vs Measured Sand Production Rate – Field B, Well 4
Figure 14 Predicted Distribution of Sand Production For Well B / 1 For Specified Producing Conditions
0 4 8 12 16 20
9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000 21000 22000
Tot Liquids (bpd)
50 60 70 80 90 100
Sand Production (pptb) Predicted Rate (pptb) WaterCut (%)
0 2 4 6 8 10 12 14 16 18 20
12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 32000
Tot Liquids (bpd)
0 10 20 30 40 50 60 70 80 90 100
0.10 1.00 10.00 100.00 1000.00 10000.00
9750 9775 9800 9825 9850 9875 9900 9925 9950 9975 10000
Depth (feet TVD.SS)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Formation Permeability (mD) Sand Production Rate (lbs/ft)