Field Lessons From Successful Application in Drilling Depleted

OTC 14278
Aphron Drilling Fluid: Field Lessons From Successful Application in Drilling Depleted
Reservoirs in Lake Maracaibo
Julio Montilva, PDVSA; Catalin D. Ivan, M-I L.L.C.; James Friedheim, M-I L.L.C.; and Rafael Bayter, M-I L.L.C.
Copyright 2002, Offshore Technology Conference
This paper was prepared for presentation at the 2002 Offshore Technology Conference held in
Houston, Texas U.S.A., 6–9 May 2002.
This paper was selected for presentation by the OTC Program Committee following review of
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Abstract
Depleted reservoirs pose numerous technical challenges in
both the construction and completion phases for wells in
dozens of producing fields, often putting into question the
economical viability of these fields. Wellbore instability,
severe lost circulation, and stuck pipe are just a few of the
problems encountered when drilling into these low-pressured
reservoir formations.
No area better illustrates the problems with depleted
reservoirs than the Lake Maracaibo region. Water-wet sands
that frequently triggered costly seepage losses and differential
sticking typify many of these zones. Some contain microfractured sandstone formations where uncontrollable losses of
whole drilling fluid previously were the norm rather than the
exception. Others are characterized by laminated sand and
shale sequences, which create the conditions for slow,
dangerous, and unduly expensive drilling. Attempts were
made with underbalanced drilling, but in addition to the extra
time and equipment required, wellbore instability lead to
failed well construction and thus seriously degrading project
economics.
Over the past two years, a specialized drilling fluid has
being utilized to drill these depleted reservoirs in Lake
Maracaibo. This fluid combines certain surfactants and
polymers to create a system of "micro-bubbles" known as
aphrons encapsulated in a uniquely viscosified system. These
aphrons are non-coalescing, therefore creating a micro-bubble
network for stopping or slowing the entry of fluids into the
formation.
The aphrons allow conventional drilling
equipment to be used to successfully complete many
reservoirs that previously would have been candidates for
underbalanced drilling only.
This paper describes the development and application of
the specialized “micro-bubbles” or aphron-based drilling fluid
for drilling depleted reservoirs by controlling downhole mud
loss and formation damage. The authors will detail the
operational procedures and the field applications of this
drilling fluid, with particular emphasis on the lessons learned
in the Lake Maracaibo implementation of the system.
Introduction
The drilling problems associated with the depleted reservoirs
intrinsic to many of the mature fields throughout the world
often make further development uneconomical. Uncontrollable drilling fluid losses frequently are unavoidable in the
often large fractures characteristic of these formations.
Furthermore, the typical laminated sand and shale sequences
create conditions that can make drilling unduly expensive and
dangerous when using conventional rig equipment.
Consequently, these and a host of associated problems have
led some operators to forgo continued development of these
promising, yet problematic, reservoirs.
The overbalance pressure generated when using
conventional drilling fluids is to blame for the majority of the
loss circulation and differential sticking problems encountered
when drilling these wells. The equipment required when using
aerated muds or drilling underbalanced is often prohibitively
expensive and meeting safety requirements can be an
exhaustive effort. Furthermore, these techniques may fail to
provide the hydrostatic pressure necessary to safely stabilize
normally pressured formations above the reservoir.
The early wells in the Lake Maracaibo area were drilled
using underbalanced drilling techniques combined with
special casing designs to isolate the Miocene and Eocene
formations. Yet, the hole instability problems associated with
this drilling technique rendered this project unprofitable.
Consequently, the operator looked for any alternative that
would return profitability to this mature reservoir by reducing
the drilling days and enhancing the production rate.
The aphron-based system was recommended as an
alternative drilling fluid to drill both the normal and
subnormal pore-pressure sections, while simultaneously
maintaining wellbore stability and controlling mud losses. The
main challenges placed upon this drilling fluid system were
solving the whole mud losses and hole instability problems
associated with drilling normal and depleted pressure intervals
2
J. Montilva, C.D. Ivan, J. Friedheim and R. Bayter
and attaining cost effectiveness through avoiding an extra
casing run.
Lake Maracaibo – Regional Geology Overview
The principal plays in the northeast area of Lake Maracaibo
are Miocene and Eocene sandstones sealed by interbedded
shales, charged from organic rich La Luna source rocks of
upper Cretaceous age. Fig. 1 is a map showing the various
fields operated in Lake Maracaibo and surrounding areas,
while Fig. 2 represents a geological cross-section through the
lake and land formations.
The API gravities of the crude in the area vary from values
as low as 14° API to 35° API. The most important reservoir
units are Miocene (Lagunillas, La Rosa Formations, Santa
Barbara and Bachaquero Members) and Eocene sandstones
(Misoa Formation B and C sands). The Miocene sandstones
have the best reservoir properties and the Bachaquero Member
of the Lagunillas Formation, consisting of thick channel sands,
is the best producer. The thickest sands occur within the
overlying, predominantly regressive Misoa B sequence, in
particular the lower Misoa B beds, a distributary mouth bar
complex. Deeper intervals consisted of a mainly transgressive
sequence with relatively thin sandstones reservoirs (Misoa C).
In general, the lower structural formations (i.e., Tia Juana,
Lagunillas, and Bachaquero) were more prone to fractured
formation losses, while the fields situated on the upper part of
the structure (Lagomar) had specific permeable sands mud
losses. The unconsolidated Miocene sands represented a
better target/candidate for the aphron-based system, as fewer
problems (i.e., mud losses) were recorded while drilling this
interval. The deeper formations (Eocene) are characterized by
localized micro-fractures that could explain the minimal lost
circulation problems recorded during drilling these intervals at
the beginning of this project.
These problems were solved by adding sized bridging
agents (i.e., calcium carbonate) to the drilling fluid system.
Judging from the amount of losses recorded, the Lagomar
field has shown the best results in using the solids-free version
of the aphron-based system. This can be explained as the C
sands (the producer in this field) have lower permeability than
the B sands (drilled in Tia Juana or Lagunillas fields).
Aphron Structure
An aphron comprises two fundamental elements1:
• A core that is commonly, but not always, spherical.
Typically, the core is liquid or gaseous.
• A thin aqueous protective shell
The aqueous shell contains surfactant molecules
positioned to produce an effective barrier against coalescence
with adjacent aphrons. As illustrated in Fig. 3, the
encapsulated shell protects the aphrons, which can attract one
another to build up complex aggregates. It should be noted
that the encapsulating soap film has both an inner and outer
surface.1 This phase has oriented surfactant molecules at the
surface that are hydrophilic pointing inwards and hydrophobic
outwards.
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Physically, the bubble in Fig. 3 is a sphere of gas, separated
from its surroundings by a thin, soapy film. The hydrophilic
head of the surfactant distributed on the molecular monolayer
is oriented towards the bulk water, while its lipophilic tail is
oriented towards the gas core.1 Thus, the foam (Fig. 4) has a
water-wet or hydrophilic boundary as opposed to the aphron,
which has a hydrophobic boundary.
The advantage of gas-core aphrons is the tendency to lump
together, creating large aggregates. Perhaps surprisingly, these
macro-structures behave in the same manner as the individual
aphron (Fig. 5). Through the meniscus that wraps all the
individual colloidal gas aphrons, this macro-structure has the
same liphophilic character and, to a certain degree, is believed
to exhibit the same behavior when in contact with a water-wet
formation.1
The “meniscus-wrapping theory” is literally endorsed by
the mechanism known as “Laplace Pressure.” This theory
simply states that when a flat liphophilic surface (i.e., plateau
border from the aphron structure) dips into a water-wet liquid
a contact angle will exist where the liquid and gas meet.1 If
two such “liphophilic charges” are close together, the effect of
the two contact angles will be the generation of a curvature of
the liquid surface between those two liphophilic droplets. This
is known as a meniscus. This mechanism may cause the
aphron macro-aggregate to be wrapped with a meniscus with
the liphophilic character.
Aphron Structure Stability
The water lamella in the aphron structure will remain stable as
long as the water film is viscosified and the minimum and
maximum thickness criteria is respected.1
First, a certain thickness is required for the water lamella to
remain stable. According to the Thin Soap Film Thickness
study by Clunie, et al,2 the water/film lamella is not stable if it
is thinner than 4 microns or thicker than 10 microns. The
study states in part that a minimum thickness created by the
interaction between the water molecules and the hydrophilic
parts of the surfactant must exist. As this “critical thickness” is
altered, such as thinning due to stretching effects when the
aphron volume increases, the soap film will break.
Another phenomenon plays an important role in water
lamella stability. This one has been described as “rate of
transfer”, which can be affected by the “Marangoni effect”.1, 3
The water molecules from the lamella tend to leave the film
and return to the bulk water (continuous phase). By
viscosifying the water through the addition of a biopolymer,
the rate of transfer is reduced to a point where the aphron
structure is stabilized.
Aphron as an Energized Microenvironment
An aphron is much more than a “gas bubble”. The viscosified
water lamella, in tandem with the surfactant layers, creates an
“energized environment.” First, when an aphron is generated
inside a liquid, a new surface must be created, which increases
in area in proportion with the growth of the bubble.1 This
expansion must be balanced by an increase in the pressure
within the bubble (Laplace pressure), thus explaining why the
OTC 14278
Aphron Drilling Fluid: Field Lessons From Successful Application in Drilling Depleted Reservoirs in Lake Maracaibo
aphron is associated with an “energized environment” or “precompressed structure.”
Aphrons contain a gas nucleus of encapsulated air and
compress when circulated downhole. The internal pressure of
these micro-bubbles increases at a rate proportional to the
external pressure being applied (Fig. 6). The combination of
increasing pressure and temperature serve to energize the
individual aphrons.4
Once the drilling bit exposes a depleted formation, the
aphrons immediately aggregate within the openings of lowpressure zones. There, a portion of the energy stored within
each aphron is released, causing it to expand. The expansion
continues until the internal and external pressures on the wall
of the aphron are in balance. Fig. 7 illustrates this energizing
process.
As the energized micro-bubbles enter formation openings,
they carry energy equal to that of the annulus. As the aphrons
crowd into the openings, external Laplace forces increase
dramatically, causing aggregation and an increase in Low
Shear-Rate Viscosity (LSRV). The microenvironment created
by this phenomenon forms a solids-free bridge.4
Aphron-Based System Composition
Table 1 shows the components of a typical aphron system. As
shown, the high-LSRV type fluid consists of a high-yield,
stress-shear-thinning (HYSST) polymer coupled with fluidloss-control additives that create and stabilize the aphrons
within the system. An aphronizer surfactant is incorporated to
achieve the desired concentration of micro-bubbles, which
typically range from 8 – 14% by volume. As the concentration
builds, it is not uncommon to observe an increase in the
Brookfield LSRV to between 120,000 and 160,000 cP.4
Once the system is circulated, the rheological properties are
easily maintained to provide optimum hole cleaning, cuttings
suspension, and a high degree of control in preventing whole
drilling fluid invasion into the lost circulation zone.
The organic and biodegradable polymers and non-caustic
pH materials in the system have allowed it to meet Gulf of
Mexico bioassay and Canadian micro-toxicity requirements.4
First Aphron-Based System Field Trial in Lake
Maracaibo
The first aphron-based system field trial was performed in the
reservoir section of the VLA 1321 well. This well was
characterized by a formation pressure gradient of 0.15 psi/ft to
0.30 psi/ft. The offset well data that were analyzed during the
planning stage of this field trial are presented in Table 2.
The aphron-based system was displaced to drill the
reservoir section after the 13⅜-in. casing was set at 5,477 ft
and the interval was drilled to 6,855 ft. The total section length
was 1,378 ft and throughout this interval 390 ft were cored
with 91% recovery. At the section total depth (TD), three
logging runs were made and the 9⅝-in. casing was run without
any problems. During all these operations (drilling, logging,
running casing and cementing), no mud losses were
experienced. The repeat formation tester data (RFT) are
presented in Fig. 8. The formation gradients were ranging
3
from 0.15 psi/ft to 0.33 psi/ft while the mud gradient varied
from 0.39 psi/ft to 0.41 psi/ft.
Further Aphron-Based System Field Applications
After the success of the first field trial of the aphron-based
system, various operators used the system in several fields in
the Lake Maracaibo field. Fig. 9 shows the evolution of the
aphron-based system in Lake Maracaibo. The system has
continuously been adjusted and fine tuned as per the lessons
learned on each specific field and application. The system
applications ranged from:
1.
2.
3.
4.
Drilling low-pressure / low-fracture gradient sections
Drilling fractured and high permeable sections
Reservoir drill-in applications
Drilling normal and low-pressure sections (high density
applications).
The low-pressure applications were mainly in the depleted
reservoirs in the Miocene formations. Owing to the depleted
nature of the sandstone formations, the aphron-based system
was formulated to bridge the porous media and prevent lostcirculation problems. All the wells drilled for this type of
application showed a pore pressure ranging from 2.5 lb/gal to
5.0 lb/gal and equivalent circulation density (ECD) between
9.5 lb/gal and 10.0 lb/gal. No mud losses were experienced.
The micro-fractured, low-pressure/low-fracture gradient
permeable formations applications were very typical for the
depleted reservoirs in the Eocene sections. For these
formations, the fracture gradient is around 9.0-lb/gal
equivalent mud weight and there are several in-situ fractures
(Fig. 10). The annular-pressure-while-drilling (APWD) data
showed that the equivalent-circulating-density (ECD) value
using the aphron-based systems was comparable with those
for a polymer-based system and the effect of the aphron
structures did was not significantly reduce the hydrostatic
pressure. Because of this behavior and in order to drill the
sections with low fracture gradient, hollow glass spheres were
introduced to the original formulation to reduce the
hydrostatic pressure. Calcium carbonate was used to provide
a matrix in the natural fracture and to create a “bridging
medium” where the aphron could work. Wells TJ 1336 and TJ
1333 were drilled using this new formulation. The recorded
ECD values were around 9.0 lb/gal. No mud losses were
reported. The biopolymer blend concentration was reduced
from 5 lb/bbl to 3 lb/bbl to optimize rheological properties and
avoid excessive ECD.
The aphron-based system was introduced for drill-in
applications for horizontal wells in the Lake Maracaibo area,
aiming to minimize formation damage through reduced mud
losses in the depleted target formations. At the same time, its
unique features of solids-free bridging and using aphron-type
structures for sealing the permeable zones were considered to
better control potential formation damage through easier
removal and smaller drop-down pressure. As a comparison, a
conventional bridging agent employed by a standard drill-in
fluid will not get removed from the productive formation
4
J. Montilva, C.D. Ivan, J. Friedheim and R. Bayter
unless a mechanical operation or an acidization process will be
performed. The main aphronizer surfactant was reduced in this
application from 1.0 lb/bbl to 0.75 lb/bbl in order to minimize
crude oil–mud emulsion.
As previously described in this paper, most of the
structures in the Lake Maracaibo field are located in the
normal and low-pressure sections covering the Miocene and
Eocene formations. Because of this geological structure
sequence, an extra casing run was usually required to drill and
case off the normal pressure section (Miocene), significantly
increasing operating costs. .
The aphron-based system was re-formulated to drill
through both low-pressure and normal pressure formations,
responding to permeable formations sealing requirements and
hole stability issues. The system was formulated as a solidsfree system using NaCl or KCl as weighting agents. Several
pilot tests were performed to evaluate the stability of the
system in the presence of salt. The test results showed no
unusual instability of the system. The maximum density used
to date is 11.5 lb/gal when incorporating NaCl salt. The TJ
1349 and TJ 1348 wells were drilled using this formulation.
Those wells are the first ones to drill with just one bit size/one
interval diameter in both the normal and subnormal sections,
thereby avoiding an extra casing run.
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system. This could be caused by the high concentration of
surfactant required to create and keep the aphron structures in
the drilling fluid system. During the field trials in Lake
Maracaibo, a compatibility test was performed prior to any
application using crude samples from offset wells and, if
emulsion was identified as a potential problem, the mud
system was treated with defoaming/anti-emulsion agents.
The driving forces behind using the aphron-based drilling
fluid system were to increase the overall profitability of the
Lake Maracaibo mature field through cost-effective drilling
operations, reduce downhole losses, and improved primary oil
recovery. The main achievements of using the aphron-based
system can be summarized as reduced drilling days (from 33
to only 13 days), savings of one to two casing strings per well,
increased cost efficiency through saving from not requiring
underbalance drilling equipment and overall improved well
productivity / oil recovery.
Acknowledgements
The authors wish to thank the management of both PDVSA
and M-I L.L.C. for permission to present this paper. A special
thanks goes to Mary Dimataris and Jim Redden from M-I
L.L.C. for professionally revising this paper.
References
Lessons Learned, Special Considerations, and
Conclusions
Any time drilling operations are conducted in a very narrow
pore pressure/fracture gradient window environment, the
hydraulics calculations are of paramount importance. The
aphron-based system appears to be a multiphase system, but
there actually is no clear model for modeling multiphase
hydraulics calculations for drilling fluid applications.
However, according to the comparison between the APWD
data and the single-phase hydraulics calculations performed
with the modified power law model, the aphron-based system
hydraulic behavior is equivalent to a polymer system. Fig. 11
presents this comparison.
Regarding the bridging capacity of the system, the
optimum system performance was obtained when the aphron
concentration was kept between 8% to 14% by volume.
However selection of the optimal aphron concentration will
depend on the formation characteristics (pore or fracture size,
pore pressure) and hydrostatic pressure. Until sufficient data
are collected for fine tuning, a minimum of 12% will be
required for any “wildcat”-type application. The aphron
concentration is controlled with the aphronizer surfactant
concentration and low-shear-rate-viscosity (LSRV) control
(higher than 50,000 cP).
Another important lesson learned from applying this
technology in Lake Maracaibo was the necessity to determine
and field-test the potential crude oil–mud emulsion. Even
though this crude-mud emulsion has not been a problem in the
field (no formation damage or production impairment related
to in-situ emulsion was recorded), in laboratory conditions, the
aphron-based system seemed to have a higher tendency to
emulsify the crude oil as compared to a standard biopolymer
1.
2.
3.
4.
Sebba, F.: Foams and Biliquid Foams – Aphrons, John Wiley &
Sons Ltd, 1987.
Clunie, J.S., Goodman, J.F. and Symons, P.C.: “Nature”, 216,
1203 (1967)
Scriven, L.E., and Sternling, C.V.: “Nature”, 187, 186 (1960)
Ivan, C.D., Quintana, J.L., and Blake, L.D.: “Aphron-Base
Drilling Fluid: Evolving Technologies for Lost Circulation
Control,” SPE 71377 2001 SPE Annual Technical Conference,
New Orleans, Louisiana, Sept30 –Oct3, 2001.
SI Metric Conversion Factors
bbl x 1.5897 E-01 = m3
°F x (°F-32) x 5/9 = °C
ft
x 3.048 E-01 = m
gal x 3.785 E-03 = m3
in. x 2.540 E-02 = m
lb x 4.536 E-01 = kg
lb/bbl x 2.853 E+00 = kg/m3
lb/gal x 1.198 E+02 = kg/m3
lb/gal x 1.198 E-01 = Specific Gravity (sg)
OTC 14278
Aphron Drilling Fluid: Field Lessons From Successful Application in Drilling Depleted Reservoirs in Lake Maracaibo
5
Land
Lake
Table 1 – Formulation of a typical aphron system
Component
Base fluid
(freshwater or
brine)
Soda ash
Biopolymer blend
Polymer blend
Functions
Provides continuous
phase for system
Formulation
0.974 bbl/final bbl
Hardness buffer
Viscosifier
Fluid-loss control
and thermal
stabilization
pH control
Aphronizer
Biocide
pH buffer
Surfactant
Biocide
0.25 lb/bbl
5.0 lb/bbl
5.0 lb/bbl
Upper
Lagunillas
Middle
Lagunillas
Bachaquero
Lower
Lagunillas
Laguna
Laguna
Lower
Lagunillas
0.5 lb/bbl
1.0 lb/bbl
5.0 gal/100 bbl
Lower
Lagunillas
La Rosa
Misoa
Upper B
Intermediate
Sta. Barbara
Misoa
Lower B
Table 2 – Offset wells general data
Well
no.
123
131
230
290
769
765
Target
zone
C-4
C-4M
C-5
C-5
C-4
C-4m
Depth
(ft)
5,775 – 5,791
5,960 – 6,006
6,562 – 6,619
6,547 – 6,600
5,770 – 5,780
6,110 – 6,279
Pressure
(psi)
1,279
1,215
1,578
1,342
1,076
864
Temperature
°F
197
196
208
206
190
194
4000’
Misoa C
Miocene/Eocene Unconformity
Eocene Formation
Miocene Formation
Producing Interval
Fig. 2 – Geological cross-section through the lake and land
formations
6000’
8000’
9000’
8000’
10000’
9000’
6000’
8000’
5000’
4000’
Tia Juana (TJ/LL)
Lagomar (VLA)
0
40
80
Km
Lagunillas (LL)
La Salina (PB/TJ)
Bachaquero (BA)
Maracaibo
Major Faults
6000’
Unconformity Datum
Fig. 1 – Various fields operated in Lake Maracaibo
Fig. 3 – Structure of colloidal gas aphron1
6
J. Montilva, C.D. Ivan, J. Friedheim and R. Bayter
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Fig. 4 – Structure of standard foam1
Fig. 6 – The aphron energizing process
Annulus
Higher Pressure Zone
Micro-environment
p
Formation
Lower Pressure Zone
Fig. 5 – The gas-core aphrons can lump together, creating large
aggregates and these macro-structures behave in the same
manner as the individual aphron
Fig. 7 – When the bit enters a low-pressure zone, the
energized aphrons aggregate instantaneously within the
formation, creating a microenvironment bridge, preventing
invasion of whole drilling fluid, filtrate and solids
OTC 14278
Aphron Drilling Fluid: Field Lessons From Successful Application in Drilling Depleted Reservoirs in Lake Maracaibo
7
RFT
Well
RFTData
Data -–VLA-1321
well VLA 1321
Mud Gradient
5500
5500
5500
5600
5600
5600
5600
5700
5700
5700
5700
DISCORD.
5800
5800
5800
5800
MISOA/C-4U2
5900
5900
5900
5900
C-4U3
6000
6000
6000
6000
C-4M
6100
6100
6100
6100
C-4L
6200
6200
6200
6200
6300
6300
6300
6300
C-5U2L
6400
6400
6400
6400
C-5U3
6500
6500
6500
6500
6600
6600
6600
6600
6700
6700
6700
6700
6800
6800
6800
6800
LA ROSA
BASAL
C-5U1
C-5U2U
C-5L1
C-5L2
C-6U1
Fig. 8 – Repeat Formation Tester Data (RFT)
Depleted sections
Low pressure and fracture
gradient intervals
La Salina – Eocene
(B-5-X, B-6-X etc.)
Drill-in applications
La Salina – Miocene (LL-03)
Tia Juana – Miocene (LL-05)
Solids free formulation
Hollow glass spheres
formulation
Aphron-base system application evolution – Lake Maracaibo
Depleted sections
Low pressure and very low
fracture gradient intervals
Normal/low pressure
sections – high density
applications
Mud weight up to 11.5 ppg
La Salina – Eocene
(B-5-X, B-6-X etc.)
La Salina – Eocene
(B-5-X, B-6-X etc.)
Hollow glass spheres and
CaCO3 formulation
NaCl, KCl, CaCO3
Fig. 9 – Aphron-base system evolution in Lake Maracaibo
0.41
0.41
0.41
0.39
5500
0.37
Mud Gradient
0.33
0.31
0.24
0.15
Formation Gradient
7.9
7.8
7.3
7.5
2157
1981
1520
1126
846
Formation Gradient
Mud
Weight,ppg
Mud weight (ppg)
@ surface
Pore Pressure (psi)
0.19
Pore Pressure
8
J. Montilva, C.D. Ivan, J. Friedheim and R. Bayter
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Micro-fractures
Field: B-6-X.25; Well TJ-872; Depth: 4345 ft
Fig. 10 – The micro-fractured low-pressure/low-fracture gradient permeable
formations are typical for the depleted reservoirs in the Eocene sections.
These formations have the fracture gradient around 9.0-ppg equivalent mud
weight and are showing several in-situ fractures
Hidraulics Evaluation
Mud weight
Mud
Weight
(ppg)
ppg
7
8
9
10
7,0
4.200
4.250
Mud
Weight
ECD Comparison
APWD Vrs Calculated Data
8,0
9,0
10,0
ppg9.0
8.0
10.0
ECD Comparison
APWD versus Calculated Data
(ppg)
surface
Surface mud
density readings
4.300
H
Depth , ft
4.350
ECD
ECD
4.400
_____APWD data
____
ECD
δH
Typical drill
Ripiosstring assembly
4.450
APWD Data
------Calculated data
- - - Calculate
4.500
Fig. 11 – Comparison between the APWD data and the single-phase hydraulics calculations performed with the modified power law
model, which shows that aphron-base system hydraulic behavior is comparable with polymer system calculations.