Analytical modeling of linear flow in single-phase tight oil and tight gas reservoirs

Abstract

Unconventional reservoirs, including tight oil, tight gas and shale gas are economically attractive, but operationally challenging, particularly for cases when complex flow behavior occurs within the reservoir. Accounting for the physics of flow in such formations is central to providing improved short- and long-term oil and gas production forecasts. At the early phase of development of these reservoirs, and in the presence of limited data, analytical models are more suited for mechanistic studies leading to improved understanding of the reservoir. Analytical models often utilize solutions to flow equations for liquids with constant viscosity, and small and constant compressibility. In tight formations, however, these assumptions simply do not apply as fluid and rock properties change with pressure drawdown. Historically, efforts have concentrated on linearizing the governing partial-differential equations to account for these effects by employing appropriately defined pseudopressure and pseudotime functions. A rigorous approach for determination of pseudotime includes the use of average pressure in the distance of investigation during transient flow.In this work, an analytical expression for average reservoir pressure in the (dynamic) drainage area is derived for constant pressure and constant rate production scenarios. By deriving an explicit relation for average pressure in the drainage area as a function of the initial reservoir pressure and the wellbore pressure, the iterative procedure for calculation of pseudotime is relaxed. Using the developed expression for average pressure in the distance of investigation, the pseudo steady-state deliverability equation is extended to model the transient period by incorporating the dynamic drainage area concept in the productivity index equation. We first verify the applicability of the developed approach for oil reservoirs and later demonstrate that the approach is considered to be useful for analysis of production data from tight gas reservoirs.The established methodology in this work provides a useful tool for rapid forecasting of tight oil and tight gas wells, allowing for the examination of the effects of different parameters on the forecast.