Simultaneous Estimation of Relative Permeability and Capillary Pressure for Non-Darcy Flow-Steady State

1996 ◽  
Author(s):  
Sezai Ucan ◽  
Faruk Civan
Keyword(s):  
Steady State ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Darcy Flow ◽  
Simultaneous Estimation

The Combined Effect of Near-Critical Relative Permeability and Non-Darcy Flow on Well Impairment by Condensate Drop Out

1998 ◽  
Vol 1 (05) ◽  
pp. 421-429 ◽  
Author(s):  
Saskia M.P. Blom ◽  
Jacques Hagoort
Keyword(s):  
Steady State ◽  
Gas Phase ◽  
Relative Permeability ◽  
Capillary Number ◽  
Radial Flow ◽  
Drop Out ◽  
Darcy Flow ◽  
Gas Reservoirs ◽  
Strongly Coupled ◽  
Original Manuscript

This paper (SPE 51367) was revised for publication from paper SPE 39976, first presented at the 1998 SPE Gas Technology Symposium, Calgary, 15-18 March. Original manuscript received for review 19 March 1998. Revised manuscript received 8 July 1998. Paper peer approved 13 July 1998. Summary We present a comprehensive numerical method to calculate well impairment based on steady-state radial flow. The method incorporate near-critical relative permeability and saturation-dependent inertial resistance. Example calculations show that near-critical relative permeability, which depends on the capillary number, and non-Darcy flow are strongly coupled. Inertial resistance gives rise to a higher capillary number. In its turn, the improved mobility of the gas phase caused by a higher capillary number enhances the importance of the inertial resistance. The effect of non-Darcy flow is much more pronounced in gas condensate reservoirs than in dry gas reservoirs. Well impairment may be grossly overestimated if the dependence of relative permeability on the capillary number is ignored. P. 421

scholarly journals Analytical modeling and correction of steady state relative permeability experiments with capillary end effects – An improved intercept method, scaling and general capillary numbers

2021 ◽  
Vol 76 ◽  
pp. 61
Author(s):  
Pål Ø. Andersen
Keyword(s):  
Steady State ◽  
Pressure Drop ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Relative Permeabilities ◽  
Total Rate ◽  
Dimensionless Numbers ◽  
End Effects ◽  
Effective Relative Permeabilities ◽  
Saturation Profile

Steady state relative permeability experiments are performed by co-injection of two fluids through core plug samples. Effective relative permeabilities can be calculated from the stabilized pressure drop using Darcy’s law and linked to the corresponding average saturation of the core. These estimated relative permeability points will be accurate only if capillary end effects and transient effects are negligible. This work presents general analytical solutions for calculation of spatial saturation and pressure gradient profiles, average saturation, pressure drop and relative permeabilities for a core at steady state when capillary end effects are significant. We derive an intuitive and general “intercept” method for correcting steady state relative permeability measurements for capillary end effects: plotting average saturation and inverse effective relative permeability (of each phase) against inverse total rate will give linear trends at high total rates and result in corrected relative permeability points when extrapolated to zero inverse total rate (infinite rate). We derive a formal proof and generalization of the method proposed by Gupta and Maloney (2016) [SPE Reserv. Eval. Eng. 19, 02, 316–330], also extending the information obtained from the analysis, especially allowing to calculate capillary pressure. It is shown how the slopes of the lines are related to the saturation functions allowing to scale all test data for all conditions to the same straight lines. Two dimensionless numbers are obtained that directly express how much the average saturation is changed and the effective relative permeabilities are reduced compared to values unaffected by end effects. The numbers thus quantitatively and intuitively express the influence of end effects. A third dimensionless number is derived providing a universal criterion for when the intercept method is valid, directly stating that the end effect profile has reached the inlet. All the dimensionless numbers contain a part depending only on saturation functions, injected flow fraction and viscosity ratio and a second part containing constant known fluid, rock and system parameters such as core length, porosity, interfacial tension, total rate, etc. The former parameters determine the saturation range and shape of the saturation profile, while the latter number determines how much the profile is compressed towards the outlet. End effects cause the saturation profile and average saturation to shift towards the saturation where capillary pressure is zero and the effective relative permeabilities to be reduced compared to the true relative permeabilities. This shift is greater at low total rate and gives a false impression of rate-dependent relative permeabilities. The method is demonstrated with multiple examples. Methodologies for deriving relative permeability and capillary pressure systematically and consistently, even based on combining data from tests with different fluid and core properties, are presented and demonstrated on two datasets from the literature. The findings of this work are relevant to accurately estimate relative permeabilities in steady state experiments, relative permeability end points and critical saturations during flooding or the impact of injection chemicals on mobilizing residual phase.

Simultaneous Estimation of Relative Permeability and Capillary Pressure for PUNQ-S3 Model With a Damped Iterative-Ensemble-Kalman-Filter Technique

SPE Journal ◽  
2017 ◽  
Vol 22 (03) ◽  
pp. 971-984 ◽  
Author(s):  
Yin Zhang ◽  
Zhaoqi Fan ◽  
Daoyong Yang ◽  
Heng Li ◽  
Shirish Patil
Keyword(s):  
Kalman Filter ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Simultaneous Estimation ◽  
Reservoir Models ◽  
Ensemble Smoother ◽  
Iterative Ensemble Smoother ◽  
Capillary Pressure Curves

Summary A damped iterative-ensemble-Kalman-filter (IEnKF) algorithm has been proposed to estimate relative permeability and capillary pressure curves simultaneously for the PUNQ-S3 model, while its performance has been compared with that of the CMOST module, iterative-ensemble-smoother (IES) algorithm, and traditional ensemble-Kalman-filter (EnKF) technique. The power-law model is used to represent the relative permeability and capillary pressure curves, while three-phase relative permeability for oil phase is determined by use of the modified Stone II model. By assimilating the observed production data, the relative permeability and capillary pressure curves are inversely, automatically, and successively updated, achieving an excellent agreement with the reference cases. Not only are the associated uncertainties reduced significantly during the updating process, but also each of the updated reservoir models predicts the production profile that is in good agreement with the reference cases. Although the damped IEnKF technique shows the highest accuracy on estimation results, history-matching results, and prediction performance for the PUNQ-S3 model, its computational expense is still high compared with the other three techniques. In addition, the variations in the ensemble of the updated reservoir models and production profiles of the damped IEnKF provide a robust and consistent framework for uncertainty analysis.

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