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Sequential indicator simulation is a commonly used method for discrete variable simulation in 3D geological modeling and a widely used stochastic simulation method, which can be used not only for continuous variable simulation but also for discrete variable simulation. In this paper, the X Oilfield in the western South China Sea is taken as an example to compare the sequential indicator simulation method and the Indicator Kriging interpolation method. The results of the final comparison show that the results of the lithofacies model established by the Indicator Kriging deterministic interpolation method are overly smooth, and its coincidence rate with the geological statistical results is not high, thus cannot well reflect the heterogeneity of the underground reservoir, while the simulation results of the lithofacies model established by the sequential indicator stochastic simulation method can fit well with the statistical law of the well, which has eliminated the smoothing effect of Kriging interpolation, thus can better reflect the heterogeneity of the underground reservoir. Therefore, the sequential indicator simulation is more suitable for the characterization of sand bodies and the study of reservoir heterogeneity.

The Zhuhai Formation of X Oilfield in Zhujiangkou Basin belongs to fan delta front sedimentary environment, where estuarine dam, front sheet sand and distal sand bar are developed, due to ocean wave modification. Fan-delta reservoir is one of the most common reservoirs in the study area. Modeling methods for sedimentary microfacies and lithofacies are now well developed, such as target-based method, sequential indicator simulation, and Indicator Kriging [

Before simulation calculation, the indicator transformation must be first carried out, that is, the process of encoding the original data into 0 and 1 according to different threshold values [

I ( u , z ) = { 1 Z ( u ) ≤ Z c 0 Others (1)

Then:

Prob { I ( u ) = 1 | ( n ) } = E { I ( u ) | ( n ) } (2)

The indicator transformation can also be used to transform some qualitative or type variables, for example, if 1 represents the occurrence of sandstone, then 0 nonoccurrence (that is, the occurrence of other rock types). It can also be interpretation and inference of geologists. Therefore data of different kinds and accuracies can be transformed into 1 and 0 for data synthesis. The above formula is an equal weight indicator weighting method, but the unequal weighting method is also usually used for predicting the unknown:

F ( z ; x | ( n ) ) = [ i ( z ; x ) ] * = ∑ j = 1 n a j ( z ; x ) ⋅ i ( z ; z j ) (3)

where, a_{j}(z; x) is the weight coefficient, which can be obtained by solving the following system of equation:

{ ∑ j = 1 n a j ( z ; x ) ⋅ C I ( z , x j ′ − X j ′ ) + μ ( z ; x ) = C I ( z , z j ) , j = 1 , ⋯ , n ∑ j ′ = 1 n a j ′ ( z ; x ) = 1 (4)

For a certain position, each threshold value corresponds to one such system of equations. In fact, within the range of variable variation, the range can be discretized with K threshold values, Z_{k}, k = 1, ∙∙∙, K. Therefore, it is necessary to solve K equation systems at each location to obtain the discrete cumulative function F(zk; xq(n)) so as to evaluate the uncertainty. The values of the cumulative density function between [Z_{K}, Z_{K}_{+1}] can be obtained by linear interpolation or other methods [

Mainly based on this concept, the sequential indicator simulation is proposed, for which one of the essential question is how to be faithful to the spatial connectivity pattern of known data and information, so that the model can reflect the heterogeneity of parameters.

The greatest advantage of indicator simulation is to simulate complex anisotropic geological phenomena and extreme values of continuous distribution. For type variables (phases) with different continuous distributions, different variograms can be specified to create anisotropic simulated images.

The biggest difference between the Indicator Kriging method and the sequential Indicator Kriging method is that the latter establishes a random probability distribution model based on the number of the random seeds, while the former establishes a deterministic model according to the index with the highest selection expectation.

The study area is located on the east side of the middle part of xx Depression in Zhujiangkou Basin. The Zhuhai Formation in the study area is a semi-anticlinal fault-nose structure controlled by the fault, with a near E-W strike, and the structure tilts north, east and south [

During the sedimentation of Zhuhai Formation, the subaqueous distributary channel came from the southeast provenance, developed fan delta front to the northwest, and extended from the delta inner front controlled by river course to the delta outer front controlled by sea wave [

The model was created by software of Petrel 2016, and the key parameters of drilling stratification, lithology type, and sedimentary microfacies type were usedtobuild the model. The lithologic curve of these wells that participate in the simulation is the result of the standardization of the logging curve. As the lithofacies are mainly divided into sandstone and mudstone in interpretation results, and that sandstone is also divided into reservoir sandstone and dry layer, hierarchical simulation is used to depict lithofacies distribution in the simulation process. Firstly, the distribution of sandstone facies and mudstone facies is simulated, and then the distribution of reservoir sandstone and dry layers in sandstone facies is simulated. The fluid phase model established by sand mudstone facies constraint can well reveal the characteristics of plane distribution and vertical superposition rules of reservoir sandstone, dry layer and mudstone.

The variogram is the key to stochastic modeling [

As can be seen from the fluid phase models of the sequential indicator simulation and Indicator Kriging (

Conventional geological model test methods include thinning testing, new well testing and dynamic verification, etc. [

Well Z2 is randomly removed from the wells in the study area, and then the lithofacies of the study area is simulated using sequential indicator simulation method [

According the comparison of the lithofacies models of the Zhuhai Formation of X Oilfield in Zhujiangkou Basin established by sequential indicator simulation and Indicator Kriging, it can be seen that the sequential indicator simulation can not only overcome the smoothing effect of the Indicator Kriging on the parameters, but can also reflect the slight changes in the parameters and characterize the uncertainty between the wells. The sequential indicator simulation method can better reflect the heterogeneity of fan-delta sand body and describe the spatial distribution of interlayer than the Indicator Kriging interpolation method.

The authors declare no conflicts of interest regarding the publication of this paper.

Wang, L.L. and Wang, Y.B. (2020) Application of Sequential Indicator Simulation in Geological Study of X Oilfield in Zhujiangkou Basin. Open Journal of Yangtze Gas and Oil, 5, 16-25. https://doi.org/10.4236/ojogas.2020.51002