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Empirical methods in production forecasting
Empirical methods are quantitative, statistically-based relationships that allow one to compare performance against a collection of analogous reservoirs using specific reservoir properties. As production forecasting analog methods states, analog methods are generally more qualitative in nature, but it often is possible to derive equations relating reservoir parameters to performance indicators. This should allow narrowing the range of outcomes rather than using the entire range of analog values.
Empirical forecasts can be highly reliable indicators of performance depending on the relevance of the analog data set used to derive the relationships, the quality of the correlations, the quality and reliability of the reservoir data, and the similarity of development conditions between the fields of the analog data set and the reservoir under consideration.
Typical performance indicators
Typical performance indicators that might be considered include:
- Initial Production Rates
- Recovery Efficiency
- Plateau Length
- Decline Rates
- Water Cut vs. Er
- Barrels of oil produced vs. barrels of water injected
- Specific Productivity (stb/D/psi-ft)
Typical reservoir parameters
Typical reservoir parameters that might be considered include:
- Absolute and relative permeabilities
- Oil, water, and gas viscosities
- Compressibilities of oil, water, gas, and rock
- Bubble-point Bo and GOR
- Pressures including initial, current, bubble point, and abandonment
- Initial water saturation, residual oil saturation
- Oil and gas gravities
- Reservoir temperature
- Mobility ratio
- Horizontal well length, number of frac stages, well spacing
- Pounds of proppant, volume of pad
- Year of development
There are several empirical relationships in the literature which are often used for quick performance predictions. An example is an equation for recovery efficiency from the API Subcommittee on Recovery Efficiency developed from a statistical study of 80 solution gas-drive reservoirs (API, 1967).
The same paper also proposed a statistically-derived equation for oil recovery for water-drive reservoirs.
Fig 1 (Petroleum Engineering Handbook, 1987) is a plot of some of the original data of 70 U.S. sandstone reservoirs (Craze and Buckley, 1945) used to derive the water-drive equation. Although residual oil saturation does increase with oil viscosity as the correlation suggests, there is considerable scatter to the analog data suggesting considering sizeable error bars when using this equation for prediction.
In addition to scatter within the original analog data set, other considerations suggest caution when applying published correlations to a new reservoir:
- How applicable is the analog data set to your current reservoir? Production forecasting analog methods page discusses selection of analog data sets, but published correlations are usually used without careful checking of the original data set.
- How accurately determined are the reservoir parameters used in the correlation? Some parameters are well known (year of development, reservoir temperature, oil gravity) but others may be subject to significant errors in data gathering and analysis (current reservoir pressure, relative permeability, residual oil saturation).
- How is your reservoir developed compared with the analog data set? A horizontal-well development could have quite a different performance (initial rates, plateau length, breakthrough times etc.) than a vertical-well development.
- How similar are operating costs and practices in the analog data set to your current reservoir? Recovery would be expected to be higher in a low-operating-cost environment than a high one. Care must be exercised, especially when comparing an offshore to an onshore development.
Developing your own empirical correlations has similar considerations but you usually know more about the analog data set, so ensuring applicability is easier. When developing your own correlation you also should have a better understanding of the tightness of the correlation and are therefore in a better position to judge the uncertainty of your predictions.
Fig 2 shows a series of normalized decline curves grouped by year of development and summarized by a table of first and second year decline rates. This approach can be very powerful, especially in mature producing areas where lots of historical data are available.
Various regression techniques can be used to develop empirical correlations. LINEST and LOGEST in Excel® are commonly-used engineering tools for multivariate analysis yielding simple linear and exponential equations. Fig 3 shows a table of 20 reservoirs where a linear correlation was developed to predict recovery factor from porosity, net pay, and viscosity.
It is also possible to use Monte-Carlo techniques to capture at least some of the uncertainty of making predictions with such an empirical equation. If we can define an uncertainty range for each input parameters in the equation (porosity, net pay, and viscosity), we can run Monte Carlo to define an S-curve for the recovery factor. This won’t capture errors associated with using an imperfect analog data set (i.e. the new reservoir differs from the analog data set in some significant way such as lithology, basin, or development plan) but it will include measurement and analysis errors of the input parameters.
With some understanding of the physics of a reservoir, variables can be grouped in logical ways – for example the “φ (1 – Sw)/Bo” group in the previous API equations relates to standard barrels of oil in a unit volume of reservoir rock. Similarly a “k/μ” group would refer to the mobility of a particular fluid. Despite these groupings, which can also be found in analytical equations, these equations remain empirical because the final form of the equation and coefficients are derived from statistical fits rather than more-rigorous material balance or transport equations.
Noteworthy papers in OnePetro
Martin Wolff - Oxy