Impact of Distance-of-Investigation Calculations on Rate-Transient Analysis of Unconventional Gas and Light-Oil Reservoirs: New Formulations for Linear Flow

Abstract

Long-term transient linear flow of hydraulically fractured vertical and horizontal wells completed in tight/shale gas wells has historically been analyzed by use of the square-root-of-time plot. Pseudovariables are typically used for compressible fluids to account for pressure-dependence of fluid properties. Recently, a corrected pseudotime has been introduced for this purpose, in which the average pressure in the distance of investigation (DOI) is calculated with an appropriate material-balance equation. The DOI calculation is therefore a key component in the determination of the linear-flow parameter (product of fracture half-length and square root of permeability, x f ffiffi ffi k p) and the calculation of contacted fluid in place. Until now, the DOI for transient linear flow has been determined empirically, and may not be accurate for all combinations of fluid properties and operating conditions.In this work, we have derived the DOI equations analytically for transient linear flow under constant-flowing-pressure and -rate conditions. For the first time, rigorous methodologies have been used for this purpose. Two different approaches were used: the maximum rate of pressure response (impulse concept) and the transient/boundary-dominated flow intersection method. The two approaches resulted in constants in the DOI equation that are much different from previously derived versions for the constantflowing-pressure case. The accuracy of the new equations was tested by analyzing synthetic production data from a series of fine-grid numerical simulations. Single-phase oil and gas cases were analyzed; pseudovariable alteration for pressure-dependent porosity and permeability was required in the analysis.The calculated linear-flow parameters, determined from our new DOI formulations for the constant-flowing-bottomhole-pressure (FBHP) case, and the input values to numerical simulation, are in good agreement. Of the two new DOI-calculation methods provided, the maximum rate of pressure response (unit impulse method) provides more accurate results. Finally, a field case was analyzed to determine the impact of DOI formulations on derivations of the linear-flow parameter from field data.Linear-flow analysis on the basis of the DOI calculations presented in this work is significantly improved over previous formulations for constant FBHP.

A review of stimulated reservoir volume characterization for multiple fractured horizontal well in unconventional reservoirs

“…It is common to regard the inner reservoir as stimulated reservoir and to characterize the permeability of the whole SRV as an equivalent permeability. The impact of distance of investigation calculation on rate transient analysis was proposed by Behmanesh et al (2015), which can be used to characterize the SRV. It proposed a new way to calculate distance of investigation (DOI) with the theory of maximum rate of pressure response.…”

“…Thought different definition of DOI can also be implemented in the integrated analysis approach to characterize the SRV, the DOI calculated based on the theory of unit impulse method is most accurate to evaluate the equivalent permeability of SRV (Behmanesh et al, 2015).…”

Discrete fracture networks modeling of shale gas production and revisit rate transient analysis in heterogeneous fractured reservoirs

“…They demonstrated that uncorrected data appear to have a very short early-time transient linear flow period, followed by apparent boundary dominated flow. Behmanesh et al (2015) proposed a new method to estimate DOI that can be used to calculate average pressure and evaluate the corrected pseudo-time. Their work shows the improved DOI and pseudo-variable calculations increases accurathe cy of linear-flow parameter estimation for unconventional reservoirs.…”

Review on gas flow and recovery in unconventional porous rocks

“…Moghanloo et al (2015) defined an asymptotic equation of DDV and within which average pressure, and applied an iterative algorithm to find their explicit formulation. Behmanesh et al (2015) and Clarkson andQanbari (2016a, 2016b) defined a new formula of distanceof-investigation only applicable for early transient-linear flow within SRV, but ignored the contributions of outer reservoirs to the long-term shale production. However, for the longterm production in shale, the flow regime would become compoundlinear flow or else with an expanding production region in outer reservoirs.…”