Log Permeability Research Articles

Sub-Gaussian model of processes with heavy-tailed distributions applied to air permeabilities of fractured tuff

Earth and environmental variables are commonly taken to have multivariate Gaussian or heavy-tailed distributions in space and/or time. This is based on the observation that univariate frequency distributions of corresponding samples appear to be Gaussian or heavy-tailed. Of particular interest to us is the well-documented but heretofore little noticed and unexplained phenomenon that whereas the frequency distribution of log permeability data often seems to be Gaussian, that of corresponding increments tends to exhibit heavy tails. The tails decay as powers of −\( \alpha \) where 1 < \( \alpha \) < 2 is either constant or grows monotonically toward an asymptote with increasing separation distance or lag. We illustrate the latter phenomenon on 1-m scale log air permeabilities from pneumatic tests in 6 vertical and inclined boreholes completed in unsaturated fractured tuff near Superior, Arizona. We then show theoretically and demonstrate numerically, on synthetically generated signals, that whereas the case of constant \( \alpha \) is consistent with a collection of samples from truncated sub-Gaussian fractional Levy noise, a random field (or process) subordinated to truncated fractional Gaussian noise, the case of variable \( \alpha \) is consistent with a collection of samples from truncated sub-Gaussian fractional Levy motion (tfLm), a random field subordinated to truncated fractional Brownian motion. Whereas the first type of signal is relatively regular and characterized by Levy index \( \alpha \), the second is highly irregular (punctuated by spurious spikes) and characterized by the asymptote of \( \alpha \) values associated with its increments. We describe a procedure to estimate the parameters of univariate distributions characterizing such signals and apply it to our log air permeability data. The latter are found to be consistent with a collection of samples from tfLm with \( \alpha \) slightly smaller than 2, which is easily confused with a Gaussian field (characterized by constant \( \alpha \) = 2). The irregular (spiky) nature of this signal is typical of observed fractured rock properties. We propose that distributions of earth and environmental variable be inferred jointly from measured values and their increments in a way that insures consistency between these two sets of data.

Extended power-law scaling of air permeabilities measured on a block of tuff

Abstract. We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q), of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence) of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q) with q, are consistent with a view of these data as a sample from a truncated version (tfBm) of self-affine fractional Brownian motion (fBm). Since in theory the scaling exponents, ξ(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well as of non-Gaussian heavy-tailed signals subordinated to tfBm, are extended by ESS. It further allows us to identify the functional form and estimate all parameters of the corresponding tfBm based on sample structure functions of first and second orders.

Improvement of Ensemble Kalman Filter for Improper Initial Ensembles

ABSTRACT Ensemble Kalman filter(EnKF) has been widely researched in petroleum industry due to uncertainty analyses and convenience to couple with commercial simulators. However, the EnKF has shown overshooting and filter divergence problems when ensemble size becomes smaller or initial ensembles are quite different from the true. These problems of the EnKF result from unified covariance between model parameters and dynamic variables. Since all ensemble members have different model parameters, especially initial ensembles are improper, it is difficult to calculate representative covariance. We introduce the concept of clustered covariance into the standard EnKF. On the assimilation step, each ensemble members can be updated using more appropriate Kalman gain rather than the unified one. From the comparison of the performances using a 2-dimensional synthetic reservoir model, the EnKF shows that root mean square (RMS) error of the logarithm of permeability increases as ensemble size becomes smaller. Furthermore, it cannot estimate the uncertainty due to incorrect dynamic prediction. It is also fluctuating with an increasing trend when assimilation time interval becomes longer. The proposed method overcomes the typical problems mentioned. It is insensitive to ensemble size and assimilation time interval, even for improper initial ensemble design cases. The RMS error is below 1 over all the cases examined including 50 ensemble size case and 100 days of assimilation time interval case. The dynamic prediction in small ensemble size is reliable with covering true performance trend despite the prediction band of initial ensemble member is failed to do so.

Extending Well-Productivity Life in a High-Pressure/ High-Temperature Tight Gas/Condensate Carbonate Reservoir by Acid Refracturing

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 142444, ’Extending Well- Productivity Life by Acid Refracturing in a High-Pressure/High-Temperature Tight Gas/Condensate Carbonate Reservoir in a Jurassic Formation of Northern Kuwait,’ by Mir Kabir, SPE, Qasem Dashti, SPE, J.R. Singh, SPE, and San Prasad Pradhan, SPE, KOC, and Ikhsan Nugraha, SPE, Liu Hai, and Hamed Al-Ghadhban, Schlumberger, prepared for the 2011 SPE Middle East Unconventional Gas Conference and Exhibition, Muscat, Oman, 31 January- 2 February. The paper has not been peer reviewed. Productivity of the subject well, which had been on production for 3 years after an initial acid-fracture treatment with almost 90% of its cumulative production occurring during the last year, was declining faster than expected. Review of the well’s performance indicated two possible causes: reservoir-pressure decline and reduced fracture-length/conductivity ratio. Acid refracturing was chosen to restore the well’s productivity by extending the fracture half-length to enhance fracture conductivity. The results showed that the productivity index (PI) increased by a factor of 2.5 during the post-treatment production test. However, after 3 months of production, this declined to 1.2. Introduction Several major fields in north-ern Kuwait, including Sabriyah, Raudathain, Umm Niqqa, Bahra, and Dhabi, produce gas from the Jurassic Middle Marrat formation, an important carbonate reservoir. Typical depth is 14,000 ft, reservoir pressure ranges from 10,000 to 12,000 psi, and the bottomhole static temperature averages 275°F. The Middle Marrat formation is mostly limestone (calcite&amp;gt;90%) with minor dolomitization. Only traces of clay and silt are found. High heterogeneity, both laterally and vertically, has been reported. Core permeability matches log permeability, and the high permeability value obtained from the core could be the result of induced fractures. Pressure-transient analyses of some wells showed dual-porosity behavior with low matrix permeability. Generally, the absolute matrix permeability is less than 1 md. The production mechanism is a combination of matrix and natural-fracture permeability. Acid Refracturing In regions where acid fracturing is common, there are questions that arise. When is the best time to refracture? What is the justification to repeat the treatment? If there is justification, what needs to be done differently in the subsequent treatment? The decision usually relies on the post-treatment production behavior compared with the pretreatment condition.

Effect of permeability variations on solute transport in highly heterogeneous porous media

The effect of aquifer heterogeneity on flow and solute transport in two-dimensional isotropic porous media was analyzed using the Monte Carlo method. The two-dimensional logarithmic permeability (ln K) was assumed to be a non-stationary random field with its increments being a truncated fractional Lévy motion (fLm). The permeability fields were generated using the modified successive random additions (SRA) algorithm code SRA3DC [ http://www.iamg.org/CGEditor/index.htm]. The velocity and concentration fields were computed respectively for two-dimensional flow and transport with a pulse input using the finite difference codes of MODFLOW 2000 and MT3DMS. Two fLm control parameters, namely the width parameter ( C) and the Lévy index ( α), were varied systematically to examine their effect on the resulting permeability, flow velocity and concentration fields. We also computed the first- and second-spatial moments, the dilution index, as well as the breakthrough curves at different control planes with the corresponding concentration fields. In addition, the derived breakthrough curves were fitted using the continuous time random walk (CTRW) and the traditional advection-dispersion equation (ADE). Results indicated that larger C and smaller α both led to more heterogeneous permeability and velocity fields. The Lévy-stable distribution of increments in ln K resulted in a Lévy-stable distribution of increments in logarithm of the velocity (ln v). Both larger C and smaller α created sharper leading edges and wider tailing edges of solute plumes. Furthermore, a relatively larger amount of solute still remained in the domain after a relatively longer time transport for smaller α values. The dilution indices were smaller than unity and increased as C increased and α decreased. The solute plume and its second-spatial moments increased as C increased and α decreased, while the first-spatial moments of the solute plume were independent of C and α values. The longitudinal macrodispersivity was scale-dependent and increased as a power law function of time. Increasing C and decreasing α both resulted in an increase in longitudinal macrodispersivity. The transport in such highly heterogeneous media was slightly non-Gaussian with its derived breakthrough curves being slightly better fitted by the CTRW than the ADE, especially in the early arrivals and late-time tails.

Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem

We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a linear uniformly elliptic partial differential equation in divergence form, in a bounded domain in dimension $d \le 3$, from measurements of the solution in the interior. We adopt a Bayesian approach to the problem. We place a prior random field measure on the log permeability, specified through the Karhunen–Loève expansion of its draws. We consider Gaussian measures constructed this way, and study the regularity of functions drawn from them. We also study the Lipschitz properties of the observation operator mapping the log permeability to the observations. Combining these regularity and continuity estimates, we show that the posterior measure is well defined on a suitable Banach space. Furthermore the posterior measure is shown to be Lipschitz with respect to the data in the Hellinger metric, giving rise to a form of well posedness of the inverse problem. Determining the posterior measure, given the data, solves the problem of uncertainty quantification for this inverse problem. In practice the posterior measure must be approximated in a finite dimensional space. We quantify the errors incurred by employing a truncated Karhunen–Loève expansion to represent this meausure. In particular we study weak convergence of a general class of locally Lipschitz functions of the log permeability, and apply this general theory to estimate errors in the posterior mean of the pressure and the pressure covariance, under refinement of the finite-dimensional Karhunen–Loève truncation.

Experimental study of the capillary pressure of supercritical CO2

Abstract Relating to the assessment of the cap rock integrity on CO 2 geological sequestration, we measured threshold pressure for supercritical CO 2 under pressure and temperature conditions of 1,000 m depth (i.e., 10 MPa and 40 °C). The present study aims to quantify various factors which affect the variability of rock’s threshold pressure and to model the threshold pressure range of a cap rock. We prepared sintered compacts composed of uniformly-sized silica glass beads (0.2–10 μm), and examined a correlation between threshold pressure and permeability for each diameter. The result revealed that threshold pressure of sintered compacts increased drastically with a decrease of component particle size. Moreover, there existed a good linearity between the logarithm of threshold pressure and the logarithm of permeability. The fitted line is an important basis specifically from a viewpoint of safety assessment because it corresponds to the lower limit of threshold pressure of homogeneous rocks.

Reservoir characterization of the Mt. Simon Sandstone, Illinois Basin, USA

Abstract The integration of open hole well log analyses, core analyses and pressure transient analyses was used for reservoir characterization of the Mt. Simon sandstone. Characterization of the injection interval provides the basis for a geologic model to support the baseline MVA model, specify pressure design requirements of surface equipment, develop completion strategies, estimate injection rates, and project the CO2 plume distribution. The Cambrian-age Mt. Simon Sandstone overlies the Precambrian granite basement of the Illinois Basin. The Mt. Simon is relatively thick formation exceeding 800 meters in some areas of the Illinois Basin. In the deeper part of the basin where sequestration is likely to occur at depths exceeding 1000 m, horizontal core permeability ranges from less than 1×10−12 cm2 to greater than 1×10−8 cm2. Well log and core porosity can be up to 30% in the basal Mt. Simon reservoir. For modeling purposes, reservoir characterization includes absolute horizontal and vertical permeability, effective porosity, net and gross thickness, and depth. For horizontal permeability, log porosity was correlated with core. The core porosity-permeability correlation was improved by using grain size as an indication of pore throat size. After numerous attempts to identify an appropriate log signature, the calculated cementation exponent from Archie’s porosity and resistivity relationships was used to identify which porosity-permeability correlation to apply and a permeability log was made. Due to the relatively large thickness of the Mt. Simon, vertical permeability is an important attribute to understand the distribution of CO2 when the injection interval is in the lower part of the unit. Only core analyses and specifically designed pressure transient tests can yield vertical permeability. Many reservoir flow models show that 500–800 m from the injection well most of the CO2 migrates upward depending on the magnitude of the vertical permeability and CO2 injection rate (CO2 velocity). Assigning a specific value of vertical permeability to model cells is dependent on the vertical height of the model cell. Measured vertical permeability on core is scale dependent, such that lower vertical permeability is expected over longer core lengths compared to smaller lengths. Consequently, a series of vertical permeability tests were conducted on whole core varying in lengths of samples from 7 cm to 30 cm that showed vertical perm could change by an order of magnitude over a 30 cm height. For one well, the results from a series of pressure transient tests over a perforated interval much smaller than the gross thickness (

Characterization of geological formations by physical parameters obtained through full waveform acoustic logging

In this paper, we will show through a field example that full wave form acoustic logging allows a quantitative evaluation of geological formations. For that purpose, conventional logs and their associated standard deviation (Std) must be computed (formation velocities, amplitudes, frequencies, etc.) since the Std is used to estimate the uncertainties associated with the log and to edit other logs. The missing values are then reconstructed by geostatistical interpolation (ordinary kriging and co-kriging). The shear velocity and density of the formation are also estimated in order to obtain mechanical parameters such as Poisson’s ratio or shear modulus. Since the converted refracted shear waves can be recorded in fast formations, a joint method based on the local measurement of the shear velocity by picking the arrival times of the refracted S wave and interpolation by co-kriging with P-wave velocity log has been used to compute a continuous shear velocity log. The Analysis of the dispersive properties of the Stoneley modes has then been used to estimate density variations and build iteratively a density log from an a priori density model. Furthermore, we will show that a dimensionless shape index can be used as a qualitative acoustic attribute to detect the presence of interfering waves, anomalic zones and to obtain a measurement of the attenuation. We will also show that P-wave attenuation , P-wave frequency and acoustic porosity logs can be fruitfully used to compute an acoustic permeability log.

Petrophysical evaluation of subsurface reservoir sandstones of Bengal Basin, Bangladesh

The present study has been carried out for core and log based petrophysical evaluation of subsurface reservoir sandstones considering at least one well from each of the Kailas Tila, Titas, Bakhrabad and Shahbazpur gas fields of Bangladesh. Core analysis results show that average core porosity, permeability and pore throat values are 20%, 209 mD and 44020 A, respectively. These measured values support that the sandstone reservoirs are categorized as good quality reservoirs. Core porosity values usually exceed thin section porosity. Different cross-plots indicate that permeability is largely dependent on porosity. Permeability and porosity are also dependent on textural parameters that include size, shape, sorting and matrix of the reservoir sandstones. It reveals from both thin section study and different cross plots that diagenetic cements are the main controlling factors of the reservoirs. Quantitative determination of the volume of cements shows that cements have inverse correlation with porosity and permeability. Log based petrophysical parameters include shale volume, porosity, water and hydrocarbon saturation, permeability, moveability index and bulk volume of water. The average values of the mentioned parameters are 20%, 22%, 26%, 74%, 110 mD, 0.28 and 0.05, respectively. The most important parameters are porosity and permeability, which indicate that log porosity exceeds core porosity and log permeability significantly lags behind core permeability. The study also reveals that 23 gas zones covering total thickness of 385 m sandstones mostly posses good quality reservoirs except few moderate quality reservoirs.

A multiscale preconditioner for stochastic mortar mixed finite elements

The aim of this paper is to introduce a new approach to efficiently solve sequences of problems that typically arise when modeling flow in stochastic porous media. The governing equations are based on Darcy’s law with a stochastic permeability field. Starting from a specified covariance relationship, the log permeability is decomposed using a truncated Karhunen–Loève expansion. Multiscale mortar mixed finite element approximations are used in the spatial domain and a nonintrusive sampling method is used in the stochastic dimensions. A multiscale mortar flux basis is computed for a single permeability, called a training permeability, that captures the main characteristics of the porous media, and is used as a preconditioner for each stochastic realization. We prove that the condition number of the preconditioned interface operator is independent of the subdomain mesh size and the mortar mesh size. Computational results confirm that our approach provides an efficient means to quantify the uncertainty for stochastic flow in porous media.

Characterization of porosity and permeability for CO2 sequestration models in the Mississippian Madison Group, Moxa Arch-LaBarge Platform, southwestern Wyoming

Porosity and permeability data for the Mississippian Madison Group in southwestern Wyoming were compiled and evaluated to relate these properties to stratigraphic facies in the Madison Group. The study was performed to provide baseline data for a geologic model required to sequester carbon in the study area. Public domain geological and petrophysical data provided the basis for the evaluation. Using the available database of wire-line logs and core from wells that penetrate the Madison Group, we place the wells within the regional structural and sequence-stratigraphic framework and detail porosity-permeability relationships. The highest porosity and permeability in the study area is present in the lower portion of the formation in dolomitic packstone-to grainstone-dominated facies near the top of the transgressive systems tract. Wire-line logs were used to calculate porosity values that correlate well with the more limited core-based data. The porosity in the Madison Group has a tri-modal distribution with porosity related to depositional facies. The first group is characterized by low porosity ( 12 percent) with a strong log permeability to porosity covariance. While lateral variations in porosity related to depositional facies can be traced over tens of kilometers, natural fractures appear to be a significant control on permeability in the lower porosity portions of the Madison.

Maximum likelihood Bayesian averaging of airflow models in unsaturated fractured tuff using Occam and variance windows

We use log permeability and porosity data obtained from single-hole pneumatic packer tests in six boreholes drilled into unsaturated fractured tuff near Superior, Arizona, to postulate, calibrate and compare five alternative variogram models (exponential, exponential with linear drift, power, truncated power based on exponential modes, and truncated power based on Gaussian modes) of these parameters based on four model selection criteria (AIC, AICc, BIC and KIC). Relying primarily on KIC and cross-validation we select the first three of these variogram models and use them to parameterize log air permeability and porosity across the site via kriging in terms of their values at selected pilot points and at some single-hole measurement locations. For each of the three variogram models we estimate log air permeabilities and porosities at the pilot points by calibrating a finite volume pressure simulator against two cross-hole pressure data sets from sixteen boreholes at the site. The traditional Occam’s window approach in conjunction with AIC, AICc, BIC and KIC assigns a posterior probability of nearly 1 to the power model. A recently proposed variance window approach does the same when applied in conjunction with AIC, AICc, BIC but spreads the posterior probability more evenly among the three models when used in conjunction with KIC. We compare the abilities of individual models and MLBMA, based on both Occam and variance windows, to predict space–time pressure variations observed during two cross-hole tests other than those employed for calibration. Individual models with the largest posterior probabilities turned out to be the worst or second worst predictors of pressure in both validation cases. Some individual models predicted pressures more accurately than did MLBMA. MLBMA was far superior to any of the individual models in one validation test and second to last in the other validation test in terms of predictive coverage and log scores.

Multiscale relationships between fracture length, aperture, density and permeability

Fractured rocks exhibit a hierarchical structure which renders their attributes scale‐dependent. In particular available data indicate a tendency for fracture length scales to be distributed according to a power law, average fracture aperture to be given by a power of the fracture length scale, and fracture density as well as log permeability to behave as random fractals. To date, no consistent theoretical relationship has been developed between fracture type (as categorized, for example, by length scale and/or aperture) and corresponding fractal attributes (such as density and log permeability). We develop and explore multiscale relationships between these fracture categories and attributes on the basis of a theory recently proposed by the author, which allows linking them in a formal way.

An Integrated Approach To Obtain Reliable Permeability Profiles From Logs in a Carbonate Reservoir

Summary Permeability is one of the key petrophysical parameters in reservoir evaluation. Information about permeability is commonly derived from cores and test data, which generally cover only part of the reservoir section, but can also be derived from logs and then extrapolated to uncored intervals and wells. Two logs provide such information: acoustic and nuclear magnetic resonance (NMR). In the Karachaganak field, an approach based on the acoustic tool was preferred because of the textural characteristics of the vuggy carbonate reservoir. The approach relies also on the use of image logs to obtain a detailed description of the reservoir-rocks texture and to discriminate between rocks with primary interparticle porosity or very small vugs and lithotypes with multimodal distribution of pores, enlarged vugs, and touching vugs. More than 900 m of core have been used to validate the permeability log derived from the analysis of Stoneley waves in 25 wells from this field. A correlation between the validated log-derived permeability and the textural facies from image logs has allowed the relationship between permeability variations and the geological framework to be established. The results have been compared with dynamic data from production logging through the definition of flow units from Stoneleywave-derived permeability and porosity-log data and the use of a stratigraphic-modified Lorenz plot (SMLP) to identify possible fluid-entry points. Three main permeability trends have been identified: For undolomitized or patchily dolomitized biohermal deposits for pervasively dolomitized lithologies characterized by lower mean permeability values for facies characterized by well-developed vuggy porosity with enhanced dissolution phenomena (i.e., touching vugs and microfracturing) Also, well-test results have highlighted the occurrence, in some wells, of very high k values in the biohermal deposits, which are clearly unmatchable by log-derived matrix permeability. Open fractures have been observed in these wells on the image logs, thus suggesting that the enhanced permeability and the improved well performances have to be related to their presence. The comparison of log-derived permeability and well-test results has given a new perspective in the interpretation of well-test results with respect to the geological framework and a well-defined sequence-stratigraphic model. The extension of this methodology to new wells could improve knowledge of the petrophysical characteristics of the reservoir and allow better prediction of reservoir productivity.

Stochastic collocation and mixed finite elements for flow in porous media

The aim of this paper is to quantify uncertainty of flow in porous media through stochastic modeling and computation of statistical moments. The governing equations are based on Darcy’s law with stochastic permeability. Starting from a specified covariance relationship, the log permeability is decomposed using a truncated Karhunen–Loève expansion. Mixed finite element approximations are used in the spatial domain and collocation at the zeros of tensor product Hermite polynomials is used in the stochastic dimensions. Error analysis is performed and experimentally verified with numerical simulations. Computational results include incompressible and slightly compressible single and two-phase flow.

Linking hierarchical stratal architecture to plume spreading in a Lagrangian‐based transport model

In this article we present a new formulation of the Lagrangian‐based model for macrodispersion of inert solutes. The formulation is based on a hierarchical expression of the spatial covariance of log permeability developed from recent findings at the well‐studied Borden research site. The covariance expression represents a two‐level hierarchy of stratal unit types with a corresponding hierarchy of permeability subpopulations. The covariance is a linear sum of terms corresponding to the probability of transitioning across stratal unit types of different scales, and these terms are directly related to quantifiable geometric attributes of the hierarchical stratal architecture at the Borden site. The new macrodispersion model is also a linear sum of terms, with different integral scales defined by the hierarchy of cross‐transition probabilities and computed from the proportions and length statistics of the stratal unit types. The model allows the study of the contribution of each term to the composite particle displacement variance and thus the study of how the hierarchical stratal architecture influences plume spreading.

Temporal evolution of DNAPL source and contaminant flux distribution: Impacts of source mass depletion

We investigated, using model simulations, the changes occurring in the distribution of dense non-aqueous phase liquid (DNAPL) mass ( S n) within the source zone during depletion through dissolution, and the resulting changes in the contaminant flux distribution ( J) at the source control plane (CP). Two numerical codes (ISCO3D and T2VOC) were used to simulate selected scenarios of DNAPL dissolution and transport in three-dimensional, heterogeneous, spatially correlated, random permeability fields with emplaced sources. Data from the model simulations were interpreted based on population statistics (mean, standard deviation, coefficient of variation) and spatial statistics (centroid, second moments, variograms). The mean and standard deviation of the S n and J distributions decreased with source mass depletion by dissolution. The decrease in mean and standard deviation was proportional for the J distribution resulting in a constant coefficient of variation (CV), while for the S n distribution, the mean decreased faster than the standard deviation. The spatial distributions exhibited similar behavior as the population distribution, i.e., the CP flux distribution was more stable (defined by temporally constant second moments and range of variograms) than the S n distribution. These observations appeared to be independent of the heterogeneity of the permeability ( k) field (variance of the log permeability field = 1 and 2.45), correlation structure (positive vs. negative correlation between the k and S n domains) and the DNAPL dissolution model (equilibrium vs. rate-limited), for the cases studied. Analysis of data from a flux monitoring field study (Hill Air Force Base, Utah) at a DNAPL source CP before and after source remediation also revealed temporal invariance of the contaminant flux distribution. These modeling and field observations suggest that the temporal evolution of the contaminant flux distribution can be estimated if the initial distribution is known. However, the findings are preliminary and broader implications to sampling strategies for remediation performance assessment need to be evaluated in additional modeling and experimental studies.

Core-Data Preprocessing To Improve Permeability Estimation From Logs

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 100748, "Core-Data Preprocessing To Improve Permeability Log Estimation," by M. Cozzi, L. Ruvo, SPE, P. Scaglioni, and A.M. Lyne, Eni E&amp;P, prepared for the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24-27 September. Two techniques of preprocessing data from core plugs were investigated to enhance the quality of synthetic permeability estimation from conventional logs by use of artificial neural networks (ANNs). A first technique consisted of "cleaning" the core-plug data set by removing measurements deemed as log-incompatible (i.e., data from plugs corresponding to log measurements having shoulder-bed effect) and those from layers with thickness less than the log vertical resolution. The second technique relies on building high-resolution digital models of cored intervals with a process-oriented-modeling (POM) approach in which the core model is populated with permeability values from core plugs and then scaled up to a log-equivalent support volume. Introduction Permeability prediction in hydrocarbon reservoirs is a challenge. Logging techniques such as nuclear magnetic resonance (NMR) enable generating permeability curves along reservoir intervals. Generally however, NMR logs are not available. In older fields, permeability measurements come from plugs sampled sparsely from bottomhole cores. Often, bottomhole cores are available only in a few reservoir intervals and/or wells, whereas conventional-log recordings (e.g., natural gamma ray (GR), density, and neutron) are available for most wells. Attempts to correlate core permeability to porosity and/or other conventional logs by use of mathematical/statistical tools date back to the early 1960s. Regression analysis has been used widely for permeability prediction. This approach assumes the permeability vs. porosity (or, alternatively, vs. conventional-log data) functional relationships to be known in advance, even though functional relationships are unknown. Nonparametric-regression techniques are used in the E&amp;P industry. Unlike conventional regression algorithms, such techniques do not make a priori assumptions with respect to the functional relationships among the investigated variables. ANNs and alternating-conditioning-expectation algorithms belong to this category. Both methods are suitable for generating synthetic permeability curves, even though the permeability data type provided as input significantly affects the final result. Tests on actual reservoirs showed that estimated permeability was very close to actual data if continuous curves of permeability from NMR logging tools, kNMR, are used as input. Conversely, when horizontal-core-plug permeabilities are used as input, the quality of the estimated permeability will be poorer than in the original core data and/or actual kNMR curves. Cross-scaling between core permeability and conventional-log data must take into account that the two types of measurement are not comparable in terms of scale and resolution. The risk of obscuring the correlation, if any, between core and log data is very high, especially when dealing with heterogeneous formations. Therefore, pre-processing core-plug-permeability data to offset core-to-log scale differences could enable integration of core data correctly into the generation of synthetic-permeability curves. Removing scale problems by scaling up core data properly should be mandatory if the only permeability measurements available as input are those from core-plug analyses.

An experimentally based approach for predicting skin permeability of chemicals and drugs using a membrane-coated fiber array

A membrane-coated fiber (MCF) array approach is proposed for predicting the percutaneous absorption of chemicals and drugs from chemical or biological mixtures. Multiple MCFs were used to determine the partition coefficients of compounds (log K MCF). We hypothesized that one MCF will characterize one pattern of molecular interactions and therefore the skin absorption process can be simulated by a multiple MCF array having diverse patterns of molecular interactions. Three MCFs, polydimethylsiloxane (PDMS), polyacrylate (PA) and CarboWax (Wax), were used to determine the log K MCF values for a set of calibration compounds. The skin permeability log(kp) of the compounds was measured by diffusion experiments using porcine skin. The feasibility of the MCF array approach for predicting skin permeability was demonstrated with the three MCFs. A mathematical model was established by multiple linear regression analysis of the log(kp) and log K MCF data set: log(kp) = − 2.34–0.124 log K pdms + 1.91 log K pa − 1.17 log K wax ( n = 25, R 2 = 0.93). The MCF array approach is an alternative animal model for skin permeability measurement. It is an experimentally based, high throughput approach that provides high prediction confidence and does not require literature data nor molecular structure information in contrast to the existing predictive models.