Geostatistics is a modern, effective tool for reservoir characterization and seismic inversion. The main purpose of geostatistics is to make property grids, which are needed as input to many types of petroleum industry software, such as cross section and visualization packages, reservoir flow simulators, and material balance programs.
Three main reasons to use geostatistics rather than other gridding methods:
Geostatistics makes more accurate grids than other gridding methods,
Geostatistics is best to quantitatively combine many different types of hard and soft data,
Geostatistics is best to quantify the uncertainty in a reservoir description.
The geostatistical methods of kriging and conditional simulation make more accurate grids than any other gridding methods.
Mathematically, accuracy can be defined as to minimize the sum of the squared error between expected and actual values throughout the grid. This is exactly what kriging does because it is the criterion from which the kriging algorithm is derived.
Another definition of accuracy is to duplicate the statistics (mean and standard deviation) and continuity of the input data. These are the criterion upon which the geostatistical method of conditional simulation is based.
In practical terms, kriging and conditional simulation will honor the control data. As far as reproducing heterogeneity in the model with limited data control, conditional simulation is the only practical method today. Other gridding methods tend to produce a grid with less heterogeneity than the real reservoir and that usually contributes to reducing the accuracy of forecasting based on the reservoir model. One typical example is permeability grid for reservoir simulation. If heterogeneity is not accurately represented in the permeability grid, it would be more difficult to make realistic prediction from the simulation study.
In addition, geostatistical gridding can be made to honor marker horizons and other boundaries. It is possible to make more accurate grid with geostatistics because more information (control data, distance and direction of control data to interpolation point, distance and direction between control data points, continuity model, horizon marker constraint, statistical distribution of control data, and degree of uncertainty in control data) is used in a systematic way compared to conventional approaches.
One of the great strengths of geostatistics is that it can quantitatively combine diverse types of data. An example of data combination is seismic and well log data.
Seismic data is considered soft data. There is usually a lot of it but it is not very accurate. On the other hand, well log data is hard data. Compared to seismic data, there are not much log data, but the log data are substantially more accurate than the seismic data. In geostatistics, these two types of data can be combined using the methods of cokriging or cosimulation.
There are many other types of data that can be combined with well data, which are almost always available to some degree. For example, data from basin deposition models can be readily used and are often valuable when seismic is not available and not many wells have been drilled. Another important type of data that is just now being integrated into geostatistical descriptions is production and well test data. Still another example is to combine well log porosity and core porosity. The relatively plentiful well log porosity is used as soft data and the relatively sparse core porosity is used as hard data.
Among different types of well data, an example is to use well log porosity as soft data to combine with core permeability which is used as hard data.
Slowly, engineers and geoscientists are realizing that not using all of the data that are available to characterize a reservoir is effectively the same as throwing perfectly good data away.
For a given set of input data, the geostatistical method of conditional simulation produces a series of grids which are consistent with the input data in terms of statistics (mean and standard deviation) and texture (variogram) in addition to honoring the same set of control data. If the reservoir is well defined (lots of data with a high degree of reservoir continuity), then there will not be much uncertainty in the reservoir description and all of the grids produced by conditional simulation will look similar. If the reservoir is not well defined, then there will be a substantial degree of uncertainty, and the grids produced will look quite different.
It’s very important in reservoir management to be able to quantify uncertainty. For example, developing different permeability grids will allow us to predict best and worst case production scenarios. This will help prevent production surprises down the road. Another example is to provide possible range of reserves. For the same set of input data, conditional simulation can provide a range of possible models so that you know how likely the reserve is going to be larger than a certain value, besides providing the most likely value.
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