An automated and iterative technique integrates decline curve analysis, type curve matching and reservoir simulation to converge to a set of reservoir characteristics. (Part one of a two-part series.)

State-of-the-art in production data analysis leaves a lot to be desired. This is especially true when pressure data are not available, which most of the time is the case when dealing with mature fields. A new technique, Intelligent Production Data Analysis (IPDA) has been developed that consists of two major components. The first component of the new technique combines three commonly used production data analysis techniques: decline curve analysis, type curve matching and reservoir simulation. The integration of these three techniques is accomplished through an iterative process that eventually converges to a set of reservoir characteristics for each well.
The second component of IPDA takes the results of the first component plus the location of each well (by its latitude and longitude) and deduces patterns that can help managers and engineers during the decision-making process. This second component is accomplished through the use of a fuzzy pattern recognition technology.
Intelligent Iterative Integration

This second process has been named Intelligent Iterative Integration (i3) because it integrates the three production data analysis techniques using an iterative process. And it uses an automation approach that was only possible to accomplish through an intelligent systems technique (Figure 1).
The process starts by plotting production rate and cumulative production versus time on a semi-log scale. An automatic optimization routine based on genetic algorithms quickly identifies the best decline curve for the given well while it simultaneously matches both rate versus time and cumulative production versus time. Decline curve analyses performed during the process provide typical rate vs. time curves plus initial production rate "Qi", initial decline rate "Di" and hyperbolic exponent "b" that are automatically identified on the bottom of the plots. Furthermore, the 30-year estimated ultimate recovery (EUR) is also calculated and shown.
The information generated as the result of decline curve analysis is then passed to a type curve matching procedure. The appropriate type curves for the type of reservoir and fluid that is being investigated should be selected.
The actual production, plotted on a log-log scale, is superimposed on top of a series of type curves developed for the same value of hyperbolic exponent that has been found during the decline curve analysis. The same production data are plotted on a set of type curves for different hyperbolic exponents. At this point, the production data can be matched with any of the curves. This is a good example of the subjectivity of the type curve matching procedure.
Refining the process
Assuming the results of decline curve analysis are satisfactory (note that the match achieved in the decline curve analysis is subject to iterative modification and can be improved; the initial match is only a starting point), there is no reason not to take advantage of the results to enhance the possibilities of success and to remove the subjectivity from the type curve matching procedure.
Having taken full advantage of the results of decline curve analysis by, a) plotting the production data resulting from decline curve analysis rather than the actual production data (the model is much better behaved than the actual production data and can provide a better and less subjective match), and b) by using the 30-year estimated ultimate recovery (EUR) that was calculated from the decline curve analysis for the well as a guide, the modeled data are moved up and down and matched to different Xe/Xf curves until a calculated 30-year EUR comparable to that of the decline curve analysis is obtained. For this particular well, the EUR is 210.9 MMcf.
Once the match is completed, the type curve matching procedure provides permeability, fracture half-length and drainage area. These parameters, as well as the EUR, are continuously updated as production data are moved on top of the type curves for the best match.
As part of the iterative process, if during the type curve matching procedure a good match cannot be achieved (a good match is defined as a match that not only looks reasonable during visual inspection but also provides reasonable values for the parameters while the EUR is reasonably close to that of the decline curve analysis), it is necessary to go back to the decline curve analysis and modify the match there in order to get a different "b" and EUR and repeat the type curve matching. If this practice yields a closer match that satisfies both methods, the right direction has been chosen. If this practice has resulted in a worse match, then the decline curve analysis must be repeated, this time in the opposite direction. Experience with this procedure shows that in most cases a single iteration achieves acceptable results.
To complete the type curve matching process, certain reservoir parameters must be known. These parameters are used during the calculation of permeability, fracture half-length, drainage area and EUR:
• Initial reservoir pressure;
• Average reservoir temperature;
• Gas-specific gravity;
• Isotropicity (kx/ky ratio);
• Drainage shape factor (L/W ratio);
• Average porosity;
• Average pay thickness;
• Average gas saturation; and
• Average flowing bottomhole pressure.
Most of the above parameters above can be (and usually are) guessed within an acceptable range for a particular field. Usually the range of initial reservoir pressures for a field or formation is known with reasonable accuracy, or it can be assumed based on formation depth. Formation depth also can be used to estimate average reservoir temperature. Gas-specific gravity can be easily calculated based on the assumed average initial pressure and reservoir temperature. In most calculations, an isotropic reservoir is assumed, meaning that the kx/ky ratio is equal to 1. The drainage shape factor is also assumed to be 1, as in a square drainage area. Average porosity, thickness and gas saturation can be calculated for each well from logs, if they are available. If they are not, an average value for the entire field can be assumed.
IPDA allows for better matches and results in a higher confidence level if wireline logs are available for the wells being analyzed. Access to logs enables porosity, thickness and saturation to be calculated and used individually for each well during the analysis. If such logs are not available or prove to be too expensive to analyze, the procedure allows the user to input an average value (as the best guess) for all wells.
The final step during the i3 process is reservoir simulation. The reservoir simulation step itself is divided into two parts - history matching and Monte Carlo simulation. During history matching all the information that has been gathered during the first two steps is used to initialize a single-well, radial reservoir simulator. It is expected that during the history matching process several of the parameters that have been used in the simulator will be modified to achieve an acceptable match. If the modifications of one or several of these parameters prove to be very significant, the user must go back to the previous two techniques and modify them in the direction that reduces the magnitude of the modifications in the history matching process. If the modifications are not significant, the user can move to the next step.
What is "significant?" This would be a judgment call based on the available information and the parameters being modified. The rule of thumb is that anywhere from a 10% to a 25% modification usually can be tolerated. The lower limit of this toleration would be for parameters with large magnitude and less uncertainty, such as initial pressure, and the upper limit would be for parameters with small magnitude and more uncertainty, such as permeability (given that wells in tight gas reservoirs are being analyzed). Since a Monte Carlo simulation is to be performed in the next step, a certain amount of uncertainty can be tolerated.
Once a history match has been achieved, all the important parameters that are involved in the simulation process are assigned a probability distribution function (PDF), and the objective function (which is the history-matched model) is run 500 to 1,000 times. Each time a run is completed, the 30-year EUR is calculated, and at the end they are plotted to form a PDF. Then the 30-year EUR calculated from decline curve analysis, and type curve matching is marked on the PDF plot. As long as the 30-year EUR calculated from these analyses is within the high-frequency area of the plot, it means that results of the analysis are s acceptable (Figure 2).
Automating the process
Reading through the last section one might think that this procedure is hopelessly long and inefficient. In fact, the process has been automated in IPDA such that performing both the decline curve analysis and type curve matching procedures takes less than 30 seconds per well. The reservoir simulation process is currently being added to the automation process. This will require minimum interaction from the user.

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