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This paper presents a three-dimensional geological reservoir model created using stochastic simulation. The oil field presented is an East African oil field formed by a structural trap. Data analysis and transformations were conducted on the properties before simulation. The variogram was used to measure the spatial correlation of cell-based facies modeling, and porosity and permeability modeling. Two main lithologies were modelled using sequential indicator simulation, sand and shale. Sand had a percentage of 26.8% and shale of 73.2%. There was a clear property distribution trend of sand and shale from the southwest to the northeastern part of a reservoir. The distribution trend of the facies resembled the proposed depositional model of the reservoir. Simulations show that average porosity and permeability of the reservoir are about 20% and 1004 mD, respectively. Average water saturation was 64%. STOIIP volume of 689.42 MMbbls was calculated. The results of simulation showed that the south eastern part of the reservoir holds higher volumes of oil. In conclusion, the model gave a better geological understanding of the geology of the area and can be used for decision making about the future development of the reservoir, prediction performance and uncertainty analysis.

3D geological models are important in the petroleum field as they give a representation of the geology of the reservoir. A good model should be as close to the real life geological scenario as possible. “However, for oil reservoirs, the real-life scenario is not fully known except in a few data points” [

Reservoir modeling involves the integration of different types of data as shown in

The main steps involved in reservoir modeling include; building the structural design of the reservoir, stratigraphy modeling, facies modeling within each stratigraphic layer and petrophysical properties modeling based on the facies. This is a

sequential approach work flow, where large scale properties are modeled first, followed by smaller uncertain properties. In the case of stochastic modeling, multiple realizations of the model can be created in order to draw statistical inferences from the set of all outcomes. The modeling steps may however vary depending on; the type of data available, time, reservoir type and human expertise.

Reservoir models are important tools in the petroleum industry for the following reasons;

・ Representation of different kinds of data (2D and 3D seismic, 4D time-lapse seismic, directly sampled rock formations in form of cuttings and cores, well logs) in a common format.

・ Estimation of the original volumes of hydrocarbons which help in economic assesment of a reservoir and drawing up appropriate development plans.

・ Optimal placement of wells.

・ Input into a simulator for dynamic analysis or visualized and used to aid in decision making.

・ Uncertainty analysis.

Geostatistics is the study of phenomena that vary in space and time [

(Semi) variogram analysis; characterization of spatial correlation [

Kriging; optimal interpolation; generates best linear unbiased estimate at each location; employs semi variogram model [

Stochastic simulation―generation of multiple equiprobable images of the variable; also employs semi variogram model [

Geostatistical routines are implemented in major reservoir modeling packages like Petrel and RMS to generate facies, porosity and permeability models. Geostatistical methods are optimal when data are normally distributed and stationary (mean and variance do not vary significantly in space). Significant deviations from normality and stationarity have a significant impact on the variogram [

1) Variogram

Geoscience data sets are distinguished from other types of data sets in one important aspect, they exhibit spatial relationship [

the appearance and flow behavior of the final model [

In this paper, variogram models are used as the input for simulating geological rock facies, porosity and permeability. The technique used to simulate these attributes is stochastic simulation, which simultaneously generates petrophysical properties, porosity and permeability, consistent with the underlying facies [

The first step in performing the spatial analysis is to estimate the value of the variograms using the hard data, i.e., well data [

In principle, experimental simulation technique will require the definition of spatial relationship, i.e., variogram, of each variable being simulated in three main directions, namely major, minor, and vertical directions. Both major and minor variograms are in the horizontal direction [

Variogram modeling is the process of representing the experimental variogram with an acceptable mathematical model that can be input in the stochastic simulation technique being used [

A variogram is basically a display of the mean square difference between two values as a function of their increment [

where, γ (h) is a semi variogram 2γ (h) is variogram, n_{h} is the number of pairs of points with the distance from each other participating in the variogram.

x_{i} is a grade in point i.

x_{i}_{+}_{h} is grade in a point with distance h from the point i.

The terms variogram and semi variogram may be used interchangeably.

a) Characteristics of the Variogram

Sill: The semi variance value at which the variogram levels off. Data is no longer auto correlated. Also used to refer to the “amplitude” of a certain component of the semi variogram.

Range: The lag distance at which the semi variogram (or semi variogram component) reaches the sill value.

Nugget: The semi variance where the separation distance is zero.

Plateau: The part of the variogram model where an increase in separation distance does not change the variogram value.

The lack of data, which makes the variogram important, also makes it difficult to calculate, interpret, and model a reliable variogram. Practitioners have been aware of this problem for some time with no satisfactory solution. Analogue data available from better-drilled fields, outcrop studies, or geological process modeling provide valuable input; however, this data must be merged with field-specific calculations to be useful [

2) Stochastic Simulation

Geostatistical model-building algorithms such as sequential Gaussian simulation, sequential indicator simulation, and truncated Gaussian simulation take an input variogram model and create a 3-D model constrained to local data and the variogram model. The variogram has an extremely important role to play in the appearance and flow behavior of 3-D models due to the sparse data available for petroleum reservoir characterization. Stochastic simulation is a way of property modeling in which multiple equiprobable realizations of the properties are generated instead of simply estimating the mean. Unlike the smoothing effect of kriging, stochastic simulation adds back in some noise to undo the smoothing effect. This gives a better representation of the natural variability of the property [

The two frequently used forms of simulation for reservoir modeling applications are sequential gaussian simulation for continuous variables like porosity and permeability and sequential indicator simulation for discrete variables like facies.

The basic idea of sequential gaussian simulation (SGS) is very simple. Kriging gives us an estimate of both the mean and standard deviation of the variable at each grid node, meaning we can represent the variable at each grid node as a random variable following a normal (Gaussian) distribution. Rather than choose the mean as the estimate at each node, SGS chooses a random deviate from this normal distribution, selected according to a uniform random number representing the probability level. Sequential indicator simulation (SIS) is very similar to sequential gaussian simulation, except that indicator kriging is used to build up a discrete cumulative density function for the individual categories at each case and the node is assigned a category selected at random from this discrete cumulative density function [

Companies in the petroleum industry have to invest very large sums of money in exploration, development, and exploitation of the petroleum reservoirs. To reduce costs and manage the risks involved with production, companies have to draw up impeccable development strategies. To do this, they need to have knowledge of the reservoir’s geological settings, reservoir heterogeneity conditions, discontinuity and continuity of the reservoir flow with consideration of fault arrangements and quantity of a recoverable hydrocarbons. Reservoir models are currently the most efficient tools in describing reservoirs. With a proper understanding of the reservoir, oil companies are able to make good development decisions and reduce most of the production challenges that come about as a result of lack of knowledge of the reservoir.

The field under study is a new field yet to start production hence a clear understanding of its geology and reserve potential is necessary.

The field under study is an East African oil field, formed by a structural trap. The field is a green field yet to start production in the coming years.

To build a representative three-dimensional geological model of the reservoir using stochastic simulation.

To calculate the ultimate reserve potential of the reservoir.

Different well data types are used to create the model using petrel software. Reservoir modeling proceeds sequentially. Large-scale bounding surfaces are modeled, then facies, and then petrophysical properties such as porosity and permeability. The variogram is needed for stochastic modeling of surfaces and petrophysical properties. Facies modeling, however, maybe performed with object-based techniques, which do not require the use of a variogram. The importance and relevance of object-based methods do not diminish the importance of thevariogram for a large fraction of reservoir modeling algorithms [

It is basically defining the architectural design of the reservoir, fault compartmentalization, and a grid network to accommodate the data. Fault modeling is an important aspect of structural modeling. They define the breaks in the grid and hence affect fluid flow in the reservoir.

Fault data was imported in form of fault sticks as shown in

Pillar gridding defines the horizontal scale of the reservoir surfaces (top, mid and bottom surface). The grid was generated using the modeled fault model. The setting for grid distance in I and J direction was set to 100 meters in I direction and 100 meters in J direction.

Stratigraphy modeling involves vertical layering of the 3D grid using horizons and layers. This is the characterization of the internal structure of the model. It involves building the vertical layering in the model. The vertical sequence of the layers mirrors the original lateral distribution of sedimentary environments and is guided by the interpreted depositional surfaces on seismic sections.

Horizons, Zones and LayersThree horizons were modeled. The reservoir was then subdivided into 8 zones based on well tops. Several layers were then added within each zone.

Property modeling is the assignment of appropriate lithological (facies modeling) and petrophysical properties to each block. Facies are lithological units with particular geological characteristics. They can be considered as an elementary part of the reservoir model. Facies are modeled first because they are of a great influence to the petrophysical properties. The modelled facies constrain the the variability

range of porosity and permeability. Saturation functions also depend on the facies. Facies distribution throughout the entire reservoir can be performed using statistical methods such as sequential indicator simulation.

Petrophysical properties; porosity, permeability and water saturation are the main properties needed to characterise the reservoir. Porosity is defined as the pore space volume. Only the effective porosity is advised to be modelled. Total porosity includes the porosity that will never be accessed. Permeability is a measure of the ease with which a fluid can flow through the pore spaces of a rock. Porosity and permeability control fluid storage and flow in a reservoir whereas fluid saturations and porosity control the amount of the hydrocarbons stored. Porosity and permeability determine the reservoir quality. The reservoir quality of a sedimentary rock is the product of the texture and composition of the original sediment. The original texture and composition are then modified by burial, compaction, diagenesis, and deformation. Core data and well logs are the main sources of the petrophysical values. Sequential guassian simulation is used to distribute the petrophysical properties within the facies and stratigraphic layers in the entire reservoir. The procedure is repeated with different random seeds to create multiple realizations (DjebbarTiab and Erle C Donaldson).

Lithology was defined and identified from SP and GR logs using alpha mapping method formula. The data was then up scaled due to the large reservoir description grid blocks compared to the support volume of the measurement. Upscaling was the first step in distributing properties values in all cells. The upscaled values were then used for the horizontal facies distribution using sequential indicator simulation in Petrel.

The petrophysical properties were simulated with Sequential Gaussian Simulation (SGS). Data Analysis was conducted on each property. Porosity underwent a normal score transformation before Sequential Gaussian Simulation. Permeability underwent a logarithmic transformation before normal score transformation.

From the log analysis shown in

BULK VOLUME STATISTICS | |||
---|---|---|---|

Axis | Min | Max | Delta |

X | 240,548.51 | 252960.52 | 12,412.01 |

Y | 130,719.79 | 149521.71 | 18,801.92 |

Z | −3544.14 | −2049.17 | 1495 |

Bulk volume | 0 | 162,770 | 162,770 |

Based on sedimentary facies analysis on each well, two basic facies are defined for facies modelling: Shale and sand. Sand had a percentage of 26.8% and shale of 73.2%. There was a clear property distribution trend of sand and shale from the southwest to the northeastern part of the reservoir. The distribution trend of the facies resembled the proposed depositional model of the reservoir. Variograms models are shown in the Figures 16-18.

Petrophysical Modelling

Simulations show that average porosity of the reservoir is about 20%.

Code | Name | % |
---|---|---|

Sand | 0 | 26.8 |

Shale | 1 | 73.2 |

horizontal direction variogram for porosity modeling.

The permeability of the reservoir is about 1004 mD.

The water saturation of the reservoir is about 64%.

NTG was also modeled to isolate the productive and non-productive parts of the reservoir.

In volumetric calculations, the amount of reserves in the reservoir is estimated to 689.42 million barrels. Most of the oil was in the southeastern part of the reservoir.

This paper has presented a case study of 3D modeling using geostatistical techniques. From the successful creation of the 3D model we can conclude that;

Two main lithologies are present in the reservoir, sand and shale.

Sand had a percentage of 26.8% and shale of 73.2%.

The average porosity and permeability of the reservoir are about 20% and 1004 Md, and the average water saturation is 64%.

In volumetric calculations, the amount of reserves in the reservoir is estimated to 689.42 million barrels. The south eastern part of the reservoir holds higher volumes of oil.

The model gave a better understanding of the geology of the reservoir and can be used for future development decisions.

Oloo, M.A. and Xie, C.J. (2018) Three-Dimensional Reservoir Modeling Using Stochastic Simulation, a Case Study of an East African Oil Field. International Journal of Geosciences, 9, 214-235. https://doi.org/10.4236/ijg.2018.94014