Capillary End Effect Research Articles

Evaluation of Relative Permeability Tests One-Step with Bump Flow and Multi-Step

The relative permeability curves obtained in the laboratory are used in reservoir simulators to predict production and decide the best strategies for an oil field. Therefore, researchers are studying several procedures to obtain relative permeability curves, among them the multiple flow rates injection methods. Thus, this work proposes to develop an experimental procedure with multiple increasing flows (multi-step). To make this feasible, simulations were initially carried out at CYDAR, aiming to establish the flow rates and necessary the time to system stabilization, within the limits of the equipment. After that, the tests were carried out and the results obtained were 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. And the capillary pressure constraints contributed to minimize the number of possible solutions of the optimization problem improving the uniqueness of solution.

Study of the decrease of the capillary end effect due to an increase in the displacement phase

Study of the decrease of the capillary end effect due to an increase in the displacement phase

Capillary End Effects in Reservoirs with Heterogeneous Wettability

A new type of capillary end effect in oil and gas reservoirs due to heterogeneous wettability has been justified. This type of capillary end effect is not related to the contrast of reservoir rock permeability or porosity. Nonlinear fliud flow in the layers with heterogeneous wettability has been established experimentally. The mechanism of this phenomenon is due to the new type of capillary end effect.

A new numerical production well model for the low-permeability gas reservoir

In the development of low permeability gas reservoirs, capillary end effect has a significant impact on the flow near the production well, and physical quantities near the production well all change dramatically, which may reduce the oil and gas production. Traditional well model cannot describe this phenomenon. In this paper, based upon the analytical solution of one dimensional radial flow, an alternative numerical well model for low permeability gas reservoir considering the end effect is constructed. The numerical results show that the gas and water productions can be predicted accurately at different grid scales using the proposed well model. In contrast, the Peaceman well model for multi-phase only can get the accurate results when the grid is enough subdivided.

Steady state relative permeability experiments with capillary end effects: Analytical solutions including derivation of the intercept method

Steady state relative permeability experiments are performed by coinjection of two (or more) immiscible fluids. The relative permeabilities can be calculated directly from the stabilized pressure drop and saturation of the core if capillary end effects and transient effects are negligible. In most cases such conditions are difficult to obtain.This work presents an analytical solution in form of explicit expressions for the spatial profiles of pressure gradients and saturation, average saturation and pressure drop for a core being injected simultaneously with two phases at steady state when capillary end effects are significant. When arbitrary saturation functions are applied, such parameters and distributions can only by obtained by numerical integration.By assumption of simplified saturation function correlations the differential equation describing steady state can be integrated. A new dimensionless capillary number N is obtained which contains the fluid and rock parameters, but also the saturation function parameters (relative permeability and capillary pressure), fluid viscosities, injected flow fraction, total flow rate and more. It is shown that when this number is of magnitude 1, end effects cover parts of the core, but parts of the core are also unaffected. For N>10 the end effects are negligible, while for N<10 end effects are dominant.This paper gives the first formal proof of the intercept method from basic assumptions. It is shown that when the inlet saturation is sufficiently close to that of a no capillary pressure situation; the average saturation changes linearly with the inverse of total rate towards the saturation corresponding to no capillary forces; also, the pressure drop divided by the pressure drop of a no end effect situation goes linearly towards 1 with the inverse of total rate.

Near-Fracture Capillary End Effect on Shale-Gas and Water Production

Summary Capillary end effect (CEE) develops in tight gas and shale formations near hydraulic fractures during flowback of the fracturing-treatment water and extends into the natural-gas-production period. In this study, a new multiphase reservoir-flow-simulation model is used to understand the role the CEE plays on the removal of the water from the formation and on the gas production. The reservoir model has a matrix pore structure mainly consisting of a network of microfractures and cracks under stress. The model simulates high-resolution water/gas flow in this network with a capillary discontinuity at the hydraulic-fracture/matrix interface. The simulation results show that the CEE causes significant formation damage during the production period by holding the water saturation near the fracture at higher levels than that using only the spontaneous imbibition of water. The effect makes water less mobile, or trapped, in the formation during the flowback, and tends to block gas flow during the production. The effect during the production is more important relative to the changing stress. We showed that the CEE cannot be removed completely but can be reduced significantly by controlling the production rate.

Nuclear Magnetic Resonance (NMR) mapping of remaining oil distribution during sequential rate waterflooding processes for improving oil recovery

At the conclusion of waterflooding phase, significant volume of oil still remains in reservoir formations. In this paper, waterflooding was performed at a designed sequential rate mode with an aim to further reduce the remaining oil saturation (Sor). Waterflooding process was monitored continuously by a low-field Nuclear Magnetic Resonance (NMR) spectrometer attempting to map pore-scale displacing behaviors and also quantify the reduction in Sorin-situ. The results showed that the main pore size of the cores ranged from 1.6 μm to 63.0 μm inferred by T2 (transverse relaxation time) distributions. The value of Sor in the cores increased towards the outlet face during waterflooding because of capillary end effect, which became more significant for heavy oil. At the termination of this waterflooding process, Sor was found to be further reduced by approximately 5.0% in the presence of thief water pathways as a result of the improved viscous forces. Water fingering and capillary imbibition effects were clearly visualized in the NMR images. These observations are expected to be useful for heavy oil waterflooding operations especially in post-breakthrough phase.

Capillary Pressure Effects on Estimating the Enhanced-Oil-Recovery Potential During Low-Salinity and Smart Waterflooding

SummaryMany experimental studies have investigated smart water and low-salinity waterflooding and observed significant incremental oil recovery after changes in the injected-brine composition. The common approach to model such enhanced-oil-recovery (EOR) mechanisms is by shifting the input relative permeability curves, particularly including a reduction of the residual oil saturation. Cores that originally display oil-wetness can retain much oil at the outlet of the flooded core because of the capillary pressure being zero at a high oil saturation. This end effect is difficult to overcome in highly permeable cores at typical laboratory rates. Injecting a brine that changes the wetting state to less-oil-wet conditions (represented by zero capillary pressure at a lower oil saturation) will lead to a release of oil previously trapped at the outlet. Although this is chemically induced incremental oil, it represents a reduction of remaining oil saturation, not necessarily of residual oil saturation.This paper illustrates the mentioned issues of interpreting the difference in remaining and residual oil saturation during chemical EOR and hence the evaluation of potential smart water effects. We present a mathematical model representing coreflooding that accounts for wettability changes caused by changes in the injected composition. For purpose of illustration, this is performed in terms of adsorption of a wettability-alteration (WA) component coupled to the shifting of relative permeability curves and capillary pressure curves. The model is parameterized in accordance with experimental data by matching brine-dependent saturation functions to experiments where wettability alteration takes place dynamically because of the changing of one chemical component. It is seen that several effects can give an apparent smart water effect without having any real reduction of the residual oil saturation, including changes in the mobility ratio, where the oil already flowing is pushed more efficiently, and the magnitude of capillary end effects can be reduced because of increased water-wetness or because of a reduction in water relative permeability giving a greater viscous drag on the oil.

Simulation Interpretation of Capillary Pressure and Relative Permeability From Laboratory Waterflooding Experiments in Preferentially Oil-Wet Porous Media

SummaryIn preferentially oil-wet porous media, laboratory waterflooding experiments are prone to capillary end effects. The wetting phase (oil) will tend to accumulate at the outlet where the capillary pressure is zero and leave a highly remaining-oil saturation at steady state (defined by a stable pressure drop and a zero oil-production rate) compared to the residual-oil saturation. Andersen et al. (2017c) derived analytical solutions describing how the capillary pressure and relative permeability of water (the injected phase) could be determined on the basis of pressure drop and average saturation at steady states obtained at different water-injection rates. Plotting these values against inverse rate reveals linear trends at high rates, with slopes and intercepts that directly quantify the saturation functions in the range of negative capillary pressures. The method is similar to the Gupta and Maloney (2016) intercept theory but quantifies entire functions rather than a single point and provides the trends also at low rates, thus using all the information.Our aim is to demonstrate how pressure drop and oil production at steady state for different water-injection rates can be used to derive relative permeability and capillary pressure from waterflooding. This is done in three ways. First, synthetic transient waterflooding tests are generated (using a core-scale simulator), applying the same saturation-function correlations as assumed in the analytical solution. Then, more-general correlations are assumed when generating the synthetic data. This is to test the robustness of the analytical solution in producing functions similar to the “true” ones. Finally, we perform a waterflooding experiment in the laboratory on a high-permeability (3 darcies) Bentheimer sandstone core, altered to an oil-wet state. Forced imbibition was started at a rate of 0.4 pore volumes (PV) per day, which was increased stepwise after approaching a steady state. Twelve rates were applied, differing overall by a factor of ≈1,000 to yield states governed by capillary forces and advective forces. The results were interpreted using both full history matching of the transient data and matching of the steady-state data with the analytical solution.The experimental procedure and model demonstrate that only water relative permeability and capillary pressure determine the steady state during waterflooding, and hence can be estimated accurately. The analytical solution could simultaneously match the trends and magnitude of a steady-state pressure drop and production with injection rate to give an estimation of the saturation functions. The estimated saturation functions from the analytical solution agreed well with the estimates from full history matching.

Steady-State Relative Permeability Measurements of Tight and Shale Rocks Considering Capillary End Effect

Relative permeability (kr) data are the key factors for describing the behaviour of the multi-phase flow in porous media. During the kr measurements of low-permeability rocks, high capillary pressure can cause a significant liquid hold-up at the core outlet. This liquid hold-up, which is known as capillary end effect (CEE), is the main difficulty for laboratory measurements of relative permeability (kr) for tight and shale rocks. In this paper, a novel method is proposed to correct the CEE during the steady-state relative permeability (SS-kr) measurements. The integrity of the proposed method is evaluated by a set of artificially generated data and the experimental SS-kr data of an Eagle Ford shale sample. It is shown that accurate kr data can be obtained using the proposed technique. This technique can be used to estimate reliable kr data without any saturation profile measurement equipment, such as CT scan or MRI.

A numerical well model considering capillary end effect for the low-permeability gas reservoir

In the recovery of low permeability reservoir, the capillary pressure has an important effect, which may reduce gas production. Due to the capillary end effect, there are two flow patterns in the vicinity of the production well: both water and gas phases can flow into the production well and only gas phase can enter the production well. Based on the analytical equations of one-dimensional radial flow considering the capillary end effect, an alternative numerical well model for low permeability gas reservoir is constructed. Numerical examples show that the proposed model can reflect the dramatic change for saturation and gas-phase pressure in the vicinity of the production well both for two flow patterns, and therefore can predict the gas and water productions accurately at different grid scales. In contrast, the original Peaceman well model for multi-phase flow, which is directly extended from that for single-phase flow, only can provide good prediction under the condition of that the grid size is enough small. Especially, for the original Peaceman well model, this problem is out of control since it is difficult to estimate a suitable grid size.

Impact of injection rate on transient oil recovery under mixed-wet conditions: a microfluidic study

Lab-on-a-chip methods were used to visualize the pore-scale distribution of oil within a mixed-wet, quasi-monolayer of marble grains packed in a microfluidic channel as the oil was displaced by water. Water injection rates corresponding to microscopic capillary numbers between Ca = 5 × 10-8 and 2 × 10-4 (Darcy velocities between 0.3 and 1100 ft/d) were considered. As expected, early-time water invasion transitions from stable displacement to capillary fingering with decreasing Ca, with capillary fingering observed at Ca ≤ 10-5. End-point oil saturation decreases with Ca over the entire range of Ca considered, consistent with the canonical capillary desaturation curve. In contrast, Sor derived from approximate numerical simulations using reasonable Pc(Sw) do not display a strong dependence on Ca. These results suggest that the Ca dependence of end-point oil saturation is largely due to capillary end effects which, under conditions considered presently, affect the entire length of the packed bed.

Experimental investigation of polymer flooding with low-salinity preconditioning of high temperature\u2013high-salinity carbonate reservoir

Application of polymer flooding in high temperature–high salinity (HTHS) carbonate reservoirs is challenging due to lack of polymers that can withstand such harsh reservoir conditions. The traditional polymers are usually sensitive to high salinity, especially at high temperature. However, injection of low-salinity make-up brines may precondition high-salinity reservoirs before initiating polymer flooding which may reduce chemical degradation of polymer. This study aims to evaluate the effectiveness of a partially hydrolyzed polyacrylamide base polymer for mobility control application in a low-salinity preconditioned carbonate reservoir and hence on the improvement of oil recovery at HTHS carbonate reservoir. Core flooding experiments using unsteady-state technique were conducted on reservoir cores with permeability range of 10–100 mD. During each experiments, salinity of the make-up brines were changed to study the effect of preflush salinity and polymer flooding in HTHS reservoir. Oil production from water flooding for all the cases was found to be between 49 and 65%. Polymer helped to reduce the mobility ratio from 4.1 to less than 1 and additional 7–11% of oil was recovered from the remaining oil saturation after water flooding. Comparisons were also made between oil recovery results based on volumetric production and in situ saturation monitoring (ISSM) data, which were found to be matching. Additionally, the ISSM helped to understand the performances of fluids injected during oil recovery stages and captured front movement of the fluids at all time. Also, high capillary end effect was confirmed from the ISSM which may lead to underestimation of the oil recovery from water flooding in the absence of ISSM. Resistance factor and residual resistance factor were also calculated during all core flooding experiments and were found to be 7.0, 2.4, 36 and 3.7, 1.4, 8.9, respectively.

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

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.

Minimized Capillary End Effect During CO2 Displacement in 2‐D Micromodel by Manipulating Capillary Pressure at the Outlet Boundary in Lattice Boltzmann Method

AbstractWe propose a new outflow boundary condition to minimize the capillary end effect for a pore‐scale displacement simulation. The Rothman‐Keller lattice Boltzmann method with multi‐relaxation time is implemented to manipulate a nonflat wall and inflow‐outflow boundaries with physically acceptable fluid properties in 2‐D microfluidic chip domain. Introducing a mean capillary pressure acting at ‐water interface to the nonwetting fluid at the outlet effectively prevents injection pressure from suddenly dropping upon breakthrough such that the continuous invasion and the increase of saturation are allowed. This phenomenon becomes most pronounced at capillary number of logCa = −5.5, while capillary fingering and massive displacement of prevail at low and high capillary numbers, respectively. Simulations with different domain length in homogeneous and heterogeneous domains reveal that capillary pressure and saturation near the inlet are reproducible compared with those with a proposed boundary condition. The residual saturation uniquely follows the increasing tendency with increasing capillary number, corroborated by experimental evidences. The determination of the mean capillary pressure and its sensitivity are also discussed. The proposed boundary condition is commonly applicable to other pore‐scale simulations to accurately capture the spatial distribution of nonwetting fluid and corresponding displacement ratio.

Well productivity enhancement by applying nanofluids for wettability alteration

Water blocking is a frequent cause for gas productivity decline in unconventional and conventional fields. It is a result of the capillary end effect near the wellbore vicinity. It creates significant formation damage and decreases gas well productivity. The alteration of the rock wettability by nanofluids is an effective way to reduce water blockage and enhance gas production. Presently, several types of surfactants and nanofluids are used in the industry for contact angle alteration. In this study, we developed an analytical model and analysed the sensitivity to several parameters. After the treatment, the porous medium in the well vicinity (or along the core) will have a stepwise constant contact angle profile. We derive analytical models for compressible steady-state two-phase linear and axi-symmetric flows, accounting for the piecewise-constant contact angle and contact-angle-dependent capillary pressure and relative permeability. The modelling reveals a complex interplay between the competing effects of compressibility, viscous and capillary forces, which influence the optimal contact angle for treatment. The optimal contact angle for treatment will depend on the initial wettability of the formation, the water cut and the capillary-viscous ratio.

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

We investigate and characterize the influence of capillary end effects on steady-state relative permeabilities obtained in pore-scale numerical simulations of two-phase flows. Our study is motivated by the observation that capillary end effects documented in two-phase laboratory-scale experiments can significantly influence permeability estimates. While numerical simulations of two-phase flows in reconstructed pore-spaces are increasingly employed to characterize relative permeabilities, a phenomenon which is akin to capillary end effects can also arise in such analyses due to the constraints applied at the boundaries of the computational domain. We profile the relative strength of these capillary end effects on the calculation of steady-state relative permeabilities obtained within randomly generated porous micro-structures using a finite volume-based two-phase flow solver. We suggest a procedure to estimate the extent of the regions influenced by these capillary end effects, which in turn allows for the alleviation of bias in the estimation of relative permeabilities.

Productivity index enhancement by wettability alteration in two-phase compressible flows

Water blocking due to the capillary end effect near the wellbore vicinity creates significant formation damage and decreases well productivity for oil and gas. The alteration of the rock wettability by a chemical well treatment is an effective way to reduce water blockage and enhance oil and gas production. Presently, several surfactants and nanofluids are used in the industry for contact angle alteration. After the treatment, the porous medium in the well vicinity (or along the core) has stepwise contact angle. The previous paper (Naik et al., 2015) develops analytical models for incompressible steady-state two-phase linear and axi-symmetric flows, accounting for the piecewise constant contact angle and contact-angle-dependent capillary pressure and relative permeability. The current paper adds the effect of compressibility, which is particularly important for high rate gas wells and wells in unconventional and tight-sand reservoirs. The obtained semi-analytical model has been validated by comparison with a set of laboratory coreflood tests. The modelling reveals a complex interplay between the competing effects of compressibility, viscous and capillary forces, yielding non-monotonic dependencies of well productivity on the wettability and the optimal contact angle. The model closely matches the productivity index data for two production wells from a field case before and after wettability treatment using surfactant.

Evaluation of low-salinity waterflooding in Middle East carbonate reservoirs using a novel, field-representative coreflood method

Low-salinity waterflooding attempts to improve recovery by reducing the salinity of the injection water, where the wettability alteration towards more water-wet state of the reservoir rock is believed to be the leading mechanism. This technology has received significant interest and a rich body of unsteady-state coreflooding test data has been reported in the past few years. However, capillary end-effect driven artifacts in conventional unsteady-state coreflooding could hinder proper understanding and interpretation of the measured results. We have developed a modified steady-state fractional-flow method to minimize capillary end effects. The fractional-flow analysis and simulation illustration of the new method has been published earlier by Gupta et al. (2015). In this work, we applied this new method to several Middle East carbonate reservoirs where slight changes in relative permeability consistent with a change in wettability can be observed but the overall uplift in recovery was very small. In addition, the results from the new method and the conventional coreflooding method were compared in selected cases to demonstrate the benefit of the new method in minimizing capillary end effect artifacts. Overall, this work demonstrates an improved laboratory screening methodology for low-salinity waterflood and similar EOR methods. The results of this work highlight the potential as well as challenges in low-salinity waterflooding in carbonates as a practical EOR technology.

Waterflooding oil-saturated core samples - Analytical solutions for steady-state capillary end effects and correction of residual saturation

Capillary end effects can play an important role when interpreting or designing a core flood experiment. The outlet of the core is characterized by a zero capillary pressure which can trap wetting phase in a region near the outlet of the core, potentially leading to a wrongful estimation of parameters such as residual saturation and relative permeability. We consider the steady state obtained in a core flooding experiment: one fluid (assumed water) is continuously injected and produced, while a second fluid (assumed oil), displaced during a transient production phase, is completely immobilized during the considered steady state due to entrapment. An analytical model is derived giving an explicit formulation of the saturation and pressure distributions, the average saturation and the pressure drop at this steady state. The model is general enough to consider different wetting states as given macroscopically by a capillary pressure curve that can vanish at a selected saturation and function shapes and magnitudes that can be adjusted. To our knowledge previous works have been limited to implicit relations between the mentioned parameters and also been restricted to strongly wetted media, which underlines one part of the novelty in this work. A second novel result from this work is that it is possible to derive meaningful capillary numbers that incorporate saturation function parameters. The model predicts a position LE (measured from the outlet) where the end effects become negligible. At the critical value 1 of our dimensionless number N (which also includes saturation function parameters) the end effects exactly reach the inlet position. The model shows different behavior according to whether N>1 (strong advective forces) or if N<1 (strong capillary forces). In the first case, both scaled pressure drop (relative to the pressure drop without end effects) and average saturation change proportionally to the inverse of N (and accordingly, the inverse of injection rate). In this regime the curves can be scaled uniquely and we can specify physically meaningful capillary numbers incorporating all saturation function parameters. The pressure drop and average saturation behave differently with the saturation function parameters and thus scale with different dimensionless numbers. For N<1 the average saturation and pressure drop do not scale easily according to one capillary number, but the model can easily and intuitively explain variations in the behavior resulting from changes in these parameters. We show that it is possible, based on a simple three-rate water flooding test to estimate the water relative permeability curve and the negative capillary pressure curve. A third novel result is that we for the first time provide a theoretical derivation of the intercept method proposed by Gupta and Maloney (2016) from the fundamental equations of multi-phase flow in porous media and extend the amount of information that is obtained from this procedure. The pressure drop trends considered in unscaled variables is equivalent to their model, stating that at high rates the pressure drop will be linear with rate. Unlike the pressure drop, the saturation will however vary linearly with the inverse of rate. The slopes provide further information about the saturation curve parameters.