The GEOSIM Model From Duke Engineering
Basic Description of the Model [1],[2]
This model considers many of the differences between conventional hydraulic fracturing and long term, lower rate water injection. One of the major differences is leak-off and thus efficiency. Fluid efficiency for stimulation fracturing is much higher than the fluid efficiency for PWRI. Therefore, the conventional Carter leakoff model was revisited in the model and a two-dimensional leakoff model adopted. This model shows that Carter’s leakoff model may underestimate leak-off by several orders of magnitude, especially for low injection rates. The model presents a mechanism to partially couple the fracturing model with reservoir simulation, where fracture dimensions are determined from the fracturing model and reservoir model is executed with the predetermined fracture. Modelling parameters can be adjusted in order for the two models to give the same injection pressure. The model is capable of considering variations in thermal stress, pore pressure and saturation in the water invaded zone. This model also considers effects of previous injection, and pre-existing propped/acid fractures. These features are important in analyzing step rate tests and fall-off tests after a period of injection.
Factors Considered
For accurate PWRI simulations, the following factors need to be considered:[3]
a) Significant pressure and saturation gradients may exist around the well from previous, long-term injection or production. It cannot be assumed that the fracture will propagate through a reservoir with constant properties.
b) Large scale reservoir heterogeneity will cause leakoff variation in the fracture path as the fracture can be a few thousands of feet in half length.[4]
c) Long-term cold water injection can create a large cooled zone around the fracture, with thermally-altered fluid properties and stresses.
d) Average reservoir pressure and stresses can change during the time of fracture propagation.
e) The leakoff zone around the fracture becomes large and has a saturation and temperature distribution, which is three-dimensional.
f) Formation damage and filter cake buildup due to solids and oil need to be considered to study the effect of water quality on injection performance. Fracture tip plugging and branching have been observed both in the laboratory and in the field. [4]
Methodology of Modelling
Two methods have been presented for modeling the change of physical parameters during injection (Figure 1). In the “parametric” or analytical leakoff model, the model assumes a one-dimensional piston-like displacement and describes the changes of physical parameters such as temperature, water saturation, relative permeability, etc, in the invaded region by their average. In the “numerical” leakoff model, the changes of physical parameters from each element of the fracture are computed by a one-dimensional (perpendicular to the fracture surface) finite difference model, which solves simultaneously for 2-phase flow, heat transfer and for the stresses.
Capabilities of the Model
Two-Dimensional Leakoff Correction
A 1-D leakoff
assumption underestimates the leak-off, especially at low injection rates. Settari (1980) [5] introduced a correction factor to the 1-D
leakoff velocity, which is a function of the dimensionless injection rate. Based on the results obtained from the
Koning’s (1988) [6] model, a relationship is given between the
correction factor and the dimensionless injection rate. This relationship shows that the 2-D
leakoff correction can be several orders of magnitude different (Figure
2). This needs to be confirmed because this has a big effect on fracture
size if this is true.
<BP Multi-Lateral Spreadsheet
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