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From time-lapse seismic inversion to history matching of water flooded oil reservoirs
The world energy demand still increases every year. As a consequence, the demand for fossil fuels, by far the first energy source, is increasing, while easily accessible fossil fuel resources are decreasing. This has stimulated research and development to the optimization of hydrocarbon recovery from existing reservoirs over the last decade. Waterflooding for enhanced oil recovery is one approach to increase the recovery of an oil reservoir.
In this thesis the monitoring of waterflooding using time lapse seismic data in combination with production data is used to improve the representative flow models of the reservoir. Such models are then used to optimize production strategies.
When constraining a reservoir model to observations, the measurement uncertainty plays a key role. The first part of this thesis is dedicated to developing an inversion methodology leading to more accurate estimates of changes in saturation and pore pressure induced by waterflooding from 4D seismic data.
Waterflooding processes induce time-lapse changes in reservoir fluid saturation and in pore pressure. These are reflected in 4D variations of seismic attributes like changes in amplitudes and time-shifts.
The improvement of the proposed 4D seismic inversion method resides in a more correct, and possibly unbiased, estimate of time-lapse changes in saturation and pore pressure. Existing methods often suffer from bias and leakage between the different estimated parameters. By making use of different combinations of time-lapse seismic attributes based on four equations: two expressing changes in pre-stack AVO attributes (zero-offset and gradient reflectivities), and two expressing post-stack time-shifts of compressional and shear waves as functions of production induced changes in fluid properties, the estimates can be considerably improved.
The impact of using different combinations of these equations is tested on a synthetic, though realistic 3D model, where seismic data have been simulated at various steps during the 30 years lifetime of the waterflooded reservoir.
Results show that the inversion accuracy increases if higher order terms in the description of the P-wave gradient reflectivity are not neglected, or if, in case S-wave data are available, the S-wave time-shift equation replaces the equation related to the P-wave gradient reflectivity. As in all inversion methods, the influence of prior porosity estimates remains very high and results improve considerably, in case lateral variations of porosity are properly taken into account.
The effect of noise on the inversion results is also investigated, with the conclusion that the method seems to be quite robust to random noise, while the introduction of systematic noise decreases the inversion accuracy more severely.
The second part of this thesis is dedicated to the investigation of the possibilities to obtain an accurate model characterization, particularly in terms of flow, through the assimilation of seismic measurements with the Ensemble Kalman Filter.
The mathematical process which identifies the parameter values that minimize a cost-function representing the mismatch between modeled and observed data is called Data Assimilation (or History Matching). In Data Assimilation, parameter estimations for the entire reservoir model, are often based only on the information related to sparsely distributed production data. It is obvious that in such a case the number of observations is much smaller than the number of parameters to estimate, making history matching a strongly ill-posed problem. The additional information acquired from (time-lapse) seismic data can be utilized to narrow the solution space down when minimizing the misfit between gathered measurements and their forecasts from numerical models.
Although in literature numerous data assimilation methods have been presented, in this thesis the Ensemble Kalman Filter has been chosen for several reasons. Firstly, the method is computationally feasible for large systems and is relatively simple to implement making use of existing simulators. Secondly, it presents a flexible treatment of any kind and number of data or uncertain parameters. Thirdly, this method has a large and active research community, and a rigorous theoretical basis.
This thesis proposes two innovative approaches to assimilate seismic measurements with the Ensemble Kalman Filter.
The first approach concerns the assimilation of time-lapse changes in fluid saturation and pore pressure available for every reservoir gridblock. This method builds directly on the results of the first part of this thesis. In this case the number of observations to assimilate can be very high, causing the problem of ’filter divergence’. Filter divergence is a consequence of an excessive reduction of ensemble parameter covariance.
The most effective method to circumvent this problem is Covariance regularization through Localization. This approach consists of multiplying the ensemble covariances element-wise by a local support matrix, resulting in a localized covariance estimate. For a correct application, localization requires the knowledge of the real covariance between measurements and states/parameters to update. Through a 2D synthetic study rules of thumb for the definition of adequate localization functions have been determined. Afterwards these rules have been successfully applied on a 3D reservoir.
The second approach of seismic data assimilation is based on the assimilation of fluid front arrival times. The major advantage of the method is, that no full inversion of seismic data to saturations for each grid block is required. The focus is only on the fronts, where changes in time lapse seismic response can be observed. In this case saturation data, impedance maps, or even simple amplitude change maps can be assimilated as waterfront arrival times.
This approach enables a very large reduction in number of data while retaining the essential information content. Furthermore, it offers a more linear sensitivity to reservoir properties and a more Gaussian distribution of simulated measurements than using saturation data. This tends to improve the functioning of the EnKF, which represents a multi-model history match that incorporates and retains geological information formulated in terms of two-point geostatistics.
This method has also been successfully applied on a slightly modified version of the benchmark Brugge field, a synthetic study reflecting to a great extent the complexity of a real field.
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The Effect of Porefill on Pre- and Post-stack Seismic Data in a Dutch Buntsandstein Reservoir
Wintershall is operating a number of Buntsandstein fields in the Southern North Sea. It has proven a major exploration challenge in the area to predict the reservoir quality of these fields based on seismic data only. The effect of salt present in the area plugging the pore space leads at first sight to similar seismic responses on post-stack data as for gas filled reservoirs. This study aims to gain better insight into the (subtle) differences in seismic response induced by water-, gas- or salt-fill scenario. The approach adopted is by studying the seismic response at various existing wells in one of the fields and the corresponding seismic responses of the processed 3D seismic survey. First a thorough analysis of the log responses of 13 wells is made and the effect of a.o. depth trends, compaction, diagenesis and facies changes to the seismic response is qualitatively investigated. Then, a match between the log data and the poststack seismic data is established by creating synthetic seismic data. Finally by using fluid substitution and more recent solid substitution theory, subtle changes in seismic response, both pre-stack and post-stack, between the different porefills are predicted. Based on these modeled predictions recommendations are made concerning the type of data analysis that should be carried out to discern the different porefills on the seismic data. The results of this research should lead to an improved characterization of the Buntsandstein reservoirs and as a consequence, to a higher success rate in drilling (i.e. less “dry wells”).
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Gravity observations for hydrocarbon reservoir monitoring
In this thesis the added value of gravity observations for hydrocarbon reservoir monitoring and characterization is investigated. Reservoir processes and reservoir types most suitable for gravimetric monitoring are identified. Major noise sources affecting time-lapse gravimetry are analyzed. The added value of gravity data for reservoir monitoring and characterization is analyzed within closed-loop reservoir management concept. Synthetic 2D and 3D numerical experiments are performed where various reservoir parameters, like permeability, porosity, reservoir structure, and aquifer characteristics, are updated using gravity and reservoir production data assimilation.
The results show that history matching a gas field with pressure data only may provide highly non-unique solutions because several parameter combinations can explain the reservoir pressure behavior observed in the wells. Therefore, additional information is needed which can be provided by time-lapse gravimetry. It is demonstrated that a joint assimilation of pressure and gravity data can provide more constrained inverse solutions and result not only in improved gas and water production forecast, but also can give more accurate reservoir reserves evaluation and reservoir state description.
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Quantifying Seismic Time-Lapse Effects of Solution Salt Mining - A Feasibility Study
In the northern part of the Netherlands the (magnesium containing) salt minerals carnallite and bischofite are extracted using solution mining methods, such as squeeze mining. As a consequence subsidence up to the surface is taking place, potentially causing harm to the environment. Given this fact the local government allows extraction of this salt under the condition that subsidence at the surface does not exceed a pre-defined limit. This makes the importance of salt mining induced subsidence evident. For an accurate prediction the 3-D characteristics of the caverns are important. Currently it is impossible to predict what effect squeeze mining has on the characteristics of the caverns, and thus on the subsidence.
This thesis addresses the question whether time-lapse seismic reflection techniques can be used to image and quantify the effects of mining magnesium salt in the north of The Netherlands. The use of seismic time-lapse techniques to indentify produced salt zones has not been investigated before and this study must be considered as a feasibility study, using synthetic seismic data. The questions addressed in this thesis are:
• Can the effects of solution salt mining be detected in seismic time-lapse mode?
• If so, can these effects be quantified?
In our approach we studied the time-lapse effects of different scenarios; representing a vertical and a lateral extension of the mine due to salt production have been evaluated. These scenarios have been transformed into different subsurface models that were an input to an acoustic and elastic finite difference scheme in order to create synthetic data. The geometric and material properties in the scenarios are based on the interpretation of real seismic data. A combination of well data and empirical relations has been used to derive the necessary seismic parameters.
The main findings can be summarized as:
1) A seismic reflection of the salt mine is visible in seismic shot records, CMP-gathers and migrated sections. The exact geometry of the mine cannot be distinguished in the data, because of interference effects.
2) To derive time-shifts and amplitude changes caused by geometry and property changes in seismic time-lapse mode, 2-D cross correlation on migrated data was used. This technique allows deriving a horizontal shift as well as a time-shift. The amplitude changes were calculated by comparing the amplitude maximum from a 2-D cross correlation window with the maximum amplitude from a 2-D auto correlation window. The difference is expressed as a percentage.
3) A vertical extension of 5 m causes a potentially detectable time shift of 1.5 ms for the acoustic case and 2.0 ms for the elastic case. The amplitude changes are respectively 5.3% and 7.1%. For a purely lateral extension of 100 m of the caverns no time shift is found for the acoustic and elastic case and the amplitude change is 0.2% and 2.0% respectively. These results show that the amplitude change caused by a vertical extension is significantly higher than the one caused by a lateral extension of the mine. In order to make lateral changes of the salt mine visible one could opt for 1-D cross correlation. The time shifts and amplitudes found are comparable as those found in literature for the oil and gas industry.
The final conclusion yields that the effects of solution salt mining can be detected and quantified in seismic time-lapse mode. Some effects in this seismic study are large enough to be seen in real seismic data. It is therefore feasible to use time-lapse seismic to monitor geometric and material changes of an underground solution salt mine.
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Borehole radar for oil production monitoring
The area of smart well technology, or closed-loop reservoir management, aims at enhancing oil recovery through a combination of monitoring and control. Monitoring is performed with a wide range of sensors deployed downhole or at the surface. These sensors allow for capturing changes in the reservoir conditions, mainly the fluid movement, at different resolutions. Downhole sensors give information of the fluid entering the well and sample only the region immediately adjacent to the well. Reservoir-imaging techniques are based on downhole or surface sensors and image large reservoir volumes typically with a resolution at the ten meter scale. Control is performed by installation of downhole flow control devices that can regulate the fluid inflow from the reservoir into the well ranging from on/off to a large number of settings. Combining monitoring and inflow technology allows using control strategies that mitigate undesired events such as premature water or gas breakthrough. Premature breakthrough of undesired fluids can reduce drastically the oil production and may cause the production well to be shut down. Generally the near-well region in the order of ten meters is poorly imaged. However, in specific reservoir environments the monitoring of the near-well region is strongly required. For example, thin oil rim reservoirs usually have a thickness in the order of few tens of meters and are characterized by early water breakthrough in individual segments of the well. Steam Assisted Gravity Drainage (SAGD) is an enhanced oil recovery technique used in heavy oil reservoirs, where oil is extremely viscous and steam injection is used to facilitate the oil flow. A pair of horizontal wells is drilled into the reservoir only a few meters apart to allow for steam injection and oil production; however, the steam chamber growth and the oil flow are largely unknown. In both these examples a better understanding of the oil displacement process in the first ten meters from the production well could help preventing early breakthrough of unwanted fluids and allow for an implementation of more effective control strategies.
We have investigated radar technology as a potential tool able to cover the monitoring requirements needed in specific oilfield environments. This feasibility study was carried out through numerical modeling and laboratory experiments.
Through the numerical simulations we conclude that a borehole radar system can be used as a monitoring tool to probe the near-well region of several meters. The main constraint is the formation water electrical conductivity; high conductivity makes attenuation and phase distortion too high for wave propagation. Water/steam front reflections are detectable in low conductivity reservoirs (σ < 0.02 S/m). A system performance above 80 dB is necessary to detect reflections in the range of 10 m (chapters 2-3).
Additional reservoir constraints are given by a high degree of time-lapse heterogeneity changes of the EM properties and the length of the transition zone from oil to water bearing rocks. The effects of changes in the reservoir can be solved by increasing the data acquisition frequency relative to the rate of the local temporal changes. A gradual transition zone reduces the water reflections, which are not detectable when the transition is in the order of the dominant wavelength of the EM signal (chapters 2-3).
Numerical simulations were performed for both simple and complex geological scenarios. A sophisticated analysis was performed coupling electromagnetic and reservoir simulations. This allowed to evaluate the GPR performance in a realistic reservoir environment. Plotting the amplitude of the two-way-time reflected signal as the water advances toward the production well, where the radar system was located, appeared in clear up-dipping events (chapter 3).
The metal components of the wellbore casing can destructively interfere with the signal emitted by the radar sensor; however a high dielectric medium around the sensor can increase the amplitude of the reflected signal and overcome the interference problem (chapter 2).
Through the laboratory experiments we conclude general considerations on the GPR ability in monitoring oil displacement process governed by water.
Water was injected in a meter-scale sand box and all the water flooding experiments presented similar characteristics. As for the modeling results, the amplitude of the two-way-time reflected signal as a function of the experiment time resulted in up-dipping events ascribable to the water front advance. According to the initial water saturation and porosity distribution continuous down-dipping events were associated to the up-dipping ones, forming wedgeshaped reflection features. The monitoring of the flow reflection features could be supported by attribute analysis, in particular, instantaneous frequency demonstrated to be a powerful tool to enhance wedge-shaped events.
The analysis of the GPR data agreed with impedance measurements taken simultaneously during the water flooding experiments. The main limitation to the GPR monitoring potential is the electrical conductivity of the residual water. The experiments at a high salinity water injection showed a strong
attenuation of the signal and a reduction of the resolution (chapter 4).
Through an analysis of measured and modeled GPR signal it was possible to take in consideration the effect of uncertainties on subsurface characterization through full-waveform inversion. Subsurface characterization through full-waveform inversion relies heavily on the accuracy with which the forward model represents the actual GPR-subsurface system. Model errors can propagate through the inversion procedure resulting in wrong parameter estimates.
The relative errors in the measured Green’s function are mainly determined by the antenna transfer functions uncertainties. Averaging over a large number of transfer function sets leads to a high-accuracy Green’s function estimate from the data, which leads to small errors in the estimated parameters obtained from full-waveform inversion. Provided the measurement conditions are respected, the inversion experiment adequately reproduces the estimated parameters. As soon as the measurement conditions are not completely respected, e.g., presence of extraneous objects, inversion experiments indicated that the accuracy of the estimates improves when calibration measurements to determine the transfer functions are acquired as close as possible to the measurement location (chapter 5).
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4D seismic reservoir characterization,
integrated with geo-mechanical modelling
Hydrocarbon production induces time-lapse changes in the seismic attributes (travel time and amplitude) both at the level of the producing reservoir and in the surrounding rock. The detected time-lapse changes in the seismic are induced from the changes in the petrophysical properties of the rock, i.e. (visco-)elastic constants as a consequence of saturation, porosity, and stress-strain changes, and by direct changes in the layer-thickness due to compaction or elongation. Usually the production effects in the surrounding rock and the effect of changes in the layer thickness are neglected, which can lead to misinterpretation of the recorded time-lapse information.
In this study we have first investigated how large each of these effects can be and what factors have the main influence. To this end we have developed different synthetic models, for which the parameters have been based on a real field cases. In more detail we adopted the following steps to investigate the time-lapse changes in the stress field both in the reservoir and in the surrounding rock for different scenarios:
- We developed a petrophysical model of hydrocarbon-saturated sandstone reservoir, based on the Hertz-Mindlin contact theory, to investigate the time-lapse changes in the seismic parameters (velocities and density) following from 4D changes in the rock parameters. The influence of the different rock properties and environmental conditions (pore pressure, water saturation and porosity) on the seismic parameters inside the reservoir has been investigated. As expected it was demonstrated that the hydrocarbon substitution by water causes an increase in the aforementioned seismic parameters, whereas an increase in the porosity and pore pressure will decrease the values of these parameters.
- We developed three different geo-mechanical models based on the
North Sea reservoirs and ran several scenarios with each of the models
to understand the development of the stress and strain fields as result
of production.
-- The first model consisted of a 2D layer-cake model and has been
used to investigate the stress distribution and vertical strain in the reservoir and in the surrounding rocks. We observed that the
distribution of the stress changes in the surrounding rock depends
on the elastic properties of the reservoir and surrounding media and is linked to the lateral boundaries between the reservoir and the surrounding rock.
-- The second model was also a layer cake model, but now with parameters and layering based on the gas field Shearwater. This model has also been used to investigate the effect of offset on the development of the time-shifts.
-- The third and final model considered of a 2D model now also
with the geometry of the gas field Shearwater. In that model we ran several scenarios changing the shape and the depleting segments of the reservoir in order to investigate their influence on the stress distribution and vertical strain.
Overall we concluded that the main factors influencing the changes
in the stress distribution and vertical displacement in a depleting gas
reservoir are: 1) the distribution and the magnitude of the pressure drop in the reservoir, 2) the geometrical shape of the reservoir and the overlaying rocks, 3) the presence of faults, and 4) the elastic properties
of the layers.
We investigated the time-shift variation as a function of offset using the second geo-mechanical model. We created synthetic time-lapse seismic data for a simple 2D model. This was done by combining the results of the geomechanical modelling with the time-shifts representative for the Shearwater data, given in the literature. We measured the time-shifts from the synthetic 4D data for different stacks in order to find the optimal value of signal-to-noise ratio without violating the requirement for vertical travel paths. From the case study we concluded that the near offset partial stack (500-1300 m) can be used in the real data example to give reliable results of the measured time-shifts.
As a second step in this study we introduced a new workflow in order to separate the effect of the changes in petrophysical properties and environmental conditions in the surrounding and reservoir rock and the physical displacement of the layers. The proposed workflow has been applied to the Shearwater 4D seismic data. The following steps have been taken:
- We measured the time-shifts using 4D data from the Shearwater field. The differences in the two-way travel time at the main reflectors were estimated and stabilized using vertical stacks of estimated time-shifts around the interfaces in order to reduce the effect of multiple reflections. Further the time-shifts are smoothed using a lateral median filter to remove the effect of the outliers, and time-shifts horizontal maps are produced for each of the main reflectors.
- We calculated the differential time-shifts in each of the geological layers using the relative ratio between the measured time-shifts at the
top and at the bottom of the layers. We used the results from the 2D
geo-mechanical modelling (vertical strain) to remove the time-shifts
caused by changes in the displacement of the layers. We observed that
the calculated differential time-shifts follow accurately the modelled
changes in the stress field for the seismic 2D line which corresponds
to the geo-mechanical model.
We concluded that the results of geo-mechanical modelling can be effectively used to eliminate the effect of displacement from the measured timeshifts. The resulting time-shifts are thus induced by changes in the seismic velocity. Furthermore, the changes in the seismic velocity are consequence of changes in the petrophysical properties and environmental conditions. This allows us to use the calculated differential time-shifts to map directly the changes in the stress field. In the Shearwater field the effect of physical displacement appeared to be negligibly small for the selected 2D line, where the geo-mechanical modelling has been applied. Furthermore, we demonstrated that the calculated changes in the seismic velocity follow
accurately the modelled stress field variations. We used the inverse relation ship between the modelled stress changes and the calculated time-shifts (induced by velocity changes) to define the changes in the vertical stress over the entire field. We conclude that the stress changes in and around a depleting hydrocarbon reservoir will always induced changes in the seismic velocity. As demonstrated in this example the correlation between the two allows an estimation of changes in the petrophysical properties and in the environmental conditions from observed velocity changes.
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