Flow Regimes and Unconventional Wells
Forecasting begins with checking and conditioning data. An incomplete list of things to think about follows:
- Use the actual number of days in the month when converting volume to rate. This will avoid sawtooth rate-time profiles.
- If you are using producing hours make sure they do not exceed the number of hours in the month.
- Look for reporting errors that are often detected from the header information. For example, a sudden short-term change in operator might indicate another operator filing with the wrong API or an unexplained and large change in volume might be a typo.
- Be consistent with your data. Time and volume are measured at month-end, but the rate is an average that would occur near mid-month. Make appropriate adjustments.
- If you have producing hours, analyze the information with producing day rates and elapsed producing time.
- Smoothing might make daily production and pressure data more useful. Some methods that might be considered are rolling average (with or without weighting), average over discrete periods (weekly, 5 days, etc.) or Bourdet
Find Linear Flow
Finding linear flow means identifying linear flow data and the coefficient a in the linear flow equation q = a t -0.5
This may be accomplished in two ways:
The first is to position a log-log rate-time ½ slope line until it aligns with a continuous trend of data as shown with the red data of Figure 1. Ideally, there will be no data, except outliers, above this line. The example uses public data from a well API 05-123-37231-00. This well is in Colorado and produces oil from the Codell formation.
A regression fit of data on the red line is simplified because the slope is known:
a = exp (sum(x) – sum(y)) / n
The second method is to calculate and plot the a coefficient for every data point as shown by green data on the right axis of Figure 1. Linear flow will show as a continuous horizontal trend and the a coefficient will be the average coefficient of the selected points (solid green dots). This approach is quite sensitive.
Two points look like they could be in linear flow based on the red dots, but not based on green dots. The inclusion or exclusion of these two data points is not critical providing they do not influence the value of the linear flow coefficient in a meaningful way. If in doubt, they are better excluded, because at this stage only the position of the linear flow line is needed.
When there is insufficient data to identify the linear flow trend (i.e. less than two points), the evaluator may consider calculating a proven reserve using the data point that results in the a coefficient with the largest value, knowing that the reserve will be understated. Of course, this will also require an estimate for the end of linear flow and an approximate b-value from other similar wells with a longer producer life.
When there is enough second segment data, a reliable forecast can be obtained by independently forecasting that segment without connecting linear and post-linear flow. Keep in mind that this independent forecast will not provide all the information needed for predicting wells that do not have enough data.
In Figure 2, the blue dashed line represents the independent forecast described above. The forecast uses the pink filled dots with the reference time, t = 0, set at the beginning of the first data month. We found equation parameters using Excel Solver™, minimizing the relative difference in rates:
The b-exponent for the forecast is 0.72. The fit is projected backward in time.
The second method is to solve for a proper modified hyperbolic equation, fitting both linear and post-linear flow. We first determine the linear flow equation as described above. One unknown is the time of transition from the first to the second segment. For a smooth transition, we use the switching time as the reference time (time = 0) and we solve for the initial rate and initial nominal decline factor from the linear flow equation or the hyperbolic approximation. The second unknown is the final b-exponent. Because secant declines depend on b-exponent, the solution is best conducted using nominal declines and switching back to secant when the calculations are complete.
We solve for the best solution using a nested iteration. The inner iteration solves for the best b-exponent, given the time of transition. The outer iteration solves for the transition time that results in the least relative difference in rates.
The results are shown as the solid red line in Figure 2. The fit has a b-exponent of 0.79 compared with 0.72 from the independent method. The transition between equations occurs at 5 months, near the middle of the previously defined linear flow period. The early transition, common for oil, results in a limiting or terminal nominal decline factor of 112 percent per year. This is much greater than the value of 15 to 20 percent per year that I see evaluators using. This huge difference is a warning call to pay attention to flow regime detection when forecasting.
While the two methods yield comparable results, we recommend forecasting using the second method, starting with the oldest wells. The objective is to obtain statistical information regarding the switch point and final b-exponent to be used when data is limited, and you will need to make estimates for these parameters.
When using statistics, it is not enough to simply build a histogram and select the most frequent. The switch point will be highly dependent on inter-fracture distance and to a lesser extent permeability. Look for these correlations in your data.
About the Author
Randy Freeborn is an SPE Distinguished Lecturer on type wells and a subject matter expert in empirical forecasting. Currently, he is a Fellow at Aucerna where he is a thought leader, responsible for identifying and inventing engineering technology and assisting clients. He has been a professional engineer for 45 years and is a member of SPEE and SPE. Freeborn has prepared numerous technical papers for presentation at conferences, workshops and industry meetings and has been a guest lecturer at the University of Houston and Texas A&M.