Unsteady-state Methods Research Articles

Effect of Heterogeneity on Capillary Pressure and Relative Permeability Curves in Carbonate Reservoirs. A Case Study for Mishrif Formation in West Qurna/1 Oilfield, Iraq

The special core analysis tests were accomplished on a set of core plugs for Mishrif Formation (mA, mB1, and mB2cde/mC units) in West Qurna/1 oilfield, southern Iraq. Oil relative permeability (Kro) data and the Corey-type fit of the data as functions of the brine saturation at the core outlet face for individual samples in the water-oil imbibition process to estimate relative permeability measurements by the centrifuge method were utilized. Identical correlations for oil and water relative permeabilities were extracted by steady-state and unsteady-state methods. For the mA samples, the gas-water capillary pressure curves were within a narrow range (almost identical) indicating that mA is a homogeneous unit. Kro curves for three mB2ab plugs were practically identical, that is referring to the homogeneity in the upper portion of the unit. The mB2 unit has a more solid‐phase concentration than other units. In addition, the general trend of low residual oil saturation is related to the raising in porosity but no reliable correlation between the residual oil saturation to water drive (Sorw) and Klinkenberg-corrected permeability (Kinf). Based on the correlation between the effective oil permeability at the initial water saturation [ko(Swi)] and (Kinf/f)1/2 for the high-permeability lithofacies mB1 plugs, ko(Swi) is approximately equal to or exceeds Kinf. While ko(Swi) was below Kinf for the other samples. New good empirical equations were obtained for effective gas permeability at final water saturation versus Kinf, as well as, for Kro and Krw versus saturation for all lithofacies.

Comparing Centrifuge, Steady-State and Semi-Dynamic Methods for Relative Permeability and Capillary Pressure Determination: New Insights

Relative permeability and capillary pressure are essential parameters for understanding multiphase flow in porous media and scenarios of production in oil or gas reservoirs. There are several experimental methods for determining the relative permeability curves: unsteady-state (USS), steady-state (SS), and semi-dynamic (SD) methods. Each method has advantages and weaknesses. Although the USS approach leads to fast data results, the interpretation neglects the capillary pressure effects and provides a limited amount of data points obtained after breakthrough. The SS method is time consuming but enables covering a wider range of saturation with data points if the test is well designed. The SD method may be more time consuming than the SS method but provides both relative permeability to the injected phase and capillary pressure. The relative permeability to the produced phase is then determined by numerical means. The main objective of this study was to compare the water-oil relative permeability curves obtained from the steady-state and semi-dynamic methods performed at reservoir conditions with live fluids. Carbonate core plugs of same rock type and same properties were selected for this experimental program. The samples were brought to the same irreducible water saturation at a constant brine-oil capillary pressure using a centrifuge before being dynamically aged with live oil. In addition to monitoring the average saturation using material balance (MB), a linear X-ray scanner was used for in-situ saturation monitoring (ISSM) along the core samples. The oil relative permeability from the SD method was simulated with fixed water relative permeability and capillary pressure by history-matching the oil production and the differential pressure signal. Two additional centrifuge tests on twin plug were performed in order to measure imbibition capillary pressure and oil relative permeability at pseudo-reservoir conditions. This comparative study shows that the SD method provides similar capillary pressure and oil relative permeability curves to those obtained by centrifuge methods. Even if all Kr curves are in an acceptable envelop, some differences are observed between SD and SS Kr curves: several investigative leads are given to explain this discrepancy. It is also shown that a better saturation method needs to be implemented, especially when dealing with heterogeneous rocks. While a more robust ISSM method is being tested at TOTAL, the results presented in this paper are very encouraging.

Research progress in damage assessment methods for tight sandstone gas reservoirs

In the process of oil and gas development, the perfect reservoir damage evaluation method is an important condition to realize the economical and efficient development of the reservoir. At present, great progress has been made in the exploration of tight oil and gas. However, due to the characteristics of low porosity, low permeability and low water saturation of tight sandstone gas reservoirs, conventional reservoir damage evaluation methods are not applicable to it, and no systematic evaluation method has been formed yet. The damage evaluation methods of tight sandstone gas reservoirs mainly include the steady-state method and the unsteady-state method. The steady-state method is mainly the high temperature and high back pressure method, while the unsteady-state methods are the pressure attenuation method and the pressure transmission method which are widely applicable. Visualization technology, microfluidic technology, flow rate evaluation method and recovery evaluation method are the new methods to evaluate reservoir damage, which are in the further research. This paper summarizes the research progress of reservoir damage evaluation methods for tight sandstone gas reservoirs, analyzes the main evaluation methods, experimental equipment and improvement measures, and points out the problems that need to be paid attention to and solved, in order to provide reference for efficient and accurate evaluation of reservoir damage in tight sandstone gas reservoirs.

Numerical modeling and experimental investigation on the effect of low-salinity water flooding for enhanced oil recovery in carbonate reservoirs

Numerous studies concluded that water injection with modified ionic content/salinity in sandstones would enhance the oil recovery factor due to some mechanisms. However, the effects of smart water on carbonated formations are still indeterminate due to a lack of experimental investigations and researches. This study investigates the effects of low-salinity (Low Sal) solutions and its ionic content on interfacial tension (IFT) reduction in one of the southwestern Iranian carbonated reservoirs. A set of organized tests are designed and performed to find each ion’s effects and total dissolved solids (TDS) on the candidate carbonated reservoir. A sequence of wettability and IFT (at reservoir temperature) tests are performed to observe the effects of controlling ions (sulfate, magnesium, calcium, and sodium) and different salinities on the main mechanisms (i.e., wettability alteration and IFT reduction). All IFT tests are performed at reservoir temperature (198 °F) to minimize the difference between reservoir and laboratory-observed alterations. In this paper, the effects of four different ions (SO42-, Ca2+, Mg2+, Na+) and total salinity TDS (40,000, 20,000, 5000 ppm) are investigated. From all obtained results, the best two conditions are applied in core flooding tests to obtain the relative permeability alterations using unsteady-state methods and Cydarex software. The final part is the simulation of the whole process using the Schlumberger Eclipse black oil simulator (E100, Ver. 2010) on the candidate reservoir sector. To conclude, at Low Sal (i.e., 5000 ppm), the sulfate ion increases sulfate concentration lower IFT, while in higher salinities, increasing sulfate ion increases IFT. Also, increasing calcium concentration at high TDS (i.e., 40,000 ppm) decreases the amount of wettability alteration. In comparison, in lower TDS values (20,000 and 5000 ppm), calcium shows a positive effect, and its concentration enhanced the alteration process. Using Low Sal solutions at water cut equal or below 10% lowers recovery rate during simulations while lowering the ultimate recovery of less than 5%.

Laboratory evaluation of flow properties of Niutitang shale at reservoir conditions

Abstract Absolute and water saturation dependent gas flow under reservoir conditions is important for the exploration of deep energy resources. Steady-state and various unsteady-state argon permeability tests were conducted on dry Niutitang shale during the confinement loading and unloading cycles, then different gases were used for steady-state permeability tests at the final confinement of 20 MPa. Permeability decreased by 36% with the confinement increasing from 5 MPa to 60 MPa, and around 66% of the permeability reductions was recovered after the unloading cycles. The apparent steady-state permeabilities were 38% higher than those derived by unsteady-state methods due to the enhanced slip flow. Two cycles of water imbibition and gas drainage tests were conducted with the long water evaporation process completed in the second gas drainage process. Argon to carbon dioxide permeability ratio ranged from 1.2 to 2.1, while the water permeability was 30–45% of the gas intrinsic permeability. The argon breakthrough pressure of water-saturated Niutitang shale sample was 8 MPa, and the permeability increased by 10 times after the long-term evaporation process. Argon permeability decreased by 90% and increased by 21.6%–29.6% respectively after the first and second gas drainage processes compared with that under dry condition with the residual water saturation being 29.7% and 11.3% respectively, which were caused by the water blockage and cracking respectively. Influences of carbon dioxide adsorption and induced swelling reached a minimum at residual water saturation.

A new low-permeability reservoir core analysis method based on rate-transient analysis theory

Unconventional reservoirs such as shales (mudrocks) and coals may exhibit an ultra-low matrix permeability (<0.001 md) challenging conventional laboratory-based methods for permeability measurement. Small-diameter core plug or crushed rock samples, combined with unsteady-state methods, are currently favored to reduce measurement times for ‘tight’ rocks. For core plug analysis, unsteady-state pulse-decay permeability (PDP) or steady-state methods (SS) are commonly employed in commercial laboratories, with the core plug sample subjected to confining stress. Analysis times, particularly for SS methods, may be excessive for ultra-low permeabilities in the nanodarcy range. Another limitation of both PDP and SS experiments applied to core plugs is that they do not represent the boundary conditions typically used to produce hydrocarbons from unconventional reservoirs in the subsurface through wells.Rate-transient analysis (RTA) is a technique used to quantitatively analyze production data from wells drilled into unconventional reservoirs to extract reservoir (e.g. permeability, hydrocarbons-in-place) and hydraulic fracture (conductivity, fracture length) properties. Multi-fractured horizontal wells (MFHWs) producing from low-permeability reservoirs commonly exhibit the flow-regime sequence of transient linear flow, where hydrocarbons flow through the reservoir orthogonal to hydraulic fractures or the horizontal well, followed by boundary-dominated flow caused by pressure interference between adjacent hydraulic fractures or wells. Transient linear flow may be analyzed using RTA methods to extract fracture or well-length (if permeability is known); the end of linear flow can be used to estimate permeability of the reservoir, and boundary-dominated flow to estimate hydrocarbons-in-place.In this work, a new experimental procedure and set-up, applied to core plugs under stress conditions, is developed to mimic well operating conditions encountered in the field (i.e. producing from a subsurface unconventional reservoir). After injection of methane gas into one end of the core plug, and pressure stabilization, the gas is flowed out of the same end of the core plug at constant pressure (with the aid of a backpressure regulator), and flow rates are measured with a flow meter. This procedure is applied to a core plug extracted from a low-permeability siltstone of the Montney Formation (western Canada). Repeated testing consistently demonstrated a transient linear flow period, as the gas pressure transient propagated along the core plug, followed by boundary-dominated flow after the pressure transient reached the end of the core plug; this sequence is identical to what is commonly observed in the field. Permeability was estimated using both the slope of a square-root of time plot (a common RTA method used to analyze transient linear flow), and the time at the end of linear flow combined with the linear flow distance of investigation (DOI) equation. Permeability from both techniques is in good agreement (±5% for both experiments performed), providing an important redundancy to the analysis procedure. Pore volume (and hence porosity, with bulk volume known) may be estimated from the time at the end of linear flow and the slope of the square-root of time plot – the calculated value is in excellent agreement (±2% for both experiments performed) with that obtained from pore volume/porosity estimates using a helium pycnometer (combined with calipered dimensions). Finally, test times for the ∼0.0007 md core plug sample, after the initiation of the production phase, are on the order of only a few minutes to obtain the two independent estimates of permeability and pore volume, which is faster than that achievable from a PDP test.The new innovative experimental procedure is successful in reproducing the physics of flow in unconventional reservoirs, with the results being analyzable with the same techniques applied to field data.

A Novel Approach to Measuring Water and Oil Relative Permeabilities in Two-phase Fluid Flow in Porous Media

In this study, direct laboratory measurements of unsteady-state imbibition test are used in a new approach to obtain relative permeability curves with no predetermined functionality assumptions. Four equations of continuity, Darcy’s law, cumulative oil production, and water fractional flow are employed in combination together under certain assumptions to present the new approach which interprets these data. We assumed that capillary pressure was previously measured and used as the input data in the method. The main difference between this work and previous unsteady-state methods is to replace the saturation profile, needed to obtain relative permeability curves, with a new saturation-dependent graph which can be measured from recovery data rather than being recorded directly during experiments. The method is demonstrated by employing recovery data from the literature, and it is then verified by a numerical simulator. The results show that the accuracy of the proposed method is comparable with accurate complex methods. Performing sensitivity analysis indicates that the proposed method can achieve more accurate results when applied to cases with a relatively high capillary number and/or low water-oil mobility ratio and when applied to media having uniformly sized pores.

Relative Permeability of CO2 in a Low-permeability Rock: Implications for CO2 Flow Behavior in Reservoirs with Tight Interlayers

In many of the underground CO2 storage sites, the sedimentary reservoirs are not petrologically uniform. Reservoir formations usually comprise high-permeability layers and low-permeability interbeds. Such sedimentary structure has been observed in CO2 storage reservoirs; for example, the Utsira formation, Sleipner, Norway, and also in the Haizume formation, Nagaoka, Japan. During the upward migration of CO2 plume from lower to upper layers, CO2 flow is inevitably affected by these tight interlayers. Therefore, it is important to know the CO2 relative permeability in these layers to predict CO2 flow behaviour. However, measurements of CO2 relative permeability in low-permeability rocks are rare in literature. The reason is perhaps due to the difficulty in controlling saturation and specific conditions for measuring relative permeability in low-permeability rocks using conventional techniques. In this study, we designed a new quasi-steady state approach for the measurement of CO2 relative permeability in a low-permeability sandstone cored from an underground formation of a CO2 storage site. The rock sample is characterized by a low permeability (approximately 0.16 mD) and relatively strong heterogeneity in subcore scale. The low-permeability characteristics make the conventional steady-state way impractical, because a very long time is necessary for building each steady-state saturation profile. Furthermore, the spatial heterogeneity also leads to that it is unsuitable for using unsteady state methods, e.g. JBN method, which is limited to the application in the displacement with uniform fluid distribution. Rock heterogeneity in the sample may lead to an incorrect estimation of relative permeability. In our new method, we use X-ray CT imaging technique to monitor the CO2 saturation changes and formation of fluid flow path during pressure adjustments. Considering the formation of CO2 flow path, we initially injected CO2 at a considerable high pressure drop until the saturation reaches a targeted value, to create the flow path. Then we lowered the pressure drop (so as to flow rate) and let the saturation profile reach a quasi-steady state and stop to increase. The saturation and fluid flow path during this operation have almost no change in the sample. Then we repeated the operation of lowering pressure drop several times and measured pressures and flow rates. If the relative permeability of CO2 has no change, the plot of pressure drop with respect to flow rate should give a linear relationship with a constant slope. Using this method, the saturation at quasi-steady states in relative permeability measurement can be controlled and the operation time can be significantly reduced. The results show a linear relationship between the pressure drop and flow rate at several quasi-steady states as expected. The results indicate the relative permeability of CO2 in low-permeability rocks can be still high as in high-permeability rocks (e.g. Berea sandstone). The changes of CO2 relative permeability are greatly dependent on the formation of CO2 flow path and the effective area of CO2 flow path in pore space as shown by the X-ray CT images. Our results are essential for understanding the behaviour of CO2 migration and trapping in CO2 storage reservoirs with low-permeability tight interbeds and the transition part of caprocks. The measurement results give important constraint in reservoir simulations for CO2 storage.

Characterization of anisotropy in the permeability of organic-rich shales

Abstract Accurate determination of permeability is essential and challenging in organic-rich shales due to the tight and heterogeneous nature of shale formations, the presence of lamination as well as induced or natural fractures and the sensitivity of fracture permeability to stress. The tight nature of shale formation makes the traditional steady-state method not to be practical. Therefore, unsteady state methods such as pulse decay or crushed-sample have been practiced for shales. However, the pulse decay method can be still time consuming and the crushed-sample method is size-dependent as our numerical simulations show. As an alternative method, the results of complex transient method are presented. Moreover, the presence of lamination and fractures causes directional dependency of permeability. To characterize this type of anisotropy, three-plug method is usually applied. However, the variation of permeability with location causes this method to be unreliable in heterogeneous formations. Similarly, the presence of artificial micro-fractures affects the reliability of the permeability measurement in shales. Using variety of methods to measure permeability, the effects of these anisotropic and heterogeneous features under stress are discussed.

Confining Properties of Carbonated Dogger Caprocks (Parisian Basin) for CO2Storage Purpose

The Géocarbone-Intégrité project, funded by ANR (Agence Nationale de la Recherche) from 2006 to 2008, has the overall objective of gaining knowledge and technology to predict storage integrity and safety for long term geological CO<sub>2<sub/> sequestration. The aim of this study (Sect. 1 and 2 of the project) is to evaluate the sealing capacities of the carbonated Dogger caprocks located on top of the reservoirs where CO<sub>2<sub/> could be injected for storage purposes in the Parisian Basin. A petrographic analysis is done on 3 different cores from geological formations of the “Comblanchien and Dalle Nacrée” tight carbonates facies. At the same time, a petrophysical study of these facies is performed. Porosity, pore size distribution and permeability are determined using special devices adapted to low permeability and tight rocks (< 10 microDarcy). Permeabilities are measured with nitrogen, helium and brine under confining pressure using unsteady-state and steady-state methods. Porosities are low and vary from 2 to 9%, depending on the facies, and single-phase permeabilities vary from 0.3 to 20 microDarcy. Using different techniques of porosity and permeability measurement allows evaluation of the uncertainties. The sealing efficiency of a caprock towards CO<sub>2<sub/> is primarily controlled by the threshold capillary pressure at <i>in situ<i/> conditions. This threshold pressure is first estimated by mercury injection (HPMI). It is also directly measured on core samples at in situ conditions with Nitrogen (N<sub>2<sub/>) and Carbon dioxide (CO<sub>2<sub/>) (to see the effect of CO<sub>2<sub/> compared to a neutral gas on the threshold pressure). Two different techniques, described in detail in this article, are used: the dynamic method and the pressure step method. For the CO<sub>2<sub/>/brine system, measured threshold capillary pressures vary from 0.4 bar to 22 bar, depending on the facies. The <i>P<i/><sub><i>t<i/><i>h<i/><sub/> values, even for the tighter facies (CH106), are probably too low to exclude penetration of CO<sub>2<sub/> into the caprock. This however does not rule out storage of CO<sub>2<sub/>, as long as it can be proved that the permeability of the caprock is low enough and its thickness large enough to limit the extent of this penetration even though overpressure is maintained for a long period.

Thermophysical characterisation of tropical wood used as building materials: With respect to the basal density

An experimental study has been carried out to determine thermophysical properties of tropical wood. Five species, covering a wide range of densities of most of the wood used in Central Africa, has been chosen. These properties which characterise the thermally insulating materials, are related to basal density in order to help predict the thermophysical properties of any tropical wood as soon as its basal density is known. Steady-state and unsteady state methods were used to measure thermal conductivity and thermal diffusivity, respectively. Specific heat and thermal effusivity were then calculated. The influences of moisture content and the principal cutting plan on the thermophysical properties of tropical wood were examined. Higher conductivity, diffusivity and effusivity in the axial direction were observed, as well as the non-directional dependence character of the specific heat. It was also observed that thermal conductivity of tropical wood increases with infradensity both in the axial and the transverse directions. Finally, it was shown that conductivity and effusivity increase and thermal diffusivity decreases with the increase of moisture content.

Determination of diffusion and distribution coefficients in polymer membranes by unsteady-state dialysis and steady-state RO methods

A new method has been developed for determination and analysis of diffusion and distribution coefficients of salts in dialysis and RO membranes based on unsteady-state dialysis and steady-state RO experimental data. The method is based on a two-part model of heterogeneous RO membranes consisting of perfect or dense and imperfect or porous parts. Such a model can be described by differential equations accounting for all water and salt fluxes entering and leaving the membrane. The method was applied to various salt solution/polymer membrane systems. Thermodynamic and kinetic parameters of the system were found to be influenced by physico-chemical parameters of the penetrant reflecting its ionic properties, chemical composition of the polymer as well as structure the membranes.

Measurement of Dynamic Saturation Profiles

Abstract Accurate relative permeability data are essential for predicting the performance of two-phase flow through porous media. Many factors, such as the rock and fluid properties, may affect the measurement of relative permeability. However, the saturation levels of the fluids flowing through a porous medium have the largest impact on the shape of the relative permeability curves. Because relative permeability is a strong function of saturation, an accurate measurement of saturation levels in various types of two-phase flow experiments is required. In addition to many non-invasive methods, weighing and volumetric methods are frequently used to estimate the average saturation during steady-state experiments. However, for unsteady-state flow experiments, material balance methods to determine the saturation levels are relatively difficult to use. This article presents a relatively new non-invasive saturation measurement method and the equipment used to obtain dynamic saturation profiles as a function of time and distance along the core-holder. The new saturation measurement system has been found to be equally good for steady-state and unsteady-state experiments. Typical dynamic saturation profiles, the equipment calibration method, and a set of typical relative permeability curves for a co-current flow experiment are presented. Based on the presented experimental results, it has been found that the new saturation measurement method and the equipment is reliable and can reproduce stable dynamic saturation profiles with a minimum level of uncertainty. Introduction Underlying the extension of single-phase flow theory for the simultaneous flow of two or more fluids are the concepts of effective and relative permeability. The effective permeability is a relative measure of the conductance of a porous medium for one fluid phase when the medium is saturated with more than one fluid(1). The relative permeability is defined as the ratio of the effective permeability of a phase to a base permeability [e.g., absolute permeability to air or water, Craig(2)]. Relative permeability data are essential for almost all two-phase flow studies related to reservoirs. The data are used in making estimations and predictions of the productivity, injectivity, and ultimate recovery from reservoirs for evaluation and future development plans. The relative permeability data can also be used to diagnose the formation damage expected under various operational conditions. Therefore, unquestionably, these data are one of the most important data sets required in reservoir engineering studies. Among several methods for obtaining relative permeability curves, laboratory techniques are considered to be the most reliable. These methods for relative permeability measurement are further classified into steady-state and unsteady-state methods. Aleman et al.(3) have concluded that the difference in the relative permeabilities obtained by the two approaches is negligible, provided that the magnitude of the local (not macroscopic) capillary number is larger than a limiting value. Numerous studies have been conducted to investigate the effect of important parameters during the measurement of relative permeability data. In addition to saturation, some of the other important parameters affecting relative permeability are wettability, IFT, flow regime, overburden pressure and temperature. Leverett and Lewis(4), Sarem(5), Saraf and Fatt(6), and Owens and Archer(7) have shown that for strongly water-wet unconsolidated sands the permeability to a wetting phase is dependent solely upon its own saturation.

The role of adsorption on the observed temperature dependencies of diffusion coefficients

In measurements of diffusion coefficients of gases in porous solids by unsteady-state (transient) methods, adsorption on the walls of the pores affects the analysis. Failure to account for the net adsorption or desorption occurring during the perturbation associated with such measurements yields apparent diffusion coefficients that are lower than the true values. Moreover, the temperature dependence is not the relatively weak dependence expected from the kinetic theory of gases for true gas diffusion coefficients, even when the pores are orders of magnitude larger than molecular dimensions. Instead it is exponential in nature, being determined largely by the temperature dependence of the adsorption process occurring in the pores. Thus, the diffusion process seems to be an activated one, although in fact there may not be a true activation barrier. The analysis presented in this paper appears to be very general, extending even to zeolites where the pore dimensions are of the order of molecular dimensions. It appears to account for the commonly reported observations in the literature that diffusion coefficients for gases in microporous solids obtained by transient methods can sometimes be as much as two to four orders of magnitude lower and can simultaneously exhibit temperature dependencies much stronger than those obtained under equilibrium conditions utilizing nuclear magnetic resonance.

The impact of wettability and core-scale heterogeneities on relative permeability

The objectives of this work were to evaluate the effects of several key parameters (e.g., wettability, saturation history and measurement methods) on the water-oil relative permeability in a mixed-wet reservoir rock. Relative permeability was first measured at its initial wettability along with its hysteresis. Wettability was altered and its impact on relative permeability was assessed. Steady-state and unsteady-state methods were compared. The relative permeabilities of the composite core were compared to those of individual plugs. A CT scanner was used to characterize the core heterogeneity and to monitor three-dimensional in situ fluid distributions during steady state and unsteady state experiments. Numerical simulation was conducted with separately characterized lithologies to describe the flow mechanism in mixed-wet porous media. Results show that an increase in oil-wettability increases the water relative permeability and decreases the oil relative permeability. A decrease of initial water saturation produces an increase in relative permeability hysteresis. Three-dimensional in situ saturations help characterize regions of different lithology and flow mechanisms. The low flow rate unsteady-state experiment can be modelled by the steady-state relative permeabilities if the heterogeneities and the capillary pressures of the composite core are considered.

The effect of velocity and interfacial tension on relative permeability of gas condensate fluids in the wellbore region

High-pressure core flood experiments using gas condensate fluids in long sandstone cores were conducted to determine the effect of flow rate and interfacial tension on relative permeability. The data are applicable to near wellbore flow in gas condensate reservoirs, because viscous forces increased over capillary forces during the tests. A relative permeability rate effect for both gas and condensate phases was observed when using steady-state and unsteady-state testing methods. The tests were repeated at increasing flow rates which showed that the relative permeability of both phases increased with the increase in flow rate. Increasing the value of interfacial tension between the phases reduced the relative permeability of the gas phase more than the condensate phase; but the relative permeability of both phases continued to increase at higher flow rates. The influence of core end-effects was shown to be negligible at the low IFT conditions used in the tests. The Reynolds number indicated that flow was within the laminar regime at all test conditions. The observed rate effect was contrary to that of the conventional non-Darcy flow where the effective permeability decreases with increasing flow rates. Relative permeability tests conducted with conventional gas oil fluids at similar test conditions did not exhibit any significant rate effects. This study is applicable to the vicinity of producing wells, where the rate effect on gas relative permeability can significantly affect well productivity.

Impact of Model Error on the Measurement of Flow Properties Needed to Describe Flow Through Porous Media

Indirect methods are commonly employed to determine the fundamental flow properties needed to describe flow through porous media. Consequently, if one or more of the postulates underlying the mathematical description of such indirect methods is invalid, significant model error can be introduced into the measured value of the flow property. In particular, this study shows that effective mobility curves that include the effect of viscous coupling between fluid phases differ significantly from those that exclude such coupling. Moreover, it is shown that the conventional effective mobilities that pertain to steady-state, cocurrent flow, steady-state, countercurrent flow and pure countercurrent imbibition differ significantly. Thus, it appears that traditional effective mobilities are not true parameters; rather, they are infinitely nonunique. In addition, it is shown that, while neglect of hydrodynamic forces introduces a small amount of model error into the pressure difference curve for cocurrent flow in unconsolidated porous media, such neglect introduces a large amount of model error into the pressure difference curve for countercurrent flow in such porous media. Moreover, such neglect makes it difficult to explain why the pressure gradients that pertain to steady-state, countercurrent flow are opposite in sign. It is shown also that improper handling of the inlet boundary condition can introduce significant model error into the analysis. This is because, if a short core is used with one of the unsteady-state methods for determining effective mobility, it may take many pore volumes of injection before the inlet saturation rises to its maximal value, which is in contradiction with the usual assumption that the inlet saturation rises immediately to its maximal value. Finally, it is pointed out that, because of differences in flow regime and scale, the effective mobilities measured in the laboratory may not be appropriate for inclusion in the data base for a reservoir-scale simulation.

Unsteady-state methods of investigation of the heterogeneous chemiluminescence of phosphor crystals

Unsteady-state methods of investigation of the heterogeneous chemiluminescence of phosphor crystals

A new method for estimating dermal absorption from chemical exposure. 3. Compared with steady-state methods for prediction and data analysis.

This paper compares unsteady-state and steady-state methods for estimating dermal absorption or analyzing dermal absorption data. The unsteady-state method accounts for the larger absorption rates during short exposure times as well as the hydrophilic barrier which the viable epidermis presents to lipophilic chemicals. Example calculations for dermal absorption from aqueous solutions are presented for five environmentally relevant chemicals with molecular weights between 50 and 410 and log10Kow between 0.91 and 6.8: chloromethane, chloroform, chlordane, 2,3,7,8-TCDD, and dibenz(a,h)anthracene. Also, the new method is used to evaluate experimental procedures and data analyses of in vivo and in vitro permeation measurements. In the five example cases, we show that the steady-state approach significantly underestimated the dermal absorption. Also, calculating permeability values from cumulative absorption data measured for exposure periods less than 18 times the stratum corneum lag time will overestimate the actual permeability. In general, steady-state predictions of dermal absorption will underestimate dermal absorption predictions which consider unsteady-state conditions. Permeability values calculated from data sets which include unsteady-state data will be incorrect. Strategies for analyzing in vitro diffusion cell experiments and confirming steady state are described.

Determination of kinetic parameters of fermentation processes by a continuous unsteady‐state method: Application to the alcoholic fermentation of D‐xylose by Pichia stipitis

A quick technique for determination of kinetic parameters of fermentation processes is proposed and applied to the transformation of D-xylose into ethanol by Pichia stipitis. The commonly used method to evaluate these parameters is based on achieving several steady states. In the proposed procedure, micro(m) and K(s) can be determined from only one steady state, by provoking a disturbance over it, after allowing the system to return to the original conditions. The main difference between the steady and unsteady state methods is the required fermentation time; while the former method lasted 350 h, the latter required a period 25 times lower. Kinetic and stoichiometric parameters were determined with both methods under anoxic and limited oxygen concentration conditions. Results from the two methods were compared, giving only 2% and 4.5% differences in the values of K(s) and micro(m) and a little over 4% for micro(m) were the deviations under the latter ones.