rezen

Reservoir Simulation Scenario Management

Overview

Visual Reservoir Software (Geo Visual Systems)

Contents

What is rezen? Functionality Uncertainty Modeling Algorithms History Matching Goodness of Fit Function History Matching Search Algorithm Project-Ensemble-Deck Hierarchy Deck Vector Plots Ensemble Vector Plots Portfolios and Canvases - User Defined Plot Layouts S-Curve Generation and P10,P50,P90 Values Ensemble and Deck Level Goodness of Fit Reporting Vector Data Export Import and Plotting of RFT Data Grids and Grid Attribute Data 2D Visualization 3D Visualization Grid Cell Views

What is rezen? rezen is a software tool for managing multiple reservoir simulation runs. There are two key motivations for wanting to do this:

History matching Handling uncertainty in forward predictions

rezen aims to support industry standard reservoir simulators such as Eclipse, VIP, CMG (IMEX, Stars, GEM) etc. Any reservoir simulator supporting Eclipse file formats is supported and with a little effort we can add support for other simulators as required. rezen aims to provide a user friendly environment for aiding the design, management and investigation of a reservoir simulation scenario. A scenario may consist of multiple related instances of a reservoir simulation model, these instances being collectively known as an ensemble. rezen supports managing a forward prediction or uncertainty modeling scenario where multiple simulation instances are generated using experimental design algorithms prior to submission to the simulator, the aim being to extract the most information from a smaller number of runs. Additionally rezen supports managing a history matching ensemble where simulation runs are made in serial, each instance being dependent on the prior runs, to optimise a set of user defined goodness of fit functions. rezen aims to provide a flexible and open framework with a transparent-box rather than a black-box approach to the internal uncertainty modeling algorithms and goodness of fit functions.

Functionality

Simulation run management Uncertainty Modeling History Matching Post-Processing

For example, rezen enables the user to do the following:

specify a set of input data/parameters (known as "variables") which: are a sub-set of the complete data set provided to the simulator. have an error, uncertainty or are the subject of a parameter sensitivity.

specify the uncertainty modeling algorithm (e.g. Tornado or Plackett-Burman or Monte-

Carlo) that will be used to generate an ensemble of multiple simulation decks to investigate the model's sensitivity to the selected variables.

for history matching, specify a set of output parameters, a set of measured data and a

"goodness of fit" function which will measure the quality of the history match. Generate and run the simulation decks.

Import the output data (either all the data or selected data) from the simulation output

files and analyse via a range of tools either individual simulation runs or the relationship between the runs.

For history matching, goodness of fit functions are available together with search

algorithms for creating the next set of simulation decks in the workflow.

Uncertainty Modeling Algorithms

Discrete cases e.g. create n runs by specifying n values of each variable.

Tornado method or one-at-a-time uncertainty analysis. Requires 3 discrete values (low, min, high) of each variable.

Monte-Carlo simulation. User can specify continuous or discrete distributions which are

randomly sampled for each run. User specifies the number of runs to do.

Plackett-Burman experimental design. Requires "+1" and "1" values of each variable, but it's usually a good idea to test for curvature, so run an all-zero case too.

Combination method or Full Factorial experimental design. Run all possible combinations

e.g. 5 variables with 3 values for each requires 35 = 243 runs. To compare how the Tornado, Plackett-Burman and Combination methods work, consider an example where we have only three variables, v1,v2 and v3. Each can have a low,mid and high value, also known as -1,0,+1. Consider the solution space cube shown below which is in the dimensions of v1,v2 and v3.

The cube has 8 corners which are at the various -1 and +1 combinations. There is a centre point of 0,0,0 which would be our base case simulation run. There are also mid points on the 6 faces and mid points on the 12 edges.

For three variables, each of which having three values, if we do all the combinations we will

generate nvaluesnvariables simulation decks, i.e. 33 = 27 decks. These are shown as the purple ovals below.

All combinations for 3 variables If we use the Tornado algorithm to generate a smaller number of decks, we generate 2*nvariables+1 decks. For three variables, this corresponds to the base case 0,0,0 and then the points in the middle of the 6 faces of the solution space cube....

Tornado for 3 variables If we use the Plackett-Burman algorithm, for three variables, this corresponds to the base case 0,0,0 and then the points at the 8 corners of the solution space cube. Note that as we increase the number of variables above 3, the chosen points in the solution space becomes more complicated.

Plackett-Burman for 3 variables Other uncertainty modeling algorithms may be implemented in the future, for example, Box-Behnken, CCD, etc.

Box Behnken CCD

History Matching Goodness of Fit Function A typical formula for a goodness of fit function is as follows:

Where x is the simulated value of the parameter, y is the measured value, s is the standard error of the measured value and w is the weighting factor (between 0.0 and 1.0) which takes into account the relative importance of matching the parameter. The quantity p represents the rank of the norm. p=1 is useful if there are gross errors as this does not place too much emphasis on outliers i.e. points which match poorly . p=2 represents conventional sum of squares errors and increasing values of p place more emphasis on outliers. History Matching Search Algorithms Radial Basis Function rezen uses a radial basis function as a proxy simulator. This is created as a function of the goodness of fit variables from the simulataneous equations created by each of the simulation deck runs. Monte Carlo simulation is used to generate a large number of proxy decks. For each proxy deck the radial basis function proxy simulator is used to calculate a goodness of fit value. A search method then selects the best proxy decks to convert into real simulation decks for the next set of history match runs.

Project-Ensemble-Deck Hierarchy

Deck Vector Plots Deck vectors are the plot data in the simulator summary or plot output files, e.g. FOPT, WWCT:well=W1 etc. These data can be imported into rezen after each deck has been run (or the data can be imported at the ensemble level for all decks in the current ensemble). An example of where a deck vector sits in the data tree is shown below...

It is possible to import only selected vectors for each deck....

Any imported vector can be quickly plotted....

If an associated history vector is available, then a goodness of fit plot (and table) is also available...

The data for any vector (and its associated vector) can be viewed and optionally exported...

Ensemble Vector Plots An ensemble vector is a collection of associated deck vectors, e.g. WWCT for well W1 across all decks D0001, D0002, .... D0019 Typically in an uncertainty modeling or history matching workflow it is just as important to analyse the relationship between different simulation decks as it is to view vector data within an individual deck. An example of where an ensemble vector sits in the data tree is shown below. Field Gas Production Total is an ensemble vector as shown on the left. Underneath it (as shown in the right) can be seen the list of deck vectors that belong to it.

FGPT for all the vectors can be displayed in a single plot...

In this case we have an uncertainty modeling ensemble with decks generated using the Tornado algorithm. We can therefore plot FGPT against the values of variable 'var1' as shown below.

Alternatively, for the Tornado algorithm, we can produce a Tornado plot as shown below. Note that we can change the timestep and the plot will dynamically update.

If history data is available for the selected ensemble vector, we can also produce a sorted goodness of fit plot showing which of the decks in the ensemble has the best fit for this vector.

In addition to the above plot, the goodness of fit of all the decks in the ensemble can be viewed as a table (and exported).

Portfolios and Canvases - User Defined Plot Layouts A hierarchy of plot layout types has been implemented in rezen. These are :-

Portfolio Canvas Panel

A portfolio can contain one or more canvases. A canvas can contain one or more panels. A panel is a plot containing one or more vectors. Each deck can have one (and only one at this stage) portfolio. Each ensemble can have a number of portfolios (typically one for each deck in the ensemble).

S-Curve Generation and P10,P50,P90 Values Consider an uncertainty modeling ensemble where our objective function is total oil production (FOPT). We define 5 variables, each of which has 3 values, i.e. -1,0,+1. If each simulation run

takes 5 hours of CPU time we do not want to run every combination (35=243 decks). We can use Plackett-Burman to generate an unbiased subset of 10 simulation decks. Plotting the FOPT objective function may end similar to the following....

Rather than try and extract accurate p10,p50,p90 values directly from this plot, we want to create a proxy simulator function and use Monte-Carlo simulation to build a proper S-curve. For the proxy simulator we can use either a simple linear function or perhaps a radial basis function. For the Monte-Carlo simulation we assign a probability distribution and associated parameters (mean, sd etc.) to each of the uncertainty variables.

We then run the Monte-Carlo simulation to generate perhaps 1,000 proxy decks. Each proxy deck is simply a set of uncertainty variable values. We run these proxy decks through the proxy simulator to generate our 1,000 objective function values (FOPT). As each of these proxy decks has the same probability (1,000 Monte-Carlo generations so each has a probability of 0.001) we can sort the decks by objective function value and then plot them as an S-Curve (FOPT vs cumulative probability)....

p10,p50 and p90 values can then be extracted from this S-curve. The data points on the S-curve can be interrogated to check the probability value, the objective function value and the variable/parameter values.

Ensemble and Deck Level Goodness of Fit Reporting

If history data is available, rezen provides goodness of fit plots for a single vector in a deck as shown below. The goodness of fit function can be modified with weights applied to different timesteps and a standard error term for each timestep.

Goodness of Fit Plot for a single vector in a deck

Further, at the ensemble vector level, rezen provides the ability to compare the goodness of fit of a single vector across all the decks in an ensemble

Goodness of Fit Histogram for a single vector across multiple decks

At the deck level, the goodness of fit of all simulation vectors with an associated history vector can be viewed in a table as shown below on the left hand side. We can then build a goodness of fit rank equation for the deck as a weighted sum of the vectors with history. On the right hand side we have added three vectors to the rank equation and adjusted the weighting of the third vector from 1.0 down to 0.1.

Having defined the rank equation for one deck, we can copy this to all the other decks in the ensemble....

We can then view and sort these deck goodness of fit rank values at the ensemble level.

Vector Data Export Vector data consists of the summary file vectors (FOPR, WGPT, etc.) that are time dependent and other data such as RFT vectors which are depth dependent. Each individual vector can be viewed and exported to a text or csv file. Additionally vectors of the same class, e.g. all those W*** vectors belonging to a specific well can be exported to a text or csv file. The Export dialog enables the user to search for and select any number of vectors from the complete list of vectors belonging to a specific simulation deck. All of this vector data can then be exported to a text or csv file.

Import and Plotting of RFT Data For Eclipse datasets, if the RFT file (either formatted or unformatted) is available, then the RFT vectors can optionally be imported as shown in the Import Deck Vectors dialog below.

On completion of the import, the RFT vectors are available under the RFT class in the Deck Vectors sub-tree for each deck...

The RFT vectors for each specific well name and timestep can be plotted against their common depth independent vector.

As for summary file vectors (FOPT, WGPR etc.), RFT vectors can be plotted on their own in a single panel view. Extensive axis options are available. The plot can be captured to the clipboard or to an image file. The data values can be exported to a csv file.

Grids and Grid Attribute Data

Hierarchical hexahedral grid geometries are supported in rezen 2.0. Local grid refinement is supported whereby the deck's main grid can have one or more LGR's. Each LGR in turn can have its own LGRs. Each grid has its own initial grid attributes (e.g. porosity, permeability, NTG, depth, etc.) and its own recurrent grid attributes (pressure, saturations etc.) Any initial or recurrent attribute will be able to be viewed or visualised in 2D and/or 3D. An example of the grid and attribute hierarchy is shown in the tree view below

In this example, the deck has two grids, a main grid and an LGR called “SWMA”. Each of these two grids has its own set of attribute data. The deck also has its own set of attributes. An example is shown below...

In this example, the deck attribute “SWAT” has its own set of deck time attributes, the first being “SWAT:0.0”. This deck time attribute itself has its own set of deck grid time attributes, namely “SWAT:0.0:main” and “SWAT:0.0:SWMA”, the latter being for the LGR.

In the case of initial attributes, rezen 2.0 supports multiple realisations. While simulators such as Eclipse, VIP etc do not require support for multiple realisations, it may well be a useful feature in rezen.

The grid definition(s) and attribute data can be imported individually for each deck...

Alternatively grid and attribute data can be imported at the ensemble level with the option of specifying which decks are enabled for import and which are not.

rezen uses the .rsspec file when importing recurrent attribute data from the restart file. This means that the actual data values themselves (i.e. the data array) is not loaded into memory until it is required. Note that unlike Review, the data is not imported into a database, it is simply kept in the native Eclipse files. Import times in rezen are therefore much faster than in Review.

2D Visualization

Simple 2D visualization of initial and recurrent grid attributes is available. An example is shown below...

This is a K layer view of Porosity. The user can interactively slide through all the layers. The data can be viewed in I, J or K. Another example....

This is a K layer view of water saturation. In addition to sliding through the layers, the user can also slide through the available timesteps. The range of values assigned to the colour range can also be interactively altered to provide a thresh-holding capability.

3D Visualization (Under Development for 2010 Q4)

The 3D visualization capabilities of the existing Review software are being incorporated into rezen. A simple example of an Eclipse corner point geometry grid with a pressure distribution is shown below...

The 3D visualization tools are based around the concepts of... a “data source”, in this case a corner point grid and associated attribute data “display modules”, e.g. a surface view or a scalar cut plane (slice)

Some examples are shown below....

Interactive slicing through the grid in the X-direction

Slice with a transparent grid

Multiple slices

Rotated slice (can be rotated interactively)

Axis Labelling

Interactive scalar cut-plane, rotated, tilted and moved through the grid.

Grid Cell Views Provided that the grid definition and attribute data have been imported, the user can build a list of cells, each of which can be viewed in its own cell view window. This list of grid cells is not built by default as it is not practical to build a cell view for every cell in the grid. The cell list below displays 8 cells in a tabular form. Each cell in the list can optionally have its own view opened.

Cell List In the cell view shown below, the user can add initial and recurrent attributes to the table displayed in the RHS panel. The cell I,J,K and the timestep displayed can be changed interactively using the sliders in the LHS panel.

Table view of multiple attributes for cell 1,16,7 at specified timestep

Additionally a single recurrent attribute can be selected to be viewed either as a table of data vs time or as a plot. This data can be exported to a text or csv file.

Table view of pressure vs time for cell 1,16,7

Plot of pressure vs time for cell 1,16,7