Click to see subtopics:Modeling is the process of history matching pressure and rate transient data based on a mathematical model. There are many different models available to match the data depending on the situation. Thus, it is important to analyze the pressure and rate transient data before modeling because it forces the analyst to think about the probable reservoir configurations and provide good estimates of reservoir parameters. Models are not unique (different model types can match the same set of data), and as a result, we recommend selecting the model type after the analysis step. The following summarizes the advantages of modeling pressure and rate transient data:
- Modeling makes use of all the information within a dataset. For example, while analyzing data from vertical wells, the analyst might try and determine permeability and skin by analyzing the data points that make up the zero slope on the derivative plot, and the semi-log straight line on the radial plot, but ignore the data points in the transition period between wellbore storage and radial flow. Models make use of the information contained in transition periods.
- Modeling takes all flow regimes into account. In multi-rate situations, analyses depend on the superposition of the equation for a single flow regime. For example, the derivation of Horner time includes the assumption that all flow, including the entire drawdown, is radial. Modeling does not assume that only one flow regime has occurred.
- With modeling, you can simultaneously analyze multiple flow periods, so that a single set of parameters can be found.
Parameter values obtained during the analysis step provide a good starting point for an appropriately chosen model type. Parameters can then be optimized by automatic parameter estimation (APE). Before using the APE method, corrupted data should be removed from the dataset to prevent the attempt to match invalid points.
Choice of model
As stated above, different models can be used to match a single set of data. Choosing a probable model type requires the consideration of a number of factors including seismic data, geology, log data, and information provided from other wells drilled in the same formation.
The choice of model can drastically change the outcome of a forecast. For example, pressure and rate transient analysis of radial flow data can be used to find the reservoir flow capacity (kh). The analyst must decide which model is better.
Model assumptions
There are many assumptions that go into the model itself which can lead or mislead the analyst. Most models assume that a reservoir is homogeneous (dual porosity excluded, where the dual porosity flow within each layer can be modeled either as pseudo-steady state or transient interporosity flow). There is no single reservoir that is actually homogeneous in nature, but many reservoirs behave as homogeneous reservoirs.
Vertical model
The vertical model simulates the pressure response in a vertical well within a rectangular-shaped reservoir with homogeneous or dual-porosity characteristics. Note that the well may be at any location within the reservoir, and that the reservoir for the vertical model has no-flow boundaries. During very early times, the cylindrical source solution is used, which is followed by the Green’s function solutions (Grindarten and Ramey, 1973). No-flow boundaries are modeled using the method of images. The result is superposed in time based on the rate history provided.
Vertical with fracture model
The fracture model simulates the pressure response in a vertical well intercepted by an infinite-conductivity vertical fracture within a rectangular-shaped reservoir with homogeneous or dual-porosity characteristics (see the figure below). Note that the well may be at any location within the reservoir, and that the reservoir for the fracture model has no-flow boundaries. During very early times, the cylindrical source solution is used, which is followed by Green’s function solutions. The Green’s function solution, as developed by Thompson et al. (1991), is used with slight modifications to simulate an infinite-conductivity vertical fracture. No-flow boundaries are modeled using the method of images. The result is superposed in time based on the rate history provided.
Horizontal model
The horizontal model simulates the pressure response in a horizontal well within a rectangular-shaped reservoir with anisotropic heterogeneities (that is, differences in permeability in the x, y, and z directions), or dual-porosity characteristics. The anisotropy is handled using a conformal mapping procedure that adjusts the boundary sizes accordingly to mimic the effect of increased or decreased permeability in each direction. The horizontal well is oriented in the x-direction, and may be at any location within the reservoir (see the figure below) and supports no-flow boundaries.
Note that the effective wellbore length (Le) defines the wellbore area open to fluid flow. The cylindrical source solution is used at very early times, which is followed by Green’s function solutions for horizontal wells, as developed by Thompson et al. (1991). No-flow boundaries are modeled using the method of images. The result is superposed in time based on the rate history provided. The following flow regimes can be handled by this model:
- Wellbore storage
- Vertical radial flow
- Linear horizontal flow
- Elliptical flow
- Horizontal radial flow
- Boundary effects
- Pseudo-steady state flow
Horizontal multifrac enhanced fracture region model
This model is a rectangular reservoir model consisting of a non-contributing horizontal well and transverse fractures. This model assumes that all the fractures are uniformly spaced with equal half-fracture length. (The reservoir can extend beyond the fracture tips.) This model has an improved effective permeability region around each fracture, and you can specify the distance from the fracture to the permeability boundary (XI).
This model takes the following linear flow regimes into account:
- linear flow within the fracture (at very early time)
- linear flow within the stimulated region towards the fractures
- linear flow within the non-stimulated regions towards the stimulated region
- linear flow within the non-stimulated region towards the wellbore
| Note: | A detailed description of the model is given by Stalgorova and Mattar (2012). |
General horizontal multifrac model
The general horizontal multifrac model is a homogeneous, single-phase, rectangular reservoir model consisting of a horizontal wellbore and transverse fractures. The horizontal multifrac solution is created through superposition of individual infinite conductivity fracture solutions in space.
You can specify the reservoir dimensions and well position, provided the entire wellbore and all fractures fit within the reservoir boundaries. In addition, each fracture can be situated anywhere along the horizontal wellbore and configured to have a unique fracture half-length and conductivity. Thus, it is possible to model the combined effects of the horizontal wellbore and multiple fractures as well as the transition into middle-time flow regimes and boundary-dominated flow for any number of different geometrical configurations. Depending on the configuration, pseudo-radial flow can be observed with this model.
Damage skin is applied along the length of the horizontal wellbore and a turbulence factor may be specified.
