*In part 2 of this article, Part 1 was first published in the March 2010 issue of ROGTEC Magazine, we look at the results & conclusions from the statistical analysis of Caspian Sea Morphometrics & Stochastic Modeling *

**Olubiyi Ishola** – biyiishola@yahoo.com

**Results & Conclusions**

The measured data reveals that the Volga delta channel ranges from 0.28 to 24.03 km in length, with a mean length of 5.41 km (Fig 5a).

The mean channel length of the hierarchy grouping ranges between 1.32 and 18.06 km. The values of the mean lengths are highest up in hierarchy 3, and lowest down the channel hierarchy 15, indicating that there are some decrease in mean length down the hierarchy (Table 5.1).

The standard deviation of the length of the channel (L) is 4.38 km (Appendix 1). The standard deviation ranges between 0.3 and 4.72 km in the hierarchy groupings, with the largest value at the top of the hierarchy and the lowest at the base (Table 5.1).

The sinuosity of the Volga delta channels range from 1 to1.5, with a mean sinuosity of 1.1.

The mean sinuosity of the hierarchy grouping ranges between 1 and 1.34 (Table 5.1). The sinuosity value is highest in hierarchy 3 and lowest in hierarchy 15, indicating a decrease in mean sinuosity down the hierarchy. This decrease is not seen in hierarchy 11 and 12 (Table 5.1).

The standard deviation for the sinuosity of the channels in the Volga delta is 0.09 (Appendix 1), and ranges from 0 to 0.1 in the hierarchy groupings (Table 5.1).

The Volga delta channels measured ranged from 70m to 833 m in width, with a mean width of 248 m and a standard deviation of 162m.

In comparison, the data from the enlarged section worked on from the Volga delta (Fig 5b) reveals a range of 0.23 to 13.42 km for channel length, a mean length of 1.61 km. The sinuosity from the enlarged section ranges from 1 to 1.33 with a mean sinuosity

of 1.07

The mean length and mean sinuosity and standard deviations of channels having similar hierarchy from the enlarged section of the Volga delta map are illustrated in Table 5.2.

The plots of length versus sinuosity, length versus hierarchy, hierarchy versus sinuosity, hierarchy versus width and sinuosity versus width of the Volga delta channels all gives a scattered graph. The R-squared values of the graphs below ranges between 0.002

and 0.12

The results of the bar chart and cumulative frequency curve of the length, width, hierarchy and sinuosity of channels in the Volga delta are shown on the plots in the figures below.

**Interpretation of results**

The results obtained from the statistical analysis are interpreted as follows; The R- squared values obtained from the scatter plots all suggest that there is no strong relationship between the variables; length, sinuosity, width and hierarchy of the Volga delta channels when plotted against each other. This is because the R-squared values obtained for all the plots are approximately zero (Figures 5.1-5.5, and 5.11-5.13).

This implies that these variables can be treated as independent and can be placed as separate entities when building a reservoir model.

Table 5.1 shows the distribution of the mean length and mean sinuosity of channel in the Volga delta as we move down the hierarchy. The value of the length in Hierarchy 3 which is 18 km suggests a major channel length. The mean channel length within the hierarchy order of 4 to 13 indicates that majority of channels within this range of hierarchies comprise major channels and branching network of distributaries which suggests movement from an upper to a lower deltaic plain environment. While the mean and standard deviation values of the mean length and sinuosity of channels in the hierarchy order from 14 to 15 suggests channels with sheet sands or lobes.

The mean length of 5.41 km when compared with the standard deviation of 4.38 km indicates that there is a wide deviation from the mean length of channels in the Volga delta. This is due to the large difference between both values, and the fact that the range of values for the channel length is distributed far from the mean value. Based on the values of mean and standard deviation, the range of channel length in most part of the Volga delta is from 1.03 to 9.79 km.

The cumulative frequency distribution indicates that majority of the channel lengths in the Volga delta are short, having an inter-quartile range of 5.25 km and median of 4 km in length (figure 5.7). The bar chart also shows a decrease in the frequency of channels with longer lengths. This suggests that the probability of getting a lower channel length is higher, while the probability of getting channels with higher length is low.

The mean sinuosity of 1.1, when compared to the standard deviation of 0.09 signifies a narrow deviation, and that most of the sinuosity values of channels in the Volga delta are closely distributed near the mean. This is due to the small difference between the standard deviation and the mean values. The river pattern is characteristic of Straight to low-sinuosity braided channels. Pattern adjustments measured as sinuosity variation are closely related to the type, size, and amount of sediment load. They are also related to bank resistance and to the discharge characteristics of the stream. The relationship between channel slope to sinuosity in an experimental river was elaborated by Schumm and Kahn (1972). Also from a research carried out by Sarker et al (1999), it was inferred that the river reduces its slope (in response to reduction in water and sediment supply upstream) by becoming more sinuous. It also endorses the observation of Adams (1919) that a distributary becomes more tortuous during their process of declination. From my results, I can conclude that most of the channels in the Volga delta have a high discharge rate.

The Sinuosity values of the channels relates to the volume of water discharged and subsequently the sediment load. This is typical of a lower delta plain environment and lower gradient of the slope. The sinuosities of the channels are straight to low sinuous.

The area extent to the lower delta plain is common where the seaward gradients of the river and channel delta are low. Most commonly in these environments, channels become more numerous and often show a bifurcating or anastomosing type on plan view. These patterns are typical of the Volga delta and can be seen from the satellite image. From the standpoint of the sand body formation, bay fill deposits, which often form thin clastic wedges, stacked, one on top of another and separated by inter-distributary bay and marsh deposits. This gives an insight into the type of heterogeneities to expect and input when constructing an object based model. Also the sinuosity is related to gradient and the volume of water discharge but independent of other variables.

The mean hierarchy of 9 and a standard deviation of 2.5 indicate that there is a moderate deviation from the mean, giving a hierarchy range of 7-12.

The bar chart reveals that most of the channel hierarchy have a normal (or symmetric) distribution, with the skewness approximately equal to zero (Figure 5.9). It can be seen that the hierarchy range from 6 to 12 are the most frequently occurring. This is also evident from the cumulative frequency plot.

The bar charts reveal a positively skewed distribution for the length, width and sinuosity of channels in the Volga delta (Figure 5.7, 5.8, 5.10 and 5.14). This indicates that most of the length, width and sinuosity of channels in the Volga delta fall within the low values, less than the mean value.

The limit of resolution of data made it difficult to determine the true mean and standard deviation of majority of the channel width in the Volga delta. But based on the result obtained, the mean width of 248 m when compared with a standard deviation of 162 m reveals a wide deviation from the mean, with a range from 86-410m. Most of the channel width that could not be measured fall within the range of 70m (51m for enlarged part) or less due to the limit of resolution on the satellite image of the delta (Appendix 1 & 3).

The cumulative frequency curve of the width of channels in the Volga delta shows that about 50% of the channels have a width of 70 m or less (51 m on the enlarged section) to 140 m. The inter-quartile range is 175 m. It also implies that the probability of getting channels with lower width is higher than getting higher channels.

From the bar chart and cumulative frequency of the sinuosity in figure 5.10 it can be interpreted that the sinuosity range from 1 to 1.8 for most of channels, followed by 1.1 to 1.2, while the least occurring sinuosity is between 1.22 to 1.4.

The cumulative frequency plot reveals that about 50% of sinuosity fall within 1-1.1, which implies that the channels have mainly low to moderate sinuosity.

Previous studies by Fielding et al, 1987 utilised dataset from width, depth and thickness of fluvial channel sandstones to show the relationship between sand body geometry and fluvial channel type. Cross plots of various channel types (such as low sinuosity channel, braided, meandering and anastomosed channels) where made to obtain width to thickness ratio and depth versus thickness. Their graph resulted in a scatter plot which shows that there is no relationship between thickness and width of channels. When compared with the dataset collected from satellite image of the Volga delta more attributes such as length, width, sinuosity, hierarchy and the drainage pattern of channels can used. However, the dataset does not provide measurements of channel thickness.

Problems with morphometrics from satellite includes poor resolution of the image, and the fact that what is in between the channels can only be based on assumptions as it might not be closely related to the real scenario.

**Application to reservoir modelling**

The dataset collected can be utilised in subsurface studies during modelling to give a general idea of the spatial distribution of sandbodies, channel geometries and connectivity which are often below seismic resolution and cannot be accurately predicted on logs.

Various parameters such as length, sinuosity and width can be input into the model independently, without worrying about the position they are in the hierarchy.

The morphometric datasets can be used to generate a stochastic model in IRAP RMS, Petrel & other reservoir modelling software using the facies channel and other techniques. The dataset will serve as a guideline for models generated in IRAP/other modelling software as inputs of various channel parameters (Length, sinuosity and width) will give a true representation of reservoir heterogeneities.

The shape, reservoir distribution and the nature of connectivity in which the dataset can be applied is typical of a low energy or mud delta, with many bifurcating distributary channels which are straight to sinuous, with discontinuous sands and mud at the shore line. This is typical of the modern Volga delta, and other examples include the Mississippi, Orinoco and Lena; all of which are river-dominated.

From the dataset obtained the, possible sand body types, which may have been deposited in the system are Major channel belt sand deposits, overbank or distributary channel sand, and lobes/sheet sands with swamp or marsh deposits.

In a large reservoir such as those of the productive series of the Caspian Sea, the dataset can be used to define the geometry of the Volga delta which will signify where in the reservoir distribution is a major channel sands or overbank/branching channel sand.

Based on the dataset obtained, the mean sinuosity of 1.1 can be modelled effectively in IRAP for all parts of the delta. This is due to the low standard deviation of 0.09 and the value of sinuosity 1.1 represents low to moderate sinuosity typical of the Volga delta. The modelling will be based on the bed load characteristics inferred from the sinuosity variations, the environment of deposition and comparison with analogue fields such as the Mississippi delta.

**Conclusions**

» The quantitative data will be useful in object based modelling of the Caspian Sea reservoirs and modelling reservoirs with systems similar to those of the modern Volga delta e.g. Mississippi, Orinoco, & Lena (all river dominated).

» The statistics from the data combined with well log & seismic data can be used to populate a reservoir to create a more detailed & accurate subsurface flow model.

» The dataset allows us to collect reservoir analogues in assessable areas and also give a general idea of the spatial distribution of sandbodies in areas below seismic resolution.

» The length, width and sinuosity of channels in the Volga delta can be input into a model independently irrespective of the position they are in the hierarchy.

» The dataset can be synthesised into cumulative probability curves which provide a quick look at P10, P50 & P90 of reservoir character.

» The dataset collected can be used to generate an object-based model in softwares such as IRAP or petrel, as inputs of variables; length, width, sinuosity will give true representation of reservoir heterogeneities.

» Measurements of quantitative architecture derived from seismic data in fluvio-deltaic systems can be integrated with measurements collected from the satellite image of the Volga delta to better improve the quality of the reservoir models.

» The use of sedimentological analysis, core reports and well logs will further assist modelling reservoirs, when combined with the dataset collected.

» More study of several datasets in fluvial deltaic facies is recommended to provide more quantitative geomorphology.

**Reference**

Bryant, I.D. and Flint, S.S., 1993. Quantitative clastic reservoir geological modelling: problems and perspectives: In Flint, S.S and Bryant, I.D., eds., The Geological Modelling of Hydrocarbon Reservoirs and Outcrop Analogues, Int. Ass. Sedimentologists Spec. Pub. 15, Blackwell, Oxford, p3-20.Chambers, J.,

Cleveland, W., Kleiner, B., Tukey, P., 1983. Graphical methods for data analysis, Wadsworth.

Fielding, C. R., Crane, R.C., 1987. An application of statistical modelling to the prediction of hydrocarbon recovery factors in fluvial reservoir sequences. In: Recent Developments in Fluvial Sedimentology (Ed. By Ethridge, F.G., Flores, R.M., Harvey, M.D.) Society of Economic Paleontologists and Mineralogist, Spec Pub. 39. 321-327

Galloway, W.E., 1981. depositional architecture of Cenozoic Gulf Coastal Plain fluvial systems. In: Recent and Ancient Nonmarine Depositional Systems: models for exploration (Ed. By F.G., Ethridge and R.M., Flores). Soc. econ. Miner., 31, 127-156. Tulsa.

Haq, B.U., Hardenbol, J., and P.R. Vail, 1988, Mesozoic and Cenozoic chronostratigraphy and cycles of sea-level change, in Wilgus, C.K., Hastings, B.S., Kendall, C.G.St.C., Posamentier, H.W., Ross, C.A., Van Wagoner, J.C., eds., Sea-level change: an integrated approach: SEPM Special Publication 42, p. 40-45.

Isaaks, E. H., Srivastava, R. M., 1989, An introduction to applied geostatistics: New York Oxford University press,

pp. 10-21

Jones, R.W., and Simmons, M.D., 1996, a review of the stratigraphy of eastern Paratethys (Oligocene-Holocene): Bulletin of the Natural History Museum (Geology Supplement), v. 52, p. 25-49

Kroonenberg, S.B., Simmons, M.D., Overeem, I., Hinds, D., Aliyeva, E.,Svitoch, A.A., Rusakov, G.V., 2001, The recent Volga delta as an analogue for the Productive Series in the South Caspian Basin. Expanded abstract, EAGE Amsterdam June 2001.

Kroonenberg, S.B., Overeem, I., Rusakov, G.V., Svitoch, A.A., 2001, Impact of Sea-Level change on river delta development: lessons from the Caspian. ICSF, Amsterdam July 2001.

Kosarev, A.N.,Yabblonskaya, E.A.,1994. The Caspian Sea. SPB. The Hague, 259 pp.

Mathword, 2005,

http://mathworld.wolfram.com/Skewness.html

NASA;

http://www.loc.gov/exhibits/earthasart/images/eaa-37s.jpg

Overeem, I., Kroonenberg, S.B., Veldkamp, A., Groenesteijn, K., Rusakov, G. V.,

Svitoch, A.A., (accepted for publ. 2002). Small-scale stratigraphy in a large ramp delta: recent and Holocene sedimentation in the Volga delta, Caspian Sea.

Pidwirny, M., 2005, Stream Morphometry: in Chapter 10: Introduction to the

geography.net)

Schmaltz, J., 2005, www.parstimes.com/MODIS/CaspianSeaTerra.jpg

Weber, K., J., Van Geuns, L.C.,1989. Framework for constructing clastic reservoir simulation models. SPE paper 19582 presented at Annual Technical Exhibition, San Antonio.