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Title: Calculation of large scale relative permeabilities from stochastic properties of the permeability field and fluid properties

Abstract

The paper describes the method and presents preliminary results for the calculation of homogenized relative permeabilities using stochastic properties of the permeability field. In heterogeneous media, the spreading of an injected fluid is mainly sue to the permeability heterogeneity and viscosity fingering. At large scale, when the heterogeneous medium is replaced by a homogeneous one, we need to introduce a homogenized (or pseudo) relative permeability to obtain the same spreading. Generally, is derived by using fine-grid numerical simulations (Kyte and Berry). However, this operation is time consuming and cannot be performed for all the meshes of the reservoir. We propose an alternate method which uses the information given by the stochastic properties of the field without any numerical simulation. The method is based on recent developments on homogenized transport equations (the {open_quotes}MHD{close_quotes} equation, Lenormand SPE 30797). The MHD equation accounts for the three basic mechanisms of spreading of the injected fluid: (1) Dispersive spreading due to small scale randomness, characterized by a macrodispersion coefficient D. (2) Convective spreading due to large scale heterogeneities (layers) characterized by a heterogeneity factor H. (3) Viscous fingering characterized by an apparent viscosity ration M. In the paper, we first derive the parameters D andmore » H as functions of variance and correlation length of the permeability field. The results are shown to be in good agreement with fine-grid simulations. The are then derived a function of D, H and M. The main result is that this approach lead to a time dependent . Finally, the calculated are compared to the values derived by history matching using fine-grid numerical simulations.« less

Authors:
;  [1]
  1. Institut Francais du Petrole, Rueil Malmaison (France)
Publication Date:
Research Org.:
BDM Corp., Bartlesville, OK (United States); American Association Petroleum Geologists, Tulsa, OK (United States)
OSTI Identifier:
508504
Report Number(s):
CONF-970317-
ON: DE97004613; TRN: 97:003410-0012
Resource Type:
Conference
Resource Relation:
Conference: 4. international reservoir characterization technical conference, Houston, TX (United States), 2-4 Mar 1997; Other Information: PBD: [1997]; Related Information: Is Part Of 4. International reservoir characterization technical conference; PB: 726 p.
Country of Publication:
United States
Language:
English
Subject:
02 PETROLEUM; 58 GEOSCIENCES; RESERVOIR ROCK; PERMEABILITY; FLUID INJECTION; FLUID FLOW; MATHEMATICAL MODELS; STOCHASTIC PROCESSES

Citation Formats

Lenormand, R., and Thiele, M.R.. Calculation of large scale relative permeabilities from stochastic properties of the permeability field and fluid properties. United States: N. p., 1997. Web.
Lenormand, R., & Thiele, M.R.. Calculation of large scale relative permeabilities from stochastic properties of the permeability field and fluid properties. United States.
Lenormand, R., and Thiele, M.R.. 1997. "Calculation of large scale relative permeabilities from stochastic properties of the permeability field and fluid properties". United States. doi:. https://www.osti.gov/servlets/purl/508504.
@article{osti_508504,
title = {Calculation of large scale relative permeabilities from stochastic properties of the permeability field and fluid properties},
author = {Lenormand, R. and Thiele, M.R.},
abstractNote = {The paper describes the method and presents preliminary results for the calculation of homogenized relative permeabilities using stochastic properties of the permeability field. In heterogeneous media, the spreading of an injected fluid is mainly sue to the permeability heterogeneity and viscosity fingering. At large scale, when the heterogeneous medium is replaced by a homogeneous one, we need to introduce a homogenized (or pseudo) relative permeability to obtain the same spreading. Generally, is derived by using fine-grid numerical simulations (Kyte and Berry). However, this operation is time consuming and cannot be performed for all the meshes of the reservoir. We propose an alternate method which uses the information given by the stochastic properties of the field without any numerical simulation. The method is based on recent developments on homogenized transport equations (the {open_quotes}MHD{close_quotes} equation, Lenormand SPE 30797). The MHD equation accounts for the three basic mechanisms of spreading of the injected fluid: (1) Dispersive spreading due to small scale randomness, characterized by a macrodispersion coefficient D. (2) Convective spreading due to large scale heterogeneities (layers) characterized by a heterogeneity factor H. (3) Viscous fingering characterized by an apparent viscosity ration M. In the paper, we first derive the parameters D and H as functions of variance and correlation length of the permeability field. The results are shown to be in good agreement with fine-grid simulations. The are then derived a function of D, H and M. The main result is that this approach lead to a time dependent . Finally, the calculated are compared to the values derived by history matching using fine-grid numerical simulations.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 1997,
month = 8
}

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  • The objective of this work is to improve determination of two-phase and three-phase relative permeabilities by the use of saturation imaging techniques. The first part of the paper reports on steady-state and unsteady-state relative permeability experiments performed on restored-state carbonate reservoir cores. The aim was to study how relative permeability test methodology impacts relative permeability curves. hysteresis and residual oil saturations in these intermediate-wet cores. Refined oil was used. Significant hysteresis was observed in both the unsteady-state water and oil relative permeabilities. The characteristics of the unsteady-state water relative permeabilities imply that viscous instabilities were present during the waterflood. Centrifugemore » capillary pressure-wettability tests performed on companion core plugs both before and after the relative permeability tests showed good agreement with the unsteady-state results, but indicated change towards less oil-wetness during the steady-state tests. The main conclusion of this work is that extensive flushing of a restored-state core with refined oil may lead to a non representative relative permeability data and should therefore be avoided. The second part of the paper presents a summary of results obtained from three-phase unsteady-state flow in water-wet sandstone (Berea and Clashach) cores. In-situ saturation measurements show that the water relative permeability is dependent on water saturation alone, and that there is no change in water relative permeability due to three-phase flow. The waterflood residual oil saturation was found reduced in the presence of a gas phase, and may depend on the phase (oil or gas) injected prior to waterflooding.« less
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