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An Analysis of Rock Typing Methods in Carbonate Rocks For Better Carbonate
Reservoir Characterization : A Case Study of Minahaki Carbonate Formation,
Banggai Sula Basin, Central Su...
Conference Paper · September 2016
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2. An Analysis of Rock Typing Methods in Carbonate Rocks
For Better Carbonate Reservoir Characterization : A Case
Study of Minahaki Carbonate Formation, Banggai Sula
Basin, Central Sulawesi
Merandy Palabiran 1, a)
and M. Nur Ali Akbar 2, b),
Sesilia Nandya Listyaningtyas 3, c)
1
Institut Teknologi dan Sains Bandung (ITSB)
2
Institut Teknologi dan Sains Bandung (ITSB)
3
Institut Teknologi dan Sains Bandung (ITSB)
a)
Corresponding author: merandypalabiran@ymail.com
b)
mn.aliakbar@gmail.com
c)
nandya_sesilia@yahoo.com
Abstract. Rock typing is very helpful in building a static and dynamic reservoir model for simulation job. Together with
doing reservoir characterization, we can estimate the reservoir reserves and predict reservoir performance with more
precisely and accurately. Several model of rock typing methods have been developed by many experts, but most of them
are not consistent to define rock types based on both geological and engineering features in carbonate reservoir rocks. So
we need a study to look at the level of consistency and suitability of a method of rock typing that applied to a field.
The object of this study is carbonate reservoir rock in Minahaki Formation, as a part of Banggai Sula Basin, Central
Sulawesi. This is a kind of reservoir rocks which most complicated to define rock types, it is because carbonate rocks is
largely controlled by its diagenesis. The method used in this study is by doing rock typing on routine core data with five
different methods which are commonly used by petrophysicists to do rock typing in a reservoir rock, they are Hydraulic
Flow Unit (HFU), Global Hydraulic Element (GHE), Pore Geometry Structure (PGS), Jennings-Lucia, and Winland R35
method. We look a consistency of each method by comparing Leverett J-Function curve that generated from Pc of each
rock type which has been determined by each method. The result presents that the best rock typing method is the method
which has concept based on integration of geological description with engineering hydraulic features, so it is very
consistent when it is compared with its own J-Function.
By the result, we can further know which rock typing method is precise to use in a carbonate reservoir characterization
based on the fundamental of M.C.Leverett theory, especially for this object of study.
Keywords: Rock typing, carbonate rocks, Leverett j-function, reservoir characterization.
3. INTRODUCTION
Core data is the data that very important and meaningful in reservoir characterization of oil and gas. Basically,
the data log which obtained from wells must be evaluated toward data from core sample analysis. In common case,
core data can be used for rock classification process (rock typing) based on its geological (lithotyping) or
petrophysical (petrotyping) characteristic (Archie et al, 1942). Rock typing on core samples is very helpful in
reservoir static and dynamic modelling. Together with doing reservoir characterization, we can estimate the
reservoir reserves and predict reservoir performance with more precise and accurate. Several model of rock typing
methods have been developed by many experts, but most of them are not consistent to define rock types based on
both geological and engineering features in carbonate reservoir rocks. So we need a study to look at the level of
consistency and suitability of a method of rock typing that applied to a field.
Reservoir rock in G-Field is dominated by carbonate rock in Minahaki Formation. Carbonate rock is a kind of
reservoir rocks which complicated to do a rock typing, it is because most of carbonate rocks is largely controlled by
its diagenesis. Because of that, we need to determine the best rock typing methods which are common used in
carbonate rock characterization based on the existing concepts. The result of each rock types will be compared with
Leverett J-Function curve that generated from capillary pressure (Pc) data which has proved the consistency of rock
typing method based on geological and engineering features (El-Khatib, 1995).
The result is, the best rock typing method is the method which has concept based on integration of geological
description of pore with petrophysical description of flow unit, so it very consistent when it compare with its own J-
Function. By the result, we can further know which rock typing method is precise to use in a carbonate reservoir
characterization based on the fundamental of M.C.Leverett theory, especially for this object of study.
The method that used in this paper are literature study and data analysis in order to give a solution based on
existing concepts to solve the problem.
METHOD
The availablity data for this study are core data with 74 sample core plugs from Routine Core Analysis (RCA),
10 sample core plugs from Special Core Analysis Laboratorium (SCAL), and several thin section data analysis.
From those data, we obtained 74 porosity and permeability from RCA, capillary pressure (Pc) curve and 10 relative
permeability (Kr) curve from SCAL. Another data that used are thin section data from petrographic analysis.
The data available are processed and then applied to each rock typing methods that used in this study. And
finally, the rock typing result will be compared in position trend of each rock typing methods in J-Function. The
following Figure 1 is a methodology flowchart of this study.
FIGURE 1. Methodology Flowchart of Research
4. DISCUSSION
I. Rock Typing Method Description
1. HFU (Hydraulic Flow Unit)
The equation from Kozeny and Carman have been modified become the mean hydraulic radius concept
(Amaefule et al, 1993). The purpose is to develop identification technique and rock characterization by Hydraulic
Flow Units (HFU) concept based on similarity of pore throat geometric. The parameter used to support this research
are porosity, Klinkenberg permeability (kklink), texture and mineral content from core sample of clastic and
carbonate. The assumption used in this study are rounded and uniform grains. The result of this study shows that the
value of flow zone indicator (FZI) were different for each HFU group. FZI is unique parameter which combine
geological attribute from texture and mineralogy as based for Hydraulic Unit determination (Amaefule et al, 1993).
Below is the rock typing by HFU method that come from concept of Kozeny-Carmen permeability equation:
S g
τ
F s
φ
φ
φ
k 1
1
(1)
and it was modified by Amaefule et al to define rock typing with :
k
RQI 314
.
0
(2)
RQI or Reservoir Quality Index is parameter of Kozeny - Carman equation that represent size of pore geometry in
μm unit, where k unit is in milidarcy, and
1
z
(3)
where ∅𝑧 is Normalized Porosity Index and ∅ is in fraction. Therefore, if equation (2) divided by equation (3)
become:
z
RQI
FZI (4)
and FZI:
S g
F s
FZI
1
(5)
equation (4) set to logarithmic become:
FZI
z
RQI log
log
log
(6)
So we can plot RQI vs Qz in log-log plot and obtaine the FZI as intercept value at ∅𝑧 = 1. To determine FZI
value in that plot, we made a straight line with a gradient of 0.5 qualitatively. Data in RQI vs ∅z plot which located
in one straight line expressed in same FZI, so that we can obtaine FZI value for each data and reveals them in
hydraulic unit group.
This method emphasized in reservoir engineering aspects while geologi aspect did not accommodate. As a result,
this method is not always successful when applied to carbonate rock because of high heterogeneity. (Wibowo and
Permadi, 2013).
2. GHE (Global Hydraulic Element
Basically, GHE method has similar concept with HFU method. But, GHE method has been developed by Peter
Corbett,et al, in 2004, by quantifying the value of FZI in the base map on a regular basis. Therefore equation (4)
modified into:
5.
0314
.
0
1
2
FZI
k (7)
As a result, this method determine FZI value for represent each kind of GHE.
TABLE 1. FZI Value for Each Kind of GHE by Peter Corbett,et al
GHE FZI
10 48
9 24
8 12
7 6
6 3
5 1.5
4 0.75
3 0.375
2 0.1875
1 0.0938
FZI value which selected in GHE were considered based on:
Porosity and permeability range in typical reservoir
Allowances of variability data from perspective engineering in the hydraulic elements of porosity
Requirement to discretization of space between porosity-permeability to eliminate unimportant value from
engineering perspective, variation or noise, significant variation from core plug set data.
3. PGS (Pore Geometry Structure)
In PGS method, there are correlation plot between Pore Geometry and Pore Structure, where Pore Geometry =
√
𝑘
∅
as y-axis, and Pore Structure =
𝑘
∅3 as x-axis. Pore Geometry is a representative of the hydraulic unit which
previously relegated by Amaefule et al. Pore Structure is a variable that developed by Permadi & Susilo (2009) as
hydraulic conductivity, that represent pore structure which affected by characterisctic of geological process in
reservoir rock. That correlation was derivatived from fractal permeability concepts. PGS Method was developed
again by Wibowo & Permadi (2013) and then generate a type curve for rock typing in reservoir rock. Therefore,
PGS method determine the rock type by plotting correlation between √
𝑘
∅
vs
𝑘
∅3 from RCA and SCAL data on rock
type curve of PGS method.
4. Jennings-Lucia Method
Jennings and Lucia (2003) determined rock classification based on correlation of rock fabric description which
defined as representative of petrophysical characteristic (initial porosity and saturation) that previously developed by
Lucia (1999). In this research, rock classification based on correlation between interparticle porosity and
permeability.
Interparticle porosity is porosity in carbonate matrix which not affected by vugs (touched or separated).
According to Lucia (1999), interparticle porosity has an important role in hydraulic flow of carbonate rock which
defined as:
v
v
inp
1
(8)
Then correlated with the size of the particles that have been analyzed visually under the microscope that do
simultaneously with percentage description of vug system in carbonate rock. Therefore acquired rock classification
6. based on rock fabric from correlation plot between interparticle porosity and permeability. To determine rock fabric,
we can use this equation below:
inp
wi
inp
d
c
d
c S
ln
ln
ln
exp
1
1
0
0
(9)
This research assumes that capillary pressure did not give big influence in saturation at zone which lies above
transition zone, pore system is not dominated by vugs and the rock has low porosity value until intermediate (5%-
30%) with pore system is interparticle porosity. In case, pore system of carbonate reservoir rock is very
heterogeneous and dominated by intraparticle porosity and vugs. Jennings & Lucia (2003) states that this generated
model should be revalidated with a reservoir which has better and complete data. This research shows that rock
physics characterization especially rock fabric have correlation with rock petrophysics and become fundamental in
application of carbonate reservoir characterization include rock typing.
5. Winland R35 Method
In 1972, H.D Winland has done a research about correlation between pore throat, permeability, and porosity. In
his research, Winland collect 300 sample from various formation and rock age, which consist of 50% clastic rock
and 50% carbonate. From 300 sample, 106 carbonate sample used for MICP test, and the rest for primary data such
as routine, SEM, etc.
Pore throat model of Winland used planar void concepts as a pore throat model in carbonate rock, as we can see
on Figure 2. Winland states that pore throat is the function of crystal size from mineral which compose carbonate
(Gunter, G.W et.al, 2014).
FIGURE 2. Planar Void model for carbonates as opposed to the pinching and swelling model (Winland, 1972)
From that concepts, Winland noted that large crystals were connected by large pores, and small crystals were
connected by small pores. So he noted, if intercrystalline pore system which filled by intergranular and solution
pore, the one which control outflow and inflow into large pore are the smallest pore system.
Winland prove his concept with the result from MICP test such as porosity, permeability and percentile 30, 35,
40, and 50 of radius of effective porosity. Statistically, there are pore throat regression with 35 percentile which have
best correlation with porosity and permeability value. As a result, Winland generates correlation between effective
pore size, permeability and porosity as follows:
log
864
.
0
log
588
.
0
732
.
0
35
log
k
R (10)
Where:
R35 : effective pore throat radius (microns) at 35%
Φ : core porosity (percent)
K : absolute permeability to air (mD)
From that equation, rock typing can be done with calculating R35 value for each sample, and then classify
sample which have same R35 value, to help this process we can make an iso-pore throat line in a graph.
II. A Case Study in Minahaki Formation
In this study, rock typing has been done for 74 plug sample from routine core analysis with all method which has
mentioned above.
For HFU method we generate a plot as follows (Figure 3):
7. FIGURE 3. Rock Typing Plot of HFU Method
From the plot by HFU method we obtained 7 type of hydraulic unit which represent as rock type for Minahaki
Carbonate Formation in G Field.
Table 2. FZI Value for Each Hydraulic Unit from rock typing by HFU method
HU FZI
1 4.5
2 1.7
3 0.52
4 0.38
5 0.25
6 0.1
7 0.053
For GHE method, we plot the data in type curve which developed by Peter Corbett, et al (2004), Rock Type
obtained from sample distribution in region of specific colour which categorized as Global Hydraulic Element by
Peter Corbett.
FIGURE 4. Plot of Rock Typing by GHE Method
From the plot by GHE method, we obtained 7 Global Hydraulic Element, there are GHE 8, GHE 7, GHE 5, GHE
4, GHE 3, GHE 2, and GHE 1. So there are 7 type of hydraulic unit which represent as rock type for Minahaki
Carbonate Formation in G Field but have different FZI range compare with HFU method.
TABLE 3. FZI Value for Each Hydraulic unit from Rock Typing by GHE Method
FZI GHE HU
12-24 8 1
6-12 7 2
1.5-3 5 3
0.75-1.5 4 4
0.375-0.75 3 5
0.187-0.375 2 6
0.093-0.187 1 7
8. For Jennings-Lucia, plot the correlation between interparticle porosity and permeability on log-log plot. Then
override the sample data from SCAL in the same plot (Figure 4). As we can see on Figure 4, Rock Type of G Field
have been distributed into all type of Rock Fabric, there are Rock Fabric 1 until Rock Fabric 4, but domination of
distribution lies around Rock Fabric 3 and 4. While distribution of sample data from SCAL dominate at Rock Fabric
3 and 4, and some data lies on Rock Fabric 2.
FIGURE 5. Rock Typing Plot by Jennings-Lucia Method
For PGS method, Rock Type determined by plotting correlation between √
𝑘
∅
and
𝑘
∅3 from RCA and SCAL data
on Type Curve of PGS Method. Figure 6 show plot by PGS Method.
FIGURE 6 Rock Typing Plot by PGS Method
From the plot by PGS Method, we get the rock type equation from regression line of type curve which stated by
Wibowo & Permadi (2013) to represent each rock type. Result of rock typing and regression equation can be seen
on Table 4.
TABLE 4. Regression Equation for each rock type which stated by Wibowo & Permadi (2013)
Rock Type Rock Type Equation
RT-1 √
𝑘
∅
= 0.5534(
𝑘
∅3
)
0.405
RT-2 √
𝑘
∅
= 0.4886(
𝑘
∅3
)
0.385
RT-3 √
𝑘
∅
= 0.4314(
𝑘
∅3
)
0.355
RT-4 √
𝑘
∅
= 0.3809(
𝑘
∅3
)
0.345
RT-5 √
𝑘
∅
= 0.3363(
𝑘
∅3
)
0.325
RT-6 √
𝑘
∅
= 0.1804(
𝑘
∅3
)
0.225
9. At the end for Winland R35 Method based on radius of effective pore, we obtained distribution of porosity and
permeability sample at iso-pore throat line as we can see on Figure 7.
FIGURE 7. Rock Typing Plot by Winland R35
From the plot we get rock type based on similarity of effective pore size for Minahaki Formation by Winland
R35 Method as Table 5.
TABLE 5. Domination of R35 Value in distribution for each sample which classified into each rock type
Winland R35
(effective pore size radius)
Rock Type
25 micron RT1
10 micron RT2
4 micron RT3
3 micron RT4
2 micron RT5
1.5 micron RT6
1 micron RT7
0.3 micron RT8
0.09 micron RT9
The table shows that there are 9 rock type for all core data, while data from SCAL lies around RT 5 and RT 6.
III. J-Function Validation with SCAL Data
J-Function is empirical equation by M.C.Leverett (1940) which is configuration from data normalization of
capillary pressure (Pc) to the water saturation (Sw). Curve of J-Function can represent the phase and pattern of fluid
flow in a pore rock by showing capillary pressure performance in the rock. Capillary pressure in the rock which has
similarity in flow unit will lie on one straight line in curve of J-Function. Therefore, if the normalization data of
Capillary Pressure J(Sw) from rock lies on one straight line in curve of J-Function, they can be classified into rock
that have similar diagenesis process, in other words they are in one rock type (El-Khatib,1995).
In this research, we observed performance of J-Function from SCAL data which has been done rock typing for
all mentioned methods. Good rock typing method will show regular pattern of J-Function for each Rock Type which
generated by each method. Curve of J-Function will have a pattern where J(Sw) that formed inclined to the left if the
rock have large pore throat and inclined to the right if the rock have small pore throat.
J-Function generated for all rock typing method after we have done rock typing for SCAL sample. After Rock
Type from all method have been classified, then calculate J(Sw) using Pc, k, and Φ for each sample with the
following equation :
k
Pc
Sw
J
cos
21666
.
0
(11)
Where :
Pc : Capillary Pressure which have corrected
σ : Interfacial Tension
θ : Interfacial Tension Angle
10. After J(Sw) have been obtained, then plot J(Sw) vs Sw for each rock type that has been determined from each
method to generate curve of J-Function as we can see on the graphs below :
FIGURE 8. (a) SCAL data Plot in Leverett J-Function, (b) Consistency of J-Function Curve by HFU Method
FIGURE 9. Consistency of J-Function Curve (a) GHE Method, (b) Jennings-Lucia Method
FIGURE 10. Consistency of J-Function Curve (a) PGS Method, (b) Winland R35 Method
We can see that J-Function which generated by HFU method has no good order, where HU 3 overlap on HU 4
and HU 5. Eventhough HU 4 and HU 5 have a good order where flow unit of HU 4 better than HU 5, however,
several data of HU 3 lies on the right HU 5 which cause an inconsistency of HFU method.
In the GHE method, the J-function curve that generated was not well ordered for each rock type. GHE 5 is the
rock type which has the highest flow unit so it should be located on the left side but it becomes on the right side.
GHE 4 is overlap with GHE 3. GHE 3 which has the lowest flow unit should be located on the right side but it
becomes on left side and the center. It can be seen on Figure 9a.
11. Rock Fabric method by Jennings-Lucia generate a better curve of J-Function which has low Rock Fabric (Rock
Fabric 3&4), but Rock Fabric 2 which has high Rock Fabric becomes on the right side, this make Jennigs-Lucia
method becomes inappropriate with J-Function which stated by M.C.Leverett (1941). So this method is still can’t be
applied well to reservoir that have high heterogeneity such as this field case. However, it indicated that Rock Fabric
concept has a good correlation between geology and petrophysics concept, especially for homogeneous rock. It can
be seen on Figure 9. There is similarity between J-Function that generated by GHE method which based on flow
unit and J-Function that generated by Jennings-Lucia which based on Rock Fabric.
For this study indicate that PGS method is the best method compared to other methods. This can be seen in the J-
Function curves generated by PGS method in Figure 10.a, that has a good order of RT 5, RT 6, to RT 8. Where it is
a good order for each petrophysical characteristics, especially for unit flow in stone.
Winland R35 method classify core data from SCAL that available in this study into 2 rock type based on value of
R35. However, the J-Function curves generated by Winland R35 was not too well ordered, where some of sample in
RT 5 is overlap to RT 6. Therefore, rock classification by Winland R35 is not too compatible for this case.
However, another result study of Winland R35 method by Potter (2010) shows that correlation of Winland R35
method which use effective pore size from permeability and porosity at percentile 35 of pore size, has a relation with
flow unit of rock, that Winland (1972) equation have similar to Kozeny-Carman equation and representated by curve
of J-Function his study. So that can prove Winland theory to be on and it can be seen too from sample of SCAL in
this case study that has a good ordered on J-Function curves on Figure 10.b (If it considered that the sample make
deviation not exist).
Another look at core sample more particularly, we found that inconsistency that happened in some methods such
as HFU, GHE, Jennings-Lucia, and Winland R35 caused by core sample number 45. Below is the characteristic of
core sample number 45:
TABLE 6. Characteristic of Core Sample Number 45
Sample ID
Depth Permeability Porosity
Description
feet mD fraction
45 7365.3 5.131 0.09 LS (PS) : crm, hrd, dru calc, calc, vuggy, om
In term of geological description, sample number 45 has same relative characteristic with other sample. Where it
is kind of packstone based on Dunham classification (1962), and there are secondary porosity of vuggy system like
the other sample.
By doing a cross-plot between porosity and permeability using all sample, and refers to research by Nelson
(1994,2005) and Akbar et.al (1995) about behaviour of porosity and permeability based on its lithological
characteristic (Figure 11a.), so there is indication that microfracture was exist in the sample (Figure 11b.).
Furthermore, we observed petrophysical characteristic from sample 45, it shows that the sample has very low
porosity but high permeability value. This may affect hydraulic unit of rock where the capillary pressure value of
sample 45 looks good with Swirr value is 0.28 or 28%. However, Swirr value of sample 45 lies under Swirr value of
another sample which classified to vuggy pore system until packstone by Nelson (1994, 2005) and Akbar et.al
(2005). It can be seen on Figure 12.
This confirm that geologic system around location of sample 45 was affected by microfracture, and it influence
flow unit of that sample. It indicates that several rock typing method very affected by fracture system, so that it can
cause inconsistency in doing rock classification based on hydraulic characteristic, it represented by inconsistency of
J-Function curve.
12. FIGURE 11. (a) Classification Behaviour of Geological Characteristic based on Porosity-Permeability by Nelson (1994,2005)
and Akbar.et al (1995), (b) Result of Classification based on Nelson (1994,2005) dan Akbar.et al (1995) Method for Minahaki
Formation.
FIGURE 12. Curve of Capillary Pressure from SCAL Data
We try to review rock typing Method by PGS that have consistent result of J-Function curve for each rock type
that has been generated. In PGS research, Wibowo & Permadi (2013) identification of microfracture cases in the
sample used (Figure 13a), and then it became consideration to develop PGS Method. Wibowo & Permadi classify
rock into 2 kind of microfracture, there are active microfracture as microfracture which affected hydraulic of rock,
and nonactive microfracture as microfracture which not affected hydraulic of rock. Based on that classification,
sample number 45 is included in active microfracture group (Figure 13b). It represented curve of capillary pressure
which shows good hydraulic ability, with Swirr value is 0.28 or 28%. Therefore it’s confirm that sample number 45
very affected by microfracture system, especially active microfracture. Furthermore, it confirmed that PGS method
has strong reason to characterize reservoir which affected by microfracture and another heterogeneity parameter,
especially in carbonate rock.
13. (a) (b)
FIGURE 13.. (a) Behaviour of microfracture classification on PGS Type Curve by Wibowo and Permadi (2013), (b)Plot result
from all sample included sample 45 on Type Curve PGS
CONCLUSION
1. Rock typing method which based on flow unit concept such as HFU, GHE, and Winland R35 is better to
applied in homogeneous reservoir (example : clean sandstone reservoir) in order to characterize hydraulic
concept of rock, however the method is not valid when applied in very heterogeneous reservoir, like this
case study on carbonate rock reservoir.
2. Rock Fabric method by Jennings & Lucia (2003), method still can not be applied well to reservoir that have
high heterogeneity (touching vug, high separated vug, porosity > 30%, etc) like this case study, because its
inconsistency show at J-Function. However in this study, it can make better consideration of the Jennings-
Lucia method which based on Rock Fabric that rock fabric has contribution to flow unit which can be
confirm by capillary pressure concept on J-Function, it can be seen at behavior of rock fabric 3 and 4 which
has a good order at its J-Function curve, which somehow Jennings and Lucia method has a similiar
arrangement with GHE method J-Function that based on flow unit as well.
3. In this G Field case, PGS method is the best method that can explain flow hydraulic concepts in reservoir,
therefore it can make consideration that hydraulic conductivity (that flow unit controlled by pore geometry
and pores structure) concept is good enough to represent flow hydraulic concept, especially in carbonate
rock.
4. Good rock typing method is method which can explain capillary pressure concept on J-Function well.
SUGGESTION
1. To use the rock typing method, we have to look at the availability and suitability of the method to the case.
2. Advanced study is needed with additional core data to make more.
3. Advanced study to compare other rock typing method to explain characteristic of carbonate reservoir,
especially for this field case.
ACKNOWLEDGMENTS
Authors would like to thanks for Indonesian Research and Development Center for Oil and Gas Technology for
supporting, when the first author in internship program, so this article can be finished. Also for Prof.Pudji Permadi
Ph.D as a lecture in Petroleum Engineering at ITSB for the deep discussion about Kozeny-Carman concept.
59 7377.30 17.77 0.23761 8.646697163
60 7377.80 9.42 0.2537 6.092830683
61 7378.60 0.01 0.05252 0.436352674
62 7379.50 15.78 0.22716 8.333861579
63 7380.20 7.58 0.21288 5.966365705
64 7380.90 6.84 0.18631 6.060011551
65 7381.55 3.18 0.17704 4.236165383
66 7382.40 10.23 0.23884 6.545257462
67 7383.30 13.29 0.26503 7.081598671
68 7384.30 5.36 0.19936 5.184690855
69 7385.40 5.23 0.23449 4.720875414
70 7386.40 4.62 0.23632 4.42198989
71 7387.20 6.60 0.25429 5.093023529
72 7387.65 5.02 0.23501 4.620853047
73 7388.30 0.64 0.2299 1.669781054
74 7388.80 8.55 0.26954 5.631125934
49 7368.8 20.35 0.259 8.864052604
42 7362.5 19.64 0.251 8.84573411
18 7344.85 18.65 0.291 8.005582245
1 7334.35 18.46 0.229 8.978382578
8.864053 67 7383.3 13.29 0.265 7.081733079
8.845734 57 7375.7 9.6 0.249 6.209204206
8.005582 22 7347.9 9.09 0.256 5.958843218
8.978383 56 7375 6.04 0.234 5.080547787
7.081733 45 7365.3 5.13 0.091 7.508237235
6.209204 4.424508016
5.958843 1 36.1 0.159 15.08286694
5.080548 4 58.0 0.173 18.31010966
7.508237 7 75.3 0.172 20.92344851
4.424508 8 144 0.189 27.63920638
3 80.3 0.160 22.40256682
10 118 0.183 25.33922853
#DIV/0!
#DIV/0!
4.62 0.236 4.424508 351.4843 RT06
Active Microfracture
Nonactive Microfracture
14. REFERENCES
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