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Following the request of a regulatory authority, a rat study was conducted to compare pharmacokinetic parameters from traditional large volume sampling and capillary microsampling. Rats were dosed with a proprietary compound in three dose groups and blood samples were collected via capillary microsampling (32 μl), immediately followed by traditional large volume sampling (300 μl) up to 24 h postdose. Resulting plasma samples were analyzed for parent drug and two metabolites. AUCs were compared between sampling techniques. There was no statistical difference between AUCs from traditional and microsampling across different doses and analytes.   Toxicokinetic parameters generated from plasma collected as a capillary microsample or traditional large volume sample are highly comparable.

 Forced and spontaneous imbibition of water is performed to displace oil from strongly water-wet Gray Berea (~130 mD) and Bentheimer (~1900 mD) sandstone core plugs. Two nonpolar oils (n-heptane and Marcol-82) were used as a non-wetting phase, with viscosities between 0.4 and 32 cP and brine (1 M NaCl) for the wetting phase with viscosity 1.1 cP. Recovery was measured for both imbibition modes, and pressure drop was measured during forced imbibition. Five forced imbibition tests were performed using low or high injection rates, using low or high oil viscosity. Seventeen spontaneous imbibition experiments were performed at four different oil viscosities. By varying the oil viscosity, the injection rate and imbibition modes, capillary and advective forces were allowed to dominate, giving trends that could be captured with modeling. Full numerical simulations matched the experimental observations consistently. The findings of this study provide better understanding of pressure and recovery behavior in strongly water-wet systems. A strong positive capillary pressure and a favorable mobility ratio resulting from low water relative permeability were main features explaining the observations. Complete oil recovery was achieved at water breakthrough during forced imbibition for low and high oil viscosity and the recovery curves were identical when plotted against the injected volume. Analytical solutions for forced imbibition indicate that the pressure drop changes linearly with time when capillary pressure is negligible. Positive capillary forces assist water imbibition, reducing the pressure drop needed to inject water, but yielding a jump in pressure drop when the front reaches the outlet. At a high injection rate, capillary forces are repressed and the linear trend between the end points was clearer than at a low rate for the experimental data. Increasing the oil viscosity by a factor of 80 only increased the spontaneous imbibition time scale by five, consistent with low water mobility constraining the imbibition rate. The time scale was predicted to be more sensitive to changes in water viscosity. At a higher oil-to-water mobility ratio, a higher part of the total recovery follows the square root of time. Our findings indicate that piston-like displacement of oil by water is a reasonable approximation for forced and spontaneous imbibition, unless the oil has a much higher viscosity than the water. 

Relative permeability ( k r ) data are the key factors for describing the behaviour of the multi-phase flow in porous media. During the k r 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 ( k r ) for tight and shale rocks. In this paper, a novel method is proposed to correct the CEE during the steady-state relative permeability (SS- k r ) measurements. The integrity of the proposed method is evaluated by a set of artificially generated data and the experimental SS- k r data of an Eagle Ford shale sample. It is shown that accurate k r data can be obtained using the proposed technique. This technique can be used to estimate reliable k r data without any saturation profile measurement equipment, such as CT scan or MRI.

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.

Traditionally, steady-state relative permeability is calculated from measurements on small rock samples using Darcy’s law and assuming a homogenous saturation profile and constant capillary pressure. However, these assumptions are rarely correct as local inhomogeneities exist; furthermore, the wetting phase tends to be retained at the outlet–the so-called capillary end effect. We have introduced a new method that corrects the relative permeabilities, analytically, for an inhomogeneous saturation profile along the flow direction. The only data required are the measured pressure drops for different fractional flow values, an estimate of capillary pressure, and the saturation profiles. An optimization routine is applied to find the range of relative permeability values consistent with the uncertainty in the measured pressure. Assuming a homogenous saturation profile systematically underestimates the relative permeability and this effect is most marked for media where one of the phases is strongly wetting with a noticeable capillary end effect. Relative permeabilities from seven two-phase flow experiments in centimetre-scale samples with different wettability were corrected while reconciling some hitherto apparently contradictory results. We reproduce relative permeabilities of water-wet Bentheimer sandstone that are closer to other measurements in the literature on larger samples than the original analysis. Furthermore, we find that the water relative permeability during waterflooding a carbonate sample with a wide range of pore sizes can be high, due to good connectivity through the microporosity. For mixed-wet media with lower capillary pressure and less variable saturation profiles, the corrections are less significant.

Relative permeability and capillary pressure are key parameters in multiphase flow modelling. In heterogeneous porous media, flow direction- and flow-rate dependence result from non-uniform saturation distributions that vary with the balance between viscous, gravitational, and capillary forces. Typically, relative permeability is measured using constant inlet fractional-flow—constant outlet fluid pressure conditions on samples mounted between permeable porous plates to avoid capillary end-effects. This setup is replicated in numeric experiments but ignores the extended geologic context beyond the sample size, impacting the saturation distribution and, consequently, the upscaled parameters. Here, we introduce a new workflow for measuring effective relative permeability and capillary pressure at the bedform scale while considering heterogeneities at the lamina scale. We harness the flexibility of numeric modelling to simulate continuum-REV-scale saturation distributions in heterogeneous rocks eliminating boundary artefacts. Periodic fluid flux boundary conditions are applied in combination with arbitrarily oriented, variable-strength pressure gradient fields. The approach is illustrated on a periodic model of cross-bedded sandstone. Stepping saturation while applying variable-strength pressure-gradient fields with different orientations, we cover the capillary-viscous force balance spectrum of interest. The obtained relative permeability and capillary pressure curves differ from ones obtained with traditional approaches highlighting that the definition of force balances needs consideration of flow direction as an additional degree of freedom. In addition, we discuss when the common viscous and the capillary limits are applicable and how they vary with flow direction in the presence of capillary interfaces.

Measurement of drainage relative permeability by the centrifuge method was first introduced by Hagoort (SPE J. 29(3):139–150, 1980). It has been shown that capillary end effects can cause error in the measurement of relative permeability if a minimum rotational speed is not honoured. To determine the minimum rotational speed that makes the capillary end effect negligible, ω min , we propose that the value of capillary-gravity number, N cg , should be of the order of 10 −2 or smaller. This conclusion is based on the use a Forward–backward scheme consisting of a forward numerical simulator developed for centrifuge experiments and applying Hagoort’s method as a backward model. The article presents the use of this Forward–backward scheme as a powerful tool for error analysis such as determining the impact of capillary end effects. By using this loop, we first determine ω min for specific core and fluid properties. Later, we generalize the ω min calculations by using the definition of N cg as a “rule of thumb” for designing relative permeability experiments by centrifuge method. We also demonstrate another use of this loop for controlling the quality of the experimental data.