Channel Depth vs. Sandstone Thickness

Channel Depth vs. Channel Width

Channel-Belt Width vs. Channel Depth

Channel-Belt Width vs. Channel Width

Onshore UK Carboniferous Analogues

UKCS Well Correlation

Statistical Modelling

Stochastic Modelling Links

Stochastic Modelling References


This work was undertaken to try and provide some constraining data on the expected reservoir architecture of the Carboniferous fluvial-deltaic systems of the UK Southern North Sea. The results were used as input to stochastic models of the then Amoco (UK) operated Cavendish Field and to understand the sensitivities inherent in the reservoir. The only "hard" data available at the time were the preserved sandstone thicknesses in offshore wells and channel architecture from outcrop in what are believed to be analogous depositional systems from the Namurian and Westphalian "A" of the UK Onshore and other areas.



Most fluvial channel deposits occur in laterally confined, elongate belts, recording the limited capacity of the depositing channel to move laterally, perpendicular to its palaeoflow. There is, however, considerable variation in the morphology of modern fluvial channels and, by analogy, ancient examples. The morphology of ancient channel belts is critical in the asssessment of the net reservoir present, the volume of reservoir connected to a given well spacing and pattern and the inter-connectivity between different sand bodies. Based on the observation of modern channels, a number of authors (see Collinson, 1978) have suggested that the width of ancient channel-belts or meander belt amplitude could be predicted from preserved sandstone body thicknesses. The summary below explains the underlying assumptions and how the results might be used in modelling of the UKCS Carboniferous offshore.

Schematic Diagram of River Channel /Meander Belt

Channel Depth vs. Sandstone Thickness

A major uncertainty is the relationship between observed sandstone[1] and the bank-full depth of the formative channel. Since channel systems may accrete vertically as well as laterally, it is likely, in many instances, that channel depths were not as deep as the preserved sandstone would suggest. In other cases, the channel may be partly filled with non-sandstone channel-abandonment facies. Figure 1 illustrates the relationship between sandbody thickness and channel-depth gathered from published data (Fielding & Crane, 1987). The ratio of Channel-Depth : Sandbody Thickness (CDST ratio) varies from an maximum of over 1 : 1 (channel partially filled with abandonment facies) to a minimum of 0.23 : 1 i.e. a preserved sandbody may be as much as 4 times as thick as the channel within which it was deposited, indicating vertical accretion or stacking. In reality, the distribution of the CDST ratios is bi-modal, with a similar distribution in all system types from braided to low sinuosity (Fig.2). The data suggests that systems are often simple (CDST ratio of approximately 1) or variably aggrading (from a minimum CDST of 0.23). The weighted average for this data population is 0.775 with two modal values at 1 and 0.55 : 1 ("Best-fit" of Fielding & Crane).

The relationship can be summarised as:

[Eq. 1] Channel Depth = Sandbody Thickness / [CDST]

where CDST ranges from 0.23 to c. 1

Figure 1: Channel Depth vs. Sandbody Thickness

Figure 2: Channel Depth/Sandbody Thickness Ratio Distribution

The range of values introduces the first uncertainty into the procedure. There is little information as to the CDST ratio which applies in the Carboniferous and it is likely that different sands will have different relationships depending on a number of factors such as accomodation space/subsidence/compaction, sediment supply, gradient and overbank composition.

A range of ratios should be used for sensitivity analysis.

[1] Etheridge and Schumm, (1978) suggested that a compaction factor of 10% is applicable to ancient sandstones and that point-bar thicknesses should be divided by 0.9 in order to approximate bank-full depths. This assumes that relict bedforms represent the fill of the entire channel depth. Compaction has partly been taken into account in both channel and channel margin/bank-full depth measurement in the data of Fielding and Crane, (1987).

Channel Depth vs. Channel Width

Leeder, (1973) published data from modern high sinuosity rivers (>1.7) on the relationship between Bankfull Channel Depth and Bankfull Channel Width (Fig.3).

A wide scatter was observed in the data for low-sinuosity channels although these are generally wider than for meandering ones (on the order of a factor of 10 for a given channel depth).

The relationship derived for high sinuosity channels is:

[Eq. 2] w = 6.8 h ^ 1.54 (StD =0.35 log units)

where w = bankfull channel width

h= bankfull channel depth

Figure 3: Bankfull Width vs. Bankfull Depth - Meandering Rivers

Channel-Belt Width vs. Channel-Depth

Fielding and Crane, (1987) also published data relating a positive correlation between modern and ancient fluvial channel-belt widths and channel-depths for various channel morphological types ranging from braided systems through meandering to anastomosed, straight and incised channels (Fig. 4). They subdivided the population into 5 cases:

1a) An extreme case - straight, non-migrating, incised channels (shoe-string)

Channel-belt Width = 0.01*ChannelDepth^2.9

1b) The upper bounding for meandering channel deposits

Channel-belt Width = 0.95*ChannelDepth^2.07

2a) The best-fit for all collected data - for use if a variety of channel types exist or type is unknown

Channel-belt Width = 12.1*ChannelDepth^1.83

2b) the published, empirical relationship for modern, truly meandering streams; fully developed meandering profiles (Collinson,1978).

Channel-belt Width = 64.6*ChannelDepth^1.54

3) the lower bounding line of all data collected; laterally unrestricted, braided fluvial systems.

Channel-belt Width = 513*ChannelDepth^1.25

From the combination of the relationships above between sandbody thickness and channel-depth and channel-depth vs. channel-belt width, one can calculate the relationship between sandbody thickness and channel-belt width, the aspect ratio (Fig.5 - assumes CDST of 0.55).

Figure 4 : Channel Belt Width vs. Channel Depth

Figure 5 : Channel Belt Width vs. Channel Sandstone Thickness

The data can also be subdivided on the basis of the channel type (braided, meandering etc.). Figures 6 and 7 illustrate the relationship for braided and meandering sub-populations, taken from Fielding & Crane, 1987, with the UK/Eire onshore data added. The onshore data has been collated from proprietary work for Amoex and published papers on the Carboniferous of England and Eire. Sandstone thicknesses described have been converted to channel depth equivalent by using the CDST ratio of 0.55 for the braided subset, 0.755 for the meandering subset. The best-fit lines were produced using Amoex linear robust-fitting techniques. The curves showing +/- 1 standard deviation show the large range in channel width for a given sandstone thickness.

Figure 6 : Channel Belt Width vs. Channel Depth (Braided Systems)

Figure 7 : Channel Belt Width vs. Channel Depth (Meandering Systems)

Best-Fit curves (Fileding &Crane Data only) derived from this approach give different equations for the relationship between Channel-Depth and Channel Belt Width than those derived by Fielding & Crane, (1987) - see above.


[Eq.4] Channel-belt Width = 230*ChannelDepth^1.435


[Eq.5 Channel-belt Width = 49.5*ChannelDepth^1.43

Meander-Belt Amplitude vs. Channel Width

Another approach, summarised in Lorenz et al., (1985), can also be used.

Data published by Leopold and Wolman, (1960) and Carlston, (1965) relates the width of the channel to the width of the meander-belt (channel-belt) (Fig. 8).

Figure 8 : Channel Width vs Meander-Belt Amplitude

The derived relationship from the combined data is :

[Eq. 6] Meander-Belt Width = 7.44 * Channel Width^1.01

Combining the above with the relationship observed by Leeder, (1973)

Eq. 2] Channel Width = 6.8 * Channel Depth^1.54 ]


[Eq. 7a] Meander-Belt Width = 7.44 * (6.8*Depth^1.54)^1.01

Assuming the same same ratio of 0.55 between Channel depth and preserved sandstone thickness as discussed above, this results in:

[Eq. 7b] Meander-Belt Width = 7.44 * (6.8*(Sandstone Thickness*CDST)^1.54)^1.01

Lorenz used a Channel Depth vs. Sandstone Thickness ratio of 1 (Fig. 5). Using a ratio of 0.55 the aspect ratio is similar to Case 2b (Fully Meandering) of Fielding and Crane, (1987). (Figs. 5, 9)

Figure 9 : Meander-Belt Width vs. Sandstone Thickness (calculated).

Onshore UK Carboniferous Analogues

There is a huge volume of published work on the Carboniferous of the onshore UK. However, little of this is specifically on the problems of sandstone reservoir distribution and architecture and AMOCO (UK) commisioned a proprietary synthesis of this work from Collinson Jones Consultants to try and provide some information on the likely lateral extent of the Namurian - Westphalian A reservoir in the UK offshore. This may be available from Collinson Jones Consultants.

The aspect ratio of modern river channel deposits is related to their type ie. braided, meandering etc. There is little agreement in the literature as to the type of depositional system present in the Carboniferous, ranging from braided (Bristow, 1993, Hazeldine, 1983) to meandering (Fielding, 1984). What is clear is that the channel belts, whatever the morphology of the individual channel systems, are of relatively low sinuosity and have a reasonably high aspect ratio, best described by Braided system equations (compare Figs. 6 and 7). The apparent width of the channel belt is probably more related to continued avulsion/channel migration which will, in turn vary throughout the succession due to a number of unpredictable factors. Furthermore, a number of sands, notably the Rough Rock and Kinderscout Grit are effectively sheet sands over large areas (1000 km2 +) and prediction of channel-belt width by reference to unit thickness in this instance is meaningless.

Published palaeogeographic maps for a number of intervals in the Westphalian A (Fielding, 1984a; 1984b) have been used to estimate the spatial distribution of these channel-belts (Fig.10). These channel systems are bounded vertically by laterally continuous and mappable coals with the intra-coal thickness is of the order of 20m (Fig. 11). This work indicates that major channel belts are generally of low sinuosity and are in the order of 2-7 km in width. It also appears from certain of the interval maps where shale "inliers" are present within broader sandstone trends that avulsion of channel-belts has occured, with amalgamation of the belts in certain locations producing wider, composite channel sand deposits

Areal net/gross (the area of sandstone channel belt presence divided by the area without major channel deposits) is in the order of 40-50% averaged over the 5 intervals for which data is available.

Assuming a vertical sandstone/shale ratio within each interval of 50% where channels are present, the average net/gross of the total system would be in the order of 20-25%, similar to the vertical net/gross calculated from offshore wells..

Figure 10 : Westphalian A Channel systems from the Durham Coalfield.

Figure 11 : Westphalian A Stratigraphy - Durham Coalfield.

UKCS Well Correlation

Correlation between UK Southern North Sea wells 43/20b-2, 44/16-2, 44/16-1, 44/16-1z and 44/21b-8 to the east of Cavendish is relatively straightforward using logs and an attempt was made to track the lateral extent of individual sandstones. The results are displayed on Figs. 12 and 13. The aspect ratios are high. This may be explained by:

1) false assumption of bed continuity between wells,

2) distance calculated may not be orthogonal to palaeoflow i.e the sands are the same but the wells are sub-parallel to channel orientation making the apparent channel width seem wider than reality. This does not appear to be true as the wells are broadly perpendicular to the palaeoflow direction (to the SW) obtained from dipmeter and CBIL data.

No such correlation can be made with confidence between wells 43/20b-2 and wells in Cavendish (43/19-1, 2a, 43/13b-4).

Figure 12 : Sandstone Thickness vs. Channel-Belt Width - Estimated Continuity between Offshore wells


The plots of curves relating Sandstone Thickness to Channel-Belt Width, derived from the methods above are shown in Figures 13, 14. As can be seen, there is a wide range in predicted Channel-Belt Widths depending on the type of channel system one believes to be present. This is further exacerbated by the unknown relationship between Sandstone thickness and original channel depth.

The amalgamation of channel-belts is also unknown and is likely to vary due to a number of factors which can not be predicted from available data, if at all.

The data from onshore Carboniferous systems, believed to be similar in depositional architecture to much of the offshore Carboniferous in the Cavendish area, is shown in Figure 13. Although there are ranges of uncertainty in that data, in terms of correlation, sand percentage in each recorded channel system etc., it appears that the average channel belt is relatively wide given the thickness of sandstone recorded.

Bounding curves for this data (Fig. 14), in the absence of other constraints, have been calculated as:


Channel-belt Width = 370*ChannelDepth^1.23 - "Mid"


Channel-belt Width = 27*ChannelDepth^1.9 - "Lower"


Channel-belt Width = 550*ChannelDepth^1.35 - "Upper"

Figure 13 : Sandstone Thickness vs. Channel-Belt Width

Figure 14 : Sandstone Thickness vs. Channel-Belt Width - Estimated Carboniferous Ranges

Statistical Modelling (after Fielding and Crane, 1987)

The documentation below is a paraphrased summary of the work of Fielding and Crane, (1987) and others and contains a brief explanation of the theory behind a computer program "CHANNEL" which may be used to estimate connected reservoir channel-belt sandstone volumes under different well spacings and various depositional system models. The program consists of an "Excell" spreadsheet template which allows the connectivity of sandbodies to be calculated using log-derived thicknesses, representative sandstone thickness/channel-belt width formulae and user-input well spacings. Contact Al Sutter for more information.


The idea of this program is to provide a means of evaluating the ranges of possibilities and sensitivities. Case specific data should be used where available and the limitations clearly recognised.

Statistical modelling of sub-surface sandstone bodies using the above methodology is only applicable to channel sandbodies. Thinner sandstones less than c.2m are likely to be the result of deposition in crevasse-splays, mouth-bar feeder channels or to have limited extent and should not be included. Similarly, thicker sandstones deposited as mouth-bars or of levee origin, common in many coastal plain sequences, are not part of this data set. However, some will contribute to connected reservoir volumes and may also help connectivity between channel sandstones and the results of the process below should be regarded as a minimum figure for connected sand volume. There is no known data on the areal extent of the mouth-bar and crevasse-splay bodies.


Using logs, core etc. all sandstones not considered to be the result of channelised processes or of non-reservoir quality should be removed from the data set.

The predicted channel-belt width for sandstones is generated using the equations discussed above.

Multiplying the thickness of a reservoir sandstone by its predicted channel-belt width gives the cross-sectional area of that sandstone perpendicular to palaeo-flow. Cross-sectional areas of all the sandstones identified may be calculated in control wells or analogous outcrop data and totalled.

If in a sequence, there are n sandstone beds s1, s2,, with thicknesses t1, t2, metres and cross-sectional widths w1, w2, ......wn metres, then the total sandstone cross-sectional area in communication with the well is :

n (Sum)ti * wi i=1

Given that the well information is representative of the sequence in the area, then any hypothetical well drilled through the section will penetrate a set of sandstone beds equivalent in cross-sectional area to those in the type well. Obviously, this does not mean exact stratigraphic correlation between sandstones either in terms of thickness or relative position.

The success rate for penetrating sandstones in the interval of interest between two proposed wells a certain distance apart is then calculated by dividing the cross-sectional area of sandstone hit by the total cross-sectional area of sandstones in existence. Since one is assuming well spacing orthogonal to palaeo-flow, cross-sectional area is proportional to volume, and the "sucess rate" may be regarded as representing reservoir volumes connected to well-bore. It is possible that some of the channel sandstones will be sufficiently wide that they cover the distance between two adjacent wells. This must be compensated for in the model by limiting the width of the sandstones considered to the distance between the wells (in a direction perpendicular to regional palaeo-flow).

Then success rate = n (Sum)ti * Minimum(wi,W) i=1 / n (Sum)ti * W i=1

Where W is the Well Spacing and "success rate" , expressed as a percentage, is defined as "the proportion of the total channel-belt sandstone reservoir volume in a given interval which will be penetrated by planned wells a certain distance apart, perpendicular to palaeo-flow".

The results of this procedure are shown in Figure 15.

Figure 15 : Borehole - Sandbody Connectivity vs. Well Spacing

It is important to remember that further sandstones could be in communication with wells through erosional interconnection between channel-belt deposits or via non- channelised sandbodies.

Theoretical simulation studies indicate that meandering channel-belt sandstones are essentially isolated if they comprise less than 50% of the total interval. Other work suggests that sequences with far lower net/gross may have considerable interconnection between channel sandstones. The data base is poor.


The model and program have a considerable number of limitations which should be borne in mind.

1) Channel-belt "wings" or overbank/minor delta deposits may contribute to sand volume and communication.

2) Sandbodies are not homogeneous reservoir units; barriers to flow/connectivity will exist.

3) Sinuous channel-belts may interconnect with each other at some point either up or down current, thereby increasing connectivity.

4) Faulting may increase or decrease connectivity.

5) The statistical distribution of sandstone bodies does not predict the actual location in space of any particular sandstone body.

6) No account of tectonic control on sandbody geometry / orientation is included.

7) The exact depositional model is unknown and may vary vertically and laterally. Theoretical relationships vary widely dependent on the type of fluvial system used as the model.

8) Channel orientation is critical in assessing connectivity with a given well pattern.

9) All ratios used are based on imprecise and variable data. The ratio of channel depth vs. observed sandstone thickness on which the work is based is the parameter with the biggest impact on aspect ratio and the range is very large. BEWARE!.

Originally compiled by A. Sutter, Feb 1996



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Lorenz, J.C., Heinze, D.M., Clark, J.A. and Searls C.A., 1985. Determination of Widths of Meander-Belt sandstone Reservoirs from Vertical Downhole Data, Mesaverde Group, Piceance Creek Basin, Colorado. A.A.P.G. v.69, No.5, p.710-721

Lowry, P. and Raheim, A., 1991. Characterisation of Delta-front sandstones from a fluvial-dominated delta system. In: Reservoir Characterisation II, eds: Lake, L.W., Caroll, H.B. and Wesson, T.C. Academic Press, Inc.

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Main References

A. Sutter: Feb 2008