^{1}

^{2}

^{2}

Reservoir quality from cored intervals has traditionally been described by grouping similar intervals according to rock type. The main shortcoming of this static modelling approach is that it lacks clarity and it is not conducive for setting up a dynamic simulation model. The alternative is to use a modelling approach based on Hydraulic Flow Zone Units (HFZUs). First proposed in the late 1980s and extensively published in the early 1990s such formulation uses the well-known Carman-Kozeny (C-K) equation. More recently, this approach has been extended to cover a wider range of geological formations with diverse pore structure types. In using a HFZU approach, a pre-processing step is customarily undertaken to first overburden correct the data and where necessary also to correct for the Klinkenberg effect (lower permeability formations, lab testing with gas). The study presented compares corrected and uncorrected data sets, to see if correction alters the overall outcome of HFZU analysis. Specifically, data sets are compared at three different conditions: ambient, overburden (only) corrected and finally data that has been corrected for both, overburden and Klinkenberg effects. In all cases it is the Flow Zone Indicator (FZI), an index representative of formation quality that is tracked, together with the type of relationship. Several comparative analysis examples are given for diverse formations. The results show that uncorrected data can yield a different correlation and FZI, especially for intervals that include low permeability samples. Results indicate that Overburden and Klinkenberg corrections should be applied before HFZU analysis.

Hydraulic Flow Zone Unit analysis was first proposed in the late 1980s and in the early 1990s several definitive papers were published [

Before conducting geological zonation using a HFZU approach it is important to make environmental corrections (for pressure and fluids), in order that valid parameters may be derived for dynamic reservoir simulation, effectively describing in-situ reservoir conditions. In particular if Special Core Analysis (SCAL) plugs are utilised (plugs used for capillary pressure and relative permeability measurement), all Routine Core Analysis (RCA) plugs need to be at least “overburden” corrected, a process described in detail below.

The initial purpose of the well-known Carman-Kozeny equation was to predict permeability as a function of pore structure parameters. However, the equation is quite complex and difficult to handle. The development of the final equation was a development over two decades, first by Kozeny and then later refined by Carman:

Kozeny equation:

where the pore characteristics parameter H_{c} has a value of 2 - 7.

Carman-Kozeny equation:

For definition of variables, see the Nomenclature towards the end of the document.

More recently this formulation was modified to be suitable for hydraulic zonation, see for example Amaefule et al. 1993 [

where:

Reservoir Quality Index

Porosity Group

Flow Zone Indicator

In 2011, Nooruddin et al. proposed a modification to the C-K equation, incorporating a lithology factor “a” and cementation exponent [

Equation (7) may be used to form a modified HFZU formulation, extending the original formulation by Amaefule et al. [

where:

Modified Flow Zone Indicator

If a formation interval has a cementation factor exponent (m) of 1, Equation (8) becomes identical to Equation (3).

The first step in HFZU analysis is to choose an appropriate interval for analysis based on geological description (deposition and facie). Grain size and sorting (related to pore throat size and variation) are also useful to consider, if they are available. It should be noted that FZI is also a measure of grain size and the determination of this parameter for each plug , as well as its variation with depth are very indicative of quality changes for a particular formation interval. For some interesting case histories untilising the above mentioned methodology see for examples [

To determine the actual relationship for a chosen interval, all data points for the interval are plotted on a log(RQI) versus log(PG) graph. Before proceeding further, the data should be quality checked for erroneous values, after which a cut-off may be applied to identify non-net sub-zones. The final step before establishing a relationship is to identify outliers (data that scatters widely from a trend) and such data may be removed if justified. A line of best fit is drawn over the remaining, selected points. If the goodness of fit, indicated by R^{2} is over 0.5 and the slope is between 0.75 and 1.25, the zone is C-K compliant. If R^{2} is over 0.5 and the slope is greater than 1.25, the interval is C-K non-compliant. A slope significantly less than unity (say less than 0.75) has no physical meaning and is typically observed for a statistically insignificant data set of very few points. For a full treatment of various geological situations, including C-K non-compliant zones, see [

^{2} of 0.88 and slope of 1.04. The C-K line has also been “reverse” modelled into a curved relationship in the lower, conventional plot.

interval with R^{2} of 0.92 and slope of 2.99.

Laboratory and the in-situ reservoir condition may differ. Typically, most RCA samples are measured in the lab at ambient conditions, while a small number are also measured at elevated pressure, so called Overburden (OB) conditions. The choice is mainly cost related, where ambient samples are significantly less costly. In order to make appropriate use of all measured data, correlations for per- meability and porosity need to be established for the smaller data set; such relationships are subsequently used to correct the majority of ambient data. As demonstrated below, this correction should ideally be applied before performing HFZU analysis. From analysing of many tests, it could be verified that the most suitable relationships are Linear and Power. It should be mentioned that these correlations are not universal; each data set requires specific parameters.

Figures 3-6 show examples of Linear and Power, OB correction relationships

for a specific data set. In this particular case, results suggest that the most

suitable correlation for permeability is Linear and for porosity it is Power, based on R^{2} and the number of points (outliers) omitted but there is relatively little difference in accuracy in this particular case.

OB correction tends to decrease both permeability and porosity data simul- taneously, leading to a modification in FZI value but not the HFZU correlation.

A second correction (permeability only) may need to be performed in certain cases, usually subsequently to OB correction, correcting for the so called

Klinkenberg effect, 1941 [

The Klinkenberg effect is more severe for low permeability samples (also at low pressure), while for samples greater than 1000 mD, the effect is negligible. Consequently, for samples with a wide range of permeability, the Klinkenberg correction not only decreases FZI values but also changes the slope of HFZU relationships.

The Laminaria oil field is located in the Timor Sea and a very comprehensive RCA data set is available for the Laminaria-2 (Lam-2) well: 361 measured plug samples covering an interval of 125.4 m. Ambient measurements were performed for all samples, horizontal air permeability and helium porosity at 400 psig. A sub-set of 174 samples were chosen for OB testing at 3950 psig. Before conducting HFZU analysis, all ambient data were corrected to OB conditions using a Power correlation for permeability and Linear relationship for porosity. The correlation equations used for correction are:

Klinkenberg correction was subsequently applied using the square-root model, Florence et al. 2007, [

A detailed HFZU analysis was performed for the Lam-2 well after application

of the corrections noted above. This analysis was guided by core photos, detailed core description, core photo-micrographs and scanning electron micrographs. A total of 19 HFZUs were identified for further study of OB and Klinkenberg correction effects, as summarised in

As indicated above, the change in slope due to OB correction is insignificant (average change less than 2%). The FZI value increases by less than 5% for OB correction alone. The specifics would be dependent on reservoir and laboratory testing conditions. A larger difference between ambient and OB pressures would yield a larger increase in FZI value.

Klinkenberg correction, on the other hand, may lead to more significant changes in both, the correlation and FZI values of individual HFZUs. For the case of Lam-2, the average increase in slope is 12%, while the average FZI decreases by 10%. Again, the precise statistics depend on specific lab and re- servoir conditions, as well as the (range of) samples.

Depth (m) | HFZU | Uncorrected | OB Corrected Only | OB and Klinkenberg corrected | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

From | To | Type | Slope | FZI | Type | Slope | FZI | Type | Slope | FZI | |

3210.22 | 3215.65 | 1 | C-K | 1.10 | 3.984 | C-K | 1.08 | 4.08 | C-K | 1.20 | 3.72 |

3215.9 | 3218.5 | 2 | C-K | 1.21 | 6.417 | C-K | 1.22 | 6.66 | C-K | 1.30 | 6.20 |

3218.91 | 3224.5 | 3 | Non-C-K | 2.55 | 12.419 | Non-C-K | 2.52 | 13.10 | Non-C-K | 2.60 | 12.67 |

3225.74 | 3231.07 | 4 | C-K | 1.20 | 9.198 | C-K | 1.19 | 9.62 | C-K | 1.27 | 9.17 |

3232.33 | 3237.4 | 5 | Non-C-K | 2.76 | 2.818 | Non-C-K | 2.75 | 2.85 | Non-C-K | 3.43 | 2.22 |

3243.95 | 3250.65 | 6 | Non-C-K | 2.42 | 8.564 | Non-C-K | 2.35 | 9.38 | Non-C-K | 2.74 | 8.05 |

3250.9 | 3254.25 | 7 | C-K | 1.21 | 14.197 | C-K | 1.18 | 15.12 | C-K | 1.24 | 14.46 |

3254.45 | 3258.1 | 8 | C-K | 0.93 | 6.865 | C-K | 0.92 | 7.12 | C-K | 0.97 | 6.75 |

3258.95 | 3265.2 | 9 | Non-C-K | 2.29 | 17.734 | Non-C-K | 2.2 | 18.99 | Non-C-K | 2.31 | 18.16 |

3265.41 | 3270.96 | 10 | Non-C-K | 2.79 | 6.609 | Non-C-K | 2.27 | 6.86 | Non-C-K | 3.03 | 6.18 |

3271.15 | 3276.45 | 11 | Non-C-K | 2.27 | 1.794 | Non-C-K | 2.25 | 1.81 | Non-C-K | 2.83 | 1.25 |

3276.8 | 3279.45 | 12 | Non-C-K | 3.06 | 0.997 | Non-C-K | 3.25 | 1.00 | Non-C-K | 4.66 | 0.59 |

3279.79 | 3284.41 | 13 | Non-C-K | 1.35 | 2.897 | Non-C-K | 1.36 | 2.93 | Non-C-K | 1.55 | 2.55 |

3284.6 | 3294.9 | 14 | C-K | 1.04 | 18.949 | C-K | 1.01 | 20.12 | C-K | 1.04 | 19.54 |

3297.45 | 3300.44 | 15 | Non-C-K | 2.95 | 17.717 | Non-C-K | 2.89 | 18.76 | Non-C-K | 2.99 | 18.18 |

3309.8 | 3312.45 | 16 | Non-C-K | 1.98 | 3.873 | Non-C-K | 2.01 | 3.96 | Non-C-K | 2.20 | 3.50 |

3315.66 | 3322.8 | 17 | C-K | 1.22 | 10.458 | C-K | 1.21 | 10.98 | C-K | 1.25 | 10.57 |

3359.1 | 3365.7 | 18 | Non-C-K | 1.96 | 8.275 | Non-C-K | 2.02 | 8.60 | Non-C-K | 2.15 | 8.13 |

3365.99 | 3369.31 | 19 | Non-C-K | 1.81 | 5.929 | Non-C-K | 1.83 | 6.14 | Non-C-K | 1.99 | 5.66 |

1) Overburden correction decreases both permeability and porosity of the samples, typically resulting in small increases in FZI values, but does not have a significant impact on the slope of HFZU relationships.

2) Klinkenberg correction decreases the permeability values (only), typically resulting in more significant modifications in both: the correlation and FZI values of HFZUs, especially for intervals that include low permeability samples.

3) It is important to perform Overburden and Klinkenberg correction (where appropriate) before final HFZU analysis, in particular when integrating SCAL plugs.

The authors acknowledge the early work by Chengzhi Yuan and Nhan B Truong in studying many data sets and deriving suitable OB correction correlations and experimenting with Klinkenberg corrections.

Hoang, T.G., Beh- renbruch, P. and Huu, M.T.D. (2017) Defining Reservoir Quality Relationships: How Important Are Overburden and Klinkenberg Corrections? Journal of Geoscience and Environment Protection, 5, 86-96. https://doi.org/10.4236/gep.2017.52007

a =Lithology factor in Nooruddin et al. equation

FZI =Flow Zone Indicator

F_{s} =Pore throat shape factor

H_{c} =Kozeny pore structure parameter

k =Absolute permeability

k_{Amb} =Ambient permeability

k_{OB} =Overburden corrected permeability

log =Logarithm base 10

m =Cementation factor in Nooruddin et al. equation

RCA =Routine Core Analysis

RQI =Reservoir Quality Index (or hydraulic radius)

R^{2} =Standard measure of accuracy in fitting a relationship

SCAL =Special Core Analysis

S_{gv} =Surface area to grain volume ratio