Pre-History Match Screening of the Prior Model

History matching is tremendously time-consuming for the reservoir engineer.  And, without question, a great deal of effort by reservoir engineers has been expended trying to history match models where there have been faulty or incorrect assumptions and interpretations input into the model.  Ideally, these assumptions and interpretations, which we denote as the "prior model", should be test before launching into the time-consuming history matching process.  One option is to simply run a (large) number of simulations varying the input parameters of the prior model, and examining the output curves to see if they "bracket" the historical data.  However, for large models and many wells, this is a difficult or impossible task.  

As described in the metric space overview, one can create a metric space consisting of an ensemble of reservoir models (derived from the prior model) using a distance measure employing one or more responses from the reservoir model.  If the model response can be compared to historical (observed) data, then the "True Earth" can be placed in metric space as well.  Using multi-dimensional scaling (MDS), one can visualize the metric space, an example of which is shown below in 2D (often, the MDS space is greater than 3D).    As is shown in the figure, we can plot the location of "True Earth", and compare its location to the ensemble of models.  In ideal circumstances, the "True Earth" should be located within the cloud of models (left).  This indicates that the prior model captures well the historical data.  However, it may often be the case that "True Earth" is located outside of the cloud of models (right).  This might be an indication that the prior model is missing some important aspect of the reservoir which is influencing the reservoir response.  One may attempt to history match in this case, but severe deviations from the assumptions and interpretations that are put into the prior model may be necessary.   It may be preferable for the reservoir engineer to take this plot on the right, visit with the geomodeling team, and figure out what is missing from the prior model, rather than proceed to a laborious history matching effort which may ultimately fail.  

An Ensemble of Reservoir Models projected into 2D MDS Space

Performing this pre-screening is straightforward, so there is little reason to not perform this pre-screening once the ensemble has been created. And, in the end, one may save a significant amount of time and effort in catching cases such as seen above (left), and avoiding attempting to history match a model (or models) when some important aspect of the reservoir is missing in the prior model.

Example:

We wish to pre-HM screen a reservoir model composed of 43,000 active grid blocks, with over 100 producing wells, supported by over 20 water injectors, with 9000 days of production.  An example of the reservoir model is shown below in Figure 1 (left).  72 reservoir models have been created, varying the spatial correlation length of the reservoir properties (low,high), angle of correlation (45,90,135 degrees), Kv/Kh ratio (0.1, 0.01, 0.001), transmissibility between the upper and lower layers (0.001, 1), and the residual oil saturation (0.2, 0.3).  The question is then whether, by modifying these parameters, we can obtain a successful history match. Figure 1 (right) displays the field oil and water production, indicating that the reservoir response from the 72 models has bracketed the historical field response quite well.  Based upon this analysis, one may conclude that the five parameters we have chosen are sufficient to obtain a good match.

Figure 1:  (Left)  One realization of the reservoir showing the injectors (blue) and producers (blue).  (Right)  the water and oil production for the 72 models, with the historical water production shown by the blue points, and the historical oil production shown by the green points.

However, the story though is quite different when we analyze the model based upon a metric space analysis.  We first create a metric space based upon a well-level flow-based distance measure (using the oil rate production over all time steps for each well).  Using MDS to visualize this space, we can see in Figure 2 (left) that the historical data, represented by a cube and identified by the blue lines, is far away from the 72 models that have been created (which are the same 72 models which bracket the field data.  For a more quantitative analysis, a plot of the Eigenvalues derived from the MDS procedure (Figure 2, right) can indicate how well the well-level response has been bracketed.  What is important to focus on is the location of the horizontal line in Figure 2 (right), which indicates that less than 50% of the variability of the well production history is captured by the 72 reservoir models.  This analysis results from the fact that the historical data is bracketed by the reservoir models in only the first dimension in MDS (associated with the first Eigenvalue of MDS).  The first dimension in MDS represents about 45% of the total variability of the well-level model response.

Figure 2:  (Left)  Plot of the MDS space using a well-level flow-based distance measure.  The history (represented by a cube) is far away from the 72 reservoir models that have been generated.  (Right)  The Eigenvalue plot of the MDS space.  What is important to focus on is the location of the horizontal line, which indicates that less than 50% of the variability of the well production history is captured by the 72 reservoir models.

Figure 2 leads us to the conclusion that the current parameterization (the 5 selected parameters and the variation of each parameter) is insufficient to obtain a good well-level history match.  An attempt to obtain a well-level history match by modifying these parameters within their given bounds will fail.  Instead of history matching, the reservoir modeling team should revisit the reservoir model, question the assumptions and the input that has gone into creating the model, and attempt to understand what uncertain parameters are missing, or too narrowly defined, what data has been poorly characterized, etc.