Sensitivity Analysis and Screening

Screening in the context of reservoir model selection is often done using simple responses such as original oil-in-place (OOIP).  Traditional screening is often done through the process of ranking, which ranks a reservoir model based upon a particular criterion (like OOIP) from lowest to highest.  Models are selected based upon particular percentiles (P10/P50/P90).  This traditional screening process poses several problems:

1. As in sensitivity analysis, screening with multiple responses (such as oil production from tens or hundreds of wells) is more complicated for the engineer and requires examining multiple ranking based upon a single response.  
2. The process of sensitivity analysis and screening are disconnected.  Sensitivity analysis varies the input parameters to understand the impact on a response.  Screening focuses on selecting models based upon a ranked response.  For proper screening, one may need to do many runs beyond what is determined using experimental design.

A Novel Approach to Sensitivity Analysis and Screening

Streamsim has developed a novel approach to sensitivity analysis, which uses the concept of a metric space (explained in the metric space overview).  First, an ensemble of reservoir models are created by varying all the uncertain parameters, discrete and continuous.  Then, a metric space is constructed using multiple responses from each reservoir model, whichever responses which may be of interest (such as cumulative oil production at 5, 10, 20, and 30 years, or well-by-well oil production rate).  Cluster analysis is then performed on the ensemble of models in metric space.  The clustering idendifies models which are similar (small distances from each other), and dissimilar (large distances).  The location of the models in metric space, the parameter values for each model, and the clusters which are created allow for novel diagnostics for sensitivity analysis.  Some examples are shown below.  

The top left figure (below) shows an ensemble of models placed in 3-dimensional space using multi-dimensional scaling (MDS space).  Each point in the plot is a reservoir model.  Points close together have small dissimilarity distances.  Those far away from each other have large dissimilarity distances.  Clustering of these points in space groups models which are similar.  One can analyze visually the effect of the uncertain parameters on the distance by coloring the points in MDS space by parameter value, shown in the top left figure below.  Here, the points (reservoir models) are colored according to the depositional direction of the sandstone (45, 90, and 135 degrees).  The separation of the colors clearly indicates that similar models (small distances) have the same angle.  In other words, models are grouped according to angle, indicating that it has a high impact on the reservoir responses used to define the dissimilarity distance.  If, on the other hand, the colors were mixed together, then that would indicate that the parameter has a low impact on the dissimilarity distance, hence on the reservoir responses employed in the distance equation.

The relationship between the models as determined by the metric space lead to other analysis plots, such as the fence diagram in the top right plot seen below.  Here, each horizontal line is a run, and each line connects on the vertical axes the parameter values for each run.  The final vertical line is a single response value of interest.  In this example, we have performed a cluster analysis and grouped the ensemble of runs into clusters.  The lines are colored by the cluster which they are found, and two clusters are highlighted in green and orange.  The fence plot can illustrate how the parameter values vary per cluster,and illuminate dependencies between parameter values.  

The histogram plot (bottom left) and the pie chart (bottom right) indicate the distribution of the parameter values per cluster.  When a cluster contains models containing a small range of values of a parameter (such as oil-water contact, shown in the pie chart), we deduce that the parameter value was important in the separation of the models spatially in metric space, and hence has a high impact on the responses used in the dissimilarity distance measure.

New methods for sensitivity analysis using metric space methods

Multi-Dimensional Scaling	Fence Diagram
Histogram	Pie Chart

In summary, the metric space separates models which are dissimilar, and groups together models with are similar as measured by the dissimilarity distance measure.  This model separation allows for some simple, visual diagnostics for sensitivity analysis.

When the sensitivity analysis stage is complete, the screening step follows naturally.  Note that the cluster analysis is a form of screening, grouping models which are similar and distinguishing models which are different.  If the goal of the screening step is to select a diverse set of models, one could then select one model from each cluster (such as the cluster centroid).  If the goal of the screening step is to select a group of models which may be closest to historical data, then one would select models from the cluster which is closest to history.  For further discussion of screening using metric spaces and history matching, click here.

Advantages of Sensitivity Analysis and Screening in Metric Space

The metric space methods for sensitivity analysis and screening described above should be considered as complimentary the classical techniques.  Note though that there are some advantages to this approach:

• No response surfaces are created - the analysis is directly using the models transformed into metric space
• Spatial uncertainty (stochastic noise) is handled naturally in this approach and is incorporated into the distance calculation
• Any type of parameter, discrete or continuous, can be analyzed in this manner.  
• The screening process follows immediately after the sensitivity analysis phase.  No new software or methods are necessary for screening.