NR has worked on methods for making realistic geological facies models for almost two decades. The goal is to reproduce the true geological heterogeneity and to describe the inherent uncertainty. Correct heterogeneity gives realistic flow patterns and the possibility to obtain unbiased forecasts from reservoir simulators. Capturing the uncertainty is important for quantifying real economical risk.

Stochastic (Monte Carlo) simulation is a tool for generating possible heterogeneous facies realiztions. A multiple of generated facies realizations spans the uncertainty range. So stochastic simulation is the tool for obtaining realistic heterogeneous geological models and for studying the uncertianty.

NR have developed a series of stochastic models for facies. Some of these are strongly linked to special types of sedimentary deposits while other are more general in nature. Below is a series of examples of the type of geometries we can generate and some types of geology they may mimic.

The Two-step Approach

It has become a standard approach to split modelling of petrophysical properties into two steps:

1. Generate the geometry of the facies.
2. Populate each facies with petrophysical properties such as porosity and permeability.

There are two main reasons for modelling the facies rather than generating the petrophysics directly:

1. The method for generating petrophysical properties requires the statistical properties to be homogeneous. If facies types with different petrophysical properties are mixed, the generated petrophysical model will have some average properties that do not behave like any of the original facies types.
2. Petrophysical properties often follow trends governed by the geometry of sedimentary deposits. Recent developments have made this a very powerful approach for reproducing realistic petrophysical trends and fluid flow patterns inside each individual facies body.

The two-step approach was established by us and others in the early 90's and has now become common practice.

Data conditioning

Generating pretty pictures are easy. Making them honour well data and seismic data are not. All our methods will honour data and we put a lot of effort into doing this consistent. A simple test to check that the conditioning algorithms work correctly is to do the following:

1. Simulate a stochastic realization and collect data for some relevant property such as connectivity.
2. "Drill" some wells in the simulated realization and keep the facies data along these "boreholes".
3. Simulate a new stochastic realization conditioned on the facies data collected in step 2. Collect data for some relevant property (e.g. connectivity) from this realization.
4. Go to step 1 and repeat say 100 times.
5. Compare the statistics for the (connectivity) data collected in step 1 and 3 for the unconditional and conditional realizations respectively.

Below is an illustration of one such experiment. The data collected is how many channels are seen in zero wells, how many are seen in one well and so on. Note that the well data collected for each run do not carry any information on the connectivity.

We observe that many channels have not been observed in any wells whereas a few have actually been observed in 8 different wells. In this case we see an excellent agreement between the uncoditional case and the case conditioned on data. This confirms that the method used for tying the channels to the observations works properly and does not introduce any artifical behaviour.

In the following we show examples of the types of geological facies models we have detailed knowledge of. All models can be conditioned to well observations and seismic data. Most of them have been developed by us in close cooperation with the oil industry.

Object based methods

Fluvial deposits

Fluvial deposits with petrophysical trends and heterogeneity following the channel geometry:

Below is a picture of deposits along the Mississippi river system. Note that the deposits are point bars. The reason the deposits look like channels are the geographic confinement of the river system in a time period. The river itself may change significantly within this time period. So the channel-like objects in the picture above are really the sum of many point bars deposited in the river valley.

Deep marine deposits - turbidites

Turbidite deposits are formed by sediments sliding down underwater channels and finally settling on the ocean floor.

Below is an underwater picture of a turbidite flow. The size of these turbidite flows can differ by many orders of magnitude from small local events to flows travelling hundreds of kilometers.

Below is a map of the ocean around India displaying the possible size of these events. We can see the channels guiding the turbidite flows quite clearly.

General point process models

Point processes can be used for many shapes. Below is a facies model with three different basic shapes: Cones (green), ellipsoids (blue), and thinner-in-the-middle (red). Note the different clustering of the different facies types. The clustering is obtained by having different spatially varying intensity for the different object types.

These facies objects have been populated with petrophysics. Different petrophysical trends are used in the different facies types.

Pixel based methods

We have significant experience with two pixel based methods: Truncated Gaussian fields and indicator kriging. We consider Markov random field models and multipoint methods promising but they still have to prove their efficiency and flexibility.

Truncated Gaussian random fields is a method where a continuous Gaussian field is mapped into discrete facies classes. In our implementation we can impose trends to force transitions from one facies to the next in a systematic fashion. A basic property with this method is that there is a strict ordering of facies. This is appropriate in certain depositional evironments where there is a systematic sequence of depositions. Below are one example showing a carbonate atoll and a few examples showing shallow marine deposits.

Carbonate atolls

Carbonates are a diverse and complex phenomenon. Some carbonates are made coral reef atolls, like the left picture:

The figure in the middle shows an intersection of an atoll with two facies simulated by truncated Gaussian simulation. To the right, we see the simulated porosity in the atoll.

Shallow marine deposits

Here we three figures of shallow marine deposits corresponding to three different situations depending on the mass transport and the strength of the wave influence. The leftmost is wave dominated whereas the rightmost is river dominated.

These three situations mimic what we see in the three areal photos below:

Indicator kriging

This is a method originally proposed for making realizations of continuous petrophysical properties such as permeability. However, the two-step approach promoting the separation of petrophysical properties into more statistically homogeneous facies has made this approach obsolete. The current popularity of indicator kriging was tremendously boosted when it was realized that it is a powerful tool for generating facies models. In particular when data are abundant and the geological constraints are vague, indicator kriging is a very efficient and useful tool.