Click to see subtopics:The most popular well design for exploiting unconventional oil & gas resources is long horizontals with multiple hydraulic fractures. Liang et al (2012) proposed a new set of typecurves for analyzing horizontal multifrac wells with the following geometry:
Figure 1: Horizontal Well Geometry
The following six flow regimes have been proposed for such a geometry:
1. Bi-linear flow caused by finite conductivity fractures
2. Primary linear flow from the formation into the fractures
Figure 2
3. Transition period between primary linear flow and compound linear flow
4. Compound linear flow, which is perpendicular to the primary linear flow
Figure 3
5. Transition between compound linear flow and boundary-dominated flow
6. Boundary-dominated flow
For unconventional reservoirs, the primary flow regimes of interest for rate-transient analysis are the primary linear flow into the fracture, the transition between primary linear and compound linear, and compound linear flow. The compound linear typecurves available in IHS RTA are based on these three flow regimes.
If the following assumptions are made regarding the horizontal multi-fractured well, Figure 1 can be reduced to a single fracture in an infinitely large reservoir:
- Fractures are equally spaced along the horizontal well
- Fractures have the same half-length and conductivity
- The horizontal well contributes negligible flow as compared to the fractures
- The reservoir is a single-layer, homogenous, isotropic system with single porosity and uniform thickness
- The fractures penetrate the entire formation thickness
- The spacing between horizontal wells is infinitely large
With these assumptions in mind, the following reservoir model was used to generate the typecurves:
Figure 4
The complete solution of the above reservoir model is based on Green’s function method of Gringarten and Ramey (1974). The dimensionless variables are defined as follows:
The constant rate solution of the equation for various Xs/xf ratios results in the following set of typecurves for normalized pressure and semi-log derivative (DER):
Figure 5
Figure 6
The square root derivative has also been introduced for the compound linear typecurve, and simply rotates the DER typecurve, resulting in a flat line during linear flow.
The typecurves presented above are based on an infinite conductivity fracture with no skin. In reality however, it is quite possible to experience a pressure drop caused by flow convergence, or finite conductivity of the hydraulic fractures. The existence of such a skin will change the shape of the data on a log-log plot, and can have a significant effect on typecurve matching if not accounted for properly. The figure below shows the effect of skin on the typecurve shape:
Figure 8
The dimensionless pressure drop illustrated in Figure 8 can be expressed as a total apparent skin using the following equation:
The same dimensionless pressure drop can be expressed in terms of an apparent FCD as follows:
The actual pressure drop due to skin is estimated using the average flow rate of the last five data points (q_(@∆p_Ds )), and the following equation:
Methodology
Data preparation
The horizontal axis is material balance time (pseudo-time for gas).
Pressure – time
For the Pressure - Time family of typecurves, the vertical axis plots are:
- Normalized pressure
- Semi-log pressure derivative
- Integral derivative
- Square root derivative
Normalized pressure
Oil wells
Gas wells
Raw data derivative
Oil wells
Gas wells
Derivative
Oil wells
Gas wells
Square-root pressure derivative
Oil wells
Gas wells
Calculation of parameters
Oil wells
Once a satisfactory match is achieved, the match point is defined as follows:
Using the dimensionless variable definitions:
along with the match point, the following variable can be calculated:
Gas wells
Once a satisfactory match is achieved, the match point is defined as follows:
Using the dimensionless variable definitions:
along with the match point, the following variable can be calculated:
Rate – time
For the Rate - Time family of typecurves, the vertical axis plots are:
- Normalized rate
- Semi-log pressure derivative
- Integral derivative
- Square root derivative
Normalized rate
Oil wells
Gas wells
Raw data derivative
Oil wells
Gas wells
Derivative
Oil wells
Gas wells
Square-root pressure derivative
Oil wells
Gas wells
Calculation of parameters
Oil wells
Once a satisfactory match is achieved, the match point is defined as follows:
Using the dimensionless variable definitions:
along with the match point, the following variable can be calculated:
Gas wells
Once a satisfactory match is achieved, the match point is defined as follows:
Using the dimensionless variable definitions:
along with the match point, the following variable can be calculated:
Boundary-dominated flow
The compound linear typecurves described above were developed for an infinitely large reservoir. Most unconventional reservoirs will, however, experience boundary-dominated flow eventually. The time at which this happens will generally depend on well spacing.
Boundary-dominated flow will appear as a straight line with a unit slope on a log-log plot, and can be expressed by the following equation using the raw data derivative:
This boundary-dominated flow line is represented by a dotted line intersecting the compound linear flow curve, and will be displayed only when a valid area or reservoir length has been entered.
Figure 9
