Methods for predicting the spreading of steam below the water table during subsurface remediation

Transcription

1 Click Here for Full Article WATER RESOURCES RESEARCH, VOL. 46,, doi: /2007wr006401, 2010 Methods for predicting the spreading of steam below the water table during subsurface remediation S. O. Ochs, 1 H. Class, 1 A. Färber, 2 and R. Helmig 1 Received 2 August 2007; revised 25 September 2009; accepted 1 December 2009; published 19 May [1] Steam injection has been efficiently applied in many cases for the remediation of contamination in the unsaturated zone; however, some effort still has to be made to establish this technology in remediation practices for contamination in the saturated zone. The main difficulty here is the lack of reliable methods capable of predicting steam propagation around the injection well in poorly layered aquifers in an early screening stage. In this paper, methods are presented for predicting steam propagation in saturated media. First, a subset of experiments conducted in a two dimensional flume is utilized to demonstrate the characteristics of steam propagation in water saturated porous media. An improved numerical model concept that for the first time accounts for the variable degrees of freedom in the researched system is successfully tested and compared with an experimental data set. The model is consequently used to derive a set of type curves for the characteristic steam propagation in saturated porous media. These type curves can be used to estimate the steam propagation and the efficiency of a measure. Finally, the applicability and the potential of the developed methods are demonstrated for a pilot scale remediation. Citation: Ochs, S. O., H. Class, A. Färber, and R. Helmig (2010), Methods for predicting the spreading of steam below the water table during subsurface remediation, Water Resour. Res., 46,, doi: /2007wr Introduction [2] In the early 1980s subsurface steam injection originally developed for enhanced oil recovery was transferred to environmental applications. Since then steam injection has proven to be an efficient remediation method at many sites. Experimental studies of varying complexity [e.g., Hunt et al., 1998; Färber, 1997; Betz, 1998; Schmidt et al., 2002] and the development of reliable numerical models [e.g., Falta et al., 1992a; Class et al., 2002; Pruess, 2004] have led to the fact that steam injection emerged as a state of the art technology for the remediation of volatile contamination in the unsaturated zone. [3] Nowadays, steam injection in saturated porous media is becoming increasingly interesting because contamination, e.g., by dense nonaqueous phase liquids (DNAPL), is not limited to the unsaturated zone alone. Although many studies on the propagation of steam in saturated porous media do exist, they usually concentrate on conditions commonly found in oil reservoirs. Here the geology is typically layered or even confined from above by a low permeable caprock, and steam is injected over large portions of the reservoir depth (see Figure 1). This and the usually large horizontal extent ( m) of such regimes cause the focus to be mainly on the horizontal spreading, thus representing a typical far field problem. In contrast, during a groundwater remediation, steam is usually injected below the contaminated target zone. The extent of such a steam 1 Institut fu r Wasserbau, Lehrstuhl fu r Hydromechanik und Hydrosystemmodellierung, Universität Stuttgart, Stuttgart, Germany. 2 Dr. Fa rber and Schwarz Acoustics Pvt. Ltd., Mumbai, India. Copyright 2010 by the American Geophysical Union /10/2007WR injection event is usually in the range of m and thus is notably smaller. This, together with the fact that steam is injected only over a small portion of the domain, results in a spreading behavior clearly different from that in oil reservoirs. For poorly layered geology, buoyancy results in a strong vertical component of the steam propagation (see Figure 1). Here the unrestrained rising of the steam front yields to a typical near field problem. However, for strongly layered systems, methods from reservoir engineering [Van Lookeren, 1983] may be applicable to predict the steam propagation. [4] Van Lookeren [1983] studied steam front propagation in a confined two dimensional oil reservoir in which steam was injected over the whole depth. He derived an analytical formulation correlating the inclination of the steam front to the ratio of viscous and buoyant forces. Basel and Udell [1989] presented a similar formulation for the inclination of the steam front and verified the method of Van Lookeren using an experimental data set. Both studies showed that buoyancy strongly influences the steam propagation. The early study of Hunt et al. [1998] showed that steam can efficiently remove residual contamination from a homogeneous water saturated column. On the basis of experimental studies, She and Sleep [1999] could demonstrate that steam flushing even has the potential for remediating low permeable regions but on the other side holds the risk of downward mobilization of the contaminant. Gudbjerg et al. [2004a] showed that conductive heating is the dominant remediation mechanism if the steam zone is not in direct contact with the contamination source. [5] Numerical models successfully applied to unsaturated conditions have shown major problems like bad convergence, stability, and robustness when modeling steam injection below the water table. Falta et al. [1992b], for 1of16

2 Figure 1. Steam injection for remediation and enhanced oil recovery. example, observed intermittent unphysical pressure fluctuations modeling steam injection into a water saturated column. Gudbjerg et al. [2004b] detected spurious backflow of water into the steam zone, causing severe problems at saturated conditions. To overcome the problems, they proposed an algorithm for blocking these nonphysical fluxes. [6] For strongly layered systems, numerical studies of pilot tests [Kuhlmann, 2002; Ochs et al., 2003] showed that the steam front propagation in the subsurface could be reasonably reproduced. With a simplified three dimensional model, Gudbjerg et al. [2005] could qualitatively simulate the steam propagation in a shallow aquifer. Steam was injected between 3 and 3.5 m below ground surface (BGS), and the water table was located at 1.7 m BGS. A numerical study with the simplified model setup showed that the geology and the injection and extraction system may strongly influence the steam propagation. [7] Currently, there is still a strong demand for reliable methods that provide an estimation of the steam propagation in the screening stage of a project, which is indispensable, if nothing else, also for the cost calculation. The objective of this study is to contribute toward the development of methods that aid the dimensioning of steam injections for remediating contaminations in the saturated zone. In a first step, a series of lab experiments is conducted in a twodimensional flume representing typical conditions. A novel numerical model, which for the first time accounts for the variable degrees of freedom in the system, is validated with experimental data. In the next step, a new dimensionless number is derived by heuristic approaches, taking into account the dominating parameters of the relevant processes. On this basis, type curves are derived that enable the approximation of the characteristic steam propagation. These type curves are intended to provide an estimation of the thermal radius of influence (TRI) in the screening stage of a project, where detailed site specific information is typically not available. The TRI is the maximum horizontal distance from the injection point up to which the entire contaminated zone can be heated to steam temperature. It is a key parameter for the design of a steam injection in the saturated zone and for the estimation of the actual costs of a planned measure. Consequently, the application of the model and the type curves is demonstrated for a field scale DNAPL remediation. The applicability and the limitations of the presented methods are discussed in section Experimental Investigations 2.1. Experimental Setup [8] The experiments were conducted in a two dimensional flume designed for performing high temperature experiments in porous media. In this study, the influence of various porous media and varying steam injection rates on the propagation of steam in saturated porous media is investigated. In Figure 2, a design plot of the flume used in the experimental investigations is shown [Van Lookeren, 1983]. 2of16

3 Figure 2. Design plot of 2 D flume used in the experiments. [9] A frame of stainless steel strengthened by additional bearings provides the basis of the flume. A temperatureresistant panel of Pyrex allows visual monitoring of the experiments. In order to minimize heat losses, insulation made of birch wood is placed between the glass and the steel bars. The interior dimension of the flume measures 0.74 m 1.1 m m (height length width), resulting in an approximate volume of 70 L. To minimize heat losses during an experiment, all parts of the flume are insulated with glass wool and foam plastic. For visual observation of the experiments, the insulation at the front is removable. Steam is injected into an injection box at the lower left corner of the flume. On the right side of the flume, a screen stretching over the full height is installed. This screen is connected to an overflow box, ensuring fully saturated conditions in the flume and well defined boundary conditions for the simulations. A cover of stainless steel containing a Viton strip seals the fume on the top Measurement Techniques Temperature Temperature Sensors [10] One hundred Pt100 temperature sensors are arranged in 10 rows and 10 columns in the flume and provide continuous point readings. The accuracy of the Pt100 sensors is ±0.4 K. Despite the large number of sensors, the spatial resolution of the temperature distribution in the flume is only about 0.1 m 0.1 m in some areas and thus is not sufficient for a proper tracking of the steam front (see Figure 2) Thermographic Camera [11] To track the steam front with a high spatial resolution, a thermographic camera, type VARIOSCAN 3022 hr, is used. The thermographic camera yields highly resolved images of the temperature distribution in the flume at a certain time. The thermal conduction in the glass panel leads to a temperature shift of about 4 C and a delay due to transient heating of the glass panel which is mostly insubstantial Saturation [12] The water saturation S w in the flume is measured using a g transmission system. A caesium (Cs 137) radiation source emits g quanta with a very high activity of 3.6E 10 Bq, allowing a fast and accurate measurement. The measuring method is based on the mitigation of radiation caused by the varying water saturation in the flume. As the emission of g quanta is a stochastic process, the uncertainty of the measurement is reduced by the square root of the measurement interval. Here a trade off between the number of measurements and the accuracy of a single measurement has to be made. Färber [1997] found a measurement interval of 2 s to result in an accuracy of approximately ±1.15%. The g robot moving source and detector (see Figure 2) allows access to any point with a precision of more than 0.1 mm. Nevertheless, feasible measurement points and their number are limited as a result of several constraints. In addition, the overall time for one sequence of measurements is limited because of the continuous propagation of the steam front. The different aspects of determining the maximum number of measurements in one sequence and their position are discussed by Ochs [2006] Steam Rate [13] A rotameter located at the outflow of the steam generation unit measures the volumetric steam injection rate. In addition, temperature and pressure are measured to derive the corresponding mass flux, with an accuracy of ±1.5%. The measurements affirmed saturated steam at almost atmospheric pressure. 3. Experimental Investigations: Results [14] In this section, the results of two experiments with a medium sand packing and steam injection rates of 3.6 kg/h and 0.72 kg/h are discussed. The properties of the sand are listed in Table 1. Although special effort was made to get a homogenous filling, local variations in permeability Table 1. Soil Properties for Medium Sand Property Symbol Measurement Value porosity permeameter test 0.34 permeability K permeameter test 6.6E 11 m 2 van Genuchten n n g density 7.4 van Genuchten a a g density Pa 1 residual water saturation S wr g density 0.12 residual gas saturation S gr by definition 0.0 3of16

4 of ±50% have been detected by tracer tests in the vicinity of the boundaries Experimental Results: High Injection Rate [15] The Pt100 temperature measurements as well as the g density measurements are point readings with a rather coarse spatial resolution. Thus, the position of the individual measurement points is essential for the interpretation of the deduced distribution of the respective quantity in the system. The positions of the Pt100 sensors are fixed and are shown in Figure 2 (circles). The different steam propagation expected in the experiments makes it necessary to adapt the g density measurement positions. For each experiment, the position of the single measurements is determined in a preliminary experiment. The measurement positions for the high steam injection rate experiments are given in Figure 2 (squares). [16] In Figure 3, the temperature and water saturation distribution in the flume is shown for three time steps (6, 12, and 18 min), each in a separate row. From left to right a thermal image, the temperature distribution derived from the Pt100 sensors, and the water saturation in the flume are presented. Note that the dark vertical bands in the thermal images show the bars of the flume (see Figure 2), indicating the significantly smaller temperature in the bearings caused by the wooden insulation between the glass and the bearings. [17] The measurements of the Pt100 sensors match the thermal images well, except for the thermal images, indicating a smaller transition zone between steam and water at ambient temperature. The reason for this is the rather coarse spatial resolution of the temperature distribution derived from Pt100 sensors, due to linear interpolation of the point readings used to derive an area plot. In reality, the steep temperature gradient between steam and water leads to the fact that the Pt100 sensors do not respond almost until the steam front arrives at the sensor. [18] The spatial resolution of the water saturation measurements is quite coarse. Thus, the discussion of the results should mainly concentrate on the point readings. The plots of the saturation distribution show that the saturation in the steam zone only is reduced significantly and reaches a minimum of 0.15 after 24 min at x and y position (0.07 and 0.1 m) close to the injection box. The results of the high rate experiments (Figure 3) show that the steam front tends to move radially at the beginning. This changes toward a more vertical spreading and an ovoid shape in the later stage of the experiment, indicating that buoyancy effects become more important; that is, a transient parameter may influences the propagation Experimental Results: Low Injection Rate [19] In Figure 4, the results of the low steam injection rate experiment are shown for the time steps 12, 24, and 60 min. Here the benefit of the high resolution thermal images is obvious. As the steam front spreads mainly vertically, the steam zone extends just over one row of sensors. This is not adequate for mapping the shape of the steam zone at all. For the same reason the position of the water saturation measurements was modified by shifting the location of the second row from 0.28 to 0.22 m to have at least two data rows. Again, the saturation measurements show that the water saturation is only reduced within the steam zone. However, the minimum at the measurement position closest to the injection port is 0.5 after 60 min. The results show that the steam front has a minor tendency to spread horizontally as in the case of the high steam injection rate because buoyancy effects are more important here Experimental Investigations: Analysis and Conclusion [20] During the experimental investigations, a series of steam injection experiments in fully saturated conditions was carried out with varying steam injection rates and for various porous media properties, although only experiments with two different injection rates are discussed here. The experimental investigations indicate that the steam zone propagation is strongly influenced by buoyancy effects. It is found that the ratio of steam injection rate to permeability (q s /K) determines the characteristics of the spreading behavior in the experiments, similar to what Van Lookeren [1983] found. For high q s /K ratios, an almost radial spreading of the steam zone around the injection port is observed in the experiments, whereas this changes toward a stronger vertical spreading for small q s /K ratios. However, unlike the invariant characteristics discussed by Van Lookeren [1983], a transient behavior has been observed in our study. This indicates that the characteristic form of the steam zone may be described by a reduced set of parameters including the q s /K ratio and a transient parameter. It can be concluded that this set of parameters, and their functional dependence are known, and characteristic type curves can be derived that describe the spreading of steam in saturated porous media for certain conditions. Such type curves could be helpful, e.g., to assess the TRI of an injection well in the screening stage of a project, which is a key factor for the practical and economic efficiency of a project. 4. Numerical Simulation of Experiments 4.1. Numerical Model Concept [21] For the simulation of the steam experiments, a novel numerical model concept is used which accounts for variable degrees of freedom in the system caused by the varying number of components locally present. The physical model concept is based on the one developed by Class et al. [2002]. Existing models of steam injection in saturated porous media show severe convergence problems [e.g., Forsyth, 1993] that could be overcome by the new model concept. The major innovation of this model concept is that it switches the primary variables not only as a function of the present phases but also depending on the number of components locally present and thus on the degrees of freedom. If we recall the Gibbs Duhem relation, the degrees of freedom (F) in a system at internal equilibrium made up of C components and P phases is F ¼ C P þ 2: In a macroscale porous multiphase or multicomponent system, however, several phases may be present at the same time. As the saturations of the phases add up to unity, the extra degree freedom is (P 1), yielding ð1þ F ¼ C P þ 2 þ ðp 1Þ ¼ C þ 1: ð2þ 4of16

5 Figure 3. Experimental results for medium sand with high injection rate: (a, d, g) thermal images, (b, e, h) temperature distribution from Pt100 sensors, and (c, f, i) water saturation in the flume after 6, 12, and 18 min (from bottom to top). 5of16

6 Figure 4. Experimental results for medium sand with low injection rate: (a, d, g) thermal images, (b, e, h) temperature distribution from Pt100 sensors, and (c, f, i) water saturation in the flume after 12, 24, and 60 min (from bottom to top). 6of16

7 Table 2. Phase States and Corresponding Primary Variables for the New Model Air a Model State Present Phases Primary Variables 1 2p2cni 11 w, g p g, S w, T 1 2p2cni 12 w p g, x a, T 1 2p2cni 13 g p g, x w g, T 0 2p1cni 10 w, g p g (T), S w 0 2p1cni 20 w p g, T 0 2p1cni 30 g p g, T a Here 1, air present; 0, air absent. Equation (2) reveals that the number of degrees of freedom depends on the number of components present. Thus, for situations in which a component disappears, the degrees of freedom are reduced by 1. A condition commonly found when steam is injected into saturated porous media is that the air, which is initially present in the system, disappears locally in the steam zone. This effect has been identified as causing convergence problems in our model. Forsyth [1993] reported the same problems and proposed adding a penalty source term, ensuring that the air component does not disappear. [22] We found that the reason for this problem is the result of the reduced degrees of freedom in the physical system, which is not considered in the numerical model concepts. This leads to the problem that the primary variables (p g, T) that ought to be independent are coupled via the saturation pressure. We implement a model concept that accounts for the variable degrees of freedom in the system by switching the primary variables as a function of the components and phases present. Moreover, this air balance equation can be locally switched off if the air component disappears. This reduces the physical model concept locally from a two phase, two component (2p2cni) model to a twophase, one component (2p1cni) model. The primary variables for the model concept are provided in Table 2. For a detailed description of the model, the reader is referred to Ochs [2006]. For this study, the steam injection process is supposed to be monotonous. Thus, once the air component is locally displaced, it does not reappear. Therefore, the model considers no reappearance of the air component Model for the Flume [23] For the simulation of the steam experiments, a twodimensional model with the dimensions of the interior flume (1.11 m 0.74 m) is set up (see Figure 2). The domain has a constant thickness of m. [24] Neumann no flow boundary conditions are used on the top, bottom, and the left sides of the flume, except for the lower left corner. Here a Neumann boundary condition representing the steam injection rate is applied. The overflow tank on the right side of the flume (see Figure 2) guarantees fully saturated conditions and a hydrostatic pressure distribution in the flume. Thus, Dirichlet boundary conditions are used here Model Parameters [25] Besides the soil properties measured for the sand and tabulated in Table 1, values for the soil grain density % sg and soil heat capacity c pm are taken from Färber [1997]. In addition to these parameters, spatially variable parameter fields for the heat capacity (C p ) and the heat losses are derived for the flume. This effort is necessary to be able to reproduce the retarding effect the flume body has on the steam propagation. For the construction of the C p field, the geometry of the flume is mapped in a first step to the finite volume mesh. Subsequently, the composition of the flume in each volume is determined and used for the calculation of the C p field. Apart from the mass and energy fluxes that are reflected by the boundary conditions, energy may also be exchanged at the front and back sides of the flume. The resulting energy losses are taken into account by an additional sink term (q loss ) in the energy balance equation. Here the simplification of a one dimensional stationary heat transfer is made. In this way, a field for the heat losses can be derived similarly to the previously mentioned C p field. The calculated heat losses have been checked experimentally [cf. Ochs, 2006] Simulation Results: High Injection Rate [26] The results of the simulation runs for the high steam injection rate of 3.6 kg/h are given in Figure 5. Figures 5a and 5b show the temperature distribution after 6 min, 12 min, and 18 min, and Figures 5e and 5f show the corresponding saturations. At the beginning (6 min), the steam zone propagates radially around the injection port at the lower left corner. As the steam zone continues to spread, the vertical growth becomes slightly greater than the horizontal one. This indicates that buoyancy effects become dominant with increasing expansion of the steam zone. The saturation distribution in the flume follows the temperature distribution as expected. A reduction of the water saturation occurs only in the steam zone. Within the steam zone, a characteristic distribution of the water saturation (S w ) arises. S w drops in large parts of the steam zone below a value of 0.4. In the vicinity of the injection screen, S w is reduced to a value of 0.15, which is close to the residual water saturation of Simulation Results: Low Injection Rate [27] For the low steam injection rate of 0.72 kg/h, the results of the simulations are depicted in Figure 6. An almost radial shape of the steam front for the first time step (12 min) is evident. However, this begins to balloon outward for the following time steps. After 60 min, a mainly vertical spreading can be observed, caused by dominant buoyancy effects (see Figure 6). In contrast to the results for the higher steam injection rate, the influence of thermal conduction is apparent here. The transition zone between the steam front and the fully saturated porous media at ambient temperature is larger than for the case with a high steam rate and extends over several elements, indicating that this is not merely an effect of numerical diffusion but rather represents thermal conduction. Water saturation in the steam zone is only reduced in the very close vicinity of the injection well to values near residual saturation. In large parts of the steam zone, values of S w > 0.4 occur. 5. Comparison Measurements and Simulations [28] The simulation results for the high steam rate (Figure 5) agree very well with the experimental data shown in Figure 3. The spreading behavior of the steam front can be reproduced with the numerical model. Not only the shape 7of16

8 Figure 5. Numerical results for medium sand, high injection rate: (a c) saturation distribution and (d f) temperature distribution after 6 min, 12 min, and 18 min. of the steam front but also the measured temperatures and water saturations match the simulation results for all time steps. Only near to the left and bottom boundaries of the flume does the propagation of the steam front in the experiments seem to be slower than the simulations predict. A possible explanation for this is that the heat capacity of the flume frame or the heat losses are underestimated in the numerical model. The measured saturation generally agrees well with the simulations. Despite this, some measurements show significant deviation from the simulation results. For example, the measured water saturation in Figure 3 (12 min) shows a value of about 0.5 at point (0.07 m, 0.4 m), whereas the simulations in Figure 5 still indicate fully saturated conditions (S w = 1.0) here. This is caused by the fact that the robot needs approximately 30 s to complete one sequence of measurements. Thus, the single measurements of a sequence do not correspond to a single time, e.g., the start of the sequence. During a sequence of measurements the steam front eventually arrives at a measurement position at which there were fully saturated conditions at the beginning. The small temperature measured with the temperature sensor and the simulation result close to point (0.07 m, 0.4 m) show that the steam front is just about to arrive at this point. The temporal shift between the start of the sequence and its completion is sufficient for the saturation to drop from 1.0 to 0.5. The propagation of the steam zone can be reproduced 8of16

9 Figure 6. Numerical results for medium sand, low injection rate: (a c) saturation distribution and (d f) temperature distribution after 6 min, 12 min, and 18 min. satisfactorily with the numerical model for the low injection rate of 0.72 kg/h. The simulated steam front is slightly faster than the measurements near to the lower and left boundary. Again, this may be the result of the simplified concepts for the heat transfer into the flume frame and the heat losses. After 60 min, the model predicts a slightly larger horizontal and smaller vertical extension of the steam zone than the measurements show. The measurements and results of the numerical simulations are very consistent. It has to be emphasized again that no fitting of input parameters was carried out in order to calibrate the model to the measured data. For the simulations, measured soil properties are used. The numerical model proved capable of reproducing the propagation of steam zones in saturated porous media. 6. Characteristic Steam Front Propagation 6.1. Procedure and Accomplished Model Runs [29] Rather than experimental results, the developed numerical model is used to investigate the characteristic steam front propagation in saturated porous media in greater detail. This is because the necessary data can be assembled at a high spatial and temporal resolution within a much smaller time frame compared with experiments. Additionally, 9of16

10 Table 3. Notation of Model Runs and Parameter Combinations a Model Run Parameter Combinations Series A A1 K A2 K/2 A3 K/4 A4 K/8 A5 K/10 A6 K/20 Series B B1 q s B2 q s /2 B3 q s /4 B4 q s /8 B6 q s /10 B6 q s /20 a Here q s = 1 g/s is constant in series A and K = m 2 is constant in series B. shortcomings of the experiments, e.g., uncertain soil properties or measurement errors, can be avoided. For the study of the general spreading behavior, a two dimensional model, similar to the one used for modeling the experiments, is used. However, the heat capacity of the flume frame and the heat losses are neglected. The experimental studies already indicated that the q s /K ratio fundamentally influences the steam front propagation in saturated porous media. On the basis of the input parameters used for modeling the medium sand experiments, several realizations with varying q s /K ratios are simulated. Two series of model runs, with constant q s and varying K (series A) and constant K and diverse q s (series B), are conducted (see Table 3). [30] First, we investigate whether the q s /K ratios could serve as an appropriate parameter combination for describing the characteristic steam propagation. To do so, the steam front propagation is compared for the corresponding instances (similar q s /K ratio). Hereby, times of equivalent energy input are compared. For two corresponding instances, the steam front propagation is visualized in Figures 7 and 8. The location of the steam front is identified by the appearance of the gas phase (S g > 0.0). Figure 8. Location of steam front for corresponding model runs A4 and B4. [31] The propagation of the steam fronts shown in Figure 7 is almost identical for the corresponding cases of series A and B. The typical shapes of the steam front for times with equal energy input fit each other very well, despite a factor 2 in the q A /q B and K B /K A ratio. [32] Comparing the results in Figure 8 shows that the fit is good at the beginning (2 and 16 min). At a later stage, a noticeable deviation for the two corresponding instances is obvious. This is especially apparent in the late time steps, e. g., 18 and 144 min. Although the shapes of the steam fronts match quite well, the results with the high injection rate (case A4) proceed slightly faster and show a larger spatial extent than the corresponding case B4. This effect is caused by thermal conduction. The energy needed to heat the porous medium in front of the steam zone by thermal conduction results in a retardation of the steam front. In order to investigate this effect in detail, simulations are carried out in which the thermal conductivity of the porous medium is set to zero (l pm = 0). In Figure 9, the results of instance A4 and the modified case B4 with l pm = 0 are plotted. Now the steam front propagation for both instances is almost identical. Figure 7. Location of steam front for corresponding model runs A2 and B2. Figure 9. Location of steam front for corresponding model runs A4 and B4 (l pm = 0). 10 of 16

11 Figure 10. Type curves for two dimensional steam propagation for series A model runs. [33] The accomplished model runs show that the spreading of the steam front is strongly dependent on the q s /K ratio. Cases with the same q s /K ratio lead to a similar spreading behavior of the steam front. However, the influence of conductive heating has to be kept in mind Dimensionless Gravity and Two Dimensional Type Curves [34] The investigations into steam propagation in saturated porous media have shown that the shape of the front strongly depends on the q s /K ratio. For steam injection in oil reservoirs with a confining layer on top and at the bottom and a constant injection rate over the total domain height, Van Lookeren [1983] derived a dimensionless expression for the steam ¼ s q s ðx b Þ bk s % s h ð% o % s Þg Gr ¼ viscous forces buoyancy forces ; ð3þ where m s is the steam viscosity, q s is the volumetric steam flux, K s is the effective permeability to steam, % o is the density of oil, % s is the density of steam, g is the gravity constant, and L b and L h are characteristic lengths describing the form of the steam zone. According to equation (3), the inclination of the steam front is a function of the dimensionless gravity number (Gr), which is a measure of the ratio of viscous to buoyancy forces [see Van Lookeren, 1983]. This formulation originates from reservoir engineering and hence represents conditions and assumptions that can be made for steam injection into oil reservoirs but in general not for the remediation scenarios that are the subject of this study. In the latter case, steam is injected below the contaminated target zone over a small portion of the domain height. Thus, the Depuit assumption applied by van Lookeren to derive equation (3) does not hold any more. However, other authors [e.g., Kopp et al., 2009] showed by dimensional analysis of the two phase governing equations for complex multiphase systems that the Gr number is a quantity substantially influencing gravity driven processes in saturated porous media. Thus, Gr should also be appropriate for describing steam front propagation during remediation. Confirming this in an analytical way mainly fails because of the complex flow field with horizontal and vertical components. Thus, a series of numerical simulations is carried out to substantiate the hypothesis. In a first step the definition of Gr in equation (3) has to be recalled and adjusted for the researched system. Obviously, the density of oil (% o ) in equation (3) has to be replaced by the density of water (% w ). In addition, the effective permeability of steam is equated with the intrinsic permeability (K s = K). While b represents the thickness of the two dimensional system, the definition of the second characteristic length h has to be examined carefully here, especially as it affects the force balance at the steam front. In van Lookeren s study, steam is injected over the full reservoir height h and thus is an adequate measure of the flux density (q/h). For the point injection, the flux density at the beginning is maximal and decreases with increasing time because of the expansion of the steam front, resulting in a time dependent characteristic length h(t) and hence a variable Gr(t). This would cause a temporal evolution of the spreading behavior of the steam fronts contrary to the invariant linear spreading Van Lookeren [1983] discussed. Such a behavior has already been observed in the experimental studies. Here the characteristic shape of the steam front changes from a radial shape at the beginning toward an ovoid shape at later times. Therefore, h in equation (3) is replaced by the transient maximum vertical extent of the steam zone y max (t), as together with q, this is a good measure of the flux density: s q s Gr ¼ bk s % s y max ðþ t ð% w % s Þg : ð4þ For the derivation of the type curves, the results of series A model runs (see Table 3) are used to minimize the influence of conductive heating on the spreading of the steam front. Besides this, only results with 0.15 < y max < 0.6 m are used to minimize the influence of the upper and lower boundary conditions. In Figure 10, characteristic type curves obtained from the simulations are assembled. A dimensionless form is used that scales the x and y coordinates with y max. This allows us to plot the type curves independently of the actual size of the steam zone. [35] For high Gr, a radial spreading around the injection port is characteristic, showing the initially negligible effect of buoyancy forces. For smaller Gr, the characteristic shape of the steam front is ovoid as the ratio of the maximum horizontal to vertical extension decreases. For very small Gr, the dominating buoyancy effects become obvious, as the steam front spreads very early mainly vertically Verification of Two Dimensional Type Curves [36] To demonstrate the applicability of the type curves developed with the numerical model and to identify possible shortcomings, the conformity of the type curves with experimental data is examined. In order to maintain a clear structure in the diagram, three different times corresponding to characteristic gravity numbers are selected from two experiments. Experimental data from experiments with a coarse and a medium sand packing with a steam injection rate of 3.6 kg/h are displayed. The time steps have been selected so that a wide range of gravity numbers is covered by the experimental data (see Figure 11). 11 of 16

12 Figure 11. Dimensionless diagram with characteristic type curves and experimental data as a function of Gr; ms indicates results of experiments with a medium sand and cs ones with a coarse sand. [37] The results of the medium sand experiments fit well into the set of type curves. Significant discrepancies occur only close to the left and bottom boundary. This is caused by the heat capacity of the flume frame and heat losses which have not been considered in deriving the type curves. The steam fronts measured during experiments with a coarse sand packing do not match that well with the type curves. Although the maximum horizontal extent of the steam front in the experiments, which is crucial for the layout of a measure, matches the type curves reasonably, the shape of the experimental steam fronts deviates in some cases from the corresponding type curve. This probably is caused by small scale heterogeneities in the coarse sand packing or could be a result of approximating the highly nonlinear relative permeability by the intrinsic permeability in the definition of Gr in equation (4). With the fact that the effective permeability affects the viscous forces rather than the intrinsic permeability in mind, a trade off has to be made. Yet using the intrinsic permeability results in a conservative approximation of the vertical steam propagation and the TRI. spreading of the steam front turns into a stronger vertical spreading for small gravity numbers. However, the individual shape of the type curves for a certain Gr number differs significantly from those derived for a two dimensional system. This is caused by the fact that in the three dimensional radial system, the width of the domain and hence that of the steam zone is not constant but increases proportionally to the horizontal extent of the steam zone. This leads to a faster pressure decline in the steam zone and thus significantly influences the ratio of viscous and buoyancy forces and consequently the spreading of the steam zone. By deriving characteristic type curves for steam propagation in saturated porous media, we provide a simple method for approximating the spreading of the steam front in the screening stage of a project, which is helpful for an early estimate of the remediation costs, for example. This method is based on a reduced set of parameters reflecting the information usually available at this stage, limited in general to the permeability and steam injection rate. For a detailed description of the steam propagation, especially in heterogenous systems, the application of a predictive numerical model, requiring sufficient field data, is still indispensable. 7. Field Application [40] To demonstrate the practical applicability of the type curves and the predictive capabilities of the numerical model, a pilot steam injection project carried out by the Research Facility for Subsurface Remediation (VEGAS) in 2005 is briefly discussed. In the runup to the pilot test, steam spreading in the saturated zone was estimated using the type curves. Additionally, the developed model was used to predict the steam propagation in the subsurface. Below and in the near vicinity of a former dry cleaning facility, severe contamination with chlorinated solvents, mainly PCE, was located. Because of the failure of a pump and treat system to remove the contamination from the subsurface, regulators considered steam injection to be an appropriate remediation technique for the site Type Curves for Three Dimensional Steam Propagation [38] In a further step, type curves for a radial threedimensional system are derived numerically. This scenario is closer to reality than the two dimensional system studied previously, as steam usually spreads radially around an injection well. The same modifications as described in section 6.2 are necessary to adapt the Gr derived by Van Lookeren [1983] for a radial steam propagation to the system we investigate, yielding s q 1=2 s Gr rad ¼ ð% o % s Þgymax 2 ðþk t : ð5þ s % s The dimensionless type curves are shown in Figure 12. [39] The set of type curves derived for the three dimensional radial system shows a behavior similar to the one for the two dimensional system. For high Gr numbers, a radial Figure 12. propagation. Type curves for three dimensional steam 12 of 16

13 Figure 13. Plan of contaminated site and layout for the pilot steam injection Setup of Pilot Steam Injection [41] The pilot installation is established at the southwestern corner of the former production facility. Extensive site investigations indicate that the zone of main contamination is located in the vicinity of the building (see Figure 13). The perchloroethylene contamination extends up to 5 7 m BGS and thus into the saturated zone. In Figure 13, the plan of the contaminated site and the arrangement of the installed wells and temperature sensors for the pilot test are shown. For the pilot test, one injection well (I6) and three extraction wells (Br38, E8, and EK2) are installed. A series of thermocouples arranged in two rows between I6 and E8 and between I6 and EK2 are used to monitor the propagation of the steam zone. Each thermocouple consists of several Pt100 sensors located at various depths Model for Pilot Steam Injection [42] To simulate the pilot steam injection, the developed numerical model is used. The water table at the site is located 3 m BGS and is overlaid by a layer of low permeable clay with a thickness of 1 2 m. Steam is injected at a depth of 7 8 m BGS. The model domain extends from 3 to 10 m BGS. Assuming a radially symmetric spreading of the steam zone around injection well I6 means that a segmental section is adequate for the simulations. A segmental model domain with an angle of 30 is used. The inner radius of the segment corresponds to the borehole radius of injection well I6, which is m. The outer radius is chosen to be 5 m. The model domain is discretized with 2240 hexahedra of various sizes. The mesh resolution decreases with increasing distance from the injection well. For the front, back, and bottom, Neumann no flow boundary conditions for water and energy are used. The left boundary is modeled using Dirichlet boundary conditions with a fixed temperature of K and hydrostatic pressure. For the top, a Dirichlet boundary condition with a constant temperature of K and a gas phase pressure equal to atmospheric pressure is applied. On the right side, a Neumann no flow boundary condition is applied except at a depth of 7 8 m BGS. Here a Neumann boundary condition representing a steam injection rate of 180 kg/h is used. Drilling cores from the installed wells indicates a layered geology at the site. A series of permeameter tests, pump tests, and borehole tests carried out by VEGAS identified six main geological units. The permeability and other soil parameters used in the simulations are provided in Table Application of the Developed Methods [43] The type curves are intended to give an estimate of the TRI in an early screening stage of a remediation project. Table 4. Model Parameters Used for the Simulations Parameter Symbol Value Permeability, 3 4 m BGS K 5.3E 12 m 2 Permeability, 4 5 m BGS K 8.0E 11 m 2 Permeability, 5 7 m BGS K 2.7E 11 m 2 Permeability, m BGS K 8.0E 11 m 2 Permeability, m BGS K 9.3E 11 m 2 Permeability, m BGS K 8.0E 11 m 2 Anisotropy ratio K xx /K yy 3 Porosity 0.4 Residual water saturation S wr 0.1 van Genuchten a a vg Pa 1 van Genuchten n n vg of 16

14 Figure 14. Temperature profiles measured and simulated for the pilot remediation at TC7, TC1, TC3, and TC5 after (1) 6 h, (b) 12 h, (c) 24 h, and (d) 36 h. Here, usually only a few data are available, including permeability and the maximum injection rate. As the TRI is known, a sound calculation of the remediation costs based on the maximum number of injection wells necessary at a site and the necessary dimension of the equipment can be carried out. However, this will be an estimate which is based on a series of simplifications the user has to be aware of (see section 6). For example, a major simplification is that the type curves are developed for a homogeneous isotropic system. This requires the determination of an effective permeability, which represents the local geology best. This is rather complex as one has to find a single scalar value that represents the usually anisotropic and heterogeneous subsurface. The investigations showed that a vertical permeability influences the spreading behavior more than a horizontal one. For buoyant flow, a harmonic averaging of the permeabilities of all geological units in the system is carried out. For the pilot study, this results in an effective permeability of 3.8 E 12 m 2, resulting in a Gr number of With the Gr number, the TRI can be estimated using Figure 12 at around 2.5 m. This value is twice as high as the number that the researcher from VEGAS initially estimated for the site. As a consequence, the cost estimate for the remediation is reduced from nearly 800,000 euro to 600,000 euro. The pilot test proved a TRI of almost 3 m, which is close to the one derived using the type curves. With the type curves, a method for determining the TRI in the screening stage and a sound basis for the cost calculation is provided. For the validation of the numerical model, the temperature measurements from the pilot field test and the simulated temperature distribution in the subsurface are compared. This is done using two dimensional plots of temperature versus depth for the thermocouples shown in Figure of 16

15 [44] Comparing the measurements with the results of the simulations shows a generally good agreement (see Figure 14). The simulated temperature distribution for TC7 and TC1, which are located in the vicinity of the injection well, match the field measurements for all time steps. The measurements for TC3 after 12 h indicate a slightly faster spreading of the steam zone than the one predicted by the model at a depth of 6 7 m BGS. This is probably the result of assigning a too low permeability to the model at this depth. Because of the fact that no measurements for TC5 below 5 m BGS are available, no statements about the degree of the fit can be made here at t = 36 h. Between 3 and 4 m BGS, the model predicts a lower temperature than that measured. This is caused by the Dirichlet boundary conditions used in the model that assume a constant temperature of K at the top. [45] With the model, the spreading behavior of the steam zone could be simulated in the runup to the pilot remediation. The results of the simulations match the measurements very well, except for minor variations caused, for example, by the Dirichlet boundary condition used on the top of the model. The high degree of conformity of the measured temperature distributions and the simulations could be used for the quantitative validation of the model. Besides this, the developed methods for predicting steam front propagation in saturated porous media were successfully tested. 8. Summary and Final Remarks [46] Two dimensional flume experiments and numerical studies with an improved model, which accounts for the variable degrees of freedom in the model domain, were used for developing methods that allow prediction of steam propagation during a subsurface remediation in the saturated zone. The experimental results indicate that the characteristics of steam front propagation are a distinct function of the q s /K ratio. For high q s /K ratios, a radial spreading at early times evolves into a more ovoid form later on. Small q s /K ratios result in a stronger vertical propagation because of dominating buoyancy effects. A series of numerical model runs was performed with the validated model aiming at the derivation of type curves that can describe the characteristic spreading behavior of steam in saturated porous media dependent on the dimensionless gravity number. These type curves allow an approximative prediction of the steam front in the screening stage of a project. Subsuming the major assumptions made for the derivation of the type curves results in the following comments. [47] 1. The type curves are derived for typical conditions commonly found during a steam injection for remediating contaminations in poorly layered aquifers (see section 7). [48] 2. The type curves are derived for homogenous systems. However, the pilot test example shows that for a poorly layered system with permeability differences less than 1 order of magnitude, an effective permeability leads to reasonable results. The same holds for anisotropic conditions. [49] 3. For strongly layered systems the applicability of the type curves is restricted to the vicinity of the well as long as the steam front does not reach a layer of distinctly different permeability. [50] 4. In remediation practice a point injection of steam below the target zone proved to be most suitable for the investigated system. Thus, the type curves are valid for such injection regimes where the height of the steam source is small compared to the total height of the aquifer. [51] 5. Saturation dependent effects of relative permeability are neglected as well as effects due to the extraction regime. [52] These simplifications were made to reduce the complexity of the method to a degree at which it gets manageable and can be used in engineering practice. However, the relevance of the type curves for practical application could be demonstrated for a field scale DNAPL remediation project. The type curves proved to be a simple while still reasonably accurate method of estimating the TRI. This is an important criterion for implementing the method to help establish steam injection as a remediation method in the saturated zone in practice. Beyond this, an improved and validated numerical model is provided that can be applied also for cases beyond the above mentioned limitations of the type curves. References Basel, M. D., and J. R. Udell (1989), Two dimensional study of steam injection into porous media, in Multiphase Transport in Porous Media, edited by K. S. Udell et al., pp , Am. Soc. Mech. Eng., New York. Betz, C. (1998), Wasserdampfdestillation von Schadstoffen in porösen Medien: Entwicklung einer thermischen in situ Sanierungstechnologie, Ph.D. thesis, Inst. fuer Wasserbau, Univ. Stuttgart, Stuttgart, Germany. Class, H., P. Bastian, and R. Helmig (2002), Numerical simulation of nonisothermal multiphase multicomponent processes in porous media. 1. An efficient solution technique, Adv. Water Resour., 25, Falta, R. W., K. Pruess, I. Javandel, and P. A. Witherspoon (1992a), Numerical modeling of steam injection for the removal of nonaqueous phase liquids from the subsurface: 1. Numerical formulation, Water Resour. Res., 28(2), Falta, R. W., K. Pruess, I. Javandel, and P. A. Witherspoon (1992b), Numerical modeling of steam injection for the removal of nonaqueous phase liquids from the subsurface: 2. Code validation and application, Water Resour. Res., 28(2), Färber, A. (1997), Wärmetransport in der ungesättigeten Bodenzone: Entwicklung einer thermischen in situ Sanierungstechnologie, Ph.D. thesis, Inst. fuer Wasserbau, Univ. Stuttgart, Stuttgart, Germany. Forsyth, P. A. (1993), A positivity preserving method for simulation of steam injection for NAPL site remediation, Adv. Water Resour., 16, Gudbjerg, J., T. O. Sonnenborg, and K. H. Jensen (2004a), Remediation of NAPL below the water table by steam induced heat conduction, J. Contam. Hydrol., 72, Gudbjerg, J., O. Trötschler, A. Färber, T. O. Sonnenborg, and K. H. Jensen (2004b), On spurious water flow during numerical simulation of stema injection into water saturated soil, J. Contam. Hydrol., 75, Gudbjerg, J., T. Heron, T. O. Sonnenborg, and K. H. Jensen (2005), Threedimensional numerical modeling of steam override observed at a fullscale remediation of an unconfined aquifer, Ground Water Monit. Rem., 25(3), Hunt, J. R., N. Sitar, and K. S. Udell (1998), Nonaqeous phase liquid transport and cleanup: 2. Experimental studies, Water Resour. Res., 24(8), Kopp, A., H. Class, and R. Helmig (2009), Investigations on CO 2 storage capacity in saline aquifers Part 1: Dimensional analysis of flow processes and reservoir characteristics, Int. J. Greenhouse Gas Control, 3, Kuhlmann, M. I. (2002), Analysis of the steam injection at the Visalia Superfund Project with fully compositional nonisothermal finite difference simulations, J. Hazard. Mater., 92, Ochs, S. O. (2006), Steam injection into saturated porous media: Process analysis including experimental and numerical investigations, Ph.D. thesis, Inst. fuer Wasserbau, Univ. Stuttgart, Stuttgart, Germany. (Available at stuttgart.de/opus/volltexte/2007/2971) Ochs, S. O., R. A. Hodges, R. W. Falta, T. F. Kmetz, J. J. Kupar, N. N. Brown, and D. L. Parkinson (2003), Predicted heating patterns during steam flooding of coastal plain sediments at Savannah River site, Environ. Eng. Geosci., 9(1), of 16