Correcting Oil/Water Relative Permeability Data for Capillary End Effect in Displacement Experiments

Qadeer, Suhail; Dehghani, K.; Ogbe, D.O.; Ostermann, Rainer

doi:10.2118/17423-ms

Cited by 20 publications

(13 citation statements)

References 5 publications

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“…This method assumes that the pressure drop measured during the experiment always represents the pressure drop across the wetting phase and the capillary effects influence only the non-wetting phase relative permeability. They based the latter assumption on the published data (Qadeer et al 1988). It has been demonstrated that capillary pressure affects both the wetting and non-wetting phase relative permeabilities (Civan and Donaldson 1989, Kalbus and Christiansen 1995, Qadeer 2001).…”

Section: Methodsmentioning

confidence: 99%

Comparison of Methods for Drainage Relative Permeability Estimation From Displacement Tests

Hussain¹,

Cinar²,

Bedrikovetsky³

2010

Proceedings of SPE Improved Oil Recovery Symposium

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This paper compares classical and contemporary methods used to obtain relative permeability from dynamic experiments. We apply a variety of analytical, semi-analytical and history matching methods to analyze experimental data of oil-water unsteadystate drainage displacements. The analysis involves two types of error: bias and variance errors. The bias error in the resultant relative permeabilities mainly comes from the smoothening and differentiation of the experimental data while the variance error represents statistical uncertainty in measurements. We elect to use our own experimental data to minimize the variance error. We compare the numerical and functional fitting methods proposed for the differentiation and apply spline and Gaussian functions for fitting production and pressure data, respectively. We use spline fitting improved by time-domain data sampling to achieve a more effective history match. This approach minimizes the effects of non-uniqueness and shape dependency of relative permeability curves. We present a modification of the semi-analytical method of Civan and Donaldson (1989).Comparison of different methods shows that analytical methods are in agreement with each other but differ from the semianalytical and history matching methods. The modified semi-analytical approach agrees well with the improved history matching. The spline and Gaussian functions for fitting experimental data are capable to preserve the data shape and yield less bias error. The function fitting methods are more effective than numerical methods in differentiation/integration of experimental data, preserving the features of the data and minimizing the errors. Semi-analytical methods provide a better first guess for history matching. Use of the cubic spline curves for relative permeability makes the relative permeability curve more flexible and any shape of the curve can be produced. There is a trade-off between the simplicity of the conventional Coreytype power law function and the accuracy of the cubic splines.

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Section: Methodsmentioning

confidence: 99%

Comparison of Methods for Drainage Relative Permeability Estimation From Displacement Tests

Hussain¹,

Cinar²,

Bedrikovetsky³

2010

Proceedings of SPE Improved Oil Recovery Symposium

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“…The frontal saturation corresponds to the tangent point between the f-f curve and the straight line drawn from the point Si,the slope of this line is equal to the displacement front velocity D, The geometric interpretation of the continuous solution (12), (13) is: the saturation value corresponds to the value of self-similar coordinate which is equal to the slope of f-f curve in the point of this saturation. This allows for a graphic-analytical construction of the saturation profile (Fig, 1).…”

Section: I-d Coreflood In Large Scale Approximation: Buckley-leversttmentioning

confidence: 99%

“…This allows for a graphic-analytical construction of the saturation profile (Fig, 1). The solution (12), ( 13) is the outer asymptotic expansionmzz for the displacement problem honouring the capillary pressure.…”

Section: I-d Coreflood In Large Scale Approximation: Buckley-leversttmentioning

confidence: 99%

“…fntroduce the shock-function which is the shock on the displacmncnt @nt in the Buckley-Leverctt solution (12), (13) The formula for the continuous solution is Two profiles are shown for moments For matddug the asymptotic solution in the .stalilized zone (A-9) with the outex solution (12), (13), we usc the methodj proposed by Erdelyiz'.…”

Section: Analytical Model For the Waterflood Honouring Capillafy Presmentioning

confidence: 99%

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Analytical Model for the Waterflood Honouring Capillary Pressure (With applications to laboratory studies)

Bedrikovetsky

Rodrigues

Britto

1996

SPE Latin America/Caribbean Petroleum Engineering Conference

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by UwSPEPmum Comillwfc4Mu _ d ,dm'rdunamlahd inmastraiwhilw by@_lhm cmtenl$Ofu'1Opapr .p-mmled, fmm ndkwnrewwd byti Sodatyd P8Murn ErWWerstimMk@ddW mdimd~b adhxahnw twml,upm-.fkas mtnOmssuJyr 6+k5myp0Mimd UmSOdyd Petmluml Engm-men u Itsmunbus wur6w8senW @SPErnwtWmuA+xl @pi#ii rww ty Edkmial Cmwnittw d llmScc@iyd Pelm4eun Ewram Pumisski710 q h MWUM Ioalaslrad dr-drncmma-lmwa-ds Hhlstrallcflsmylwltac ap!sdllma)slrm 81mum~~d w41efeaRdbywcfn nb3fMfmr w#prm.sfwwiIa AbstractAn analytical model for the coreflood honouring the capillary pressure is developed. The analytical solution for the problem of the displacement of oil by water taking into account the capillary pressure is obtained using the method of matched asymptotic expansions.The model is based on the matching of the capillarity-free Buckley-Leverett solution with two asymptotic expansions irr regions of strong capillary pressure effects: with the continuous stabilized-zone solution in the neighbourhood of the displacement front, and with the end-effect solution near to the core outlet. Numerical simulation shows the high accuracy of the analytical solution proposed. The analytical solution is used for regularization of the inverse problem for determination the relative permeabilities tiom the coreflood data. Analytical solution allows to transform the inverse problem, which is the ill-posed one in the general formulation, to the system of two integral equations. The system can be solved asymptotically using the regular small parameter method. SPE 36130P. BEDRIKOVETSKY, J.R.P.RODRIGUEZ, P.R.P. BRIITCI So the misbalance is of an order of E, and it is also negative. It is zero

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“…Therefore, this approach may give stable results only for fixed analytical expressions of relative permeability (Batycky et al 1981;Richmond et al 1990;Qadeer et al 1988;Chardaire-Riviere et al 1992;Sigmund and Mccaffery 1979). Nevertheless, very different shapes of relative permeability have been reported in the literature (Honarpour et al 1986;Kerig and Watson 1986), which reduces the stability of the optimization method.…”

Section: Introductionmentioning

confidence: 99%

A Semi-Analytical Model for Two Phase Immiscible Flow in Porous Media Honouring Capillary Pressure

2011

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This article describes a semi-analytical model for two-phase immiscible flow in porous media. The model incorporates the effect of capillary pressure gradient on fluid displacement. It also includes a correction to the capillarity-free Buckley-Leverett saturation profile for the stabilized-zone around the displacement front and the end-effects near the core outlet. The model is valid for both drainage and imbibition oil-water displacements in porous media with different wettability conditions. A stepwise procedure is presented to derive relative permeabilities from coreflood displacements using the proposed semi-analytical model. The procedure can be utilized for both before and after breakthrough data and hence is capable to generate a continuous relative permeability curve unlike other analytical/semi-analytical approaches. The model predictions are compared with numerical simulations and laboratory experiments. The comparison shows that the model predictions for drainage process agree well with the numerical simulations for different capillary numbers, whereas there is mismatch between the relative permeability derived using the Johnson-Bossler-Naumann (JBN) method and the simulations. The coreflood experiments carried out on a Berea sandstone core suggest that the proposed model works better than the JBN method for a drainage process in strongly wet rocks. Both methods give similar results for imbibition processes.

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Correcting Oil/Water Relative Permeability Data for Capillary End Effect in Displacement Experiments

Cited by 20 publications

References 5 publications

Comparison of Methods for Drainage Relative Permeability Estimation From Displacement Tests

Comparison of Methods for Drainage Relative Permeability Estimation From Displacement Tests

Analytical Model for the Waterflood Honouring Capillary Pressure (With applications to laboratory studies)

A Semi-Analytical Model for Two Phase Immiscible Flow in Porous Media Honouring Capillary Pressure

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