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

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.

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.

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.

Formation Characterization and Production Forecast of Tight Sandstone Formations in Daqing Oilfield Through Digital Rock Technology

2021 ◽  
Author(s):  
Danhua Leslie Zhang ◽  
Xiaodong Shi ◽  
Chunyan Qi ◽  
Jianfei Zhan ◽  
Xue Han ◽  
...  
Keyword(s):  
High Resolution ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Surfactant Solution ◽  
Fluid Models ◽  
Pore Scale ◽  
Field Development ◽  
Digital Rock ◽  
Small Pore ◽  
Sem Imaging

Abstract With the decline of conventional resources, the tight oil reserves in the Daqing oilfield are becoming increasingly important, but measuring relative permeability and determining production forecasts through laboratory core flow tests for tight formations are both difficult and time consuming. Results of laboratory testing are questionable due to the very small pore volume and low permeability of the reservoir rock, and there are challenges in controlling critical parameters during the special core analysis (SCAL) tests. In this paper, the protocol and workflow of a digital rock study for tight sandstones of the Daqing oilfield are discussed. The workflow includes 1) using a combination of various imaging methods to build rock models that are representative of reservoir rocks, 2) constructing digital fluid models of reservoir fluids and injectants, 3) applying laboratory measured wettability index data to define rock-fluid interaction in digital rock models, 4) performing pore-scale modelling to accelerate reservoir characterization and reduce the uncertainty, and 5) performing digital enhanced oil recovery (EOR) tests to analyze potential benefits of different scenarios. The target formations are tight (0.01 to 5 md range) sandstones that have a combination of large grain sizes juxtaposed against small pore openings which makes it challenging to select an appropriate set of imaging tools. To overcome the wide range of pore and grain scales, the imaging tools selected for the study included high resolution microCT imaging on core plugs and mini-plugs sampled from original plugs, overview scanning electron microscopy (SEM) imaging, mineralogical mapping, and high-resolution SEM imaging on the mini-plugs. High resolution digital rock models were constructed and subsequently upscaled to the plug level to differentiate bedding and other features could be differentiated. Permeability and porosity of digital rock models were benchmarked against laboratory measurements to confirm representativeness. The laboratory measured Amott-Harvey wettability index of restored core plugs was honored and applied to the digital rock models. Digital fluid models were built using the fluid PVT data. A Direct HydroDynamic (DHD) pore-scale flow simulator based on density functional hydrodynamics was used to model multiphase flow in the digital experiments. Capillary pressure, water-oil, surfactant solution-oil, and CO2-oil relative permeability were computed, as well as primary depletion followed with three-cycle CO2 huff-n-puff, and primary depletion followed with three-cycle surfactant solution huff-n-puff processes. Recovery factors were obtained for each method and resulting values were compared to establish most effective field development scenarios. The workflow developed in this paper provides fast and reliable means of obtaining critical data for field development design. Capillary pressure and relative permeability data obtained through digital experiments provide key input parameters for reservoir simulation; production scenario forecasts help evaluate various EOR methods. Digital simulations allow the different scenarios to be run on identical rock samples numerous times, which is not possible in the laboratory.

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