1/44 revised : 09/12/2016 rabiller geo-consulting · thomeer's models or on the use of...

1(c) Rabiller Philippe Rabiller Geo-Consulting

1/44 revised : 09/12/2016

In this presentation the characterization of facies is discussed only in terms of porosity, or rather storage capacity and in terms of capacity to let the fluid flow, through the permeability and pressure mechanisms, in drainage conditions. Obviously those parameters are meant to be used as input for a full characterization of rock facies through their integration with logs.

Logs, actual depth and well names are intentionally omitted to avoid any confidentiality issue.

The most obvious goal of the method is to derive from MICP measurements:• The total Porosity as investigated by the Mercury injection • The porosity that contributes to flow through permeability/pressure mechanism in

drainage condition. • The permeability and the radius of the pore throat class contributing most to

permeability. Indeed this radius is the parameters which condition the flow at a given position above the FWL.

The sealing efficiency of the rocks can also be derived from the proposed method using the logic developed by Winland and Pittman. This specific subject was addressed in a poster presented by the author at the AAPG/EAGE workshop "Hydrocarbon Seals of the Middle East" held 18‐20/01/2016 in Muscat.


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The presentation will cover 4 groups of points and will deliberately focus on how to use MICP to calibrate RCA Poro Perm measurements so that the latter can be used as proxy of MICP. Particularly we discusses the FZI method in the light of MICP.

Example of PSD facies will be shown to illustrate how the MRGC‐CFSOM clustering method can be used to define Porous Network facies, without any user bias. For the sake of clarity of illustration, the example used is deliberately based on a very small set of data points (138) from a single wells.

Because logs cannot be used here it is not possible to illustrate the up‐scaling of PSD by means of the method described in "The Iterative Use of Clustering and Modeling to Improve Permeability Prediction"Philippe Rabiller, Jean‐Pierre Leduc, Total Fina Elf Shin‐Ju Ye, Halliburton Energy Services; SPWLA 42nd Annual Logging Symposium, June 16‐20, 2001

Also it is not the core of the subject, we illustrate how saturation height modeling can be carried seamlessly because of the design of the method.


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This slide illustrates the back bone of the flowchart of the method and the way the results of the MICP curves interpretation are displayed with respect to depth.

The software used is Geolog (Paradigm Geophysical). All the processes are proprietary, they were created using the Geolog/Loglan module which is the standard Geolog programming module. The process is fully integrated, all the data are stored in the Geolog data base and can be displayed in Frequency, Xplots and layouts.

In a first step, carried in a single well mode, the data are loaded into the Geolog Data base. Then the Saturation and the Pressure are re‐sampled on a standard Pressure (Radius) scale. This operation • Does not require any assumption or user defined parameter;• Results in an array log which is comprised of 240 bins and can be displayed both in X‐

plots and most importantly in Layouts for easy visualization with any other core or log data indexed with respect to depth. The number of bins of the array can be changed easily.

Although this number of bins is a remnant of windows 32 bits, still in use in 2009 during the early stage of this development, it is a good comprise for multi‐well projects with data sets composed of MICP measurements whose number of pressure steps may range from about 40 up to about 200 with a 0,1 to 60000 psi pressure range. Increasing the number of bins would certainly results in a greater accuracy but at the expense of the compactness of ".well" files.


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Drainage and imbibition curves, as well, can be processed and displayed.

Saturation scale (0‐100) or log10 saturation scale are also available for display and they are used for several trial solutions methods.

Once they are stored in the standard format the suite of the processes can be carried in multi‐well mode.


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Contrary to other processes described in the recent years, and based on the use of Thomeer's models or on the use of Gaussian fitting function to describe the Pore Throat Size Distribution (PSD), no statistical assumption is imposed on the shape of PSD.

Indeed using either Thomeer's model or Gaussian fitting results in a varied number of parameters to describe each subset of the PSD and varied number of parameters simply precludes • the use of clustering or prediction method in a subsequent step. • The use of Histogram upscaling method.

The process embed an automatic • correction for conformance (closure) which can be graphically edited by the user • Detection of the Katz and Thompson Entry and Threshold pressure, which can also be

graphically edited should the user feel the need for it.

Aside of the implementation of the published work of several authors on permeability modeling, the use of trial solution methods is extended to the Purcell method and to the search of the features characterizing the PSD curves : local minima and maxima , inflexion points. The number and position of modes within the PSD is defined from those features.

Implementing the varied methods proposed by: KATZ and THOMPSO, PITTMAN, WALLS & AMAEFULE, NOKKEN & HOOTON , is a way to explore the data and check the consistency and efficiency of the process.


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This slide illustrates how the display of MICP data can be integrated seamlessly with Saturation Height modeling.Because Saturation, PSD and the contribution to permeability: K_Dis and NK_Dis (Normalized K_Dis) of each class of pore throat, are displayed using a Pressure scale which is also a Radius scale, then, if Field/lab conversion parameters and density of fluid (down hole conditions) are known, it is possible to display the Buoyancy pressure developed by the fluids on the same track, partition the array using this pressure pressure and visualize how PSD or Saturation curve are partitioned by the pressure.

The 3rd track from left superimposes the PSD (green wiggle and orange background) with the contribution to permeability of each class of pore throat. It clearly visualizes that not all the pore volume contribute to permeability. Only the largest pore throat classes actually contribute to permeability despite that the volume of pores which can be accessed through them can be relatively small.

On the 4th track 3 DP buoyancy curves computed for varied position of FWL (2580m, 2610m, 2641 m) are superimposed to the K_DIS array and they can be used to partition this array, or simply to check which rock facies will contribute to flow in a specific pressure context.


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This slide illustrate the display of the data used in saturation height modeling.

The background of the leftmost track is color coded for static classes of Pore Throat Size. Using such static classes it is possible, manually or algorithmically, to affix a "name" to each samples however such a classification fails to account for the complexity of the porous network. The sticks on the 3rd track symbolize the classes of PSD to which each sample belongs to.

The 8th track from left display the saturation computed for 3 position of FWL.


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Saturation values are binned on a regular scale function of Pc (I.e.: radius of Pore throat). The number of bins of the array is such that in most cases not all the bins are filled by a value measured in a single pressure step. Bins devoid of value are filled by linear interpolation. In case several pressure steps just fit in the same bin, then only the one with the greatest saturation is retained. Missing values are not a option if use of clustering or prediction methods is considered in a subsequent step.

Once all the bins are filled by linear interpolation the saturation curves are smoothed using a sliding window whose size is user defined and should be kept minimal (default value is 5 bins).

The frequency plot on the left hand side of the slide illustrates effect of binning and smoothing. The average error is centered and its standard deviation is small. The percentage of error is not insensitive to Pore Throat size radius. It is only sensitive to the rapid variations of Saturation in the range of pore throat size close to the entry /displacement pressure. Because an accurate determination of entry or displacement pressure is a must the size of the smoothing window must be kept minimal. (with the default values adopted here the size of the window is 0,125 logarithmic decade).


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This slide is meant documenting the effect of binning Pc value. It is negligible.


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This slide illustrate the accuracy of permeability modeling by Purcell method.

The leftmost X‐plot displays the computed permeability by Purcell method with the RCA permeability measured on same samples.

The rightmost Xplot is a screen copy from a Buiting and Clercke's publication. The red (X‐plot axis) and black frames (data points) are defined on the rightmost X‐plot and transferred on the leftmost to ease the comparison. Buiting and Clercke results are used as a reference for the process we propose here and which provides with a similar match between computed and measured permeability values.


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This slide does not duplicate the previous one although it displays the same X‐Plots.

It is meant to draw the attention on the ways the permeability were computed in the 2 processes and then question the reasons of their differences.

While in the left most Xplot displaying the result of our method the permeability is computed without specifying any subset of PSD, Buiting and Clercke clearly mention that their permeability equation must be applied only on "the largest pore throat system present in our multimodal samples".

Using only the "the largest pore throat system present" requires that this system is delineated and so a rule is set for that purpose. The Purcell permeability model we use eliminates the need for the user to explicitly set up such a rule and defines classes of pore throats – the "porositons" according to the terminology proposed by Clercke.

The fact that the Purcell model, without any intervention of the user, provides with a similar accuracy, is simply understood if one considers that the contribution to permeability is computed for each class of pore throat and the permeability is obtained by their summation. Displaying the contribution to permeability of each class of pore Throat makes it easy to visualize that only the classes of largest pore throat contribute to permeability.

Whatever the method used the results obtained stress the fact that only a fraction, of varied importance, of the total porosity contribute to permeability. Henceforth it is of


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utmost importance to defined accurately this fraction.


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Defining without any user input the class of pore throat size that contribute most to permeability is straightforward using in the framework of Purcell modeling.

Picking the apex of the distribution of the contribution to permeability is possibly the optimal way to pick the upper limit of the pore throat class as it can be compared with the results of the Katz and Thompson trial solution for the Hydraulic conductance and is possibly less sensitive to processing errors than is the Entry or Displacement pressure. Further the difference in porosity values is rather negligible between the two picking options.

The concept of PHI_Z should also impact our way to interpret resistivity Indeed in the invaded zone the filtrate displace only the fluids "within" PHI_Z.

If we can know with some certainty what is the value of PHI_Z in the virgin zone and what is the PHI not invaded by Hc then the Hc content estimation can be improved.


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This slide illustrates graphically how PHI_Z is defined as the set of pore throat whose minimum radius is MHR and the maximum radius is NK_DIS_Apex).

It also shows that Total Porosity and PHI_Z may differ very significantly.

The rightmost track displays "PHI Total" and "PHI_Z" , their difference is emphasized by the orange background between the 2 curves.

The computed and measured permeability are displayed on the last but one right track.


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The frequency plot on the left hand side of the slide shows the distribution of the value of the contribution to permeability by the pore throat size class whose radius is MHR. The median is 0,00773, while the maximum is 0,01454.

The Xplot on the right hand side of the slide displays the radius of MHR on X axis and the radius of the Apex of the Pittman Trial solution. The radius at the Apex of the Pittman trial solution defines the sealing efficiency of a rock, i.e.: the capillary pressure it can withstand and hence the maximum height of the hydrocarbon column it can trap . The Two characteristics are in good agreement.

Thus for practical purpose it is legitimate to consider that pore throat classes whose radius is smaller than that of MHR do not contribute to Permeability.


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The left hand side X‐plot of this slide display the measured (X axis) and the computed permeability using Purcell model. In this case, the permeability was computed using "Total Porosity"

The frequency plot displays the ratio Computed/Measured Permeability in log scale. Note the value of Mean, Mode and Standard deviation.


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The left hand side X‐plot of this slide display the measured (X axis) and the computed permeability using Purcell model. In this case, the permeability was computed using "PHI_Z" porosity.

The frequency plot displays the ratio Computed/measured Permeability in log scale. Note the value of Mean, Mode and Standard deviation.


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The two frequency plots display the ratio Computed/measured Permeability in log scale. • In the left hand side plot the permeability was computed using Total Porosity• In the right hand side plot the permeability was computed using PHI_Z

Note the values of Mean, Mode and Standard deviation for the 2 cases. The use of PHI_Z to compute the permeability provides with a significantly better fit between measured and observed. The average is well centered and the standard deviation is significantly reduced if PHI_Z is used.


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The concept of PHI_Z should also impact our way to interpret resistivity Indeed in the invaded zone the filtrate displace only the fluids "within" PHIZ

If we can know with some certainty what PHI_Z is in the virgin zone and what is the PHI not invaded by Hc then we can better estimate the Hc content


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The two Xplot in this slide display Porosity on X axis and permeability on Y axis. • On the left hand side Xplot the porosity is Total Porosity• On the Right hand side Xplot the porosity is PHI_Z

The color coding is function of the Log10 of The radius of K_DIS apex which is the best characteristic to compare with the FZI functions.

Note that the pattern of color conforms to that of the FZI functions in the right hand side X‐Plot while colors are scattered w/r to FZI functions in the left hand side X

This simple fact together with the observation that the distribution of the contribution to permeability differs significantly from the distribution of Pore throat size support the idea that the usual way to compute RQI and FZI using the total porosity is somehow inappropriate.


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This slide is similar to the previous one and call for the same comments repeated here below for greater convenience. The only difference being that instead of displaying data from a single wells it displays data from 6 different wells. It is important to state that the process of MICP was made in multi‐well modes and that no manual editing of Closure correction and Katz and Thompson entry was made, the Purcell lithological factor is the same for all wells. Despite this multi‐well processing the color pattern remains clear.

The two Xplot in this slide display Porosity on X axis and permeability on Y axis. • On the left hand side Xplot the porosity is Total Porosity• On the Right hand side Xplot the porosity is PHI_Z

The color coding is function of the Log10 of The radius of K_DIS apex which is the best characteristic to compare with the FZI functions.

Note that the pattern of color conforms to that of the FZI functions in the right hand side X‐Plot while colors are scattered w/r to FZI functions in the left hand side X

This simple fact together with the observation that the distribution of the contribution to permeability differs significantly from the distribution of Pore throat size support the idea that the usual way to compute RQI and FZI using the total porosity is somehow inappropriate.


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The two Xplot in this slide display Porosity on X axis and permeability on Y axis. • On the left hand side Xplot the porosity is PHI_Z• On the Right hand side Xplot the porosity is Total Porosity

The color coding is function of the Number of modes observed in the PSD. The greater the number of modes the more complex is the "texture" of the porous network.

There is clearly a pattern in the colors: complex texture is associated with highest values of FZI.

This color pattern explains why it is so difficult to define foolproof PHI‐K laws or equations. If the porous network texture somehow largely controls the distribution of permeability with respect to porosity then it is impossible to find a satisfactory relationship by considering only Porosity and Permeability.


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The frequency plot displayed on the left hand side shows the distribution of the number of modes observed in the PSD. If mono‐modal PSD are the most frequent instances they account for less than half of the total population. Multimodality is not an exception it is rather the rule.

The Xplot on the right hand side displays • Total Porosity on X axis • PHI_Z porosity on Y axis, • The color code is a function of the number of modes – the complexity of the texture

of the porous network.

The Xplot clearly shows that : • PHI_Z is always smaller than PHI_Total – this is simply explain by Purcell's equation

and the fact that the radius at MHR defines the lower limit of pore Throat Size classes contributing to permeability.

• The ratio PHI_Z / PHI_Total decreases with increasing number of modes, that is by increasing complexity of the texture of porous network

The relationship between complexity of texture and PHI_Z suggests that this complexity of porous network, if assess from description of thin section, possibly with automatized analysis techniques, could be used to evaluate PHI_Z even if MICP measurements are not available.


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This slide illustrate further the conclusions drawn in previous slide. The color code is for log10 Permeability.

Clearly the greatest permeability values are dominantly associated to high values of pore network complexity.


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This slide provides graphic material to discuss the possibility to define fixed (static) classes or sets of pore throats, "porositons", characterized by a specific value of their mode, as proposed for example by Clercke for the Ghawar field.

The Frequency plot display the distribution of the radius for all the modes of the PSD. The X‐plot on the right hand size display the permeability computed for each mode (Y axis) versus the radius of the mode, the color code for the number of modes.

In the example above the possibility to define unambiguously such porositons is unclear.


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The slides 22 and 23 were illustrating the fact that the FZI plots are consistent with the FZI concept, developed by J. Amaefule and his coworkers, only if the PHI_Z porosity is used in lieu of the Total porosity. It is deduced from this observation, that, if the Permeabilities computed by means of the Purcell equation fit the permeabilities measured in RCA measurements is because the RCA permeability values are actually constrained by the PHI_Z of the rock samples. The fact that the PHI_Z values are not measured directly in the RCA process does not affect the actual working of the porous network.

In the framework of the above reasoning it can be further deduced that if a relationship between RQI and Permeability can be brought into evidence from SCAL measurements, then RQI (if its actual value is not deduced with accuracy, at least its minima and maxima could be evaluated) could be estimated from Permeability and from the estimated RQI values the range of PHI_Z could be also obtained.

PHI_Z and Total porosity are easily computed if MICP measurements are available and less so if they are not available. It is then highly desirable to find a way to obtain PHI_Z over logged intervals where only RCA measurements are available.

Indeed if such a means is found then it would be possible to • cross‐check and cross validate the actual and predicted values of PSD and PHI_Z ,

measured on SCAL, and the PHI_Z estimated from RCA porosity and permeability. • Try and establish local, regional or general law for deriving PHI_Z from RCA.


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This slide and the 2 next ones expose the steps of the principle of calibration of RQI

The first step consists in defining the trend RQI_SCAL versus Radius at the apex of the distribution of contribution to permeability.

It is preferable to define a trend for the Radiusmax and a trend for the Radiusmin . The trend should not be defined using a regression method, since the residues of the prediction by regression would not be randomly distributed. Indeed the data points, exemplified here and used in view of calibration are not randomly scattered, on the contrary their spread is due to the complexity of the Porous network which control the shape of the distribution of contribution to permeability.


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This slide illustrate the comparison between RQI_SCAL and RQI_RCA computed on the same rock samples.

The scattering of the data points over the Radiusmax is related to complexity of porous network.


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This slides illustrate the principle of the procedure for retrieving RQImax "RCA" from the Raw RQI_RCA, once the trends Radiusmax and Radiusmin versus RQI_SCAL are calibrated. The "raw" RQI_RCA is the one computed using the Total Porosity.


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This slide illustrates how to predict RQI_RCA from RCA poro‐perm using logs as predictors and multiple k‐NN algorithm.

In a fist step an unsupervised electrofacies model is created using the wireline logs.The model allows detecting the major facies boundaries, those creating shoulder effects. After detection of shoulder effects, two options are possible: 1. The RCA in the intervals with Shoulder effects are deleted2. A prediction model is used to restore the logs. In this case all the RCA measurements

can be used.

A k‐NN model is created to predict the RCA poro‐perm . • The k‐NN is used to predict jointly the porosity, the permeability and the electrofacies

of the 1st, 2nd, 3rd,….10th Nearest neighbors (in data space ) of each depth increment. • The RQI is computed for the 1st, 2nd, 3rd,….10th Nearest neighbors and only the values

of the nearest neighbors belonging to the same electrofacies facies ‐ or the facies in its vicinity in data space‐ defined at the specific depth increment are validated and binned in an array log whose Y scale is porosity and X scale is pore throat radius. If 2 values of predicted RQI fit in the same bin their values are cumulated. As a result a proxy of the distribution of contribution to permeability is obtained.

• Because the Y scale of this array log is porosity‐ that is a scalar variable‐ upscaling can be performed.

It is then possible to superimpose on this array the Pcfield, using appropriate scaling.


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The slide illustrate the result of the classification of PSD curves by the MRGC‐CFSOM method.

All the bins of the PSD array are taken into accounts. The unsupervised classification is performed in a data space of 240 dimensions.

• On the left hand X‐plots all the data points are plotted.• On the right hand X‐plots only the points in the inner part of the clusters are

displayed, that is to say the points most typical of each PSD facies.


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The slide illustrate the result of the classification of PSD curves by the MRGC‐CFSOM method. Each facies is shown on a separate X‐plot.

Because the total number of points is rather small the sorting of points does not look optimal in the sense that a number points are grouped in the dark green colored facies as if this facies was kind of dust bin. Indeed if data points are too few and yet they differ significantly then regrouping them is never satisfactory.


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In the left hand X‐plot, the color code symbolize the PSD facies. In the right hand X‐plot, the color code symbolize the number of modes.

The complexity of the porous network is reflected by the PSD Facies.

Note the position of the dark green colored facies, discussed in the previous slide: low porosity and texture of varied complexity.


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The colors are symbolic of facies of "Contribution of PSD bins to permeability " the K_Dis array.


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On the left hand side X‐plot the color code is for log10(FZI) computed on SCAL with PHI_Z . The colors fit the FZI function functions.

On the Right Hand side Xplot the color code is for the facies of K_DIS defined by unsupervised MRGC‐CFSOM method (in the 240 dimensions of the data space) The colors are organized along the FZI functions, the apparent scattering is due to the fact that the clustering takes into account the 240 dimensions defining the distribution while only each samples is plotted using only 2 dimensions: RQI and PHI_Z . Thus the finer scale details contained in the whole distribution are lost and generate this apparent scattering.


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A new way to process MICP "drainage" data was presented. It drastically minimizes the user bias, it does not impose any predefined model to the shape of MICP or PSD curves. Although this was not exemplified here it is suitable for imbibition data.

The method embeds the computation of several parameters characteristic of MICP curves proposed by several previous researchers. The consistency observed between the results exemplifies the robustness of the method

It was shown that the logic of the method allows a seamless integration of Saturation Height modeling together with Permeability modeling and definition of Pore Type by clustering techniques.

The method was used here to subdivide total porosity in 2 components: • PHI_Z which is the porosity which

• contributes to the essential of flow through permeability/pressure mechanisms

• Is accessed through the set of pore throats whose radius is greater then MHR• The second component (it could be termed as PHI_STO) which is the difference

between Phi_Total and PHI_Z • contribute to storage • May contribute to flow by imbibition.

FZI method proposed by Amaefule and his co‐workers should be used with PHI_Z .


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We have briefly exposed the principle of • PHI_Z retrieval from RCA if calibration on SCAL is first performed.• RQI (and then PHI_Z) prediction using k‐NN method and logs as predictors.


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1/44 revised : 09/12/2016 rabiller geo-consulting · thomeer's models or on the use of...

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