A method for quick assessment of CO2 storage capacity in closed and semi-closed saline formations

Saline aquifers of high permeability bounded by overlying/underlying seals may be surrounded laterally by low-permeability zones, possibly caused by natural heterogeneity and/or faulting. Carbon dioxide (CO₂) injection into and storage in such “closed” systems with impervious seals, or “semi-closed” systems with non-ideal (low permeability) seals, is different from that in “open” systems, from which the displaced brine can easily escape laterally. In closed or semi-closed systems, the pressure buildup caused by continuous industrial-scale CO₂ injection may have a limiting effect on CO₂ storage capacity, because geomechanical damage caused by overpressure needs to be avoided. In this research, a simple analytical method was developed for the quick assessment of the CO₂ storage capacity in such closed and semi-closed systems. This quick-assessment method is based on the fact that native brine (of an equivalent volume) displaced by the cumulative injected CO₂ occupies additional pore volume within the storage formation and the seals, provided by pore and brine compressibility in response to pressure buildup. With non-ideal seals, brine may also leak through the seals into overlying/underlying formations. The quick-assessment method calculates these brine displacement contributions in response to an estimated average pressure buildup in the storage reservoir. The CO₂ storage capacity and the transient domain-averaged pressure buildup estimated through the quick-assessment method were compared with the “true” values obtained using detailed numerical simulations of CO₂ and brine transport in a two-dimensional radial system. The good agreement indicates that the proposed method can produce reasonable approximations for storage–formation–seal systems of various geometric and hydrogeological properties.     

Assessing the economic feasibility of regional deep saline aquifer CO2 injection and storage: A geomechanics-based workflow applied to the Rose Run sandstone in Eastern Ohio, USA

Typical top-down regional assessments of CO₂ storage feasibility are sufficient for determining the maximum volumetric capacity of deep saline aquifers. However, they do not reflect the regional economic feasibility of storage. This is controlled, in part, by the number and type of injection wells that are necessary to achieve regional CO₂ storage goals. In contrast, the geomechanics-based assessment workflow that we present in this paper follows a bottom-up approach for evaluating regional deep saline aquifer CO₂ storage feasibility. The CO₂ storage capacity of an aquifer is a function of its porous volume as well as its CO₂ injectivity. For a saline aquifer to be considered feasible in this assessment it must be able to store a specified amount of CO₂ at a reasonable cost per ton of CO₂. The proposed assessment workflow has seven steps that include (1) defining the storage project and goals, (2) characterizing the geology and developing a geomechanical model of the aquifer, (3) constructing 3D aquifer models, (4) simulating CO₂ injection, (5,6) evaluating CO₂ injection and storage feasibility (with and without injection well stimulation), and (7) determining whether it is economically feasible to proceed with the storage project. The workflow was applied to a case study of the Rose Run sandstone aquifer in the Eastern Ohio River Valley, USA. We found that it is feasible in this region to inject 113 Mt CO₂/year for 30 years at an associated well cost of less than US $1.31/t CO₂, but only if injectivity enhancement techniques such as hydraulic fracturing and injection induced micro-seismicity are implemented.     

CO2SINK—From site characterisation and risk assessment to monitoring and verification: One year of operational experience with the field laboratory for CO2 storage at Ketzin, Germany

The CO₂SINK pilot project at Ketzin is aimed at a better understanding of geological CO₂ storage operation in a saline aquifer. The reservoir consists of fluvial deposits with average permeability ranging between 50 and 100 mDarcy. The main focus of CO₂SINK is developing and testing of monitoring and verification technologies. All wells, one for injection and two for observation, are equipped with smart casings (sensors behind casing, facing the rocks) containing a Distributed Temperature Sensing (DTS) and electrodes for Electrical Resistivity Tomography (ERT). The in-hole Gas Membrane Sensors (GMS) observed the arrival of tracers and CO₂ with high temporal resolution. Geophysical monitoring includes Moving Source Profiling (MSP), Vertical Seismic Profiling (VSP), crosshole, star and 4-D seismic experiments. Numerical models are benchmarked via the monitoring results indicating a sufficient match between observation and prediction, at least for the arrival of CO₂ at the first observation well. Downhole samples of brine showed changes in the fluid composition and biocenosis. First monitoring results indicate anisotropic flow of CO₂ coinciding with the “on-time” arrival of CO₂ at observation well one (Ktzi 200) and the later arrival at observation well two (Ktzi 202). A risk assessment was performed prior to the start of injection. After one year of operations about 18,000 t of CO₂ were injected safely.     

Analytical solution to evaluate salt precipitation during CO2 injection in saline aquifers

Carbon dioxide sequestration in deep saline aquifers is a means of reducing anthropogenic atmospheric emissions of CO₂. Among various mechanisms, CO₂ can be trapped in saline aquifers by dissolution in the formation water. Vaporization of water occurs along with the dissolution of CO₂. Vaporization can cause salt precipitation, which reduces porosity and impairs permeability of the reservoir in the vicinity of the wellbore, and can lead to reduction in injectivity. The amount of salt precipitation and the region in which it occurs may be important in CO₂ storage operations if salt precipitation significantly reduces injectivity. Here we develop an analytical model, as a simple and efficient tool to predict the amount of salt precipitation over time and space. This model is particularly useful at high injection velocities, when viscous forces dominate.First, we develop a model which treats the vaporization of water and dissolution of CO₂ in radial geometry. Next, the model is used to predict salt precipitation. The combined model is then extended to evaluate the effect of salt precipitation on permeability in terms of a time-dependent skin factor. Finally, the analytical model is corroborated by application to a specific problem with an available numerical solution, where a close agreement between the solutions is observed. We use the results to examine the effect of assumptions and approximations made in the development of the analytical solution. For cases studied, salt saturation was a few percent. The loss in injectivity depends on the degree of reduction of formation permeability with increased salt saturation. For permeability-reduction models considered in this work, the loss in injectivity was not severe. However, one limitation of the model is that it neglects capillary and gravity forces, and these forces might increase salt precipitation at the bottom of formation particularly when injection rate is low.     

Integration of counter-current relative permeability in the simulation of CO2 injection into saline aquifers

Carbon dioxide (CO₂) injection into saline aquifers is one of the promising options to sequester large amounts of CO₂ in geological formations. During as well as after injection of CO₂ into an aquifer, CO₂ migrates towards the top of the formation due to density differences between the formation brine and the injected CO₂. The time scales of CO₂ migration towards the top of an aquifer and the fraction of CO₂ that is trapped as residual gas depends strongly on the driving forces that are acting on the injected CO₂.When CO₂ migrates to the top of an aquifer, brine may be displaced downwards in a counter-current flow setting particularly during the injection period. A majority of the published work on counter-current flow settings have reported significant reductions in the associated relative permeability functions as compared to co-current measurements. However, this phenomenon has not yet been considered in the simulation of CO₂ storage into saline aquifers.In this paper we study the impact of changes in mobility for the two-phase brine/CO₂ system as a result of transitions between co- and counter-current flow settings. We have included this effect in a simulator and studied the impact of the related mobility reduction on the saturation distribution and residual saturation of CO₂ in aquifers over relevant time scales. We demonstrate that the reduction in relative permeability in the vertical direction changes the plume migration pattern and has an impact on the amount of gas that is trapped as a function of time. This is to our best knowledge the first attempt to integrate counter-current relative permeability into the simulation of injection and subsequent migration of CO₂ in aquifers. The results and analysis presented in this paper are directly relevant to all ongoing activities related to the design of large-scale CO₂ storage in saline aquifers.     

Petrophysical analysis to investigate the effects of carbon dioxide storage in a subsurface saline aquifer at Ketzin, Germany (CO2SINK)

To test the injection behaviour of CO₂ into brine-saturated rock and to evaluate the dependence of geophysical properties on CO₂ injection, flow and exposure experiments with brine and CO₂ were performed on sandstone samples of the Stuttgart Formation representing potential reservoir rocks for CO₂ storage. The sandstone samples studied are generally fine-grained with porosities between 17 and 32% and permeabilities between 1 and 100 mD.Additional batch experiments were performed to predict the long-term behaviour of geological CO₂ storage. Reservoir rock samples were exposed over a period of several months to CO₂-saturated reservoir fluid in high-pressure vessels under in situ temperature and pressure conditions. Petrophysical parameters, porosity and the pore radius distribution were investigated before and after the experiments by NMR (Nuclear Magnetic Resonance) relaxation and mercury injection. Most of the NMR measurements of the tested samples showed a slight increase of porosity and a higher proportion of large pores.     

Coupled hydromechanical modeling of CO2 sequestration in deep saline aquifers

Sequestration of carbon dioxide (CO₂) in deep saline aquifers has emerged as an option for reducing greenhouse gas emissions to the atmosphere. The large amounts of supercritical CO₂ that need to be injected into deep saline aquifers may cause large fluid pressure increases. The resulting overpressure may promote reactivation of sealed fractures or the creation of new ones in the caprock seal. This could lead to escape routes for CO₂. In order to assess the probability of such an event, we model an axisymmetric horizontal aquifer–caprock system, including hydromechanical coupling. We study the failure mechanisms, using a viscoplastic approach. Simulations illustrate that, depending on boundary conditions, the least favorable moment takes place at the beginning of injection. Initially, fluid pressure rises sharply because of a reduction in permeability due to desaturation. Once CO₂ fills the pores in the vicinity of the injection well and a capillary fringe is fully developed, the less viscous CO₂ displaces the brine and the capillary fringe laterally. The overpressure caused by the permeability reduction within the capillary fringe due to desaturation decreases with distance from the injection well. This results in a drop in fluid pressure buildup with time, which leads to a safer situation. Nevertheless, in the presence of low-permeability boundaries, fluid pressure continues to rise in the whole aquifer. This occurs when the radius of influence of the injection reaches the outer boundary. Thus, caprock integrity might be compromised in the long term.     

Laboratory calibration of the seismo-acoustic response of CO2 saturated sandstones

Ultrasonic experiments were undertaken on CO₂ flooded sandstone core samples, both synthetic sandstones and core plugs from the CRC1 CO₂ injection well in the Otway Basin, Victoria, South Eastern. Australia. The aim of these laboratory tests was to investigate the effects of CO₂ as a pore fluid on the seismo-acoustic response of the sandstone and ultimately to provide an indication of the sensitivity of time-lapse seismic imaging of the eventual CO₂/CH₄ plume in the Otway, Waarre C formation.The synthetic sandstones were manufactured using both a proprietary calcium in situ precipitation (CIPS) process and a silica cementing technique. Samples were tested in a computer controlled triaxial pressure cell where pore pressures can be controlled independently of the confining pressures. The pressure cell is equipped with ultrasonic transducers housed in the loading platens. Consequently, effective pressures equivalent to those expected in the reservoir can be applied while ultrasonic testing is undertaken. Both compressional, P and shear waves, S were recorded via a digital oscilloscope at a range of effective pressure steps. Pore pressures were varied from 4 MPa to 17 MPa to represent both the gaseous and liquid phase regions of the CO₂ phase diagram. Similar experiments were conducted on core plugs from the Waarre C reservoir horizon obtained from the CRC1 injection well, but with an intervening brine-saturated step and in some cases with a CO₂/CH₄ mix of 80%/20% molar fraction which is representative of the field situation. However, the pore pressure in these experiments was held at 4 MPa. Finally, acoustic impedances and reflection coefficients were calculated for the reservoir using Gassmann theory and the implications for imaging the CO₂ plume is discussed.     

The impact of heterogeneity on the distribution of CO2: Numerical simulation of CO2 storage at Ketzin

Numerical modelling of multiphase flow is an essential tool to ensure the viability of long-term and safe CO₂ storage in geological formations. Uncertainties arising from the heterogeneity of the formation and lack of knowledge of formation properties need to be assessed in order to create a model that can reproduce the data available from monitoring. In this study, we investigated the impact of unknown spatial variability in the petrophysical properties within a sandy channel facies of a fluviatile storage formation using stochastic methods in a Monte Carlo approach. The stochastic method has been applied to the Ketzin test site (CO₂SINK), and demonstrates that the deterministic homogeneous model satisfactorily predicts the first CO₂ arrival time at the Ketzin site. The equivalent permeability was adjusted to the injection pressure and is in good agreement with the hydraulic test. It has been shown that with increasing small-scale heterogeneity, the sharpness of the CO₂ front decreases and a greater volume of the reservoir is affected, which is also seen in an increased amount of dissolved CO₂. Increased anisotropy creates fingering effects, which result in higher probabilities for earlier arrival times. Generally, injectivity decreases with increasing heterogeneity.     

Monitoring of the microbial community composition in saline aquifers during CO2 storage by fluorescence in situ hybridisation

This study reveals the first analyses of the composition and activity of the microbial community of a saline CO₂ storage aquifer. Microbial monitoring during CO₂ injection has been reported. By using fluorescence in situ hybridisation (FISH), we have shown that the microbial community was strongly influenced by the CO₂ injection. Before CO₂ arrival, up to 6 × 10⁶ cells ml⁻¹ were detected by DAPI staining at a depth of 647 m below the surface. The microbial community was dominated by the domain Bacteria that represented approximately 60% to 90% of the total cell number, with Proteobacteria and Firmicutes as the most abundant phyla comprising up to 47% and 45% of the entire population, respectively. Both the total cell counts as well as the counts of the specific physiological groups revealed quantitative and qualitative changes after CO₂ arrival. Our study revealed temporal outcompetition of sulphate-reducing bacteria by methanogenic archaea. In addition, an enhanced activity of the microbial population after five months CO₂ storage indicated that the bacterial community was able to adapt to the extreme conditions of the deep biosphere and to the extreme changes of these atypical conditions.     

Seismic monitoring and modelling of supercritical CO2 injection into a water-saturated sandstone: Interpretation of P-wave velocity data

This paper reports on an integrated laboratory and numerical simulation study of ultrasonic P-wave velocity response to supercritical CO₂ displacement of pore water in Tako sandstone. The analysis of dynamic velocity data recorded using an array of piezoelectric transducers mounted on a core sample showed that the P-wave velocities at different positions displayed a similar trend in time, i.e., an initial sharp fall followed by a more gradual decline. Considerable variations observed in the measured P-wave velocity reductions across the sandstone core could largely be attributed to the final state of saturation (e.g. uniform, patchy or in-between) attained by the two-phase fluids. Numerical simulation of the injection test using a simple 1D model was carried out to provide an estimation of the phase saturation changes underlying the measured P-wave velocity reductions. A second order polynomial correlation between the measured ultrasonic P-wave velocity reductions and the estimated CO₂ saturation was established. Comparison with the Gassmann velocities showed that the empirically established relationship marks a clear deviation from both the patchy and uniform saturation velocity curves.     

Model prediction on the rise of pCO2 in uniform flows by leakage of CO2 purposefully stored under the seabed

A numerical study was conducted to predict pCO₂ change in the ocean on a continental shelf by the leakage of CO₂, which is originally stored in the aquifer under the seabed, in the case that a large fault connects the CO₂ reservoir and the seabed by an earthquake or other diastrophism. The leakage rate was set to be 6.025 × 10⁻⁴ kg/m²/sec from 2 m × 100 m fault band, which corresponds to 3800 t-CO₂/year, referring to the monitored seepage rate from an existing EOR field. The target space in this study was limited to the ocean above the seabed, the depth of which was 200 or 500 m. The computational domain was idealistically rectangular with the seabed fault-band perpendicular to the uniform flow. The CO₂ takes a form of bubbles or droplets, depending on the depth of water, and their behaviour and dissolution were numerically simulated during their rise in seawater flow. The advection–diffusion of dissolved CO₂ was also simulated. As a result, it was suggested that the leaked CO₂ droplets/bubbles all dissolve in the seawater before spouting up to the atmosphere, and that the increase in pCO₂ in the seawater was smaller than 500 μ atm.     

Modelling of CO2 arrival time at Ketzin – Part I

The injection of CO₂ at the Ketzin storage site and the chemical detection of its arrival in the observation well allowed testing of different numerical simulation codes. ECLIPSE 100 (E100, black-oil simulator), ECLIPSE 300 (E300, compositional CO₂STORE) and MUFTE-UG were used for predictive modelling applying a constant injection rate of 1 kg s^?1 CO₂ and for a history match applying the actual variable injection rate which ranged from 0 to 0.7 kg s^?1 and averaged 0.23 kg s^?1. The geological model applied, is based on all available geophysical and geological information and has been the same for all programs.The results of the constant injection regime show a good agreement among the programs with a discrepancy of 21–33% for the CO₂ arrival times. However, it is determined from the comparison of the cumulative mass of CO₂ at the time of CO₂ arrival that the injection regime is an important factor for the accurate prediction of CO₂ migration within a saline aquifer. Comparing the actual variable injection regime with the simulations applying a constant injection rate the results are relatively inaccurate.Regarding the actual variable injection regime, which was evaluated using all three simulators, the computational results show a good agreement with the data actually measured at the first observation well. Here, the calculated arrival times exceeded the actual ones by 8.1% (E100), 9.2% (E300) and 17.7% (MUFTE-UG).It can be concluded that irrespective of the deviations of the simulations, due to combinations of different codes and slight differences in input parameters, all three programs are well equipped to give a reliable estimate of the arrival of CO₂. Deviations in the results mainly occur due to different input data and grid size choices done by the different modelling teams working independently of each other. Deviations of the simulations results compared to the actual CO₂ arrival time result from uncertainties in the implementation of the geological model, which was set up based on well log data and analogue studies.     

CO2 transportation for carbon capture and storage: Sublimation of carbon dioxide from a dry ice bank

Climate change is being caused by greenhouse gases such as carbon dioxide (CO₂). Carbon capture and storage (CCS) is of interest to the scientific community as one way of achieving significant global reductions of atmospheric CO₂ emissions in the medium term. CO₂ would be captured from large stationary sources such as power plants and transported via pipelines under high pressure conditions to underground storage. If a downward leakage from a surface transportation system module occurs, the CO₂ would undergo a large temperature reduction and form a bank of “dry ice” on the ground surface; the sublimation of the gas from this bank represents an area source term for subsequent atmospheric dispersion, with an emission rate dependent on the energy balance at the bank surface. Gaseous CO₂ is denser than air and tends to remain close to the surface; it is an asphyxiant, a cerebral vasodilator and at high concentrations causes rapid circulatory insufficiency leading to coma and death. Hence a subliming bank of dry ice represents safety hazard. A model is presented for evaluating the energy balance and sublimation rate at the surface of a solid frozen CO₂ bank under different environmental conditions. The results suggest that subliming gas behaves as a proper dense gas (i.e. it remains close to the ground surface) only for low ambient wind speeds.     

Methodology for CO2 chain analysis

The paper presents a methodology for CO₂ chain analysis with particular focus on the impact of technology development on the total system economy. The methodology includes the whole CO₂ chain; CO₂ source, CO₂ capture, transport and storage in aquifers or in oil reservoirs for enhanced oil recovery. It aims at supporting the identification of feasible solutions and assisting the selection of the most cost-effective options for carbon capture and storage. To demonstrate the applicability of the methodology a case study has been carried out to illustrate the possible impact of technology improvements and market development. The case study confirms that the CO₂-quota price to a large extent influence the project economy and dominates over potential technology improvements. To be economic feasible, the studied chains injecting the CO₂ in oil reservoirs for increased oil production require a CO₂-quota price in the range of 20–27 €/tonne CO₂, depending on the technology breakthrough. For the chains based on CO₂ storage in saline aquifers, the corresponding CO₂-quota price varies up to about 40 €/tonne CO₂.     

Pipeline design for a least-cost router application for CO2 transport in the CO2 sequestration cycle

CO₂ capture and geological storage (CCS) is considered as a viable option to mitigate greenhouse gas emissions during the transition phase towards the use of clean and renewable energy. This paper concentrates on the transport of CO₂ between source (CO₂ capture at plants) and sink (geological storage reservoirs). In the cost estimation of CO₂ transport, the pipeline diameter plays an important role. In this respect, the paper reviews equations that were used in several reports on CO₂ pipeline transport. As some parameters are not taken into account in these equations, alternative formulas are proposed which calculate the proper inner diameter size based on flow rate, pressure drop per unit length, CO₂ density, CO₂ viscosity, pipeline material roughness and topographic height differences (the Darcy–Weisbach solution) and, in addition, on the amount and type of bends (the Manning solution). Comparison between calculated diameters using the reviewed and the proposed equations demonstrate the important influence of elevation difference (which is not considered in the reviewed equations) and pipeline material roughness-related factor on the calculated diameter. Concerning the latter, it is suggested that a Darcy–Weisbach roughness height of 0.045 mm better corresponds to a Manning factor of 0.009 than higher Manning values previously proposed in literature. Comparison with the actual diameter of the Weyburn pipeline confirms the accuracy of the proposed equations. Comparison with other existing CO₂ pipelines (without pressure information) indicate that the pipelines are designed for lower pressure gradients than 25 Pa/m or for (future) higher flow rates. The proposed Manning equation is implemented in an economic least-cost route planner in order to obtain the best economic solution for pipeline trajectory and corresponding diameter.     

Legal and regulatory challenges in the implementation of CO2 geological storage: An Alberta and Canadian perspective

Alberta is the province with the largest CO₂ emissions in Canada, with approximately two-thirds of emissions originating from large stationary sources. Due to the fortuitous association of large CO₂ sources with the storage capacity offered by the underlying Alberta basin, it is expected that large-scale CO₂ geological storage in Canada will occur in Alberta first, and both levels of governments are contemplating measures to facilitate implementation. A review of the current provincial and federal legislation and regulations presented in this paper indicates that the existing legal and regulatory regime is reasonably sufficient, with some modifications, to accommodate the active injection phase of CO₂ capture and storage (CCS) operations, and the early takers of this new technology. However, governments in Alberta and Canada, and likely everywhere, need to address several pressing issues dealing mainly with the CCS post-operational phase. These issues, reviewed in this paper from an Alberta and Canadian perspective, fall into several categories: jurisdictional, property (ownership), regulatory and liability. Because Alberta is a landlocked province, matters relating to CO₂ storage under the seabed will not be addressed here except when discussing matters of jurisdiction and CO₂ classification. Possible models for post-injection liability transfer to the state are also presented. Although this review is focused on western Canada conditions, the issues are broad enough to be of interest in other jurisdictions, which may also adopt parts of the legal and regulatory framework that is quite well developed in Alberta.     

Dynamis CO2 quality recommendations

In the carbon capture and storage (CCS) chain, transport and storage set different requirements for the composition of the gas stream mainly containing carbon dioxide (CO₂). Currently, there is a lack of standards to define the required quality for CO₂ pipelines. This study investigates and recommends likely maximum allowable concentrations of impurities in the CO₂ for safe transportation in pipelines. The focus is on CO₂ streams from pre-combustion processes. Among the issues addressed are safety and toxicity limits, compression work, hydrate formation, corrosion and free water formation, including the cross-effect of H₂S and H₂O and of H₂O and CH₄.     

Dissolution of a CO2 lake, modeled by using an advanced vertical turbulence mixing scheme

The dissolution of CO₂ from a CO₂ lake with and without a hydrate layer, located at a flat bottom at 3000 m depth has been modeled using the MIT General Circulation Model coupled with the General Ocean Turbulence Model (GOTM). The vertical turbulent mixing scheme takes into account density effects and should give more realistic results for the CO₂ plume than previously used constant eddy diffusivity models. The introduction of a third direction gives qualitatively different results for the spreading of the CO₂ plume than previous 2D results. The dissolution rate and near field dissolved CO₂ concentrations approach a steady state for a given far field ocean current within less than a day. The dissolution rate is highly dependent on the velocity of the ambient current and is reduced with 1.6 when a hydrate layer is introduced.     

Comparison of several packings for CO2 chemical absorption in a packed column

CO₂ capture and storage has gained widespread attention as an option for reducing greenhouse gas emissions. Chemical absorption and stripping of CO₂ with hot potassium carbonate (K₂CO₃) solutions has been used in the past, however potassium carbonate solutions have a low CO₂ absorption efficiency. Various techniques can be used to improve the absorption efficiency of this system with one option being the addition of promoters to the solvent and another option being an improvement in the mass transfer efficiency of the equipment. This study has focused on improving the efficiency of the packed column by replacing traditional packings with newer types of packing which have been shown to have enhanced mass transfer performance. Three different packings (Super Mini Rings (SMRs), Pall Rings and Mellapak) have been studied under atmospheric conditions in a laboratory scale column for CO₂ absorption using a 30 wt% K₂CO₃ solution. It was found that SMR packing resulted in a mass transfer coefficient approximately 20% and 30% higher than that of Mellapak and Pall Rings, respectively. Therefore, the height of packed column with SMR packing would be substantially lower than with Pall Rings or Mellapak. Meanwhile, the pressure drop using SMR was comparable to other packings while the gas flooding velocity was higher when the liquid load was above 25 kg m⁻² s⁻¹. Correlations for predicting flooding gas velocities and pressure drop were fitted to the experimental data, allowing the relevant parameters to be estimated for use in later design.