AFA Documentation
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Hyperbolic (Arps) and Flow Regime Identification

In the studies provided by Rushing et al. [2007] and Lee and Sidle [2010] these authors showed that the unconstrained use Arps' hyperbolic rate relation (particularly for cases where the b-values are greater than 1) can and almost always does yield significant overestimates of reserves. However, Colllins [2016] showed that Arp’s relations (for high b values) could be reduced to the simple relations shown in the table below, and explains why the Arps' hyperbolic relation often adequately fits production data from MFHW in the early time (transient flow).

For scenarios with b>1, discussion (and clarification) has shown it is a possible indication of flow regimes encountered at early times for a horizontal well with multiple hydraulic fracture stages (as many as 30) as well as extension other completions.

The following table is provides specific reservoir signatures or periods that do not require an entire model from transient to PSS.


Flow Regime

Slope

Generalized Relation

Theoretical Rate Relation

b value

Linear Flow

  • Highly conductive fractures in MFHW

  • Refer to

1:2 Slope

2

Bilinear Flow

  • Low Conductivity Fractures in MFHW

1:4 Slope

4

Radial Flow

0 Slope



Multi-Fractured Linear Flow

1:3 Slope


3

Pseudo-Steady State Flow

Unit Slope



Boundary Dominated Flow





Recall:

and assuming that bDit >> 1, mathematical derivation for many of the above regimes can be derived from Arps.

References:

  • Practical Considerations for Decline Curve Analysis in Unconventional Reservoirs — Application of Recently Developed Time-Rate Relations, V. Okouma, N. Hosseinpour-Zonoozi, D. Ilk,, T.A. Blasingame, SPE 162910.

  • Rushing, J.A., Perego, A.D., Sullivan, R.B., and Blasingame, T.A. 2007. Estimating Reserves in Tight Gas Sands at HP/HT Reservoir Conditions: Use and Misuse of an Arps Decline Curve Methodology. Paper SPE 109625 presented at the SPE Annual Technical Conference and Exhibition, Anaheim, CA, 11-14 November.

  • Lee, W.J. and Sidle, R.E. 2010. Gas Reserves Estimation in Resource Plays. Paper SPE 130102 presented at the 2010 SPE Unconventional Reservoirs Conference, Pittsburgh, PA, USA, 23-25 February.doi:10.2118/119897-MS.

  • Anderson, D.M., and Mattar, L. 2003. Material-Balance-Time During Linear and Radial Flow. Presented at PETSOC Canadian International Petroleum Conference in Calgary, Alberta, Canada, 10–12 June. PETSOC 2003-201. http://dx.doi.org/10.2118/2003-201 .

  • Anderson, D.M., and Nobakht, M., Moghadam, S., and Mattar, L. 2010. Analysis of Production Data from Fractured Shale Gas Wells. Presented at SPE Unconventional Gas Conference in Pittsburgh, Pennsylvania, USA, 23–25 Februrary. SPE-131-787-MS. http://dx.doi.org/10.2118/131787-MS .

  • Fulford, D.S., and Blasingame, T.A. 2013. Evaluation of Time-Rate Performance of Shale Wells using the Transient Hyperbolic Time-Rate Relation. Presented at SPE Unconventional Resources Conference – Canada in Calgary, Alberta, Canada, 5–7 November.

  • Patrick William Collins “Decline Curve Analysis for Unconventional Reservoir Systems - Variable Pressure Drop Case” Professional Studies, M.Sc . Texas A&M University, 2016.