Shape factors for the pseudo-steady state flow in fractured hydrocarbon wells of various drainage area geometries

Pseudo-steady state (PSS) flow is an important time-dependent flow regime that

quickly follows the initial transient flow regime in the constant-rate production of

a closed boundary hydrocarbon reservoir. The characterization of the PSS flow

regime is of importance in describing the reservoir pressure distribution as well as the

productivity index (PI) of the flow regime. The PI describes the production potential

of the well and is often used in fracture optimization and production-rate decline

analysis. In 2016, Chen determined the exact analytical solution for PSS flow of a

fully penetrated vertically fractured well with finite fracture conductivity for reservoirs

of elliptical shape. The present work aimed to expand Chen’s exact analytical solution

to commonly encountered reservoirs geometries including rectangular, rhomboid,

and triangular by introducing respective shape factors generated from extensive

computational modeling studies based on an identical drainage area assumption. The

aforementioned shape factors were generated and characterized as functions for use

in spreadsheet calculations as well as graphical format for simplistic in-field look-up

use. Demonstrative use of the shape factors for over 20 additional simulations showed

high fidelity of the shape factor to accurately predict (mean average percentage error

remained under 1.5 %) the true PSS constant by modulating Chen’s solution for

elliptical reservoirs. The methodology of the shape factor generation lays the ground

work for more extensive and specific shape factors to be generated for cases such as

non-concentric wells and other geometries not studied.