Click to see subtopics:Extended periods of linear flow have been observed in many gas wells. These wells are usually in very tight gas reservoirs with hydraulic fractures designed to extend to the drainage boundary of the well. Wattenbarger et al. (1998) presented new typecurves to analyze the production data of these gas wells.
They assumed a hydraulically fractured well in the center of a rectangular reservoir. The fracture is assumed to be extended to the boundaries of the reservoir.
They showed that the solution in case of constant rate production and closed reservoir is:
Where dimensionless variables are defined as:
The typecurves based on this equation are shown below. Wattenbarger et al. (1998) showed that there are different typecurves for different values of xf / Ye.
The solution for linear flow can be rewritten as:
where:
This equation shows that plotting [(xf / Ye) * pD] against tDye gives only one curve for any rectangular geometry, rather than families of typecurves with different values of xf / Ye.
In RTA, this analysis has been modified as follows:
- [(Ye / x’e) * qD] is plotted against tDye instead of [(xf / Ye) * pD].
- The typecurves are generated for cases where the well is not in the center of the reservoir (different values for Ye / Yw).
- In addition to dimensionless rate, the inverse of semi-log pressure derivative curve is included.
Methodology
Data preparation
The horizontal axis is material balance time (pseudo-time for gas).
On the vertical axis, two variables are plotted:
- Normalized rate
- Inverse of semi-log pressure derivative
Normalized rate
Oil wells
Gas wells
Inverse of semi-log pressure derivative
Oil wells
Gas wells
Analysis
The normalized rate and inverse semi-log pressure derivative are plotted against the material balance time on a log-log scale of the same size as the typecurves. This plot is called the “data plot”. Any convenient units can be used for normalized rate or time because a change in units simply caused a uniform shift of the raw data on a logarithmic scale. It is recommended that daily operated-rates be plotted, and not the monthly rates; especially when transient data are analyzed.
The data plot is moved over the typecurve plot, while the axes of the two plots are kept parallel until a good match is obtained. Several different typecurves should be tried to obtain the best fit of all the data. The typecurve that best fits the data is selected and Ye / Yw value is noted.
Calculation of parameters
Oil wells
Using the definition of [qD (Ye / Xe)]:
k Xe / Ye is calculated as follows:
where (q / Δp) and [qD (Ye / Xe)], are read off from each of the raw data and typecurve graphs at a selected match point.
From the definition of dimensionless time based on reservoir width (tDye):
(Ye / √k) is calculated as follows:
Substituting the equation for [(k Xe / Ye)] into the above, we get:
Additional reservoir parameters are now calculated:
(Acres)
(Mbbl)
Gas wells
Using the definition of [qD(Ye / Xe)]:
(k Xe / Ye) is calculated as follows:
where (q / Δpp) and [qD (Ye / Xe)] are read off from each of the raw data and typecurve graphs at a selected match point.
From the definition of tDye,
(Ye / √k) is calculated as follows:
Substituting the equation for (k Xe / Ye) into the above, we get:
Additional reservoir parameters are now calculated:
(Acres)
(Bscf)