Approximate solution for pressure behavior during a multiple rate injectivity test

Abstract

The pressure response during a well test provides important information about reservoir properties, well productivity or reservoir performance. In order to have an option to replace traditional production tests, avoiding the gas flaring and increasing operational safety, injectivity test began to play an important role in the management of reservoirs. Although analytical models are able to describe injection and falloff periods, multiple rate models still need to be developed. This work presents a new formulation to compute pressure response when performing multiple rate injectivity test in a water injection well operating in an oil zone. First, the proposed formulation is compared to injection/falloff models and after a multiple rate scheme is performed. This formulation extends prior models presented in the literature. The accuracy of the proposed solution was assessed by comparison with a numerical simulator. The proposed formulation is also used to determine the reservoir equivalent permeability in any specific period of injection or shut-in. Keywords Well-testing • Injectivity test • Partial differential equation • Reservoir evaluation List of symbols B Phase formation volume factor c to Total compressibility c r Rock compressibility f w Fractional flow of water h Thickness (m) k l Absolute permeability (= o,) k rl Relative permeability (= ,) M Mobility ratio p i Initial pressure p l Pressure (= , w) p wf Well bottom-hole pressure q inj Injection rate q o Oil rate q w Water rate r f Waterfront radius r w Wellbore radius S w Water saturation t Time t

An Analytical Model for Injectivity Tests in Multilayered Reservoirs With Formation Crossflow

“…Finally, Bonafé et al [4] presented a new formulation to approximate the pressure response at the well during injectivity tests. The solution considered multiple flow rates in a single layer reservoir.…”

Pressure Transient Analysis for Injectivity Tests in Multilayer Reservoirs

“…Injectivity tests are an alternative to conventional well testing [1,7,8]. This procedure is based on pressure transient analysis due to the injection of an external fluid into the reservoir [9,10].…”

“…This procedure is based on pressure transient analysis due to the injection of an external fluid into the reservoir [9,10]. Injectivity tests have gained more attention recently, as they are operationally safer and avoid dealing with the produced fluid disposal or flaring -hence, presenting lower environmental impact than conventional well testing [7,8]. The reduced carbon footprint compared to conventional well testing becomes particularly important considering that many oil field companies committed to substantially decrease greenhouse gas emissions in a foreseeable future.…”

“…The solutions for single-phase [3,5,20] and two-phase flow [8,11,12,16] in multilayer reservoirs with vertical wells are already known. Formulations for well testing in single-layer reservoirs with horizontal wells are also available [4,18,21,22,23,24,25,26].…”

“…(2-14) Thus, rearranging Eq. (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12), layer flow-rate may be computed as:…”