A review of the validity of a reservoir simulation model does not need to address whether the model is perfect overall. Rather, a review should address whether or not, a model can be used for a particular purpose.
Model verification is done usually with a history match, which may be as limited as a single-point test. A good history match, however, does not guarantee a good model. What does is the total package, consisting of the construction, the history match, and most importantly, reasonable projections.
In general, most individuals have limited time to review models, even though very detailed, complex models are products of many months or years of work.
Reservoir models
A simulation model represents an oil and gas reservoir in its size, shape, and physical characteristics. Its main intent is numerically to duplicate reservoir performance by incorporating physical parameters that dictate subsurface flow in porous media. The model predicts future reservoir performance under a specified development plan.
One can draw various inferences from a properly constructed reservoir model. It can be used to evaluate or confirm static conditions, such as the original oil in place (OOIP), and dynamic issues, such as well deliverability and production decline.
But the model must be verified because one cannot observe, measure, and test every aspect of a hydrocarbon reservoir. At best, one measures an extremely small portion of the reservoir, and many measurements may be erroneous or contradictory.
Models are history matched so that under historical production constraints the model behaves similar to actual wells.
The assumption is that once the model reacts under historical constraints, as did the actual wells, then it will behave the same as the actual wells under future constraints. But this is often incorrect, and misused models are common.
One should not use modeling results that contradict common reservoir engineering principles. Often professionals tend to place a higher than justified level of confidence on model results, simply because they were calculated with a sophisticated approach.
It seems obvious, however, to remember that the model is not the res ervoir itself. The model is only a representation or an analogy of the reservoir.
Once the model is built, history matched, and verified, it can be used for many purposes. Among these is to test alternative development scenarios for a field or reservoir to try to optimize either recovery or economic returns. This is an attempted optimization because no one ever knows the best depletion scenario. One can only compare reservoir performance from a relative standpoint.
Problems in determining whether a model represents the actual reservoir for a particular forecast depend on input data quality, reservoir complexity, availability of appropriate data, and level of detail, effort, and skill used to construct the model.
Regardless of the quality of these inputs, a history match can validate the model and support its subsequent use for planning purposes.
Each petroleum accumulation, simulation model, and history match is different. Some models have decades of history while others may not have any history. Thus when evaluating a model, one must look at many items, in addition to the history match.
Although one can construct a good model without a history match, there would be little basis with which to determine if the predicted reservoir performance is reasonably correct. This strictly theoretical model does not take advantage of the strongest tool of simulation, namely history matching. This is why evaluators often have little confidence in non-history matched models.
For instance, the reservoir engineering staff at the US Security and Exchange Commission (SEC) says proved reserves can be derived from a model only if it features a good history match.
History matching
In modeling, two time-consuming tasks are data gathering and history matching. Short cuts in gathering data often increase the time needed for history matching because either limited or bad data require additional trial-and-error iterations.
The initial prehistory-match model incorporates all known reservoir data and information, such as:
- Measured hard data, such as formation tops.
- Softer data inferred from analysis, such as permeability from a well test.
- Soft data that are qualitatively inferred from production trends or geological insight, such as connectivity and anisotropy.
One generally runs the initial model specifying, as a target, the observed historical production rates for each simulated well at the appropriate time. That is for each month, one specifies that each well produces the monthly volume reported in production records.
One can constrain either the rate of one phase or the total fluid or liquid volumes (Fig. 1). It is generally not possible, for example, to order a well to produce 100 bo/d and 62.5 bw/d, simultaneously. Rather, the model predicts the bottomhole pressure required for producing the specified phase rate and calculates the other phases produced based on the reservoir conditions surrounding the well.
Alternatively, wells could be constrained to produce at a certain bottomhole pressure (BHP) or tubinghead pressure (THP). In this case, the model predicts each phase's rate at the given pressure.
Even though one constrains the model to produce the known production rates, the model will calculate the well and reservoir pressures at each time step, as well as the relative phase ratios based on the fluid properties, relative permeability, and near-wellbore saturation.
Phase choices
The history-match quality cannot be determined by simply checking the match of the specified rates or cumulative production because the model continues to match specified (phase) rates as long as the reservoir has enough energy and mobility.
The phase chosen to constrain the history match is less important than the quality of the history match.
One usually starts a history match with the total liquid rate. This helps in obtaining a reasonable field-wide material-balance match, although the phase ratios will generally be poor in the first pass (Fig. 2).
Engineers first focus on obtaining a good pressure match by refining pore volume, aquifer strength, etc. Next, they adjust factors likely to improve the phase-ratio match, and eventually they will match the hydrocarbons recovered from individual wells.
A field-wide liquid match helps size total pore volume and aquifer strength. It also obtains an overall phase-ratio match. If the reservoir contains predominately gas or condensate, engineers use total fluid rate, including gas, to replace total liquid rates.
When one completes this field match with liquid rate constraints, the authors suggest that one continue to improve the history match by including specific phase rate constraints.
An oil rate usually is the best constraint for a black-oil reservoir, whereas a gas rate constraint is best for a reservoir that produces dry gas and water.
Engineers specify a particular phase if certain wells produce predominately that phase. For example, the oil phase may give poor results for a well producing 99 bw/d and 1 bo/d. Thus, one should constrain most wells by the primary phase of interest except for those wells producing extreme phase ratios. In these, the predominant phase should be the constraint.
The main reason for switching from liquid or fluid rate constraint to phase rate is that the final history match will have the correct amount of the primary phase produced throughout and at the end of the match. This allows for more straightforward, reliable future recovery projections.
Furthermore, reported oil or gas volumes usually are more accurate and reliable than the reported water volumes, which are included in the liquid and fluid rates.
Iterations
Even with the model constrained to historical oil or liquid rates, one also needs to match other parameters.
First, one has to compare average reservoir pressure and simulated well pressures, as calculated by the model, with observed values from the field.
A particular pressure will be associated with a given volume withdrawn from the reservoir. When compared to history, the pressures indicate how well the model compares to reported values. From this comparison, engineers also obtain ideas on how to get a better match.
If the model pressures are low compared to measured values, the evaluators need to add energy to the system by altering different parameters, specifically those parameters for which they have the least confidence.
The primary parameters for pressure matching include pore volume, permeability, hydrocarbon volume, aquifer configuration, and compressibility. These parameters will change from model to model, both in respect to the parameters themselves and the relative uncertainty therein.
In general, after one obtains the field-wide pressure match, the next step is the saturation match.
The match of water cut or oil-water ratio and the GOR or oil-gas ratio dictates the saturation match (Fig. 3). For a dry gas reservoir, this might only be a match of the water-gas ratio. In this process, the history match moves back and forth between field-wide match and well-by-well match.
One might have a good field-wide match with individual wells matching poorly. An example could be water encroachment from the wrong side of an anticline. The overall fluid rate and ratio matches could be excellent, but the well-by-well match could tell a different story.
A poor match of individual wells may lead to offsetting errors, thereby creating the illusion, on a field-wide basis, that one has a good history match.
Some parameters used for matching the saturation include individual layer permeability, vertical to horizontal permeability ratios, and local geological features such as channels, faults, and barriers. Saturation matching can be time consuming because in many cases changes to one well impact other wells.
The time and resources required for history matching depend on such factors as:
- Years of historical data to match.
- Number of wells.
- Number of grid blocks.
- Number of phases or formulation (oil, gas, water, fully compositional).
- Software functionality.
- Hardware.
- Geological model and reservoir description accuracy.
- Experience of analysts.
- Time and budget limitations.
- Scope and objectives.
- Ultimate use.
Usually experience in constructing and history matching models will help one gain a sense of the time required to complete history matches, although the time needed is difficult to estimate. In many cases, the simulation engineers never believe that they have completed the history match because history matches are subjective and the engineers usually feel that a better match is only a few runs away.
The level of satisfaction will in most cases be a compromise among remaining time, budget, accuracy, and ultimate use of the results.
As a general approach, we have identified the following nine steps to organize a history match review:
- Determine ultimate use of the model results.
- Check for reasonableness in model construction.
- Assess quality of field pressure and produced volume match.
- Assess quality of local well pressure and saturation match as warranted.
- Look for reasonableness in modifications to achieve match.
- Review the simulated transition from history match to prediction mode.
- Evaluate reasonableness of status quo case and other forecast cases.
- Assess overall quality and validity of model.
- Use results as analogy to actual field.
No real rules of thumb are in place for determining the quality of a model history match, but the duration of a history match period is important. A model with a 15-year history is probably more reliable than one with only 2 months. But a model with only 2 months of history may be more reliable if constructed to higher standards and history matched with more reasonable assumptions.
Ultimate use
Individual well matches may not be important if one requires only general field deliverability estimates for a quick sanctioning decision or a rough estimate for initial sizing of field facility.
For reserves certifications, development well planning, or completion optimization, evaluators most likely require a strong critique of the model and history match.
Reasonableness
The reviewer checks the reasonableness of the model construction to assess what data were included and whether it was used appropriately. The reviewer needs to investigate discrepancies between mapped structural and stratigraphic features and those incorporated into the model. This can be a concern if the model is used to assess reserves because reserves guidelines often place strict limitations on geological features, such as contacts, sand thickening, etc.
In the overall assessment, an engineer should consider if fluid and rock properties, saturation functions, and well descriptions and placements are consistent before and after a history match. Where significant discrepancies exist, additional review can determine if model assumptions that contradict observed field data are justified.
One should note that in many cases gross assumptions must be made during the review because availability of actual data or time limitations preclude detailed checks of input parameters.
Pressures, produced volumes
After determining that the model was constructed prudently, the reviewer can begin to evaluate the quality of the history match, starting with the overall pressure and material-balance match.
Global reservoir pressures should be reasonably matched throughout the duration of the history-matched period.
A clear-cut tolerance that dictates a good or poor quality match does not exist because many factors influence the overall history-match evaluation as well as the general fluctuation and error inherent in pressure measurements, which are point measurements that represent field-wide values.
One test may be to check that observed pressures fluctuate near to model-calculated average regional pressures. If calculated pressures are within about 5% at all times, one should consider the pressure match to be very good.
Similar to the field-wide pressure match, the field-wide phase match should be the next item to be considered. The model's calculated rates and cumulative volumes of the non-specified phases, such as water and gas for an oil reservoir, should be compared to the historically observed values.
The primary hydrocarbon phase rates and cumulative volumes should be within about 2-3% of historical values, especially for reserves evaluation.
Cumulative volumes may match at the end of the history match, even though the rate profile prior to that point is radically different. The difference in historical rate profiles, however, portends significant divergence between the simulated future rate stream and the actual rate stream that the field will realize. Thus, simply obtaining the correct cumulative volumes of each phase by the end of the history match does not, in itself, constitute a good history match.
The combination of a good pressure match and phase volume match ensures that the overall field material balance is reasonable. One may then expect this model to provide reasonable approximation of field-wide performance as opposed to local or well-by-well bases.
Well pressure, saturation
The individual well history match is the next level to evaluate. The model should match the individual well shut-in pressures and produced phase volumes reasonably well.
Very rarely will all wells in a model have a good match. In general, one should look for overall field-wide quality. That is, one can discount the poorer matched well if it is surrounded by a few wells with good matches.
A model cannot capture all heterogeneities or geological features, especially given limited data, time, and budget. A poor match may also indicate the poor quality of the measured field rate or pressure data and may not indicate a poorly constructed and matched model.
When nearby wells indicate a similar, poorly matched response, an evaluator may infer that some reservoir dynamics are not fully understood and thus are not properly modeled for that area. In this case, the engineer conducting the history match or model documentation may clarify the reason for the mismatch.
Modifications
In the next step, the engineer needs to determine whether the changes made to achieve a match are reasonable. One should view the model results with skepticism if it has a good match but the changes were unrealistic.
One should seriously question the model's forecasts if changes to obtain a match are difficult to justify geologically. For instance, placing hydrocarbons in an unlikely area usually indicates problems with the model.
Potential problems with the model may be:
- Input parameters, such as high porosity, low residual saturations, or high compressibility
- Geologic features, such as permeability barriers surrounding a single well or grid-cell pipelines connecting an aquifer to a single well.
Of course, many unusual items can be justified based on data observations or performance. But concerns should be focused on items with no reasonable justifications and on models that could have been matched with other, more reasonable history matching adjustments.
Of special concern are modifications of single wells. Frequently, modelers will history match by making alterations in the immediate vicinity of individual wells. These modifications can include transmissibility modifiers to stave off advancing water, increased or decreased pore volume to better match pressures, and alterations to relative permeability end points.
Often, they make such changes to the cell column of a vertical well, possibly including surrounding columns. Such changes, if common in a model, may indicate a degree of heterogeneity not properly expressed throughout the rest of the model. In this case, one should distribute this heterogeneity or compartmentalization throughout the model. Otherwise, infill wells added later will not include the heterogeneity shown by the history match.
It is unusual for a model not to require any changes from the original description to match the historically observed well performance. In such a case, the model itself helps verify the initial model construction and geological interpretation.
Transitions
One usually has to reconfigure the final history matched model to predict future behavior. These forecasts, typically referred to as prediction cases, usually are set up by specifying either the BHP or THP for the wells.
The simulator will calculate the produced volumes and phase portions based on the specified pressure, the completion data, and the surrounding reservoir conditions. For artificially lifted wells, an alternative is to impose a constant liquid or gas rate until the wells reach a minimum flowing BHP or THP.
In general, either a total liquid rate or a flowing THP or BHP is assigned to wells for future predictions.
The phase rate profiles should be smooth in the transition from history matching to prediction, unless new wells are added, existing wells are shut-in, or the fundamental constraints on the wells are changed. This should be true for the field-wide and well production rates. A shift when transitioning from the history match mode to prediction mode usually indicates noncalibrated wells.
One often needs to adjust each well's productivity in the prediction mode because during the history match the well's productivity may not be that important. Note that production rates are specified during the history match and that the main emphasis is on material balance and reservoir fluid movement.
Usually, one adjusts a productivity factor to tie the recent production rates to recent flowing BHP within the model. This productivity adjustment is referred to as the calibration mode.
This process, typically iterative, depends on the interference between the wells. This step ensures that the wells in the model reasonably predict the future performance of actual wells.
In some cases, one may not require adjustments for robust models and mod els that incorporate many of the parameters influencing individual well productivity, such as skin damage, partial penetrations, and stimulation treatments.
Validating forecasts
This discussion of the evaluation of a history match has been primarily qualitative and not quantitative because of the variability in model types and history matches.
The status quo forecast is an expeditious test to help evaluate a model quantitatively. This test can determine whether a model is inappropriate but it cannot its appropriateness.
In the status quo case, one continues the past operating practices into the future. As an example, one can consider a model's predictions of a depletion-drive reservoir as good if the predicted decline rate is consistent with the historical and extrapolated decline curves.
Of course, if the drive mechanism changes, for instance to a waterflood, the future predictions have some uncertainty. Also, if the status quo case indicates unrealistic future projections and declines, the model should be considered as being invalid for predictive purposes, unless this anomaly could be explained (Fig. 4).
Once the status quo case is checked, one can predict with more confidence the influence of new operating practices, such as operating pressure changes and infill drilling.
The engineer evaluating the model must determine whether a predicted process did not exist in the past, and as such, has not been subject to history matching. If, for instance, the model starts with depletion drive and then changes to a field-wide waterflood in the prediction mode, the engineer must determine a level of confidence in the forecast.
If the field history included a waterflood pilot project with the model history match capturing this response reasonably well, the engineer would have a high confidence in the field-wide waterflood. On the other hand, without a history-matched pilot project there is less confidence.
Engineers must base their confidence on:
- Whether the process has been history matched.
- Whether the data that drive the process have been laboratory measured or merely assumed.
- Whether the results are reasonable for the process.
In cases without a pilot, a modeler can obtain data from a wealth of sources, which may include fine-scale mechanistic models and lead to additional models to review. In many cases, a new exploitation process will not depend upon characteristics determined through history matching.
For instance, vertical permeability variances might make almost no difference in the history match of a depletion-drive gas reservoir exploited by vertical wells. On the other hand vertical permeability might make a tremendous difference in the forecast rates and recovery if horizontal wells are added to the prediction run (Fig. 5).
Thus, if good data are not available for a non-history matched process, one may need to do sensitivity studies to assess the variability of potential recovery and rate forecast to parameters that were only poorly resolved during the history match (Fig. 6).
While stimulation is a powerful tool, acceptance of its forecasts should be predicated by appropriate review. Even with a favorable review, simulation results must be viewed in light of their intrinsic limitations, which can be associated with a particular model or modeling in general.
The authors
Dean Rietz is vice-president and manager of reservoir simulation at Ryder Scott Co., Houston. He has concentrated on the use of numerical approaches to evaluate oil and gas reservoirs. Rietz holds a BS in petroleum engineering from the University of Oklahoma and an MS from the University of Houston. He is a member of SPE and is a registered professional engineer in Texas.
Miles Palke is a petroleum engineer working in reservoir simulation for Ryder Scott Co. Houston. He has more than 5 years of reservoir engineering experience with emphasis on reservoir simulation studies. Palke holds a BS in petroleum engineering from Texas A&M University and an MS from Stanford University. He is a member of SPE.
