Technique forecasts production from waterflooded reservoirs

Nov. 24, 2003
A proposed technique using the observed trend of log water-oil ratio (WOR) vs. cumulative oil produced (Np) can predict oil well decline rates on a time basis.

A proposed technique using the observed trend of log water-oil ratio (WOR) vs. cumulative oil produced (Np) can predict oil well decline rates on a time basis.

An oil reservoir in the mature stages of waterflooding has historical well data, acquired during production, well tests, and cased-hole logging.

These mature assets require a simple and accurate but fast analytical method for predicting future production performance. Conventional forecasts with exponential decline curves tend to be conservative when predicting future oil rates because they do not explicitly consider the water cut.

Also in the latter stage of a field's life, reservoir simulation may help identify by-passed oil potential, but these simulations are often poor at predicting individual well performance that typically requires an extensive effort to obtain a unique history match.

The proposed technique is fast, efficient, and incorporates the time dimension into production and reserves forecasting.

The technique is robust and the authors have used it widely throughout the shallow marine and turbidite reservoirs of the UK continental shelf.

Background

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Analysis of production performance for a North Sea Brent formation reservoir undergoing waterflooding in the early 1990s showed a consistent linear trend of WOR in log WOR-vs.-Np plots (Fig. 1).

Since then, the authors have observed this trend in a wide range of these shallow marine reservoirs as well as in Paleocene turbidite reservoirs.

The industry has used log WOR for predicting reserves potential to a limiting water cut for a long time, and some commercial production database software incorporate this method1 but not for predicting production rates.

Based on observed water-cut development, the challenge was to make the method time-based rather than volume-based to enable the linear trends to predict production rates.

Production data from an example well in the UK North Sea (Fig. 1) illustrate how one derives and employs the proposed forecasting method.

Calculations

Equation 1 (see Equation box) describes a trend line through the log WOR data. In the equation, m is the slope of the log WOR trend line and c is the intercept.

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Fig. 2 shows that the example well has a very good WOR trend.

One should note that the trend-line slope increases after a workover shuts off some of the swept zones in the well.

This phenomenon implies that a workover allows a more rapid but ultimately lower recovery of reserves.

The phenomenon obviously is specific to a well and reservoir, but it can highlight the need of a future recompletion because of a prematurely shut-off interval.

An analogy to the steady-state solution of the material balance equation allows one to introduce time into the calculations.

If one assumes that average reservoir pressure does not change over time, injection water and aquifer influx (We) must completely replace the voidage created by the oil and water production, as expressed by Equation 2.

In this equation, Qo and Qw are the oil and water rates and Bo and Bw are the oil and water formation-volume factors, respectively.

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Because WOR is simply the ratio of produced water rate to produced oil rate, one can rearrange Equation 2 by substituting it for Qw, which equals (Qo.3.WOR), to obtain Equations 3a and 3b.

In fact, water influx due to aquifer support is minimal in the example field and support comes virtually entirely from water injection; hence the We term can be neglected in the example.

One then uses Equations 1 and 3a to predict rates, for both oil and water phases with the following procedure:

  • Obtain the fluid properties, Bo and Bw, from either pressure-volume-temperature (PVT) measurements or correlations. For the example field, the produced oil has a high GOR, which is reflected in its Bo of 1.5 reservoir bbl/stock tank bbl (rb/stb). The produced water is of low-to-medium salinity and has a Bw of 1.035 rb/stb.
  • For the time from when the forecast will begin, such as the last production data point, obtain the last known total liquid production rate from the well. In the example well, the last known total liquid rate was 9,721 b/d at surface conditions. Because we assumed 100% voidage replacement, this rate will be the required downhole injection rate Qwi.
  • Estimate the slope m of the log WOR vs. Np trend. Fig. 2 shows the slope as 3E-7.
  • Obtain the values of Np and WOR at initial reservoir conditions for the time from when the forecast is to start. Note that WOR equals water cut/(1 – water cut). In the example well, Np was 5,661,747 bbl of oil, water cut was 0.802, and WOR was 4.062.
  • For the forecast period, calculate a new intercept c from [log WOR – mNpi]initial time step. This was –1.0873 for the example well data shown in Fig. 2.

Time steps

The example uses monthly time increments, although one can use any time increment.

There is a small systematic error in the proposed method because Equation 3 assumes WORi represents the entire time increment i to i + 1.

This is not a significant error and it can be reduced by use of an alternative estimate for WOR in Equation 3, such as shown in Equation 4.

To use this estimate, however, one requires an estimate for WORi+1 at time increment i. This is obtained with Taylor's theorem, where one obtains successively better estimates with Equations 5 and 6.

Studies have shown Equation 5 can reduce the time increment and systematic calculation errors to acceptable levels.

Substituting Equations 4 and 5 into Equation 3a results in Equation 7a that improves the Qo estimate in time increment i to i+1.

Equation 7a can replace Equation 3a in the stepwise estimate of rates, if required.

One can incorporate production uptime into the model with an efficiency multiplier, between 0 and 1, in Equation 3a or Equation 7a, or with an explicit setting of liquid rates to zero, as shown in Equation 7b.

In the example well, uptime efficiency was a very high 98%.

Quality control

It is worth plotting the historical production data in order to compare with data from the predictive model. Plotting oil rate and water cut vs. time (Fig. 1) allows one to quality-control the forecast oil rate and water cut trends compared with historical data.

The benefit of plotting the historical trend of log WOR vs. Np trend (Fig. 2) is that we can readily assess the coherency of the initial WOR data, which will subsequently be used for predicting production rates.

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Fig. 3 shows the results of the exercise, where the results are compared with the predicted decline from an exponential fit to the production data (post workover).

As seen in Fig. 3, the exponential decline is much more pessimistic about the future performance of the example well than the proposed prediction model.

In fact, it is common for high-rate producers with high water cut in the UK North Sea to outperform the early production forecasts based on an exponential decline.

It was partly for this discrepancy that the authors developed this technique.

Forecast applications

The presented technique has been used in a wide range of applications such as:

  • Field performance prediction with an evaluation of production at a well level.
  • Field performance prediction with an evaluation at a zone level, using spinners surveys to split well production to the reservoir zone level.
  • Production and field performance monitoring, including evaluating the impact of workovers.
  • Asset evaluations.

Once set up in a spreadsheet, one can readily copy the equations to enable multiwell forecasts. The latest spreadsheets facilitate automation of the calculations with the set up of query links to corporate production databases.

These links can be configured to enable automatic data update upon file opening.

One can extend this technique of integrating the steady-state material balance rate equation with the linear trend of log WOR vs. Np to any of the standard cumulative oil production decline curves, such as water cut vs. Np, oil cut vs. Np, etc., to ultimately calculate a time dependent decline forecast.

Acknowledgment

Thanks are due to Steve Burford for his original idea and help with this article. F

Reference

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1. Dake, L.P., Fundamentals of Reservoir Engineering, Elsevier Scientific Publishing, 1978.

The authors
Bob Harrison ([email protected]) is a director of TriPhase Consulting Ltd. working as a petroleum engineering advisor and trainer on international prospect evaluation issues and petrophysical matters. He previous worked with British Gas E&P, Enterprise Oil PLC and Maersk Oil & Gas AS. Harrison has a BS in electrical engineering from the University of Science and Technology in Manchester, an MS in petroleum engineering from Imperial College, and an executive MBA from Cranfield School of Management.

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Andrew Warnock is a senior reservoir engineer with EnCana UK Ltd., currently working on the Scott and Telford fields in the Central North Sea. He has formerly worked for Amerada Hess Corp., Enterprise Oil PLC, and ChevronTexaco Inc.