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Monday, 29 March 2010

Caspian Sea: Morphometrics & Stochastic Modelling

Many reservoir models rely on populating reservoir zones with objects whose dimensions are taken from statistical databases of analogue sandbodies. While this attributes may be sufficient to characterise single channels, they do not adequately describe branching networks such as deltaic distributary channels.

This study examines morphometrics of deltaic distributary channels using satellite image data from the modern Volga Delta, Russia.

The Volga delta is an extreme example of a fluvial-dominated delta that is characterised by extraordinary pronounced distributary branching. Several reservoir intervals are deposited by the palaeo-Volga Delta in the Pliocene Productive Series reservoirs of the offshore Caspian Sea.

A quantitative database of key geometrical measurements the length, width and sinuosity was collected from the branching network of channels on the satellite image of the Volga delta. The channel segments were assigned hierarchies using an ordering classification system.

Various statistical analyses were carried out to obtain the mean, standard deviation, Inter-quartile range and coefficient of skewness of the length, width and sinuosity of the Volga Delta channels. Also, various cross plots of length, width, sinuosity and hierarchy were made and their R2 values obtained to reveal the associations between these variables.

The statistical analyses reveal that there are no relationships between these variables; length, sinuosity, width and hierarchy.

This implies that these variables can be treated as independent and can be placed as separate entities in object-based reservoir modelling of the Pliocene Productive series reservoirs of the offshore Caspian Sea.

The results enables us to define shapes and dimensions of channel objects for models of the Pliocene Productive Series reservoirs of the offshore Caspian Sea, such as the Pereriv Suite in BP's giant ACG field.

This study, 'morphometrics of deltaic distributary channels for object based reservoir modelling' was undertaken as a three month project in Imperial College as the final individual project for the Imperial College Msc in Petroleum Geoscience.

The aim of the project is to collect a quantitative database of key geometrical measurements of a network of deltaic distributary channels with its case study from the Volga Delta, Russia.

The requirements of the project are as follows:

  • To measure key geometrical/morphometric data for a connected distributary channel network;
  • To compare this dataset to standard statistical databases used to condition object-based models of deltaic reservoirs; and
  • To define shapes and dimensions of channel objects for models of reservoir analogous to the modern Volga Delta (Productive Series reservoirs, Caspian Sea)

Many reservoir models rely on populating reservoir zones with objects whose dimensions are taken from statistical databases of analogue sandbodies. This approach requires: (1) robust matching of the subsurface reservoir interval to an analogue (e.g. ancient systems at outcrops, modern system), and (2) measurements of the key geometrical attributes of analogue sandbodies. Typically, the geometrical attributes of channels in such databases are width/depth ratio and sinuosity. While these attributes may be sufficient to characterise single channels, they do not adequately describe branching channel networks such as deltaic distributary channels. This project will characterise the morphometrics of such network in the Volga delta, an extreme example of a fluvial-dominated delta that is characterised by extraordinary pronounced distributary branching. The results have several applications to several intervals deposited by the palaeo-Volga Delta in the Pliocene Productive Series reservoirs of the offshore Caspian Sea, where the channel dimensions, geometry and connectivity are key unknowns that may have large impact on reservoir behaviour.

Morphometric Techniques
Morphometry can be defined as the measurement of the shape, whereby measurements are then manipulated statistically or mathematically to discover inherent properties. Morphometric techniques aim at developing methods or a set of tools that measures both general and specific geomorphometric features.

In the field of hydrology, morphometric studies were first initiated by R.E. Horton and A.E. Strahler in the 1940s and 1950s. The main purpose of their work was to discover holistic stream properties from measurement of various stream attributes.

The attributes to be first quantified was the hierarchy of stream segments according to an ordering classification system as illustrated in Figure 2.1.

In this system, channel segments were ordered numerically from the stream’s headwaters (i.e. the upper portion of stream's drainage system) to a point somewhere down stream. Numerical ordering begins with the tributaries at the stream’s headwaters being assigned the value of 1. A stream segment resulted from the joining of two 1st order segments was given an order of 2. Two 2nd streams formed a 3rd order stream and this went on. The analysis of the data generated revealed some interesting relationships (Pidwirny, 2005).

R.E Horton applied morphometrics analysis to a variety of stream attributes and from his studies a number of laws of drainage composition were proposed. Horton’s law of stream strengths suggested that a geometric relationship existed between numbers of stream segments in successive stream orders. The law of basin areas indicated that the mean basin area of successive ordered systems formed a linear relationship when plotted on a graph.

These results and studies of other natural branching networks have revealed patterns similar to the stream order model. In morphometry the geomorphological significance of the Hortonian stream-order relationship is limited.

The stream numbering technique used by Horton is quite similar to the technique applied during this study to number and assign hierarchy to channel segments of the Volga delta. In this study, the channel segments were first of all numbered randomly from the first segment to the last seen on a map view of the delta. The ordering of the stream segments according to their hierarchy was then assigned the number '1', from the Volga River, at the apex of the delta.

In a situation whereby a single channel is assigned the value of 1 in the first order in the hierarchy, when it splits or bifurcates into two or three channel segments, they are assigned the value '2' in the second order of the hierarchy. If two of the channel segments converge, the channel segment that results from this is assigned the hierarchy number of the previous single channel that bifurcated. In this way, the ordering according to hierarchy goes on until the last channel segment has drained into the Caspian basin.

Object-based reservoir modelling
Reservoir models are essential tools used during the exploration of hydrocarbon reserves. According to Bryant and Flint, 1993, the general methodology for building a geological reservoir model is to;

  • Define the space occupied by reservoir interval
  • Identify the geological/genetic units within this space
  • Assign realistic shapes and geometries to these geological/genetic units
  • Arrange these units within the defined space (i.e. determine the reservoir’s internal geometry or 'architecture'); use either deterministic or stochastic (object-based) methods
  • Assign reservoir properties to the genetic units (use deterministic, stochastic and/or other geostatistical methods)

The concept of object-based modelling techniques (also termed 'marked point processes) follows naturally from the concept of genetic reservoir units. An object-based is defined as a 3-D geometric shape which can represent a genetic reservoir unit, or shale, or any other reservoir or non reservoir interval which can be defined in space and which has clearly distinguishable boundaries.

An object-based model is a model that simulates the distribution of objects defined by specific geometries, in 3D space, with simulations usually constrained by well data.

A reservoir will typically contain many objects of a certain type (e.g. channels), which have a similar geometry but which differ in size (e.g. different thickness, width and length), location and orientation. If the location of the objects are 'conditioned' to well data (objects have been identified in the wells and the realisation must honour this) then the well data is modelled before the inter well volume.

Object-based modelling uses the stochastic method of approach in building probabilistic models on a particular object with various modelling software such as IRAP and Petrel. These types of modelling have variable input parameters, commonly derived from probability-density functions (pdfs), and therefore have multiple outcomes; as a consequence model runs must be repeated many times and subsequently averaged.

The goal of object-based modelling in sedimentary geology is to predict sedimentary architecture and stratigraphy. Uncertainties associated with object-based modelling include; limited data available about reservoir dimensions and architecture, Complex spatial disposition of reservoir building blocks or facies, and spatial heterogeneity of rock properties. (Bryant and Flint, 1993).

According to Bryant and Flint, 1993, the stochastic reservoir modelling provides improved integration of geoscientific information, uncertainty quantification by generation of many plausible relations, reservoir characterisation during exploration, appraisal and production stage and convenience, and speed of stochastic methods.

Object-based modelling is commonly applied to fluvial reservoirs.

The method employed for stochastic reservoir modelling of fluvial channel sand bodies includes:

  • Conditioning data
  • Honoring well data: whereby sand bodies are randomly located to coincide with sands in the well. This ensures that the channel positions are controlled.
  • Inter well bodies: Here random bodies conflict with the well and must be dropped or moved
  • Final realisation: Sand is added until net-to-gross ratio reaches desired level.

Problems can arise with object based techniques when there are objects present in the well which cannot be matched because the stop criteria has been reached too soon, there are too many conflicts, or the objects being drawn into the reservoir volumes have an inappropriate geometry. Problems are also associated with objects that are very large (It is easier to fit a group of small objects together than large ones). Other problems occur when the wells are closely spaced to the size of the objects; this is ironic as more wells yield better constrained models. The methodology can distort the statistics, whereby larger object are placed near the well and smaller objects between wells.

Data used is as follows:

  • Publicly available satellite imagery of the modern Volga delta
  • Enlarged section of the delta with better resolution showing more pronounced distributary channel patterns.
  • Cartoon map of the Volga showing the area covered by the satellite image.

Methodology and Data Collection
The channel segments were traced-out from the satellite image map of the Volga delta using sheets of tracing paper, & the channel segments numbered from 1 to 270

Measurements of length along the stream (L), horizontal length (H) & width of channels were obtained; using a ruler and a long string, and the sinuosity (L/H) was calculated.

The channel segments were assigned a hierarchy with numbering starting from 'one', from the Volga River, at the apex of the delta through the network of branched and converging stream channels to the region represented on a traced-out, satellite image of the Volga delta. The numbering of the channel hierarchy continued from there, through the drainage system to where the stream channel drains into the Caspian Sea. Some channels close to the sand dunes and deserts were observed and measured.

A section of the delta showing a pronounced branching pattern was looked at and measured as above.

The Sinuosity for each channel segment was calculated by dividing the channel length along a floodplain stream (L) by the horizontal channel length (H).

All the records of measurements were properly labelled and tabulated on an Excel work sheet.

Statistical analysis; mean, standard deviation, frequency & cumulative frequency were obtained from the dataset collected via Excel worksheet.

Part 2 of this article with the findings and conclusions will be published the June issue of ROGTEC Magazine.
posted by The Rogtec Team @ 11:25 


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