Intercept Method - A Novel Technique to Correct Steady-State Relative Permeability Data for Capillary End-Effects

2014 ◽  
Author(s):  
Robin Gupta ◽  
Daniel Riney Maloney
Keyword(s):  
Steady State ◽  
Relative Permeability ◽  
End Effects ◽  
Novel Technique ◽  
Permeability Data

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.

scholarly journals Influence of capillary end effects on steady-state relative permeability estimates from direct pore-scale simulations

2017 ◽  
Vol 29 (12) ◽  
pp. 123104 ◽  
Author(s):  
Gaël Raymond Guédon ◽  
Jeffrey De’Haven Hyman ◽  
Fabio Inzoli ◽  
Monica Riva ◽  
Alberto Guadagnini
Keyword(s):  
Steady State ◽  
Relative Permeability ◽  
Pore Scale ◽  
End Effects

Intercept Method—A Novel Technique To Correct Steady-State Relative Permeability Data for Capillary End Effects

2015 ◽  
Vol 19 (02) ◽  
pp. 316-330 ◽  
Author(s):  
Robin Gupta ◽  
Daniel R. Maloney
Keyword(s):  
Steady State ◽  
Relative Permeability ◽  
Data Interpretation ◽  
End Effect ◽  
Fractional Flow ◽  
End Effects ◽  
Flow Rates ◽  
Pressure Drops ◽  
State Tests ◽  
State Measurement

Summary In laboratory measurements of relative permeability, capillary discontinuities at sample ends give rise to capillary end effects (CEEs). End effects affect fluid flow and retention. If end-effect artifacts are not minimized by test design and data interpretation, relative permeability results may be significantly erroneous. This is a well-known issue in unsteady-state tests, but even steady-state relative permeability results are influenced by end-effect artifacts. This work describes the intercept method, a novel modified steady-state approach in which corrections for end-effect artifacts are applied as data are measured. The intercept method requires running a steady-state relative permeability test with several different flow rates for each fractional flow. Obtaining multiple (three or four) sets of rates (Q), pressure drops (ΔP), and saturation data allows for assessment of CEE artifacts. With Darcy flow, a plot of pressure drop vs. total flow rate is typically linear. A nonzero intercept or offset is an end-effect artifact. To correct for the effect, the offset is subtracted from measured pressure drops. Corrected pressure drops are used in permeability calculations. The set of saturations from measurements at the target fractional flow is used to calculate a corrected final saturation. Because corrections for end effects are made during the test rather than after the test is complete, any discrepancies can be resolved by additional measurements before moving on to the next fractional flow. Rates are then adjusted to yield the next target fractional-flow condition, and the same protocol is repeated for each subsequent steady-state measurement. The method is validated by theory and is easy to apply.

Computation of Relative Permeability From In-Situ Imaged Fluid Distributions at the Pore Scale

SPE Journal ◽  
2018 ◽  
Vol 23 (03) ◽  
pp. 737-749 ◽  
Author(s):  
S.. Zou ◽  
F.. Hussain ◽  
J.. Arns ◽  
Z.. Guo ◽  
C. H. Arns
Keyword(s):  
Steady State ◽  
Relative Permeability ◽  
Pore Space ◽  
Large Field ◽  
Pore Scale ◽  
Ct Scanner ◽  
End Effects ◽  
The Core ◽  
In Situ Conditions

Summary Image-based computations of relative permeability require a description of fluid distributions in the pore space. Recent advances in imaging technologies have made it possible to directly resolve actual fluid distributions at the pore scale, thus capturing a large field of view for arbitrary wetting conditions, which are numerically difficult to reproduce. In previous studies, fluid distributions were not imaged under in-situ conditions, which may cause the oil (nonwetting) phase to snap off. Consequently, computed oil relative permeability is underestimated, particularly at low oil saturations. This study extends our previous work by imaging fluid distributions under in-situ conditions as a basis for numerical computations. In this study, we perform a steady-state flow test on a homogeneous outcrop sandstone (Bentheimer) core. First, the dry core is imaged in our microcomputed-chromatography (micro-CT) facility. Afterward, the core is fully saturated with 0.4 molar sodium iodide (NaI) solutions. The saturated core is then mounted in a specially designed flow cell that allows the flow experiment to be performed with the core mounted on the CT scanner. Afterward, a steady-state injection of oil and brine is performed at four different oil/water-injection ratios. For each injection ratio, steady-state pressure drop is noted, and in-situ fluid distributions are imaged under flow conditions. These imaged fluid distributions are used to compute image-based relative permeability, whereas the measured pressure drops are used to calculate experimental relative permeability. Results demonstrate that imaging in-situ fluid distributions allows us to overcome significant limitations of our previous work: Namely, measured and computed oil relative permeability are in close agreement across the whole saturation range, and laboratory capillary end effects at the core outlet can be imaged, which allows us to apply a correction to the laboratory-measured data.

Steady-State Measurements of Relative Permeability for Polymer/Oil Systems

1982 ◽  
Vol 22 (01) ◽  
pp. 79-86 ◽  
Author(s):  
F.N. Schneider ◽  
W.W. Owens
Keyword(s):  
Steady State ◽  
Relative Permeability ◽  
Oil Recovery ◽  
Water Saturation ◽  
Flow Behavior ◽  
Residual Effect ◽  
Sweep Efficiency ◽  
Residual Resistance ◽  
Reservoir Permeability ◽  
Permeability Data

Abstract Means for increasing tertiary oil recoveries from previously waterflooded viscous oil reservoirs are receiving added attention today as a result of industry-wide efforts to improve U.S. oil producing rates and reserves. Injection of a bank of polymer solution that precedes injection of a miscible slug (e.g., a micellar fluid) can reduce reservoir permeability contrasts and result in improvement of the sweep efficiency of the process. To evaluate the potential magnitude of improved recovery and economics of prior polymer slug injection, there is a need for basic polymer/oil relative permeability data for use in performance evaluation calculations. Such relative permeability data were measured by steady-state procedures on a suite of 18 out-crop and formation core samples ranging, in permeability from about 50 to 1,200 md. Six different polyacrylamide polymers were tested, and resistance and residual resistance data were obtained on each. Data were obtained in both oil-wet and water-wet systems. The observation in these studies was that the presence of polymers in the water phase had a significant and consistent effect, lowering water relative permeability over the entire water saturation range. In many of the tests, the presence of flowing polymer or its residual effect during subsequent brine flow had no effect on oil relative permeability. In several tests, polymer contact actually improved oil mobility through increases in oil relative permeability at all levels of oil saturation. Permeability level and polymer type produced no clear-cut differences in flow behavior. The obvious differences in core wettability resulted in widely varying relative permeability characteristics, but again the effect of polymer contact was about the same, qualitatively, as obtained on the water-wet cores. Introduction The steady decline of U.S. oil reserves and rapidly, increasing, prices obtained for each barrel of crude produced are strong incentives to maximize recoveries for all reservoirs. Various enhanced oil recovery techniques are being tested and used for recovering some of the oil left behind after conventional waterflooding. The added recovery achievable with such processes, however, is influenced to a large degree by one of the same factors leading to inefficient waterflooding - i.e., reservoir heterogeneity. Numerous laboratory studies using, both physical and mathematical models, plus numerous field projects, have shown that when contrasts in reservoir permeability increase, recovered by any external injection recovery process decreases as a result of reduced sweep efficiency. Thus, if recoveries from the more heterogeneous reservoirs are to be maximized, procedures must be developed for reducing the permeability contrasts before application of an EOR process or by mobility adjustment within the process itself. Preinjection of polymers in advance of a micellar flood has been proposed as a means for improving reservoir sweep efficiency by reducing permeability contrasts. Laboratory tests of this process demonstrated that, in both linear and five-spot stratified systems, the residual resistance effect achieved by preinjection of poly-acrylamide polymers resulted in improved sweep and additional recovery by subsequent micellar flooding. In the one reported field test of this process, tertiary oil was mobilized and recovered, but insufficient data are available to indicate whether the preinjected polymer resulted in improved sweep efficiency. Mathematical model studies provide a reliable means for evaluating potential benefits of polymer preinjection. However, such studies require input data that permit the model to simulate the physical processes that may occur in the reservoir. This laboratory study was conducted to provide such data. SPEJ P. 79^

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