Injectivity of Completions for Soft Formations
A. Settari, TAURUS Reservoir Solutions Ltd., Calgary (updated 01/05/01)
Introduction
Part of the work in Task 3 is to investigate two aspects of various completion
configurations for soft formations.
a) Choice of the best completion method for a specific reservoir, and
b) the injectivity of the specific completion configuration.
The first task was addressed in the Completions Workshop and resulted in a
Completion Selection Tool which is essentially a “knowledge base” of the Sponsors
and accounts for factors such as sand production, screen plugging, operational
considerations, etc.
This report deals with some aspects of the
calculation/estimation of the injectivity of various completions, assuming that there
is no mechanical or chemical damage or plugging due to PWRI. This will establish a
baseline for comparison, on which the effects specific to PW need to be
superimposed.
On the whole, it is believed that the completion selection criteria will override
injectivity considerations, which will be therefore secondary to completion choice.
Accordingly, the various calculations are not treated in detail, except for some
aspects that are not generally recognized.
1.
Injectivity of Different Well Completions in Matrix mode
1.1
Openhole Completion
This is the reference case. The most convenient way of expressing the effect of
other completions is to compare their injectivity to an openhole completion. The
injectivity can be calculated from radial flow equations. Note that assumptions
about boundaries must be made; the usual case is to assume a constant pressure
outside boundary. As a consequence, the absolute value of the injectivity depends
slightly on the outside radius, re. For liquid, single phase, steady-state flow, this is
the familiar equation (e.g., Pucknell and Mason, 1992).
P = 141.2 qL L BL [ln(re/rw) + S + D qL] /(kR hR)
(1)
where P is the drawdown (Pe – Pwf), qL is the rate, BL is the fluid formation volume
factor (FVF), re and rw are the outside and wellbore radii, S is the mechanical skin,
D is the non-Darcy skin, kR is the reservoir permeability and hR is the reservoir
thickness. The constant 141.2 applies for metric units (qL in m3/d, L in cp, kR in
md, hR in m). For an openhole completion, the only component of mechanical skin
is due to permeability damage or enhancement (no perforations), denoted by Sk.
If the area of the injection well has not been completely waterflooded to the
external radius, multiphase injectivity estimates can be obtained by simulation or
from analytical extension of the above equation for a radially composite mobility
system. Note that in this case the injectivity varies with time.
1.2
Openhole Screens and Slotted Liners
The additional pressure drop in wire wrap screens is probably small (without
plugging) although at extremely high rates there may be entrance effects and
possibly turbulence. Generally, the pressure drop across the screen is small and
the screen does not alter the radial flow pattern in the formation. Asadi and Penney
(2000) measurements give pressure drop of 0.05-0.1 psia at an injection rate of 6
– 18 BPD/ft of length. Figure 1 shows their data extrapolated to higher rates using
the assumption that the pressure drop is proportional to velocity squared.
Pressure drop through clean screens v2 extrapolation
100
Test 1
pressure drop (psia)
Test 2
10
Extrapolation
1
0.1
0.01
1
10
100
1000
flow rate (BPD/ft of length)
Figure 1. Pressure drop through clean screens extrapolated from data of Asadi
and Penny (2000)
Therefore, openhole screen completions should be similar in terms of Injectivity
Index to openhole completions except at extremely high rates. It must be stressed
that the results on Figure 1 are extrapolated; operator experience suggests that the
screen pressure drop is not nearly quadratic. Also, the screens tested by Asadi and
Penny are not typical wire mesh screens which would have lower resistance.
Slotted liners have also small pressure drop across the liner (when clean), but
cause convergent flow to the slot in the formation, which is the largest contribution
to slotted liner skin (also called the slot factor). The skin as a function of slot open
area or density, and width is shown in Figure 2 (Figures 3 and 4 from Kaiser et al.,
2000).
Figure 2. Skin factors for slotted screens.
Another factor increasing the skin is present if there are sections of the liner
without slots. If the area ratio of the slotted sections to entire liner area is B, this
effect can be estimated (according to Kaiser et al., 2000) by a “partial coverage”
skin of
SB = ln(re/rw)(1-B)/B
Manufacturers of screens and liners should also provide data on screen skin, Sscr,
and then Equation (1) can be used with S = Sk + Sscr.
1.3
Cased and Perforated Completion
For perforated completions, the mechanical skin is due to the combination of the
geometry of the perforations and any previous damage (assumed to be radial). In
addition, matrix acidizing after completion will contribute a negative component,
primarily due to permeability enhancement around perforations.
Extensive literature exists for predicting the perforation skin Sp from different
perforating geometries, in both laminar and turbulent flow. This includes finite
element simulations by Tariq (1987), semi-analytical methods for laminar and
turbulent flow (Karakas and Tariq, 1988; McLeod, 1982) and finite difference nearwellbore reservoir simulation (Behie and Settari, 1993). Typically, the results are
expressed in terms of the productivity ratio, PR, defined as the productivity of the
perforated completion divided by the productivity of an openhole, single phase,
undamaged completion. This concept can be applied directly to injection wells. If
the flow rate in the actual completion is q and the corresponding pressure drop is
P = Pe – Pw, the injectivity ratio IR is given by:
IR 
r
r
Cq
Cq
ln e /(p 
ln e )
2kh rw
2kh rb
(3)
where rb is the outside radius of the model which was used to generate the result
(not necessarily the same as re). C is a conversion constant. For field units, if q is
in bbls/d, k in md, h in ft and  in cp, C=1866.9; for metric units, if q is in m3/d, k
in md, h in m and  in cp, C=149.19. Typically the IR is correlated with perforation
phasing, shots per foot (spf) as well as perforation length and diameter. The
majority of this data is for single phase flow (without or with turbulence). For
multiphase flow it is recommended that the results be obtained by simulation
(Behie and Settari, 1993) because the analytical techniques (Perez and Kelkar,
1988) are too simplified.
For laminar flow, IR is independent of rate. The effect of reservoir turbulence is
theoretically dependent on rate. Numerical work (Behie and Settari, 1993) showed
that the reduction of IR due to reservoir turbulence in liquid flow is small for
permeabilities up to 800 md. This is shown in Figure 3 for a perforating pattern
with 0° phasing, 4 spf, fluid viscosity 0.7 cP, perforation diameter rp = 0.4 inch and
wellbore diameter rw = 0.5 ft. Much larger effects are possible in gas injection.
IR chart, 0 deg phasing, 4 spf, 0.7 cp, rw = 0.5 ft
0.95
0.90
Injectivity ratio
0.85
0.80
150 md, laminar
0.75
150 md,
turbulent
0.70
400 md,
turbulent
0.65
0.60
800 md,
turbulent
0.55
0.50
0
5
10
15
perf length (in)
Figure 3. An example of the effect of reservoir turbulence on cased hole injectivity
for clean empty perforations.
As a final note, the perforation program evaluated in Figure 3 would leave a
positive skin compared to openhole. Large shot density and tunnel length are
needed to achieve or exceed an openhole Injectivity Index. The equivalent skin
corresponding to a given IR is
S = ln(re/rw) (1- IR)/IR
(3)
The data on Figure 1 translates into skins of approximately 1 to 4.
Filled or Collapsed Perforations
The above calculations apply for clean perforations, i.e., when the perforation
tunnel remains empty. In PWRI injection, there is a possibility of solids
accumulation in the perf tunnel itself. Since the solids are very fine, the
permeability in the tunnel can be potentially very small. In addition, in soft
formation, there is a possibility of the perforation collapse if formation failure is
reached. The collapsed region may be dilated and therefore have a higher porosity
and permeability than the formation. However, there may be a compacted lower
permeability zone around the dilated zone. These zones will probably have a
different shape from the original tunnel.
The IR of filled or collapsed perforations can be significantly lower compared to
clean perforations. Calculations were done in this project using the model described
in Behie and Settari (1993) with the perforation filled by a material with different
permeability. The results are shown in Figure 4 for laminar flow, for permeability of
438 md, porosity of 25% and perforation diameter of 0.4 inch.
4 spf, laminar, filled perf, k p=k x 0.01, 0.1, 1, 10, infinity
IR
1
0.1
360 deg
180 deg
90 deg
90 deg, empty perf
0.01
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
perf length (ft)
Figure 4. Injectivity of perforated completion with filled perforations.
Note that the (standard) case of the empty perforation is obtained as a limiting
case of kp >> k.
In addition, turbulence in the perforation can now play a significant role. The
turbulence can be also included in the simulations using the Behie and Settari
model. Such calculations have been performed for the empty as well as filled
perforations for the same data as for Figure 4 (k=438 md). The results are best
expresses as a ratio of the IR with turbulence to IR obtained without turbulence.
The results are shown in Figure 5.
2 spf, laminar, filled perf, effect of turbulence
1
kp = 0.1 x k
0.9
kp = k
kp = 10 x k
0.8
(IR)turb/(IR)noturb
kp = inf x k (empty perf)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.00
0.05
0.10
0.15
0.20
perf length (ft)
0.25
0.30
0.35
Figure 5. Effect of turbulence on injectivity of perforated completion with filled or
collapsed perforations, k=438 md.
The total IR for a filled perforation is then obtained by taking the value from Figure
4 and multiplying it by the factor from Figure 5. This can lead to significant skin
factors. For example, taking kp=k, IR= 0.32 x 0.3 = 0.096 and from Equation (3),
taking ln(re/rw) ~8, S= 75.
1.4
Cased Hole Screens
The addition of the screen introduces additional pressure drop as discussed above
for openhole screens. For clean screens, the completion PI should be close to the
same completion without a screen.
1.5
Gravel Packed Cased Hole
This case has been treated in detail by Pucknell and Mason (1992). A cased gravel
packed completion has poorer injectivity than the alternatives. Additional pressure
drops result from the gravel pack layer between the screen and casing, and from
the gravel packing the perforation tunnel itself. The latter is expected to be more
significant.
The resistance between the screen and the casing can be expressed as laminar and
non-Darcy skin contributions, Ss and Ds:
Ss = (kR/kgr) ln ( rc/rs)
(4)
where kgr is the gravel pack permeability, rc is the inner radius of the casing and rs
the outer radius of the screen.
Ds = Dconst  gr (1/rs – 1/rc)
(5)
where:
gr is the turbulence factor of the gravel and
Dcnst = 1.02 x 10-14  B kR hR /(heff2)
is the constant term in Equation (5). The height heff is not explained in Pucknell and
Mason (1992), but it is understood to be an effective height, which corrects the
radial flow equation for the converging nature of the flow. A more accurate method
accounting for the convergence of the flow towards the perforation tunnels is given
by Yildiz and Langlinais (1991). The turbulence factor can be correlated with gravel
permeability in the same manner as for fracturing proppants and turbulence
measurements for proppants can be used to estimate  gr.
The effect of gravel permeability in the perforation tunnel is the largest factor
reducing gravel pack injectivity. It can be expressed in terms of an “effective
length” of a perforation, Lpe, defined as the length of a perforation without the
gravel pack, which would have the same IR as the actual gravel packed perforation
with a length Lp. Numerical solutions with the simulator described by Behie and
Settari (1993) were used by Pucknell and Mason to correlate the ratio L pe/Lp with
(kgr/kR)(rp/Lp)3/2. This correlation is shown in Figure 6. Once Lpe is known, the
standard methods for empty perforations can be used to calculate the perforation
skin.
The effect of turbulence in the gravel packed tunnel can be evaluated by the same
numerical model, but to our knowledge, there is no correlation currently available.
The above method can be used for “intact” perforations. A different calculation
method was developed by Pucknell and Mason (1992) for “collapsed” perforations.
They approximate the collapsed geometry by hemispheres filled with gravel,
with size determined from the perforation geometry. The total pressure drop is
determined using radial flow in the reservoir up to the envelope of the hemispheres
and then using hemispherical flow from the outside radius of the hemisphere to the
radius of the perforation.
Effective Perforation Length for Gravel Pack
Effective Perforation Length/
Actual Length Lpe/Lp
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.1
1
10
100
3/2
Dimensionless group (kgr/kR)(rp/Lp)
Figure 6. Effect of gravel packing on the effective perforation length.
1.6
Propped Fracture (Injection Below Fracture Pressure)
It may be difficult to operate this type of completion, because the injection pressure
must be kept below the current fracture pressure at all times. This means that
either sophisticated prediction and monitoring tools should be employed, or a
sufficient safety margin in injection pressure must be maintained, which reduces
achievable injection rates.
However, a propped fracture completion in a cased and perforated hole can be
common in converted producers.
For long-term injectivity estimates, the effect of a fracture can be expressed by a
fracture skin Sf in the radial flow equation, or converted to an equivalent wellbore
radius rwe according to:
rwe = rw e-Sf
(6)
For an infinite conductivity fracture, the well known result is rwe = Lf/ 2, which gives
a skin
Sf = ln (2 rw/Lf)
(7)
However, since PWRI often occurs in high permeability formations, the conductivity
of the fracture may not be infinite. In that case, Equation. (7) overpredicts
injectivity. A simple adjustment can be made by using the result of Cinco-Ley and
Samaniego for finite conductivity fractures (Cinco-Ley and Samaniego, 1981),
which gives rwe/Lf as a function of dimensionless fracture conductivity FcD
FcD = kf bf/(kR Lf),
(8)
where kf is the fracture permeability and bf is the fracture width (assumed constant
along the length). The function rwe/Lf = f(FcD) is shown in Figure 7. As a rule of
thumb, fractures with an FcD greater than 10 can be considered to be infinite-acting
(i.e., of infinite conductivity).
Effective wellbore radius vs dimensionless frac conductivity
Ratio rwe/Lf
1
0.1
0.01
0.1
1
10
100
1000
Dimensionless frac conductivity Fcd
Figure 7.
Correction to the infinite conductivity fracture skin calculation.
Note that all of these results assume a vertical fracture with the same height as the
reservoir pay, in a homogeneous reservoir and in single phase flow. Also, these
methods cannot be used to look at short-term (transient) data. Finally, the method
of Figure 7 - for correcting the fracture skin for finite conductivity of the fracture becomes unreliable when the fracture (proppant) and reservoir permeabilities are of
the same order of magnitude. This is easily seen by considering the case of kf = kR
in which the skin should be zero regardless of the value of FcD ( = bf/Lf in this case).
In such cases, numerical modeling should be employed.
Effect of turbulent flow
In gas wells, turbulence can reduce the benefits of fracturing to the extent that a
fractured well only achieves the performance of an unfractured well without
turbulence (the concept of “neutral skin”; refer to Stark et al., 1998 ). Turbulence is
usually thought to have a negligible effect for liquid flow. However, careful analysis
shows that it can be significant at high rates, as shown for production wells in Bale
et al. (1994).
A general correlation for predicting the reduction in injectivity due to turbulence has
been developed recently by TAURUS and Statoil (Bale, 1999) and made available to
the PWRI project. The correlation is based on a large database of fine-grid,
accurate solutions of steady-state, single phase flow. The final correlation is quite
complex and it is expressed as:
IR = (II)turb / (II)noturb = f(QD, FcD, Fc, kR)
(9)
where QD is a dimensionless injection rate and Fc = kfbf is fracture conductivity.
An example of the effect of turbulence for data typical of Ewing Bank FracPack
completions is shown in Figure 8. The case is based on Marathon's presentation at
the Soft Formations Workshop (Angel, 1999) and the data used are as follows:
Proppant .......................................................................... 20/40 Econoprop or frac sand,
Proppant Diameter .................................................................................. 0.0252 inches,
Proppant Porosity ................................................................................................... 0.4,
Proppant Density...................................................................................... 165.3 lbm/ft3,
Proppant Permeability (Stressed) ............ 180,000 mD * 0.6 (gel reduction) = 108,000 mD,
Fracture Turbulence Factor,  ............................................................ 32789.00 (1/psia),
Fracture Geometry ..........................................penny-shaped (approximated by a square),
Reservoir Height ................................................................................................ 100 ft,
Reservoir Permeability ..................................................................................... 1600 md
Effective Fluid Viscosity ........ 0.5 cP (corresponding to an injection temperature of 60-80°F),
Injection Rates ......................... from 5,000 to 35,000 BPD (50 – 350 BPD/ft of formation).
Based on our experience with fracturing design, it is difficult to achieve average
proppant coverage of more than 3-4 lb/ft2. Results on Figure 8 indicate that at 2
lb/ft2, turbulence can account for up to 11% reduction in the Injectivity Index,
while at 3 lb/ft2 the effect decreases to 5% reduction. However, more serious
effects are present in transversely fractured high angle wells (Settari, 2000).
Finally, it should be noted that the correlations used in the above example have
been developed for a permeability range of 20 – 200 md. For higher permeability
(as in the example data), the actual permeability value was used for calculating the
dimensionless groups, but the correlating functions for 200 md were used.
Extension for high permeability sands is possible.
Effect of turbulence on injectivity
1
0.95
IR = IIturb / IIno turb
0.9
0.85
0.8
0.75
Q = 5,000 B/d
0.7
Q = 15000 B/d
Q = 25000 B/d
0.65
Q = 35000 B/d
0.6
0.55
0.5
0.000
0.500
1.000
1.500
2.000
2.500
3.000
3.500
prop coverage (lb/sqft)
Figure 8.
2.
Effect of turbulence on typical PWRI Fracpack completions.
Injectivity in fracture mode
Induced (dynamic) fractures are commonly propagated in PWRI. Equivalent fracture
permeability, from the theory of laminar flow between parallel plates, is kf = b2/12;
this estimate is usually too high by orders of magnitude due to roughness,
tortuosity, etc. ,Even then, the conductivity of an open fracture is usually high
enough to be infinite-acting.
For a given fracture length, estimates for a propped fracture with infinite
conductivity could be used to calculate skin. However, this value will be misleading
for two reasons:
a) induced fractures are growing and a true steady state Injectivity Index does not
exist unless the fracture stabilizes in length
b) The standard definition of Injectivity Index is not applicable for a well with a
propagating fracture.
2.1
How To Measure Injectivity For A Well With Dynamic Fracture?
The relation between bottomhole pressure and rate below fracture pressure
(including a well with propped or acid fracture) is a function of completion geometry
and reservoir properties. One can define the true Injectivity Index as:
II = dQ/dpwf = (Q1 – Q2) / (pwf1 – pwf2)
(10)
where Q1 and Q2 are the stabilized rates corresponding to flowing pressures pwf1
and pwf2. This definition is the analog of the definition below fracture pressure.
However, if we use this II to compute the expected rate for a “drawdown” (pwf – pR)
the standard equation
Q = II (pwf – pR)
(11)
clearly does not give the correct answer. Conversely, one could interpret II from
the long-term p and Q data by simply applying Equation (11) and that is how much
of the PWRI data is analyzed. However, the II computed from Eqn. (11) is not
independent of rate.
For a well with a propagating fracture, pwf is dominated by in-situ stress and rock
mechanical data, and can be expressed in several ways, e.g., as:
pwf = pfoc(t) + pfric + ptip + pentr
(12)
where pfoc(t) is the (variable) fracture opening/closure pressure, pfric is the
pressure drop due to friction in the fracture, ptip represents tip effects (plugging,
plasticity), and pentr represents all entrance effects (tortuosity, perforations, …).
The pressure drops inside the fracture are governed by the fracture mechanics such
that the resulting crack opening satisfies both elasticity and fluid flow equations. In
water injection, where there is leak-off dominated fracture propagation, pfric is
usually small. The dominating factor is the change of the pfoc, which is essentially
the current total stress on the fracture face. Competition between the poroelastic
and thermoelastic stresses can make pfoc vary in time in a complex manner, even if
Q is constant. Therefore, one cannot use Equation (11) to compute the Injectivity
Index. Use of the definition in Equation (10) will typically give much larger values,
compared to the Injectivity Index below frac pressure II. However, even this can
be used only after the poro- and thermoelastic effects have stabilized, or only
during a short time frame. In summary, while Equation (10) is still useful to
measure the resistance to fracture propagation, the Injectivity Index cannot be
used to predict BHP or rate via Equation (11). This aspect is discussed in detail in a
related PWRI report (Settari, 2000a).
Fracture Propagation Aspects
The second aspect of the evaluation is the propagation rate of the fracture. In
practical terms, one can inject at almost any rate at the entrance to the fracture,
and the real limitation will be the THP, given the pressure losses in the wellbore and
entrance to fracture. However, changes in rate do translate to different rates of
propagation, or different stabilized fracture length.
This will bring other
considerations into play. For example, if PWRI is used for waterflooding (as
opposed to disposal), fracture propagation will have an effect on pattern sweep and
therefore the injectivity cannot be considered in isolation from sweep.
2.2
Matrix Injection After Fracture Injection
If the rate is cut back, it is possible that the dynamic fracture will close and the well will
return to a pseudo-matrix mode of injection. Fracture closure is also possible if the
permeability is stress-dependent and becomes sufficiently enhanced over time. This was
seen in the data for the Maersk MFB-07 pilot injector where the injection pressure after
about 2 years of injection started declining below fracture pressure at a constant rate which
was earlier interpreted as being in fracture mode (by SRT’s). The pressure decline was not
due to a change in stress, which was measured as slightly increasing with time by SRT’s
until that point.
In the case of a closure there is usually some residual conductivity in the closed fracture,
which will make the post-fracturing pseudo-matrix Injectivity Index higher than its prefracturing equivalent. The existence of residual conductivity has been well documented in
conventional fracturing without proppant. In soft formations, the conductivity may heal
with time due to plastic deformation if sufficient compressive stress is present. The role of
the solids deposited in the fracture during PWRI is not clear; they could be providing
permeability or, more likely, forming a seal.
Currently we are not aware of any methods to predict the magnitude of the residual
conductivity, in particular for PWRI fractures. The conductivity can be measured by PTA
techniques, but it may be too small to be clearly diagnosed. It should be however
measurable in a laboratory under simulated conditions.
The residual conductivity phenomena may be also important for interpretation of fall-off
tests.
3.
Example Calculations of Completion skin.
Consider a reservoir with the following data (partly already used in the previous example):
Pay height .......................................................................................................... 100 ft
Permeability ................................................................................................... 1600 md
Porosity ............................................................................................................. 25 %
Reservoir Temperature ...................................................................................... 170 °F
Injection Temperature ........................................................................................ 80 °F
Reservoir pressure ......................................................................................... 2500 psia
Initial minimum stress .................................................................................... 3500 psia
Water FVF ............................................................................................................ 1.03
Water viscosity ................................................................................................... 0.4 cP
Drainage radius ................................................................................................ 1750 ft
Wellbore radius ............................................................................................... 0.4616 ft
Initial (openhole) skin .............................................................................................. 20
Perforating pattern: 4 spf, 90 deg phasing, 0.4 inch diameter, 6 inch length.
The following II (Injectivity Index) estimates are calculated, based on different
assumptions:
1) Openhole:
II = qL/P = (kR hR) / {141.2 L BL [ln(re/rw) + S + D qL] }
Without considering the skin, in laminar flow, and assuming maximum dp = 1000
psia, the results are:
II = 333 bbls/day/psi
Qmax = 333,000 bbls/d
With the initial drilling skin of 20, the corresponding values are:
II = 97.37 bbls/day/psi
Qmax = 97,000 bbls/d
2) Openhole with a screen:
Assuming that the pressure drop data of Figure 1 can be extrapolated quadratically
with rate, the equation for pressure drop across the screen can be fitted by:
Dps = 0.00045 (Qinj/H)2
Then one can solve iteratively for Dps and Q given the total pressure drop, which
results in:
Dps = 243.7 psia
II = 73.58 bbls/day/psi
Qmax = 73587 bbls/d
Therefore there is a significant effect of a screen.
3) Cased and perforated:
Assuming clean perforations and laminar flow, one can use a chart similar to Figure
3, but for the specific perforating pattern and other parameters. This chart has
been generated and the values are shown below.
Length
(ft)
Phasing
360
180
90
0.1
0.5487
0.6222
0.6558
0.125
0.58
0.6604
0.697
0.15
0.6051
0.6907
0.7294
0.2
0.6413
0.736
0.7787
0.5
0.7573
0.8717
0.9212
Applying this and assuming that the drilling damage is not relevant, one gets clean
perf, laminar flow IR= 0.92. For the effect of turbulence we use Figure 5 to
estimate a factor FT of 0.85 (one should generate specific chart for the given
conditions since FT depend on permeability). This gives
Laminar flow:
Skin= 0.717
II = 306 bbls/day/psi
Qmax = 306,000 bbls/d
Corrected for turbulence:
Skin= 2.298
II = 260 bbls/day/psi
Qmax = 260,000 bbls/d
This is still an optimistic value. If we now assume that perforation is filled with
material of permeability = 1/10 of reservoir, we obtain from Figure 4 IR=0.11 (in
absence of a graph for the correct permeability). From Figure 5, we estimate the
multiplying factor for turbulence as 0.35 (for 2 spf in absence of 4 spf correlation
and for the permeability of 438 vs 1600 md). This results in total IR=0.0385 which
results in the following values:
Laminar flow:
Skin= 66.7
II = 36.68 bbls/day/psi
Qmax = 36,680 bbls/d
Corrected for turbulence:
Skin= 205
II = 12.88 bbls/day/psi
Qmax = 12,840 bbls/d
Note again that it would be possible to generate the charts for the turbulence factor
specific to the given permeability and other parameters.
Discussion
The example illustrates several points:

The openhole, undamaged calculation gives very large, unrealistic values

There may be a significant pressure drop across screens at high rates. Lab or
field data at representative rates is necessary to confirm this.

Perforation skin can be high if the perfs are filled, and can account for a large
portion of the observed total skin in the field.

There is a large variation in predicted injectivity (333,000 – 12,000 bpd)
depending on the completion configuration and assumptions used.
Note also that all the above calculations were made without plugging in reservoir
matrix. When this is accounted for, the large skins seen in the field are not
surprising.
References
Angel, R. (1999): MOC GOM Soft Rock Completions Ewing Bank Area, Presentation to
Completion workshop, PWRI, Edinburgh, December 1999.
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