Efficient hydrologic tracer-test design for tracer-mass estimation and sample-collection frequency, 1, method development

We explore the use of efficient streamline-based simulation approaches for modeling partitioning interwell tracer tests in hydrocarbon reservoirs. Specifically, we utilize the unique features of streamline models to develop an efficient approach for interpretation and history matching of field tracer response. A critical aspect here is the underdetermined and highly ill-posed nature of the associated inverse problems. We have investigated the relative merits of the traditional history matching ('amplitude inversion') and a novel travel time inversion in terms of robustness of the method and convergence behavior of the solution. We show that the traditional amplitude inversion is orders of magnitude more non-linear and the solution here is likely to get trapped in local minimum, leading to inadequate history match. The proposed travel time inversion is shown to be extremely efficient and robust for practical field applications. The streamline approach is generalized to model water injection in naturally fractured reservoirs through the use of a dual media approach. The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems. A detailed comparison with a commercial finite difference simulator shows very good agreement. Furthermore, an examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large-scale field applications. We also propose a novel approach to history matching finite-difference models that combines the advantage of the streamline models with the versatility of finite-difference simulation. In our approach, we utilize the streamline-derived sensitivities to facilitate history matching during finite-difference simulation. The use of finite-difference model allows us to account for detailed process physics and compressibility effects. The approach is very fast and avoids much of the subjective judgments and time-consuming trial-and-errors associated with manual history matching. We demonstrate the power and utility of our approach using a synthetic example and two field examples. We have also explored the use of a finite difference reservoir simulator, UTCHEM, for field-scale design and optimization of partitioning interwell tracer tests. The finite-difference model allows us to include detailed physics associated with reactive tracer transport, particularly those related with transverse and cross-streamline mechanisms. We have investigated the potential use of downhole tracer samplers and also the use of natural tracers for the design of partitioning tracer tests. Finally, we discuss several alternative ways of using partitioning interwell tracer tests (PITTs) in oil fields for the calculation of oil saturation, swept pore volume and sweep efficiency, and assess the accuracy of such tests under a variety of reservoir conditions.

Erosional incidents have heightened the necessity of studies regarding rock mass erosion in unlined dam spillways. Enhanced comprehension of hydraulic erodibility necessitates an investigation into the geomechanical and hydraulic aspects of erosional phenomena. Controlled blasting is commonly employed to establish unlined spillways in rock masses, and this process results in irregularities along the spillway surface profile. Recent research has identified key geometric parameters of rock masses that impact erosion in unlined spillways, such as joint opening, dip and dip direction, and joint spacing. However, the effect of spillway surface irregularities on hydraulic parameters remains uncertain. Numerous studies have examined the surface roughness of rock at the millimeter scale within the domain of hydraulic engineering. Despite these efforts, a noticeable gap persists in our understanding of how surface irregularities specifically exert influence over hydraulic parameters. Currently, there is a lack of a clear equation or methodology to incorporate irregularities into hydraulic erosive parameters. The main aim of this study is to show how such irregularities affect the hydraulic parameters. This study is dedicated to emphasizing the importance of considering these irregularities. Building upon the findings obtained, the core aim of this research is to facilitate the formulation of an equation in future investigations that effectively accounts for these irregularities when calculating hydraulic erosive parameters. To assess the significance of surface irregularities in unlined spillways, computational fluid dynamics (CFD) with ANSYS-Fluent software was employed to analyze 25 configurations of spillway surface irregularities and their effects on various factors, including pressure (total, dynamic, and static pressures), shear stress, flow velocity, and energy. The findings indicated that irregularities significantly influenced the hydraulic parameters. Specifically, an increased irregularity height led to a decrease in maximum velocity, total pressure, and shear stress. Conversely, total energy loss increased, amplifying the rock mass’s vulnerability to erosion due to these irregularities.

The dispersion phenomenon has resulted from the various water flow magnitude and direction in porous media. The dissolved tracer tends to spread due to dispersion and then travel time of tracer through the porous media increases. In unsaturated porous media, dispersion coefficient varies with non-linear Darcy’s velocity and the water content. These nonlinear dispersions were observed in both of the laboratory scale sand and soil columns (20 cm). The unsaturated infiltration column and tracer tests have been used to interpret the relationships between Darcy’s velocity and the water content together with the dispersion coefficient. However, the dispersivity coefficient cannot be measured directly; it has to be determined from advection-dispersion equation (ADE), which can be used to model the tracer transport in unsaturated porous media. The model was used to describe the non-linear functions of water contents and dispersivities for both porous media. The simulations have been verified that the dispersion of tracer through soil is higher than that of sand column and also the travel time of tracer through soil is longer than that of sand column. Even though, soil has very low degree of pore velocity, high dispersivity is observed in the simulations. The water content and tracer concentration profiles reveal that the increase of dispersivity induces the increase of flow path distance and the decrease of pore velocity. The maximum dispersivity was observed when the water content of porous media is relatively low; this leads to the maximum of spreading of tracer.

In modern systems of automated architectural and construction design, the method of creating three-dimensional models of objects under development is widely used. This method allows to visualize the object, determine various geometric object parameters, calculate its strength characteristics, solve issues related to production technology, etc. In most up-to-date graphics systems, standard solid-state objects, such as a parallelepiped, a cylinder, a ball, etc., are used as input data when creating three-dimensional models. At the same time, when creating complex models consisting of standard bodies, it is nec-essary to determine the type of object, its position and geometric parameters. The paper considers algorithms for recognizing some standard solids and determining their basic geometric parameters. The algorithms are implemented using ObjectARX technology for the AutoCAD system. The algorithms developed in the article can be applied in the problems of designing various objects, using technologies for creating three-dimensional models.

Faults in some deep mudstones have poor hydraulic connectivity owing to high normal stress on the fault planes. Designing a method for modelling solute transport pathways in such faults/fractures using available data is a critical issue vis-à-vis the safety assessment of radioactive waste disposal. In this study, faults in deep siliceous mudstones with low swelling capacity are investigated using cross-hole hydraulic and tracer tests between two boreholes. The water pressures observed during the hydraulic test are reproduced via hydraulic simulations, assuming a one-dimensional (1D) flow channel with a length 8–80 times the linear distance (4.5 m) between the two borehole test sections. This flow channel length indicates a tortuosity remarkably higher than that previously reported in discrete fracture network simulations and laboratory experiments using a single fracture (i.e. 1–5). Advection–dispersion simulations using a pipe model with a tortuosity of 8–80 reproduces a time series of tracer concentrations observed during the tracer test. The radius of the pipe simulated in the tracer test was 7–39 times the flow channel radius estimated via the hydraulic test, which is in agreement with the ratio of 5–20 previously reported based on in situ tracer and hydraulic tests of faulted/fractured rocks. The simulated longitudinal dispersivity is 1/9–1/20 of the estimated flow path lengths, in agreement with the laboratory and field tracer study values. These results indicate that transport pathways in faults with low hydraulic connectivity can be modelled using a highly tortuous 1D pipe flow path.

Fractional flow in fractured chalk; a flow and tracer test revisited


 
 
 Tracer tests are fundamental in characterizing fluid flow in underground formations. However, the setting of appropriate boundary conditions in even simple analytical models has historically been controversial, mainly due to the lack of sufficient physical evidence. Determining the relevance of boundary conditions on tracer test analysis becomes therefore a topic of renewed interest. The subject has been previously disscused by studying the tracer breakthrough curve sensitivity to diverse model parameter values. In our present work we examine the issue from a new practical reservoir characterization perspective. Two well-known equivalent elementary tracer transport models having different boundary conditions are matched to the same tracer test data. The resulting model parameter difference quantifies the effect of boundary conditions on reservoir property determination. In our case a tracer pulse injected in a homogeneous one-dimensional porous medium and moving at constant speed dominated by advection and dispersion is considered. The tracer transport models to be used yield conditions (i) on the tracer concentration, and (ii) on the tracer flux. Three data sets from tracer tests performed in different oil reservoirs are used to fit the models and determine the parameter values. We found that boundary conditionsbecome more important as Peclet number gets smaller. The cases analyzed have Peclet numbers 25.0, 5.4 and 3.7. The largest parameter difference obtained in each case is 5%, 18% and 37% respectively. These differences are large for laboratory experiments, but less relevant for tracer tests in oil fields, where data variability is frequently high. Nevertheless, attention should be paid when small Peclet numbers are present.
 
 

SUMMARY A study has been made of the response of production wells to the injection of a tracer pulse into an injector in watered-out reservoirs. Two response functions can be distinguished: (i) the tracer production rate and (ii) the cumulative tracer recovery both as functions of time. It is shown that the tracer response to pulse injection can be obtained from the results of a unit-mobility-ratio, equal-density miscible displacement. The cumulative tracer recovery is identical with the production rate of the displacing phase. The tracer production rate follows from differentiation of the production rate of the displacing phase with respect to time. For some simple flow systems, analytical solutions are presented that bring out the general features of the responses of interwell tracer tests. Linear flow solutions indicate the effect of longitudinal mixing to be negligible, whereas transversal mixing is important in layered reservoirs only if the individual layers are relatively thin (cm-dm scale). Solutions for a homogeneous two-spot show the effect of a pattern. The production-rate response is slide-shaped: a sudden rise followed by a fairly extensive fall-off period. This fall-off period becomes shorter for more linear patterns. In stratified reservoirs each layer produces its own ‘slide’ response. The responses of the less prolific layers, however, may be completely swamped by those of the more prolific layers. A procedure is indicated to model ‘single-colour’ and ‘multi-colour’ field tracer tests with the help of a conventional black oil simulator. It is based on the mathematical similarity that exists between two-phase immiscible flow and two-component miscible flow. For accurate simulation results a fine grid system (at least seven grid blocks between injector and producers) must be employed. The study may find application in the planning, design and interpretation of field tracer tests in watered-out reservoirs. The results of this study also apply to tracer tests in gas cycling projects.

Tracer Tests for Characterizing Malm Geothermal Reservoirs Within the German BMWi Project TRENDS: A Feasibility Study

This paper presents the numerical analysis results of a field tracer test. The objective of this test was to measure the dispersivity and the effective porosity of a permeable sedimentary layer. The tracer test was performed using two vertical bore holes 90 meters in depth and located 7 meters apart. The sedimentary layer, composed of sandstone, conglomerate, and weathered granite, was 10 meters thick and started 80 meters below the surface. One bore hole was used to inject groundwater with tracer and the other to recover to recirculate groundwater. We used a tracer solution containing Br. Before the tracer was injected, groundwater was circulated through the sedimentary layer between the two bore holes to establish a steady state of groundwater flow. The circulation flow rate and Br concentration initially injected were determined by using Gelhar's analytical solution so that the detectable tracer concentration (several ppm) could be recovered within one month. When the groundwater level at the recovery hole became stable, the tracer was injected into the injection hole and the concentration of Br was analyzed at the recovery hole. The circulation flow rate was 7800cm³/ min. The initially injected Br- tracer concentration was 8300 ppm. Thirty eight hours later, the concentration of Br at the recovery hole reached a maximum level of 10 ppm.The convection-dispersion equation was used for the tracer test's numerical analysis. This differential equation was transformed by F. E. M. Half of the horizontal section of the analytical region was used for numerical analysis and meshes like a semi-circle were used for the circulation-line above the surface between the two bore holes. A dispersion coefficient depends upon flow velocity, dispersivity, and diffusion. Initially, the flow velocity distribution and the permeability of layer were analyzed using F. E. M. as a seepage problem. The analyzed permeability of the layer was 2.2×10-5cm/sec.According to the F. E. M. analysis result, using the breakthrough curve of Br at the recovery hole and the matching technique, the effective porosity was determined to be 7% and the dispersivity 3.5 meters. The effective porosity was determined to be 4.5% and the dispersivity 3.5 meters by Gelhar's analytical solution. The 7% or 4.5% effective porosity value was smaller than the 30% porosity value with the boring core samples. This suggests that the measurement of effective porosity using a field tracer test is important in evaluating groundwater flow velocity and mass transport. The relationship between the dispersivity 3.5 meters and the distance 7 meters agreed well with those of Leonhart (1985).

Tracer tests have been widely used in the petroleum industry to determine qualitative information about underground reservoirs, such as the existence of flow barriers, directional flow paths, etc. This paper describes how well-to-well tracer tests can be used to obtain quantitative information about the geostatistical parameters (variance and correlation scale) of permeability. Both theoretical and experimental results are presented. In the theoretical work, a catalog of tracer production curves for different sets of geostatistical parameters for five-spot flooding patterns is produced. This catalog is computed with the help of a new numerical technique that is stable and devoid of any numerical dispersion. The effects of variance of the natural logarithm of permeability (ranging from .14 to 2.25), dimensionless correlation scale (ranging from .2 to .5), and of numerous realizations are quantified. The general effect of areal heterogeneity is that multiple peaks appear in the output tracer concentration curve, even when the flow is confined to a single layer. An increase in variance generally increases the number of prominent peaks in the output concentration profile, decreases the time between the emergence of peaks, and increases the time span of the occurrence of the tracer. An increase in correlation scale generally decreases the number of peaks. By using a sufficient number of permeability realizations, an attempt is made to assess variance and correlation length of the permeability field from the tracer and output concentration curves. In the experimental work, a slab of rock (Arizona flagstone) representing a quarter of a five-spot pattern was selected. A simple minipermeameter was used to measure areal permeability on grids of points on both the top and bottom surfaces of the rock. A tracer test was performed and the tracer output concentrations were measured at six intervals along the depth of the rock at the production well. Six different types of concentration curves were obtained, showing that downhole sampling of the tracer would be important in achieving adequate information about the reservoir rock. Permeabilities measured with the minipermeameter were used as input into the simulator and the numerical production curves were compared with the experimental profiles. The occurrences of similar patterns of multiple peaks confirms the numerical technique and strongly suggests that well-to-well tracer tests in oil fields and aquifers could be used to estimate the geostatistical parameters of the permeability field.

Residence time distribution analysis in the transport and compressing screws of a biomass pretreatment process

The advection‐dispersion equation (ADE) fails to describe commonly observed non‐Fickian solute transport in saturated porous media, necessitating the use of other models such as the dual‐domain mass‐transfer (DDMT) model. DDMT model parameters are commonly calibrated via curve fitting, providing little insight into the relation between effective parameters and physical properties of the medium. There is a clear need for material characterization techniques that can provide insight into the geometry and connectedness of pore spaces related to transport model parameters. Here, we consider proton nuclear magnetic resonance (NMR), direct‐current (DC) resistivity, and complex conductivity (CC) measurements for this purpose, and assess these methods using glass beads as a control and two different samples of the zeolite clinoptilolite, a material that demonstrates non‐Fickian transport due to intragranular porosity. We estimate DDMT parameters via calibration of a transport model to column‐scale solute tracer tests, and compare NMR, DC resistivity, CC results, which reveal that grain size alone does not control transport properties and measured geophysical parameters; rather, volume and arrangement of the pore space play important roles. NMR cannot provide estimates of more‐mobile and less‐mobile pore volumes in the absence of tracer tests because these estimates depend critically on the selection of a material‐dependent and flow‐dependent cutoff time. Increased electrical connectedness from DC resistivity measurements are associated with greater mobile pore space determined from transport model calibration. CC was hypothesized to be related to length scales of mass transfer, but the CC response is unrelated to DDMT.

This study has investigated and outlined the possible quantification and mapping of the distributions of advective solute travel times through hydrological catchments. These distributions are essential for understanding how local water flow and solute transport and attenuation processes affect the catchment-scale transport of solute, for instance with regard to biogeochemical cycling, contamination persistence and water quality. The spatial and statistical distributions of advective travel times have been quantified based on reported hydrological flow and mass-transport modeling results for two coastal Swedish catchments. The results show that the combined travel time distributions for the groundwater-stream network continuum in these catchments depend largely on the groundwater system and model representation, in particular regarding the spatial variability of groundwater hydraulic parameters (conductivity, porosity and gradient), and the possible contributions of slower/deeper groundwater flow components. Model assumptions about the spatial variability of groundwater hydraulic properties can thus greatly affect model results of catchment-scale solute spreading. The importance of advective travel time variability for the total mass delivery of naturally attenuated solute (tracer, nutrient, pollutant) from a catchment to its downstream water recipient depends on the product of catchment-average physical travel time and attenuation rate.

Water flow and solute transport processes are more complex in frozen than in unfrozen soils. The objective of this study was to determine the effects of freezing and thawing on water flow and solute transport in field soils. Experiments were conducted at two field sites each containing soil with a distinct texture (clay loam and sandy loam). Bromide (Br−) was used as a tracer, and soil water content and tracer concentrations were measured at different depths and times. A mass balance method was proposed to estimate mean values of water and solute fluxes (apparent soil water and Br− fluxes) in frozen, transition, and unfrozen zones during a freezing period and conduction and thawed zones during a thawing period. During freezing, soil water content significantly changed below and above the freezing front. Because of the presence of solute, relatively high liquid water content was found at soil temperature below zero. Soil water fluxes were mainly affected by the phase changes during freezing and thawing periods in the clay loam soil and by changes in the hydraulic properties related to liquid water content in the sandy soil. The contribution of water flux to the change of liquid water was much larger in the frozen zones than in the transition zones. During freezing, Br− ions excluded from ice and the different directions of dispersion and convection fluxes resulted in increases and then decreases of the apparent Br− concentration to mean measured Br concentration ratios. During thawing, the movement of liquid water and the superposition of convection and dispersion fluxes resulted in Br− concentration peaks and higher variation of the ratios. The water flow process was less synchronous with the solute transport process in unfrozen soils than in frozen soils.