Effects of Dispersion and Dead-End Pore Volume in Miscible Flooding

1977 ◽  
Vol 17 (03) ◽  
pp. 219-227 ◽  
Author(s):  
L.E. Baker
Keyword(s):  
Pore Volume ◽  
Field Application ◽  
Column Height ◽  
Published Data ◽  
Model Parameters ◽  
Mixing Zone ◽  
Dead End ◽  
Capacitance Model ◽  
Capacitance Effects ◽  
Dispersive Mixing

Abstract The design of the solvent slug size for a miscible flood process can be improved with data on holdup (or capacitance process can be improved with data on holdup (or capacitance effects) and dispersion of the solvent slug in the reservoir. A modified version of the Coats-Smith dispersion-capacitance model and an improved solution method for the model were used to study dispersion and capacitance effects in cores. The velocity dependence of the model parameters is shown. A correlation is developed for estimating effective dispersion coefficients for field application. The method described provides a means for characterizing the properties of dispersive mixing and microheterogeneity of reservoir properties of dispersive mixing and microheterogeneity of reservoir cores and aids in the design of the volume of solvent for miscible floods. Introduction The amount of solvent that must be injected is a critical factor in the success of a miscible flood. Because of the cost of miscible solvents such as carbon dioxide or rich gas, slug processes generally are used. If the solvent slug used is larger processes generally are used. If the solvent slug used is larger than necessary, the solvent cost will be increased without compensatory increases in oil recovery. If too small a slug is used, some of the oil that could have been moved will be left behind. The slug size required is affected by many variables, including reservoir geometry, interwell spacing, gravity effects, mobility ratios, etc. Slug degradation is caused by mixing (by dispersion) of solvent with oil at the leading edge of the solvent bank and with chase fluid (for example, dry gas) at the trailing edge. Trapping of oil and solvent in microscopic heterogeneities (regions of dead-end pore volume or relatively stagnant flow) also contributes to the mixing-zone growth. This trapping, known as capacitance may be caused by rock heterogeneities or by shielding of oil and solvent by water films. This paper is concerned with predicting solvent slug requirements in an idealized linear system where gravity, mobility ratio, and areal sweep effects are unimportant, but where longitudinal dispersion (mixing at the leading and trailing edges of the bank) and capacitance effects are significant. An example might be a miscible displacement in the pinnacle reef formations of Alberta. A prediction of the effects of dispersion and capacitance was needed for the design of a miscible flood of this type. The oil-column height was about 350 ft, and the flood advance rate was to be downward at 0.0384 ft/D. The oil/solvent viscosity ratio of 10 was unfavorable; however, it was expected that the unfavorable mobility effects would be largely compensated for by the stability effects of gravity at the low flow rate. Published data relating to similar reservoirs indicated that "stagnant volume" that could cause trapping and degradation of the solvent slug might be as much as 10 percent of the reservoir volume. Based on these data, preliminary calculations were made using the Coats-Smith dispersion-capacitance model to predict the mixing-zone profiles. The results indicated that this level of stagnant volume might cause the solvent requirement to be increased by 30 to 90 percent over the amount predicted by a simple dispersion model without capacitance effects if the peak solvent concentration in the enriched gas bank did not drop below 99 percent throughout the life of the flood. Coats and Smith indicated that tests in short cores would show extended mixing zones if capacitance effects were present, but that if the magnitude of the transfer group M(D) = M(L)/u was large (as it would be in a field situation, where L may be very large), the influence of capacitance would be minimized. The prediction of a 30- to 90-percent increase in solvent requirements for the case described above prompted a review of methods for measuring capacitance effects and a search for a more convenient method for predicting the severity of capacitance effects in field application. predicting the severity of capacitance effects in field application. An improved method for modeling data from short core tests was developed, and experimental work was performed to investigate the factors influencing the capacitance-model parameters. SPEJ P. 219

Dead-End Pore Volume and Dispersion in Porous Media

1964 ◽  
Vol 4 (01) ◽  
pp. 73-84 ◽  
Author(s):  
K.H. Coats ◽  
B.D. Smith
Keyword(s):  
Porous Media ◽  
Diffusion Model ◽  
Concentration Profile ◽  
Pore Volume ◽  
Concentration Profiles ◽  
Simple Diffusion ◽  
Effluent Concentration ◽  
Dead End ◽  
Capacitance Model ◽  
Simple Diffusion Model

Abstract Experiments in which calcium chloride displaced sodium chloride from four cores showed the extent of asymmetry in the resulting effluent concentration profiles. These results provided a check on how validly the mixing process is modeled by a differential (i.e., not finite-stage) capacitance mathematical model. The effluent concentration profile from two consolidated cores exhibited considerable asymmetry, while two unconsolidated cores yielded nearly symmetrical profiles. All runs resulted in breakthrough of the 30 per cent concentration significantly before one pore volume was injected. In addition, velocity appreciably affected the effluent concentration profile from a Torpedo sandstone core. The differential capacitance model matched the data significantly better than a simple diffusion model. The capacitance model allows determination of the amount of dead-end pore space in a porous matrix and the effect of velocity on the rate of diffusion into this space. An experimental program yielding insight into the physical validity of the capacitance effect is described. Introduction Axial dispersion - the mixing accompanying the flow of miscible fluids through porous media- has been the subject of many relatively recent studies and a comprehensive review of the topic has been given by Perkins and Johnston. This dispersion is of practical interest in studies of the miscible displacement process, fixed-bed chemical reactors, and the adsorption of solutes from a flowing stream onto the surface of a porous medium. In the latter case, the effect of dispersion must be considered when adsorption parameters are determined from the nature of concentration profiles.In general, early studies of dispersion assumed applicability of a simple diffusion equation and were concerned with correlation of the experimentally determined "effective" diffusion coefficient with system properties over a large range of the latter. Recent investigators have been concerned with the deviations between the asymmetrical effluent concentration profiles observed and the symmetrical ones predicted by the diffusion model.In the present study, effluent concentration profiles were obtained from consolidated and unconsolidated cores. These profiles were compared with those predicted by a differential (i.e., not finite-stage) capacitance model. Solutions to the simple diffusion model, for three sets of boundary conditions, were compared with one another and with the experimental profiles. SUMMARY OF PREVIOUS WORK The reader is referred to Perkins and Johnston for an extensive review of studies of dispersion in porous media. Many investigators have employed the simple diffusion model characterized by Eq. 1 below: (1) The dispersion coefficient D for unconsolidated systems is correlated by ....................(2) for 2 less than less than 50, where v is interstitial velocity and dp is particle diameter. Since heterogeneity of the sand pack affects the mixing, this equation is also expressed as (3) where a is proportional to the degree of heterogeneity and is about 3.5 for random packs of unconsolidated sand. Eq. 3 holds for. For a homogeneous (regular) type of packing, a should be 1 or less. Aris and Amundson and Carberry and Bretton consider a to be the number of particle lengths per mixing cell in the finite-stage model. Data from consolidated cores indicate a dp to be about 0.36 cm for outcrop rocks, Torpedo sandstone having a reported value of 0.17 cm. SPEJ P. 73^

scholarly journals New Mathematical Modeling Approach for Predicting Microbial Inactivation by High Hydrostatic Pressure

2007 ◽  
Vol 73 (8) ◽  
pp. 2468-2478 ◽  
Author(s):  
Bernadette Klotz ◽  
D. Leo Pyle ◽  
Bernard M. Mackey
Keyword(s):  
Microbial Inactivation ◽  
Inactivation Kinetics ◽  
Published Data ◽  
Model Parameters ◽  
Order Kinetic ◽  
Square Root ◽  
Additional Time ◽  
Decimal Reduction Time ◽  
First Order ◽  
Primary Model

ABSTRACT A new primary model based on a thermodynamically consistent first-order kinetic approach was constructed to describe non-log-linear inactivation kinetics of pressure-treated bacteria. The model assumes a first-order process in which the specific inactivation rate changes inversely with the square root of time. The model gave reasonable fits to experimental data over six to seven orders of magnitude. It was also tested on 138 published data sets and provided good fits in about 70% of cases in which the shape of the curve followed the typical convex upward form. In the remainder of published examples, curves contained additional shoulder regions or extended tail regions. Curves with shoulders could be accommodated by including an additional time delay parameter and curves with tails shoulders could be accommodated by omitting points in the tail beyond the point at which survival levels remained more or less constant. The model parameters varied regularly with pressure, which may reflect a genuine mechanistic basis for the model. This property also allowed the calculation of (a) parameters analogous to the decimal reduction time D and z, the temperature increase needed to change the D value by a factor of 10, in thermal processing, and hence the processing conditions needed to attain a desired level of inactivation; and (b) the apparent thermodynamic volumes of activation associated with the lethal events. The hypothesis that inactivation rates changed as a function of the square root of time would be consistent with a diffusion-limited process.

Predicting Dead-End Pore-Volume in a Reservoir from Single Tracer Experiment

2017 ◽  
Author(s):  
Jyoti Phirani ◽  
Shantanu Roy ◽  
Harish J. Pant
Keyword(s):  
Pore Volume ◽  
Tracer Experiment ◽  
Dead End

scholarly journals Joint inversion of proxy system models to reconstruct paleoenvironmental time series from heterogeneous data

2020 ◽  
Vol 16 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Gabriel J. Bowen ◽  
Brenden Fischer-Femal ◽  
Gert-Jan Reichart ◽  
Appy Sluijs ◽  
Caroline H. Lear
Keyword(s):  
Time Series ◽  
Ad Hoc ◽  
Joint Inversion ◽  
Environmental Variable ◽  
Heterogeneous Data ◽  
Published Data ◽  
Model Parameters ◽  
Qualitative Comparison ◽  
Bayesian Hierarchical ◽  
Proxy Reconstructions

Abstract. Paleoclimatic and paleoenvironmental reconstructions are fundamentally uncertain because no proxy is a direct record of a single environmental variable of interest; all proxies are indirect and sensitive to multiple forcing factors. One productive approach to reducing proxy uncertainty is the integration of information from multiple proxy systems with complementary, overlapping sensitivity. Mostly, such analyses are conducted in an ad hoc fashion, either through qualitative comparison to assess the similarity of single-proxy reconstructions or through step-wise quantitative interpretations where one proxy is used to constrain a variable relevant to the interpretation of a second proxy. Here we propose the integration of multiple proxies via the joint inversion of proxy system and paleoenvironmental time series models in a Bayesian hierarchical framework. The “Joint Proxy Inversion” (JPI) method provides a statistically robust approach to producing self-consistent interpretations of multi-proxy datasets, allowing full and simultaneous assessment of all proxy and model uncertainties to obtain quantitative estimates of past environmental conditions. Other benefits of the method include the ability to use independent information on climate and environmental systems to inform the interpretation of proxy data, to fully leverage information from unevenly and differently sampled proxy records, and to obtain refined estimates of proxy model parameters that are conditioned on paleo-archive data. Application of JPI to the marine Mg∕Ca and δ18O proxy systems at two distinct timescales demonstrates many of the key properties, benefits, and sensitivities of the method, and it produces new, statistically grounded reconstructions of Neogene ocean temperature and chemistry from previously published data. We suggest that JPI is a universally applicable method that can be implemented using proxy models of wide-ranging complexity to generate more robust, quantitative understanding of past climatic and environmental change.

Fitting Foam-Simulation-Model Parameters to Data: II. Surfactant-Alternating-Gas Foam Applications

2014 ◽  
Vol 18 (02) ◽  
pp. 273-283 ◽  
Author(s):  
W. R. Rossen ◽  
C. S. Boeije
Keyword(s):  
Steady State ◽  
Capillary Pressure ◽  
Oil Recovery ◽  
Water Saturation ◽  
Field Application ◽  
Model Parameters ◽  
Fractional Flow ◽  
Sweep Efficiency ◽  
Water Fraction ◽  
Foam Model

Summary Foam improves sweep in miscible and immiscible gas-injection enhanced-oil-recovery processes. Surfactant-alternating-gas (SAG) foam processes offer many advantages over coinjection of foam for both operational and sweep-efficiency reasons. The success of a foam SAG process depends on foam behavior at very low injected-water fraction (high foam quality). This means that fitting data to a typical scan of foam behavior as a function of foam quality can miss conditions essential to the success of an SAG process. The result can be inaccurate scaleup of results to field application. We illustrate how to fit foam-model parameters to steady-state foam data for application to injection of a gas slug in an SAG foam process. Dynamic SAG corefloods can be unreliable for several reasons. These include failure to reach local steady state (because of slow foam generation), the increased effect of dispersion at the core scale, and the capillary end effect. For current foam models, the behavior of foam in SAG depends on three parameters: the mobility of full-strength foam, the capillary pressure or water saturation at which foam collapses, and the parameter governing the abruptness of this collapse. We illustrate the fitting of these model parameters to coreflood data, and the challenges that can arise in the fitting process, with the published foam data of Persoff et al. (1991) and Ma et al. (2013). For illustration, we use the foam model in the widely used STARS (Cheng et al. 2000) simulator. Accurate water-saturation data are essential to making a reliable fit to the data. Model fits to a given experiment may result in inaccurate extrapolation to mobility at the wellbore and, therefore, inaccurate predicted injectivity: for instance, a model fit in which foam does not collapse even at extremely large capillary pressure at the wellbore. We show how the insights of fractional-flow theory can guide the model-fitting process and give quick estimates of foam-propagation rate, mobility, and injectivity at the field scale.

The Growth of Mixing Zone in Heterogeneous Porous Media

2012 ◽  
Author(s):  
M. R. Othman ◽  
R. Badlishah Ahmad ◽  
Z. May
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Short Duration ◽  
Dispersion Coefficient ◽  
Fluid Velocity ◽  
Heterogeneous Porous Media ◽  
Mixing Zone ◽  
Zone Size ◽  
Model Mixing ◽  
Dispersive Mixing

Dengan menggunakan penyelesaian analitikal yang merangkumi fraktal eksponen, pembesaran jarak pencampuran telah dapat ditentukan bagi model satu dimensi. Size zon pencampuran didapati meningkat apabila media berliang menjadi semakin heterogen. Dalam media berliang yang heterogen, saiz zon pencampuran meningkat apabila pemalar penyerakan meningkat terutama sekali pada aliran jangkamasa singkat relatif. Terdapat tiga faktor penting mempengaruhi saiz zon pencampuran penyerakan, ΔxD. Perkara terpenting dalam kajian ini ialah keheterogenan takungan, yang dipersembahkan oleh fraktal eksponen, β. Hasil kajian mendapati bahawa apabila β menjadi kecil (media berliang menjadi semakin heterogen), saiz zon pencampuran meningkat. Satu lagi faktor mempengaruhi ΔxD ialah pemalar penyerakan bersandar masa, Κ(tD). Di dalam takungan heterogen, zon pencampuran meningkat dengan peningkatan nilai pemalar penyerakan pada aliran jangkamasa singkat relatif. Bagi aliran jangkamasa panjang relatif, bagaimanapun, ΔxD terus meningkat walaupun Κ(tD) menjadi tetap. Faktor ketiga ialah purata kelajuan bendalir, ν. Zon pencampuran mempunyai perkaitan songsang dengan kelajuan bendalir dengan cara ΔxD meningkat apabila ν berkurangan. Kata kunci: Kehomogenan; keheterogenan; pekali penyerakan; eksponen fraktal; zon pencampuran; media berliang Utilizing currently available analytical solutions that incorporate fractal exponent, the growth of mixing length of injected solvent was determined for a one-dimensional model. Mixing zone size was found to increase as porous medium becomes increasingly heterogeneous. In a heterogeneous porous media, mixing zone size increases as dispersion coefficient increases particularly at relatively short duration of flow. There are three important factors influencing the size of the dispersive mixing zone, ΔxD. Of particular importance in this study is reservoir heterogeneity, which is represented by a fractal exponent, β. It was discovered that as β becomes smaller (porous medium becomes increasingly heterogeneous), the size of the mixing zone increases. Another factor affecting ΔxD is time dependent dispersion coefficient, Κ(tD). In a heterogeneous reservoir, mixing zone increases with increasing value of dispersion coefficient at relatively short duration of flow. For relatively long period of flow, however? ΔxD continues to increase even though Κ(tD) remains constant. The third factor is average fluid velocity, ν. Mixing zones have inverse relationship with fluid velocity in that ΔxD increases as ν decreases. Key words: Homogeneity; heterogeneity; dispersion coefficient; fractal exponent; mixing zone; dimensionless concentration; porous media

Early Surgery Versus Biologic Therapy in Limited Nonstricturing Ileocecal Crohn’s Disease—A Decision-making Analysis

2020 ◽  
Vol 26 (11) ◽  
pp. 1648-1657
Author(s):  
Efrat Broide ◽  
Adi Eindor-Abarbanel ◽  
Timna Naftali ◽  
Haim Shirin ◽  
Tzippora Shalem ◽  
...  
Keyword(s):  
Crohn’S Disease ◽  
Crohn's Disease ◽  
Markov Model ◽  
Treatment Strategy ◽  
Early Surgery ◽  
Published Data ◽  
Model Parameters ◽  
Decision Analysis Model ◽  
Biologic Treatment ◽  
Life Years

Abstract Background Surgery is the preferred option for patients with symptomatic localized fibrostenotic ileocecal Crohn’s disease (CD) but not for those with predominantly active inflammation without obstruction. The benefit of early surgery in patients with a limited nonstricturing ileocecal CD over biologic treatment is still a debate. Objective Our objective is to formulate a decision analysis model based on recently published data to explore whether early surgery in patients with limited nonstricturing CD is preferred over biologic treatment. Methods We constructed a Markov model comparing 2 strategies of treatment: (1) early surgery vs (2) biologic treatment. To estimate the quality-adjusted life years (QALYs) and the costs in each strategy, we simulated 10,000 virtual patients with the Markov model using a Monte Carlo simulation 100 times. Sensitivity analyses were performed to evaluate the robustness of the model and address uncertainties in the estimation of model parameters. Results The costs were $29,457 ± $407 and $50,382 ± $525 (mean ± SD) for early surgery strategy and biologic treatment strategy, respectively. The QALY was 6.24 ± 0.01 and 5.81 ± 0.01 for early surgery strategy and biologic treatment strategy, respectively. Conclusion The strategy of early surgery dominates (higher QALY value [efficacy] and less cost) compared with the strategy of biologic treatment in patients with limited ileocecal CD.

On the estimation of specific surface per unit pore volume from induced polarization: A robust empirical relation fits multiple data sets

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. WA105-WA112 ◽  
Author(s):  
Andreas Weller ◽  
Lee Slater ◽  
Sven Nordsiek ◽  
Dimitrios Ntarlagiannis
Keyword(s):  
Specific Surface ◽  
Surface Area ◽  
Pore Volume ◽  
Empirical Relation ◽  
Induced Polarization ◽  
Single Frequency ◽  
Model Parameters ◽  
Data Sets ◽  
Multiple Data ◽  
Multiple Data Sets

We analyze the relationship between induced polarization (IP) parameters and the specific surface area normalized to the pore volume [Formula: see text] for an extensive sample database. We find that a single linear imaginary conductivity-[Formula: see text] relation holds across a range of single-frequency IP data sets composed of sandstones and unconsolidated sediments that lack an appreciable metallic mineral content. We also apply a recent approach defined as Debye decomposition (DD) to determine normalized chargeability [Formula: see text], a global estimate of polarization magnitude from available spectral IP (SIP) data sets. A strong linear relationship between [Formula: see text] and [Formula: see text] is also found across multiple data sets. However, SIP model parameters determined for samples containing metallic minerals are approximately two orders of magnitude greater than for the model parameters estimated for the nonmetallic sample database. We propose a concept of “polarizability of the mineral-fluid interface per unit [Formula: see text]” to explain this difference, which is supported by the observed dependence of IP parameters on fluid conductivity between sample types. We suggest that this linear IP-[Formula: see text] relation can be considered the IP equivalent of the classical Archie empirical relation. Whereas the Archie relation describes a power-law relation between electrical conductivity due to electrolytic conduction through the available interconnected pore volume, the IP-[Formula: see text] relation is an equivalent relation between mineral-fluid interfacial polarization and available pore surface area.

scholarly journals Data Assimilation of Volcanic Aerosols using FALL3D+PDAF

2021 ◽  
Author(s):  
Leonardo Mingari ◽  
Arnau Folch ◽  
Andrew T. Prata ◽  
Federica Pardini ◽  
Giovanni Macedonio ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Volcanic Ash ◽  
Volcanic Eruptions ◽  
Column Height ◽  
Model Parameters ◽  
Eruption Column ◽  
Mass Loading ◽  
Multiple Model ◽  
Volcanic Aerosols ◽  
Forecast Quality

Abstract. Modelling atmospheric dispersal of volcanic ash and aerosols is becoming increasingly valuable for assessing the potential impacts of explosive volcanic eruptions on infrastructures, air quality, and aviation. Management of volcanic risk and reduction of aviation impacts can strongly benefit from quantitative forecasting of volcanic ash. However, an accurate prediction of volcanic aerosol concentrations using numerical modelling relies on proper estimations of multiple model parameters which are prone to errors. Uncertainties in key parameters such as eruption column height, physical properties of particles or meteorological fields, represent a major source of error affecting the forecast quality. The availability of near-real-time geostationary satellite observations with high spatial and temporal resolutions provides the opportunity to improve forecasts in an operational context by incorporating observations into numerical models. Specifically, ensemble-based filters aim at converting a prior ensemble of system states into an analysis ensemble by assimilating a set of noisy observations. Previous studies dealing with volcanic ash transport have demonstrated that a significant improvement of forecast skill can be achieved by this approach. In this work, we present a new implementation of an ensemble-based Data Assimilation (DA) method coupling the FALL3D dispersal model and the Parallel Data Assimilation Framework (PDAF). The FALL3D+PDAF system runs in parallel, supports online-coupled DA and can be efficiently integrated into operational workflows by exploiting high-performance computing (HPC) resources. Two numerical experiments are considered: (i) a twin experiment using an incomplete dataset of synthetic observations of volcanic ash and, (ii) an experiment based on the 2019 Raikoke eruption using real observations of SO2 mass loading. An ensemble-based Kalman filtering technique based on the Local Ensemble Transform Kalman Filter (LETKF) is used to assimilate satellite-retrieved data of column mass loading. We show that this procedure may lead to nonphysical solutions and, consequently, conclude that LETKF is not the best approach for the assimilation of volcanic aerosols. However, we find that a truncated state constructed from the LETKF solution approaches the real solution after a few assimilation cycles, yielding a dramatic improvement of forecast quality when compared to simulations without assimilation.

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