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.

Prediction of mobile water in a tight gas sandstone reservoir using NMR and fractional flow model

2014 ◽  
Vol 54 (2) ◽  
pp. 1
Author(s):  
Maria Anantawati ◽  
Suryakant Bulgauda
Keyword(s):  
Steady State ◽  
Relative Permeability ◽  
Flow Model ◽  
Bound Water ◽  
Free Water ◽  
Development Project ◽  
Asia Pacific ◽  
Fractional Flow ◽  
Reservoir Properties ◽  
Mobile Water

One of the objectives of petrophysical interpretation is the estimation of the respective volumes of formation fluids. With traditional interpretation using conventional openhole logs it is only possible to determine the total amount of water. The challenge is to determine the volumes of bound water (clay-bound and capillary-bound) and free water. At the moment, NMR is the only measurement that can help distinguish the volumes of each water component (clay-bound, capillary-bound and mobile), using cut-offs on T2 (transverse relaxation time). However NMR interpretation also requires information on reservoir properties. Alternatively, steady-state relative permeability and fractional flow of water can be used to determine the potential of mobile water. The study area, located in the Cooper Basin, South Australia, is the target of a planned gas development project in the Patchawarra formation. It comprises multiple stacked fluvial sands which are heterogeneous, tight and of low deliverability. The sands are completed with multi-stage pin-point fracturing as a key enabling technology for the area. A comprehensive set of data, including conventional logs, cores and NMR logs, were acquired. Routine and special core analysis were performed, including NMR, electrical properties, centrifuge capillary pressure, high-pressure mercury injection, and full curve steady state relative permeability. A fractional flow model was built based on core and NMR data to determine potential mobile water and the results compared with production logs. This paper (SPE 165766) was prepared for presentation at the SPE Asia Pacific Oil & Gas Conference and Exhibition, held in Jakarta, Indonesia, from 22–24 October 2013.

CFD Challenge: Solutions Using the In-House Finite-Element-Based Solver NEWTETR

2012 ◽  
Author(s):  
Yiemeng Hoi ◽  
David A. Steinman
Keyword(s):  
Steady State ◽  
Pressure Measurements ◽  
Surface Geometry ◽  
Flow Rates ◽  
Pressure Drops ◽  
Or Groups ◽  
Giant Cerebral Aneurysm ◽  
Pulsatile Pressure ◽  
Nominal Surface

Briefly, this Challenge aims to test the sensitivity of steady and pulsatile pressure drops as predicted by different CFD solvers or groups, and ultimately against in vitro pressure measurements. The current study focuses on the Phase I of the Challenge. We simulated steady state and pulsatile pressure drops based on the nominal surface geometry and specific inlet flow rates on a giant cerebral aneurysm with proximal stenosis.

Work With Chemical Additives Advances Understanding of Relative Permeability Shifts

2021 ◽  
Vol 73 (09) ◽  
pp. 37-38
Author(s):  
Chris Carpenter
Keyword(s):  
Steady State ◽  
Relative Permeability ◽  
Flow Rate ◽  
Pressure Difference ◽  
Effective Permeability ◽  
Constant Flow ◽  
Chemical Additives ◽  
Flow Rates ◽  
Steady State Method ◽  
Tight Rocks

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 201520, “Advances in Understanding Relative Permeability Shifts by Imbibition of Surfactant Solutions Into Tight Plugs,” by Mohammad Yousefi, Lin Yuan, and Hassan Dehghanpour, SPE, University of Alberta, prepared for the 2020 SPE Annual Technical Conference and Exhibition, originally scheduled to be held in Denver, Colorado, 5–7 October. The paper has not been peer reviewed. Various chemical additives have been proposed recently to enhance imbibition oil recovery from tight formations during shut-in periods after hydraulic fracturing operations. In the complete paper, the authors develop and apply a laboratory protocol mimicking leakoff, shut-in, and flowback processes to evaluate the effects of fracturing-fluid additives on oil regained permeability. A conventional coreflooding apparatus is modified to measure oil effective permeability (koeff) before and after the surfactant-imbibition experiments. Methodology Proposed Technique for Measuring Oil Effective Permeability. Despite the simplicity of the steady-state method, measuring permeability of tight rocks with this technique is challenging because of its time-consuming nature and the fact that accurate measurement is necessary of extremely low flow rates corresponding to low injectivity of tight rocks. The authors use a pair of plugs from a well drilled in the Montney formation that is a stratigraphic unit of the Lower Triassic age in the western Canadian sedimentary basin located in British Columbia and Alberta. It is mainly a low-permeability siltstone reservoir. In the modified coreflooding apparatus, the authors reduce the effect of compressibility in order to reduce the duration of the transient period by approximately one order of magnitude. Because monitoring changes in pressure is much easier and more accurate than monitoring flow-rate changes, a constant flow-rate mode is used and pressure is recorded with time. Oil is injected at different constant flow rates (qo), and the inlet pressure is monitored. The stable pressure difference across the plug is recorded for each flow rate. After steady-state conditions are reached based on the pressure profile, the qo is increased. This process is repeated until four stable pressure differences corresponding to four different qo are obtained. After the highest qo is reached, it is decreased in similar steps to check the repeatability of each data point. The permeability is calculated with the Darcy equation and slope of the qo vs. stable pressure difference across the plug.

scholarly journals EVALUATION OF CAPILLARY END EFFECT IN WATER-OIL PERMEABILITY TESTS USING MULTIPLE FLOW RATES TECHNIQUE

2021 ◽  
Vol 14 (04) ◽  
pp. 259-267
Author(s):  
I. C. A. B. A. Santos ◽  
F. M. Eler ◽  
D. S. S. Nunes ◽  
P. Couto
Keyword(s):  
Relative Permeability ◽  
Flow Rate ◽  
Optimization Problem ◽  
Oil Field ◽  
End Effect ◽  
Flow Rates ◽  
Experimental Procedure ◽  
Injection Methods ◽  
Relative Permeability Curves ◽  
Capillary End Effect

Relative permeability curves obtained in laboratory are used in reservoir simulators to predict production and establish the best strategies for an oil field. Therefore, researchers study several procedures to obtain relative permeability curves. Among these procedures are the multiple flow rates injection methods. Thus, this work proposes to develop an experimental procedure with multiple increasing flows. To make this feasible, simulations were initially carried out at CYDAR, aiming to establish flow rates and time necessary to achieve system stabilization, within the limits of the equipment. After that, tests were carried out establishing the minimum time of 5 hours to stabilize the oil production, and the differential pressure at each flow rate. The accounting and minimization of the capillary end effect in these tests were also evaluated. Capillary pressure constraints contributed to minimize the number of possible solutions to the optimization problem improving the fit of solutions for a specific case.

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 Research on the Correction Method of the Capillary End Effect of the Relative Permeability Curve of the Steady State

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4528
Author(s):  
Yanyan Li ◽  
Shuoliang Wang ◽  
Zhihong Kang ◽  
Qinghong Yuan ◽  
Xiaoqiang Xue ◽  
...  
Keyword(s):  
Steady State ◽  
Pressure Drop ◽  
Relative Permeability ◽  
Stability Factor ◽  
End Effect ◽  
Relative Permeability Curve ◽  
Steady State Method ◽  
State Method ◽  
The Impact ◽  
Capillary End Effect

Relative permeability curve is a key factor in describing the characteristics of multiphase flow in porous media. The steady-state method is an effective method to measure the relative permeability curve of oil and water. The capillary discontinuity at the end of the samples will cause the capillary end effect. The capillary end effect (CEE) affects the flow and retention of the fluid. If the experimental design and data interpretation fail to eliminate the impact of capillary end effects, the relative permeability curve may be wrong. This paper proposes a new stability factor method, which can quickly and accurately correct the relative permeability measured by the steady-state method. This method requires two steady-state experiments at the same proportion of injected liquid (wetting phase and non-wetting phase), and two groups of flow rates and pressure drop data are obtained. The pressure drop is corrected according to the new relationship between the pressure drop and the core length. This new relationship is summarized as a stability factor. Then the true relative permeability curve that is not affected by the capillary end effect can be obtained. The validity of the proposed method is verified against a wide range of experimental results. The results emphasize that the proposed method is effective, reliable, and accurate. The operation steps of the proposed method are simple and easy to apply.

scholarly journals Two-Phase Flow in Rough Fractures – Insights from 3D-Printed Fractures

2021 ◽  
Author(s):  
Tomos Phillips ◽  
Jeroen Van Stappen ◽  
Tom Bultreys ◽  
Stefanie Van Offenwert ◽  
Arjen Mascini ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Fluid Flow ◽  
Relative Permeability ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Fractional Flow ◽  
Two Phase ◽  
Flow Rates ◽  
3D Printed ◽  
Flow Pathways

<p>Fractures can provide principal fluid flow pathways in the Earth’s crust, making them a critical feature influencing subsurface geoenergy applications, such as the storage of anthropogenic waste, emissions or energy. In such scenarios, fluid-conductive fault and fracture networks are synonymous with two-phase flow, due to the injection of an additional fluid (e.g. CO<sub>2</sub>) into an already saturated (e.g. brine) system. Predicting and modelling the resulting (partly-)immiscible fluid-fluid interactions, and the nature of fluid flow, on the field-scale, requires an understanding of the constitutive relationships (e.g. relative permeability and capillary pressure) governing fluid flow on the single-fracture scale. In addition to capillary and viscous forces, fracture relative permeability is influenced by aperture heterogeneity, arising from surface roughness. The degree to which surface roughness controls relative permeability behaviour in fractures remains unclear. As all fractures display roughness to various degrees, furthering our understanding of two-phase flow in fractures benefits from a systematic investigation into the impact of roughness on flow properties. To this end, we performed co-injection experiments on two 3D-printed (polymeric resin) fractures with different controlled and quantified surface roughness distributions (Joint Roughness Coefficients of 5 & 7). Brine and decane were simultaneously injected at a series of incrementally decreasing brine fractional flow rates (1, 0.75, 0.5, 0.25, and 0), at low total volumetric flow rates (0.015 mL/min). Steady-state fluid occupancy patterns, preferential flow pathways and overall fluid saturations in each fracture were imaged and compared using an environmental laboratory-based μ-CT scanner with a 5.8 μm voxel size (EMCT; Ghent University Centre for X-ray Computed Tomography). Experimental results highlight the importance of roughness on the relative permeability behaviour of fractures, which is, for example, a principal control on leakage rates from geological stores.</p>

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
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