A Model of the Hydraulic Fracturing Process for Elongated Vertical Fractures and Comparisons of Results With Other Models
- I.D. Palmer (Oral Roberts U.) | C.T. Luiskutty (Oral Roberts U.)
- Document ID
- Society of Petroleum Engineers
- SPE/DOE Low Permeability Gas Reservoirs Symposium, 19-22 March, Denver, Colorado
- Publication Date
- Document Type
- Conference Paper
- 1985. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 4.1.2 Separation and Treating, 2.2.2 Perforating, 5.4.2 Gas Injection Methods, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 3 Production and Well Operations
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A summary is given of a fracture model that calculates fracture height as a function of distance from the wellbore for the case of a continuous payzone bounded by zones in which the minimum in situ stress is higher. The model is applicable if the vertical fracture is highly elongated, with length/height ratio greater than 3.5. The fluid flow therefore is essentially one-dimensional along the fracture length. The flow can be non-Newtonian. Leak-off is included, as well as spurt loss, but pumping rates and injected fluid properties are constant with time. Elastic properties properties are constant with time. Elastic properties do not vary from one zone to another. The model calculates width profiles in each vertical section of the fracture. Finally, both fracture height and bottomhole pressure are calculated as a function of time.
A comparison is made between the results of this model (ORU model) and the AMOCO, MIT, and TERRA-TEK variable-height models. There are areas of agreement and disagreement. A critical assessment is made of assumptions that differ in the models in an effort to reconcile the models. The conclusion is that the ORU AMOCO, and TERRA-TEK models are in basic agreement for highly elongated fractures.
In the past few years, several variable-height fracture models have been developed, and are in use to predict hydraulic fracture growth during well predict hydraulic fracture growth during well stimulation. However, there has been no concerted attempt to compare the predictions of these models, nor to account for the resulting discrepancies. This we do here.
The components of our fracture model (ORU model) are first summarized, including a new formulation for fracture width, to create a basis for detailed comparison with the other fracture models.
Next we compare the published results from each of three other fracture models with the ORU model. A penetrating analysis of these models allows some discrepancies to be resolved, though not all. This paper is a first try at normalizing these fracture paper is a first try at normalizing these fracture models, some of which are difficult to understand.
SUMMARY OF ORU MODEL
The geometry and principal parameters relating to a highly elongated fracture are shown in Figure 1. The fracture expands from the payzone (S ) into zones of higher (but equal) minimum in-situ stress (S ). The equations which govern the fracture expansion are:
(a) Width equation. As described previously, the fracture is divided into vertical sections, each of which is treated as an independent 2D or line crack, giving the width profile as a function of net pressure and height (see Appendix A):
(b) Pressure gradient equation. Assuming laminar flow along the payzone direction, the pressure drop across a typical vertical section is a function of the width profile, the height, and the flow rate (Appendix B): profile, the height, and the flow rate (Appendix B): (2)
The pressure drop also depends on the fluid parameters n and k (power law fluid) or parameters n and k (power law fluid) or viscosity p (Newtonian fluid).
(c) The criterion for fracture expansion. We use K = K where K is stress-intensity factor and K is fracture toughness.
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