Data types

In essence, the purpose of ERT is to pass uncertain parameter values to a forward model and then store the resulting outputs. Forward models include all necessary pre-processing and post-processing steps, as well as the computational model (e.g., a physics simulator like ECLIPSE) that produces the predictions. Consequently, ERT must be able to read and write data in a format compatible with the forward model.

Data managed by ERT are organized into distinct data types, each of which will be detailed in this chapter. The data types in ERT can be classified based on two main criteria:

  1. Dynamic behaviour: whether the data type is a static input to the simulator, such as porosity or permeability, or an output of the simulation.

  2. Implementation: this includes the type of files it can read and write, how it is configured, and so forth.

Note: All data types share a common namespace, meaning that each keyword must be globally unique.

Scalar parameters with a template: GEN_KW

This section describes the distributions built into ERT that can be used as priors. For detailed description and examples on how to use the GEN_KW keyword, see here.

The algorithms used for updating parameters expect normally distributed variables. ERT supports other types of distributions by transforming normal variables as outlined next.

  1. ERT samples a random variable x ~ N(0,1) - before outputting to the forward model this is transformed to y ~ F(Y) where the distribution F(Y) is the correct prior distribution.

  2. When the prior simulations are complete ERT calculates misfits between simulated and observed values and updates the parameters; hence the variables x now represent samples from a posterior distribution which is Normal with mean and standard deviation different from (0,1).

The transformation prescribed by F(y) still “works” - but it no longer maps to a distribution in the same family as initially specified by the prior. A consequence of this is that the update process can not give you a posterior with updated parameters in the same distribution family as the Prior.

Reproducibility

When ERT samples values there is a seed for each parameter. This means that if ERT is started with a fixed RANDOM_SEED each prior that is sampled will be identical. When running without a random seed ERT will output which random seed was used, so it is possible to reproduce results as long as that is kept.

This section only applies if a fixed seed is used:

  • If the ensemble size is increased from N -> N+1 the N first realizations will be identical to before

  • Parameter order is irrelevant

  • Parameter names are case sensitive, PARAM:MY_PARAM != PARAM:myParam

NORMAL: Gaussian Distribution

The NORMAL keyword allows assigning a Gaussian (or normal) prior to a variable. It requires two arguments: a mean value and a standard deviation.

Syntax

VAR NORMAL <mean_value> <standard_deviation>

Parameters

  • <mean_value>: The mean of the normal distribution.

  • <standard_deviation>: The standard deviation of the normal distribution.

Example

For a Gaussian distribution with mean 0 and standard deviation 1 assigned to the variable VAR:

VAR NORMAL 0 1
../../_images/normal.png

Notes

The NORMAL keyword is integral for scenarios demanding priors that reflect typical real-world data patterns, as the Gaussian distribution is prevalent in many natural phenomena.

LOGNORMAL: Log Normal Distribution

The LOGNORMAL keyword is used to assign a log normal prior to a variable. A variable is considered log normally distributed if the logarithm of that variable follows a normal distribution. The logarithm in question is the natural logarithm. If \(X\) is normally distributed, then \(Y = e^X\) is log normally distributed.

Log normal priors are especially suitable for modeling positive values that exhibit a heavy tail, indicating a tendency for the quantity to occasionally take large values.

Syntax

VAR LOGNORMAL <log_mean> <log_standard_deviation>

Parameters

  • <log_mean>: The mean of the logarithm of the variable.

  • <log_standard_deviation>: The standard deviation of the logarithm of the variable.

Example

Histogram from values sampled from a lognormal variable specified with log-mean of 0 and log standard deviation 1.

VAR LOGNORMAL 0 1
../../_images/lognormal.png

TRUNCATED_NORMAL: Truncated Normal Distribution

The TRUNCATED_NORMAL keyword is utilized to assign a truncated normal distribution to a variable. This distribution works as follows:

  1. Draw a random variable \(X \sim N(\mu,\sigma)\).

  2. Clamp \(X\) to the interval [min, max].

Syntax

VAR TRUNCATED_NORMAL <mean> <standard_deviation> <min> <max>

Parameters

  • <mean>: The mean of the normal distribution prior to truncation.

  • <standard_deviation>: The standard deviation of the distribution before truncation.

  • <min>: The lower truncation limit.

  • <max>: The upper truncation limit.

Example

VAR TRUNCATED_NORMAL 2 0.7 0 4
../../_images/truncated_ok.png

UNIFORM: Uniform Distribution

The UNIFORM keyword is used to assign a uniform distribution to a variable. A variable is considered uniformly distributed when it has a constant probability density over a closed interval. Thus, the uniform distribution is fully characterized by it’s minimum and maximum values.

Syntax

VAR UNIFORM <min_value> <max_value>

Parameters

  • <min_value>: The lower bound of the uniform distribution.

  • <max_value>: The upper bound of the uniform distribution.

Example

To assign a uniform distribution spanning between 0 and 1 to a variable named VAR:

VAR UNIFORM 0 1
../../_images/uniform.png

Notes

It can be shown that among all distributions bounded below by \(a\) and above by \(b\), the uniform distribution with parameters \(a\) and \(b\) has the maximal entropy (contains the least information).

LOGUNIF: Log Uniform Distribution

The LOGUNIF keyword is used to assign a log uniform distribution to a variable. A variable is said to be log uniformly distributed when its logarithm displays a uniform distribution over a specified interval, [a, b].

Syntax

VAR LOGUNIF <min_value> <max_value>

Parameters

  • <min_value>: The lower bound of the log uniform distribution.

  • <max_value>: The upper bound of the log uniform distribution.

Example

To assign a log uniform distribution ranging from 0.00001 to 1 to a variable:

VAR LOGUNIF 0.00001 1
../../_images/loguniform.png

Notes

The log uniform distribution is useful when modeling positive variables that are heavily skewed towards a boundary.

CONST: Dirac Delta Distribution

The CONST keyword ensures that a variable always takes a specific, unchanging value.

Syntax

VAR CONST <value>

Parameters

  • <value>: The fixed value to be assigned to the variable.

Example

To assign a value of 1.0 to a variable:

VAR CONST 1.0
../../_images/const.png

DUNIF: Discrete Uniform Distribution

The DUNIF keyword assigns a discrete uniform distribution to a variable over a specified range and number of bins.

Syntax

VAR DUNIF <nbins> <min_value> <max_value>

Parameters

  • <nbins>: Number of discrete bins or possible values.

  • <min_value>: The minimum value in the range.

  • <max_value>: The maximum value in the range.

Example

To create a discrete uniform distribution with possible values of 1, 2, 3, 4, and 5:

VAR DUNIF 5 1 5
../../_images/dunif.png

Notes

Values are derived based on the formula: \(\text{min} + i \times (\text{max} - \text{min}) / (\text{nbins} - 1)\) Where \(i\) ranges from 0 to \(\text{nbins} - 1\).

ERRF: Error Function-Based Prior

The ERRF keyword allows creating prior distributions derived from applying the normal CDF (involving the error function) to a standard normal variable. Note that the CDF is not necessarily the standard normal, as SKEWNESS and WIDTH corresponds to its negative mean and standard deviation respectively. This allows flexibility in creating distributions of diverse shapes and symmetries.

Syntax

VAR8 ERRF MIN MAX SKEWNESS WIDTH

Parameters

  • MIN: The minimum value of the transform.

  • MAX: The maximum value of the transform.

  • SKEWNESS: The asymmetry of the distribution.

    • SKEWNESS < 0: Shifts the distribution towards the left.

    • SKEWNESS = 0: Results in a symmetric distribution.

    • SKEWNESS > 0: Shifts the distribution towards the right.

  • WIDTH: The peakedness of the distribution.

    • WIDTH = 1: Generates a uniform distribution.

    • WIDTH > 1: Creates a unimodal, peaked distribution.

    • WIDTH < 1: Forms a bimodal distribution with peaks.

Examples

  1. For a symmetric, uniform distribution:

    VAR ERRF -1 1 0 1
../../_images/errf_symmetric_uniform.png

  1. For a right-skewed, unimodal distribution:

    VAR ERRF -1 1 2 1.5
../../_images/errf_right_skewed_unimodal.png

Notes

Keep in mind the interactions between the parameters, especially when both SKEWNESS and WIDTH are adjusted. Their combination can result in a wide range of distribution shapes.

DERRF: Discrete Error Function-Based Distribution

The DERRF keyword is a discrete version of the ERRF keyword. It is designed for creating distributions based on the error function but with discrete output values. This keyword facilitates sampling from discrete distributions with various shapes and asymmetries.

Syntax

VAR DERRF NBINS MIN MAX SKEWNESS WIDTH

Parameters

  • NBINS: The number of discrete bins or possible values.

  • MIN: The minimum value of the distribution.

  • MAX: The maximum value of the distribution.

  • SKEWNESS: The asymmetry of the distribution.

    • SKEWNESS < 0: Shifts the distribution towards the left.

    • SKEWNESS = 0: Produces a symmetric distribution.

    • SKEWNESS > 0: Shifts the distribution towards the right.

  • WIDTH: The shape of the distribution.

    • WIDTH close to zero, for example 0.01: Generates a uniform distribution.

    • WIDTH > 1: Leads to a unimodal, peaked distribution.

    • WIDTH < 1: Forms a bimodal distribution with peaks.

Examples

  1. For a discrete symmetric, uniform distribution with five bins:

    VAR_DERRF1 DERRF 5 -1 1 0 1
../../_images/derrf_symmetric_uniform.png

  1. For a discrete right-skewed, unimodal distribution with five bins:

    VAR_DERRF2 DERRF 5 -1 1 2 1.5
../../_images/derrf_right_skewed.png

TRIANGULAR: Triangular Distribution

The TRIANGULAR keyword is used to define a triangular distribution, which is shaped as a triangle and is determined by three parameters: minimum, mode (peak), and maximum.

Syntax

VAR TRIANGULAR MIN MODE MAX

Parameters

  • XMIN: The minimum value of the distribution.

  • XMODE: The location (value) where the distribution reaches its maximum (or peak).

  • XMAX: The maximum value of the distribution.

Description

The triangular distribution is a continuous probability distribution with a probability density function that is zero outside the interval [XMIN, XMAX], and is linearly increasing from XMIN to XMODE and decreasing from XMODE to XMAX.

Example

To define a triangular distribution with a minimum of 1, mode (peak) of 3, and maximum of 5:

VAR_TRIANGULAR TRIANGULAR 1 3 5
../../_images/triangular.png

3D field parameters: FIELD

The FIELD keyword is used to parametrize quantities that span the entire grid, with porosity and permeability being the most common examples. For detailed description and examples see here.

2D Surface parameters: SURFACE

The SURFACE keyword can be used to work with surface from RMS in the irap format. For detailed description and examples see here.

Simulated data

The datatypes in the Simulated data chapter correspond to datatypes which are used to load results from a forward model simulation and into ERT. In a model updating workflow instances of these datatypes are compared with observed values and that is used as basis for the update process. Also post processing tasks like plotting and QC is typically based on these data types.

Summary: SUMMARY

The SUMMARY keyword is used to configure which summary vectors you want to load from the (Eclipse) reservoir simulation. In its simplest form, the SUMMARY keyword just lists the vectors you wish to load. You can have multiple SUMMARY keywords in your config file, and each keyword can mention multiple vectors:

SUMMARY  WWCT:OP_1  WWCT:OP_2  WWCT:OP_3
SUMMARY  FOPT FOPR  FWPR
SUMMARY  GGPR:NORTH GOPR:SOUTH

If you in the observation use the SUMMARY_OBSERVATION to compare simulations and observations for a particular summary vector you need to add this vector after SUMMARY in the ERT configuration to have it plotted.

You can use wildcard notation to all summary vectors matching a pattern, i.e. this:

SUMMARY WWCT*:* WGOR*:*
SUMMARY F*
SUMMARY G*:NORTH

will load the WWCT and WWCTH, as well as WGOR and WGORH vectors for all wells, all field related vectors and all group vectors from the NORTH group.

RFT data

RFT data represents measurements or simulated values of formation properties such as pressure and saturation at specific locations within wells. These measurements are typically taken at discrete depth points and specific times during the reservoir’s production history.

Understanding RFT files

Reservoir simulators (e.g., ECLIPSE, OPM Flow) can generate RFT files that contain simulated pressure, saturation, and other formation properties at well measurement locations. These files are produced alongside summary files and use the same basename specified by the ECLBASE keyword.

For example, if your configuration specifies:

ECLBASE MY_FIELD
The simulator should generate files such as:

  • MY_FIELD.RFT - Binary RFT file

  • MY_FIELD.SMSPEC - Summary specification file

  • MY_FIELD.UNSMRY - Summary data file

Ert will expect the MY_FIELD.RFT to be produced by the reservoir simulator when either rft observations or rft responses is used. When the SUMMARY keyword is used, ert expects MY_FIELD.SMSPEC and MY_FIELD.UNSMRY to be produced by the reservoir simulator.

For the OPM simulator, the keywords WRFT and WRFTPLT enables output of the RFT file.

Working with RFT observations

RFT data is loaded into ERT automatically when you define RFT_OBSERVATION entries in your observation configuration file. ERT reads the RFT files generated by your forward model and extracts the simulated values at the locations (specified by NORTH, EAST, and TVD coordinates) and times (DATE) defined in your observations.

Each RFT observation specifies:

  • WELL: The name of the well where the measurement was taken

  • DATE: The date of the measurement in ISO format (YYYY-MM-DD)

  • PROPERTY: The property being measured (e.g., PRESSURE, SWAT, SGAS)

  • VALUE: The observed value

  • ERROR: The measurement uncertainty

  • TVD: True vertical depth below sea level

  • NORTH and EAST: Horizontal coordinates of the measurement location

Example observation configuration:

RFT_OBSERVATION prod_rft_2015 {
   WELL=PROD_01;
   DATE=2015-06-15;
   PROPERTY=PRESSURE;
   VALUE=3850;
   ERROR=25;
   TVD=2150.5;
   EAST=456789.2;
   NORTH=6789012.3;
};

For loading multiple RFT observations from a CSV file, see the RFT_OBSERVATION documentation.

Exporting RFT data for visualization

The EXPORT_RFT workflow job exports RFT observations and simulated responses to CSV files compatible with the webviz-subsurface RftPlotter plugin. This workflow job is a replacement for the MERGE_RFT_ERTOBS forward model when using RFT_OBSERVATION instead of the legacy GENDATA_RFT method.

To use it, add the workflow job to your ERT configuration, e.g. with the HOOK_WORKFLOW_JOB keyword:

HOOK_WORKFLOW_JOB export_rft_data EXPORT_RFT POST_SIMULATION

By default, the output file is written to share/results/tables/rft_ert.csv in each realization’s runpath. A custom filename can be specified as a parameter:

HOOK_WORKFLOW_JOB export_rft_data EXPORT_RFT custom_rft.csv POST_SIMULATION

Note

To include SGAS, SWAT, and SOIL saturation values in the exported CSV, SGAS and SWAT properties must be listed in the RFT response configuration to make ERT extract these properties from the RFT files. For example:

RFT WELL:PROD DATE:2015-02-01 PROPERTIES:PRESSURE,SWAT,SGAS

General data: GEN_DATA

The GEN_DATA keyword is used to load text files which have been generated by the forward model. For detailed description and examples see here.