Corporate fracturing simulator: from a mathematical model to the software development

UDK: 622.
Key words: hydraulic fracturing, HF, fracturing design, fracturing simulation, minifrac, mathematical modeling, geomechanics, hydrodynamics, rock deformation, fracture fluid flow, proppant transport, fluid leakage into the formation, numerical methods
Authors: A.V. Aksakov, O.S. Borschuk, I.S. Zheltovа (RN-UfaNIPIneft LLC, RF, Ufa), A.V. Dedurin, Z. Kaludzher, A.V. Pestrikov, K.V. Toropov (Rosneft Oil Company PJSC, RF, Moscow)

Article is devoted to mathematical modeling of the fracturing mechanics and software development for fracturing simulation and decision making support in design and conduct of fracturing treatments. We discuss the basic software elements for modeling hydraulic fracturing, the existing mathematical models of hydraulic fracturing process (KGD, PKN, Radial, Cell-based-Pseudo3D, Lumped-Pseudo3D, Planar3D), history of development, characteristics and limitations. It is noted the practical importance for the fracturing planning tasks and risk minimization to correctly describe the fracture height growth, this pushed the development of Pseudo3D (P3D) and Planar3D (PL3D) models.

We show the general mathematical formulation of hydraulic fracturing process, based on coupled solution of the formation elasticity equations, fluid hydrodynamics and proppant transport. In details discussed the mathematical formulation for Planar3D model and common assumptions that are made. Software interface examples are shown for common methods of fracturing injection tests analysis and hydraulic fracturing design simulation on the example of corporate fracturing simulator. Typical functional requirements for hydraulic fracturing simulators are given. It is noted that the combination in a one fracturing simulator Planar3D and Cell-based-P3D models provides a flexible software solution to specific geological conditions and requirements for the calculation speeds. It has been shown that for certain geological conditions fracturing simulations using Planar3D and Pseudo3D models may vary in term of evaluating hydraulic fracture geometry. The attention made that the task of speed increasing for Planar3D-models is the actual point of application for scientific and engineering community efforts.


1. Nolte K.G., Fracture evaluation using pressure diagnostics. Reservoir stimulation,

3rd ed., Chichester: Wiley, 2000, 856 р.

2. Adachi J., Siebrits E., Peirce A., Desroches J., Computer simulation of hydraulic

fractures, International Journal of Rock Mechanics & Mining Sciences,

2007, pp. 739-757.

3. Sneddon I.N., The distribution of stress in the neighbourhood of a crack in

an elastic solid, Proceedings of the Royal Society of London A: Mathematical,

Physical and Engineering Sciences, 1946, V. 187, no. 1009, pp. 229-260.

4. Khristianovich S.A., Zheltov Y.P., Formation of vertical fractures by means of

highly viscous liquid, Proceedings of Fourth World Pet. Congress, Rome, 1955,

V. 2, pp. 579-586.

5. Geertsma J., de Klerk F.A., Rapid method of predicting width and extent of

hydraulic induced fractures, J. Pet Tech., 1969, V. 12, pp. 1571-1581.

6. Perkins T.K., Kern L.R., Widths of hydraulic fractures, J. Pet. Tech., 1961,

pp. 937-949.

7. Nordgren R.P., Propagation of a vertical hydraulic fracture, SPE 3009-PA,


8. Carter R.D., Derivation of the general equation for estimating the extent of

the fractured area, Drilling and Production Practice, New York: American Petroleum

Institute, 1957, pp. 261-269.

9. Mack M.G., Warpinski N.R., Mechanics of hydraulic fracturing, Reservoir

stimulation, 3rd ed., Chichester: Wiley, 2000, 856 р.

10. Cleary M.P., Analysis of mechanisms and procedures for producing

favourable shapes of hydraulic fractures, SPE 9260-MS, 1980.

11. Meyer B.R., Design formulae for 2-D and 3-D vertical hydraulic fractures:

model comparison and parametric studies, SPE 15240-MS, 1986.

12. Smith M.B., Klein H.A., Practical applications of coupling fully numerical

2-D transport calculation with a PC-based fracture geometry simulator,

SPE 30505, 1995.

13. Barree R.D., A practical numerical simulator for three-dimensional fracture

propagation in heterogeneous media, SPE 12273-MS, 1983.

14. Clifton R.J., Abou-Sayed A.S., On the computation of the three-dimensional

geometry of hydraulic fractures, SPE 7943-MS, 1979.

To buy the complete text of article (a format - PDF) or to read the material which is in open access only the authorized visitors of the website can. .