History Matching
When the geological model is complete,you should verify that it reproduces the observed rates and pressures during a simulation run. This is commonly used to prove that the model makes a reasonable prediction for the future. Usually users run tens or maybe hundreds of different simulations, in order to find the best match. The History Match Analysis in Petrel allows you to easily and quickly analyze hundreds of simulation runs to find the best match. It is recommended to start off at a high level and then examine in more detail all the way down to obtain a data curve for every well.
The Calculations (History Matching)
The History match analysis tool calculates the absolute difference between the observed and the simulated values at each time step and then divides by the number of points used, to give users an averaged difference value or what we call the match value (M). It also normalizes the value by dividing the difference by a normalization parameter σ:
Here M is the match value, N is the number of time samples, Si is the simulated values and Oi the observed values at time i.
By setting the normalization values correctly, you can force the match value to be in a given value range. Hence every vector will have the same importance in the combined match. The normalization can also be used for weighting purposes, that is, choosing weights of different size will put more weight on selected vectors in a combined match.
Zero values from the observed data can be filtered out. This way you can disregard data from times when the well is shut in, so that if all values from the observed data are zero for a well, the data points in this interval will not be used in the calculation.
History Matching Analysis
TheHistory match analysis process is located under Simulation in the Processes pane.
If no History Match Statistics sets have been created then the first time the panel is displayed users will only be able to select Create new match. A unique name for the match set will be calculated automatically, but it can be edited via the appropriate edit field in the panel. The Observed Data Set will contain a list of all the observed data sets previously loaded and will default to the first one found.
If History Match Statistics sets have previously been generated then the default selected option is Edit existing match. If a History Match Statistic set has been selected in the Results Pane then it will be the default selection. The Observed Data Set shown will be the one that was used to create the History Match Statistic set. If you do not want to edit an existing History Match Statistic set, then simply select Create new match.
Select the Observed Data Set that you would like to use in this match set. In the white box in the bottom part of the panel you can find all the vectors that have been found in both the observed data sets and in all the cases. Set to Use Default for all, or highlight any combination of vectors and deselect Use Default to specify individual settings. You do not need to specify the wells or cases, as the History Match Analysis will be automatically performed on all wells in all cases. The calculations are relatively fast so this does not pose a problem.
Note: If you change the Observed Data Set, the list of vectors will be recalculated and any customized settings made to the old set will be lost.
Sample
Choose between Simulation frequency and Observed frequency.
Simulation frequency: In this instance, the observed data is sampled forward, that is, is regarded to be constant from one observed data point to the next. The values for the observed data are averaged and compared with the simulated data at every time step.
Observed frequency: In this instance, the simulated data is considered to be constant from one time step and backwards to the previous time step. These values are compared with the observed data at all observed data points.
Normalization
This process is used to normalize the values. More specifically:
1. it will make the match unitless;
2. it will make the result be in a certain ’normalized’ range;
3. it can also be used as weighting when combining matches.
Choose between Average (%) and Absolute. The first option will divide the error (difference between simulated and observed) with the given % of the average observed value; the Absolute option will use the value you specify.
By using an Absolute value of 1, the match value will be the un-weighted average error for the time interval in the original unit. The match value is an absolute value and will always be positive, independent of whether or not the simulated value is less or more than the observed.
Note: This stage of the process only performs the ‘expensive’ sampling and normalization of the data. The remaining thresholding and summation of the partial match values are done ’on the fly’ when toggling the various vector matches, identifiers and cases, whilst displaying the plots/maps.
History Matching Statistics
TheHistory Match Statistics folder is on the Results Tree and holds all theMatch Sets. It also contains two subfolders:
1.Vector Matches contains all the different vectors (curves) that are available for matching analysis;
2.Identifier contains all the wells.
The combination of those and of what is selected in the Cases pane, will decide what is calculated and displayed.
Settings
In the Settings panel for a particular match set there is a Settings tab where you can define threshold values.
Threshold
A threshold is used when displaying Qualitative matches. Qualitative matches are graded from 1 (good) to 5 (poor). Any raw match value below ‘Min’ will be graded 1. All raw values above ‘Max’ will be graded 5. The interval in between is divided into three equally sized intervals, graded 2-4.
In cases where the user chooses to display Quantitative match values, the raw match value will be displayed and the threshold value will not be used. The color map used for Quantitative plots will be continuous, while for Qualitative plots it will be discrete.
Case Comparison
This is used when comparing two cases in map view. When you compare two cases it is very unlikely that they will have exactly the same value down to the last decimal, therefore, for practical purposes, we will consider two cases to be equal, where the absolute difference is less than the Equality value set here.
Statistics
Under Settings for a particular Match set there is a Statistics tab. This contains the information generated from running the initial part of the process (the sampling and normalization of the data). This is a more detailed version of the data that is written out to the log window when the History Match Analysis process is run. The table has six columns:
Simulation & Vector
It displays the name of the case and the match vector.
Minimum & Maximum
It displays the minimum and maximum match values found. This should help you when trying to determine the threshold settings.
Zero data
This reports whether zero data values have been found in both the observed and summary data (this can happen if the well is shut in). Such information should help you determine whether you need to switch on the Zero Data Filtering option in the main process panel.
Note: It is only possible to switch on or off the Zero Data Filtering on a vector-by-vector basis. You cannot switch it on or off on a case-by-case basis.
Wells matched
This reports the number of wells that had both the observed and summary data for the vector in the case. This is a simple way of checking that the expected number of wells had data for the vector.
Style
Under Settings for History match statistics you find the Style tab, which has three further tabs:
General
General style settings, such as Labeling, Marker size and color templates can be found here. Optimizing the colors (min/max value range) when displaying your results in a map window is recommended The Auto Size option automatically sizes the font used to display the labels in such a way that they do not overlap. This can result in very small labels that are difficult to read; therefore, the option is switched off by default. Printers have a far higher resolution than a typical screen so it can be useful to switch this option on, prior to producing a hard copy output.
Function window
Choose coloring to indicate the best and worst matches. Choose between single vector mode and combined vector mode. Combined vector mode (see How combined vectors are computed) will combine (sum) the selected matches when displayed. The combine mode is also selectable via thetoolbar and the popup menu of the History match statistics set.
If the combine vector mode is selected then a single point will be plotted for all the vectors using the Match color. If the single vector mode is selected then points will be plotted for each vector selected. There are options on this panel for how the points should be colored, either using the property from the subject or evenly across the current color map.
Map window
Choose between Well compare mode and Case compare mode.
Well compare mode displays match values for wells for a selected case. Their value can be displayed as either qualitative or quantitative. Bubble plots are available for this mode where the size of the marker is determined by how good the match is. This makes it very easy to see which wells are producing good and bad matches. Options are available in the panel to specify the minimum and maximum marker size for the bubbles. Qualitative or Quantitative matches can be selected using the radio buttons on this panel or via the popup menu of the Case subject.
Case Compare mode compares two selected cases.
History matching workflow example
The aim of this example is to give an idea of how to conduct such an analysis and also how to interpret the results you see.
Before you start
If you have not observed yet data and simulation results in your project, you will first need to import some. Observed data can be imported onto the Wells folder in the Input pane; ECLIPSE simulation results can be imported into the Case pane.
Run the history matching process
Configure the options as described above, under Settings for History match statistics, then select Apply or OK. A new Match Set will be created under the History match analysis folder in the Results pane.
General plotting notes
There is an option on the root menu of the Cases pane (right-click in the Cases pane) to select or deselect all the cases. This option can be very useful as there is no top-level root node to toggle on/off all child nodes.
There is no need to select a Match statistics set, as this will be done automatically once you have selected a valid combination of vectors, wells and cases.
To make a vector or well display on the X-axis rather than on the Y-axis, right-click on the appropriate vector or well, and choose Select as X.
Petrel will determine the type of plot you want, by analyzing the items you have selected. It is therefore possible, with certain combinations, that a plot cannot be generated. These scenarios will produce an empty plot; this should not be confused with plots that are valid, but for which no valid data can be found. These are indicated by the text “No Valid Data found” being written across the plot.
The wells and vectors are initially listed in the Results pane in the order that they were found when the History match analysis process was run. It is possible to sort the wells or vectors by name or property by right-clicking on the corresponding folder and selecting one of the various Sort By… options.
The X- and Y-axis ranges will often change, due to different types of plots being generated. To normalize the view.
Rank cases
Open a function window and then select your choice of:
Cases of interest (from the Cases pane1)
2. Vector Matches of interest (under the Vector Matches folder of the History match statistics folder of the Results pane)
3. Wells to include (under the Identifier folder of the History match statistics folder of the Results pane)
The plot above shows Match Value Vs Case. This is a very easy way to find the good and bad cases. The superimposed arrow indicates that the match value is decreasing when we do more simulations. This shows that we are improving the model for this particular match.
If a single vector is selected, its name will be displayed on the Y-axis. If multiple vectors are selected, the name for the Y-axis will change to indicate that it is a combination. If multiple vectors have been selected, then you can use thetoolbar button to display a marker for each vector match, rather than a single marker representing the combined match for all.
Cross plotting vectors
Open a function window and then select your choice of:
1. Cases of interest (from the Cases pane)
At least t2. wo vector matches (under the Vector matches folder of the History match statistics folder of the Results pane). One vector must be designated as the X-axis. To do this, right-click on it and select the menu option ‘Select as X’. The other vectors will be combined, if necessary, and placed on the Y-axis.
Wells to include (under the Identifier folder of the History match statistics folder of the Results pane)3.
The plot above shows a cross-plot of Oil Production Rate Match Values Vs a Combination of other Match Values. This can be used to see trends in your data. An example would be if you were able to improve one match while something else is made worse. This type of plot will very quickly show you any negative correlations. The box, in the lower left corner, indicates the optimal position for the match values to appear. Those are the cases with low difference in Match Values for all Vectors being plotted. The superimposed green arrow indicates a good trend (both are improving) where as the superimposed red arrow indicates a bad trend (one match value is improving whilst another is getting worse).
Cross plotting wells
Open a function window and then select:
1. Cases of interest (from the Cases pane)
2. Vector Matches of interest (under the Vector matches folder of the History match statistics folder of the Results pane)
3. At least two wells (under the Identifier folder of the History match statistics folder of the Results pane). One well must be designated as the X-axis. To do this, right-click on it and select the menu option ‘Select as X’. The other wells will be combined, if necessary, and placed on the Y-axis.
Plotting well matches in map view
Be sure to select Well compare (Single case select mode) in the Map window tab of the Settings panel for History match statistics, or deselect the Case comparetoolbar button.
Open a map window and then select:
1. Case of interest (from the Cases pane)
2. Vector Matches of interest (under the Vector matches folder of the History match statistics folder of the Results pane)
3. Wells to include (under the Identifier folder of the History match statistics folder of the Results panel)
The map above shows the qualitative match for a specific case on a map window. Values are given by coloring, and the bubble plot mode has been enabled so that the size reflects the mismatch. We immediately see the three red wells that match poorly. Switch between qualitative and quantitative in the History Match Statistics Settings or via the popup menu options of the case.
Note: Only one case at a time can be selected in this mode. Nothing will be displayed until only one case has been selected. Once the map is displayed, selecting a case will automatically deselect the previous one.
Comparing two cases in map view
Be sure to select Case compare (dual case select mode) in the Settings panel for History match statistics, or press the Case Comparetoolbar button.
Open a map window and then select:
1. The two cases of interest (from the Cases pane).
2. Vector Matches of interest (under the Vector Matches folder of the History match statistics folder of the Results pane)
3. Wells to include (under the Identifier folder of the History match statistics folder of the Results pane)