SPE 152392

Probabilistic Production Forecasts Using Decline Envelopes L.E. Brito, SPE, F. Paz, SPE, D. Belisario, SPE, CBM Mexico

Copyright 2012, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Latin American and Caribbean Petroleum Engineering Conference held in Mexico City, Mexico, 16–18 April 2012. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract One of the most frequently method used for production forecasting is the decline curves analysis, which can be harmonic, exponential or hyperbolic; being the most commonly used the exponential decline curve.

However there are wells that exhibit complex production behaviors, where the exponential decline curve does not fit the entire production history. One of the solutions that have been used is to divide the production history into several segments and then apply different decline factors for each segment. This complex behavior results from a long transient period observed in formations with very low permeability that have been stimulated with hydraulic fractures.

In this paper, we propose an approach that considers a table of time-dependent factors; each factor results from dividing the production rate at time t, q (t), by the initial production rate, q (0), so the production history becomes a profile of factors with values between 0 and 1, which represents more accurately the behavior of the well decline. When this method is used to analyze a reservoir or a field, each well produces a decline profile, and using the information from all wells generates an area in which a profile for each well can be found. This area is defined by two envelopes, an upper bound, representing the most favorable performance, with lower production decline, and a lower bound which represents the worst performance with higher production decline. The upper bound is generated using the maximum function, and then a smooth curve is found with a hyperbolic fit; for the lower bound a similar process is used but using the minimum function. Additionally an average curve is determined.

In order to perform a probabilistic production forecast using these envelopes, a profile is generated within the envelopes using a probabilistic distribution of the ubication. A random value between 0 and 1 is generated and added to the respectives values for each month of the lower envelope, to get a new profile. Using this profile a production forecast can be made and multiple simulations can be performed to obtain a probability distribution curve of all the possible outcomes.

Introduction The production data analysis is one of the tools that are used commonly in the industry to make production forecasts. Arps equations are in use since the 1940’s and more modern approachs such as Fetkovich et al, Mc Cray, Blassingame et al, are in use since the 1980’s. All these method are appropriate to make forecasts in a deterministic way within its own limitations. The aim of this paper is to propose a simplified methodology for making probabilistics production forecasts using the historical production data without the need to be dealing with complex analytical or numerical models that would require more geological and reservoir data, not always available.

This kind of approach is very suitable for a preliminary assessment of the economic evaluation of a well, reservoir or field taking into account the risk and uncertainties, and can be used in the visualization phase of development plans (FEL).

The production behavior of very low permeability, stimulated wells is very complex, due to the presence of a relative long period of transient flow condition. Using the transient data to make long time forecast is considered incorrect and misleading.

The experience in the analysis of production data from fields that produce from low permeability formations that have been hydraulic fractured indicate that these wells have relatively high oil production rates at the beginning with very high declination, and then lower declinations. This kind of behavior can not be modeled with a single declination curve, and the solution used in some cases is to split the production history in two or three segments, each one with a different percent of declination. A simpler approach that can be used in a probabilistic way have been developed in this paper and consists, basically, in getting normalized and sincronized curves that can be used as models for predicting the behavior of new wells drilled in these areas.

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Methodology As we are interested in comparing the production behavior of several wells within an area the first step is to define an adimensional factor for each value of the production curve, this value is called the production factor, Factor(t). Using the production factor we get a normalized production curve for each well. The other process used in the methodology is called synchronization, and it means to put all the production curves from all the wells in the same time scale as if they were producing from the same starting date. The final process consists in determining the curve envolepes that contain within its limits all the production behaviors observed. Then, the decline envelopes are used to generate probabilistic production forecasts. Production Factor. Factor(t) The production factor is used to represent more closely the complete behavior of the wells and is the normalized production rate with respect to the initial rate.

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Factor(t) results from dividing each production rate by the initial production rate, Eq. 1. The set of all the factors constitute the decline profile for each particular well. As the factors cover all the production history, a better match is always found, even when the well is still in the transient flow period.

Table 1 and Fig. 1 show an example of application of this concept. In the table values of oil production every month are

shown, and the calculated factors, Factor (t) making a decline profile. Fig. 1 shows with green dots normalized values. The exponential curve, in red, does not adjust the initial production stage.

Table 1.- Production history and Factor(t) profile.

Date b/d Time, month Factor(t)

15/11/1971 200 0 1.00

15/12/1971 87 1 0.44

15/01/1972 62 2 0.31

15/02/1972 49 3 0.25

15/03/1972 12 4 0.06

15/04/1972 34 5 0.17

15/05/1972 27 6 0.14

Fig. 1.- Graph of Normalized Rate vs Time. Green dots represent the values of the normalized production rate for each time and the red curve represents the exponential fit. The curve does not match the early flow period.

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To reproduce the production history once we had determined the values of Factor(t) we use Eq. 2.

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Next are listed the steps to follow when applying the methodology of Decline Envelopes. Inspection of production histories. Selection of pure decline periodos. Synchronization of production histories. Normalization of production histories. Composite graphs of all wells. Determination of Decline Envelopes. Determination of Frequency Distribution of initial production rates. Determination of Production Type Curves, P10, P50 and P90, with a corresponding cumulative production curve.

Inspection of Production History The first step is the inspection of the production history of the well to determine if the data has the quality to be analyzed, if there is no erratic behavior or values that seem suspicious at first sight, such as spikes or sharp production declines or monotonous measurements. Fig. 2 shows the behavior of a well producing from a stimulated low permeability formation. The history spans over a period of more than ten years. This behavior looks, in general, quite normal and acceptable for analysis.

Fig. 2.- Inspection of production history. This behavior looks acceptable for analysis. The production history covers a period of more than ten years.

Fig. 3 shows a production history with an erratic behavior, no suitable for analysis. Fig. 4 also shows a production history with repeated measurements and erratic behavior that is not adequate for decline analysis. This kind of behavior results from changes in the operating conditions of the wells, workovers, repairs, choke changes, shut in, and other events that distort the decline behavior of the well. Another problem that arises in the analysis of some production histories is when you find monotonous measurements that could be indicative of repeated measurements.

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Fig. 3.- Production history with erratic behavior, not appropriate for analysis.

Fig. 4.- Production history with repeated measurements and erratic behavior, not appropriate for analysis. Selection of Pure Decline Periods From the production history pure decline periods are extracted to avoid discontinuities in the profiles caused by changes in the production conditions of the well, such as changes of chokes, stimulations, repairs and other activities that can generate abrupts behavior changes. The aim is to obtain a declining profile from the production history.

According to the theory a well that flows at constant bottomhole pressure in a closed drainage area with no flow at the outer limit will experience a declining behavior. The first stage corresponds to the transient flow period, and the second stage to the pseudo static flow period.

In this step, graphs of production rate vs time are made and inspected to select the time periods where a declining behavior is observed and there are no abrupt changes in the production behavior.

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SPE 152392 5

Fig. 5.- Selection of pure decline periods from the production history.

Fig. 5 shows that most of the production history can be extracted, eliminating some points at the start of the production period until it reaches the maximum value of production, and from this point information can be used for comparison with the production histories of other wells.

Fig. 6 shows another production history and the selection of the of pure decline period. There is a somewhat erratic behavior during the first months of production; there is a point beyond which a period of decline is observed. Fig. 7 shows another production history with a pure decline behavior. Now it can be seen that there are patterns of behavior.

Fig. 6.- Selection of pure decline periods from the production history.

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Fig. 7.- Selection of pure decline periods from the production history

Synchronizing Production Histories When comparing various production histories on the same graph, a similar pattern can be seen, as shown in Fig. 8.

Fig. 8.- Comparison of different production histories in the same graph.

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In order to compare all these histories what is done is to synchronize them to the same start date as shown in Fig. 9,

placing all production beginnings at the same time. This type of plot where multiple synchronized profiles are in the same graph helps to get an overview of the initial production rate and overall decline behavior.

Fig. 9 shows the synchronization of multiple wells from a low permeability field. Even though there are differences in the initial production rate a similar decline behavior can be seen.

Fig. 9.- Synchronized production histories of several wells.

Normalization of Production Histories and Composite graphs of all wells (Set of Decline Profiles) As we are interested in the decline profile, the next step, after synchronizing, is the normalization of production histories, which results from dividing each production rate by the value of the initial production rate. When all production histories are normalized, what you get is a group of decline profiles, with values ranging from 0 to 1 that generate a band of decline, which represents an area where any decline profile can be found from the possible decline profiles exhibited by the wells, see Fig. 10. The width of the band is indicative of the dispersion showed in the decline behavior of all the wells, and the uncertainty associated with production forecasts.

Fig. 10.- Set of Synchronized and Normalized Production histories.

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Decline Envelopes To reduce the complexity that represent many lines, see Fig. 10, these were replaced by two envelopes, an upper envelope, which represents the most favorable decline behavior, with lower decline, and a lower envelope representing the worst performance, with the highest decline. This method has been called the decline envelope. In addition to the envelopes a third curve has been added, which represents the average decline value. The decline envelopes are obtained from the tables with the values of the decline profiles of all the wells analyzed. Functions minimum and maximum are used monthly to create two vectors of values, one corresponding to the minimum values and the other to the maximum values. Then these vectors are smoothed using an hyperbolic correlation to get two curves, which represent the upper and lower decline envelopes as shown in Fig. 11.

Fig. 11 shows a graph which defines the decline envelope and the average decline curve. The aim of these envelopes is to

define an area where it is likely to find a decline profile for a well. If a proper probability distribution is defined, these envelopes can be used to generate probabilistic production forecasts in a simple manner.

Fig. 11.- Profiles of maximum, minimun and average values and their corresponding smoothed curves. Upper and Lower Envelopes and Average Curve.

You can use a uniform probability distribution, where every value between the lower and upper envelopes has equal

probability of occurrence, a BetaPert distribution can also be used, which uses three parameters to describe the distribution: minimum, maximum and most probable. The minimum value is 0, represents the lower decline envelope. The maximum value is 1 and represents the upper decline envelope. Any other value between 0 and 1 represents a decline path within the envelopes.

To use the decline envelope method for probabilistic production forecasts two elements are required: the probability distribution for the initial production rate and the decline envelopes with its probability distribution associated. Fig. 12 shows a schematic of this concept, applied to the prediction of a single well, resulting in a well type, which in the graph is represented by three curves, P10, pessimistic profile, P50, average profile, and optimistic profile P90 , 80% chance of occurrence is between P10 and P90 profiles.

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Fig. 12.- Schematic of the use of the decline envelopes for probabilistic production forecasts.

Determination of Frequency Distribution of Initial Production Rates With the values of initial production rates used in the normalization process a frequency distribution curve is determined, and the parameters describing this distribution then can be used to make probabilistic production forecasts. Fig. 13 shows an example of a curve of probability distribution of initial production rates.

Fig. 13.- Frequency distribution for initial production rate.

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Determination of Production Type Curves, P10, P50 and P90 The final product gives the probabilistic behavior of a type well, which results from combining two probability distributions: a distribution for the initial production rate that has already been described and a distribution of decline profile location within the decline envelope. To define the distribution of the profile location within the envelope curves a uniform distribution can be used where there is equal probability of occurrence of any value between the envelopes, or a BetaPert distribution, which requires three parameters: minimum, maximum and most likely. The minimum value is 0, and represents the lower envelope of decline. The maximum value is 1, represents the upper envelope. The most probable value is obtained by defining the relative position of the average decline profile with respect to the lower decline envelope. The relative position of the average decline profile is calculated as follows, equation 3:

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Using this method a probability distribution for each time could be found, but we are interested in using a single probability distribution for the entire decline profile, to make things easier, then what is done is to get an average value of all readings. Equation 4:

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After calculating the “Most likely value”, a value of the Decline location is calculated, then a profile is generated using the lower envelope, equation 5. For each iteration a value of position between the envelopes is generated and used to calculate a production profile. At the end we will have a distribution of oil production rates for each time.

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Using the values of the percentiles 10, 50 and 90 from each time, for the calculated production rates, curves for each percentile can be generated, as can be seen in Fig. 14. The separation between the curves of the percentiles 10 and 90 is an indicative of the uncertainty and risk in the production forecast.

Fig. 14.- Probabilistic production behavior of the type well.

The method developed, called decline envelope model produces a forecast of the well, using the production histories from

many wells, it generates a band of decline, limited by an upper and a lower bound, which makes this method suitable for making probabilistic production forecasts.

Conclusions 1. A model for analyzing the behavior of production was developed called "Production Decline Envelopes". This method allows the analysis of multiple wells to define a decline band, which can be used in probabilistic production forecasts.

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2. Most of the wells analyzed showed high initial decline behavior, and then a smooth decline, which was reproduced by simulation, considering low-permeability formations subjected to hydraulic fracturing. 3. The production behavior indicates that the initial flow period is transient, and its duration is relatively long. This is the expected behavior for low permeability formations and high values of porosity by compressibility. 4. The method developed is relatively simple, and avoids having to explicitly define the flow regime (transient, pseudo-static) and select the type of decline to use (exponential, hyperbolic, harmonica).

Acknowledgements We thank CBM, México for their support and permission to publish this paper. References Lee, W. J. and Wattembarger, R. A.: “Gas Reservoir Engineering”, SPE Textbook Series, Vol 5, Richardson, TX (1996). Benedict, J.: “Mathematics of the Decline Analysis”, Nortex Gas & Oil Company, Houston, TX (1981). Doublet, L. E.; McCollum, T. J. and Blasingame, T. A.: “Decline Curve Analysis of Oil Well Production Data Using Material Balance

Time: Application to Field Cases.”, SPE paper 28688, presented at the 1994 Petroleum Conference, Mexico, 1994. Fetkovich, M. J.; Vienot, M. E.; Bradley, M. D. and Kiesow, U. G.: “Decline-Curve Analysis Using Type Curves-Cases Histories”. SPE

Formation Evaluation, December 1987. SI Metric Conversion Factors Bbl x 1.589 873 E-01 = m3

ft x 3.048 E-01 = m