The Improvement Of Kriging Algorithm

On the scientific and effective prediction of reservoir parameters, which always are hot and difficult points of Petroleum Geology. Initially using the traditional methods of mathematical statistics, but such a pure mathematical method does not consider the spatial continuity and relativity between reservoir parameters, without any Geological significance, which is the great limitations for the prediction of reservoir parameters. The geostatistics method based on the theory of regionalized variable taking full account of the spatial variation trend and directional of geological parameters and interdependence of the two samples’parameters, then using the interpolation and extrapolation of kriging method to characterize the changes’rule of reservoir parameters. And use this rule to predict the spatial distribution of the parameters (such as porosity, permeability, etc). The application of geostatistics method realized the leap that the prediction of the pure mathematics to geological understanding+the prediction of mathematics.The kriging method is an important part of geostatistics, also is the core of geostatistics. The estimate methods of geostatistics are mainly various kinds of kriging methods. Kriging method widely used in groundwater simulation, soil drawings and other fields, and is a very useful geological statistical grids method. Kriging also known as the best interpolation method of spatial autocovariance, is also an optimal interpolation method. Condition of using kriging method is that the regionalized variables have the spatial correlation. Kriging is based on the different space locations of samples and the different relativity between samples, assigning the different weights to each sample, then sliding weighted average to estimate the average grade of Centre block.Kriging interpolation is brought up by South Africa mining engineer D. G. Krige is based on the specific circumstances of the gold deposit of South Africa in1952, so the naming is the kriging method. Later G. Matheron, France scholar, studied the kriging method and reasonably improved the statistics based on the spatial distribution, which is a new method of a combination of traditional methods and statistical methods. And the professor Matheron put forward the concept of regionalized variables, and founded the geological statistics. The development of kriging technology has been more than50years history, and the technology is in constant development and improvement. Kriging have been widely used in our country mining and oil industry. In the mining and petroleum industries, data are usually collected along drillholes or wells. So the data are along strings. When kriging is used with these finite strings of data it can be frequently observed that outlying data in the strings receive higher weights than all other data. This counterintuitive weighting, referred to as the string effect. The string effect lead to the results of kriging doesn’t in accord with the actual situation. So we need to correct the string effect.Through the delicate dissecting of geostatistical kriging algorithm, and combined with some understanding of the geology, multidisciplinary theories and methods, improved the existing algorithm to correct the string effect of kriging. There are two new methods to correct the string effect:the distance constrained kriging(DCK) and the finite domain kriging(FDK). The two approachs have been programmed by FORTRAN language and been tested with some small examples, to make the results of the stochastic modeling of geological development in oilfield more tally with the actual situation. Which have important theoretical and realistic significance to deepen the stochastic modeling theory of development geological in oil field and effective dig the remaining oil of reservoir.The two new approaches of distance constrained kriging and finite domain kriging can correct the string effect of kriging, and the correction is a local correction. As with the traditional kriging techniques, the two new approaches have the following characteristics:the estimators are unbiased and exact interpolators, they take into account the redundancy of data in the string and closeness of the data in the string to an estimation location, and they provide estimates for the unsampled value of the variable of interest according to its spatial continuity. In this particular case study, finite domain kriging was shown to result in stronger correction; however, distance constrained kriging performed better in jackknife validation.