P.A. Fokker

Pipe viscometry of foams

This paper describes a method for extracting useful information from small‐scale pipe viscometer measurements of foam rheology. The rheology of a foamed polymer solution at a given temperature, pressure, and quality was determined in pipes of five diameters. The flow curves showed a marked dependence on the diameter of the pipe. The concept of apparent slip could be used to explain the phenomenon. The classical slip correction of Mooney was not applicable, but the method developed by Jastrzebski (based on the previous work of Oldroyd) provided a consistent means of apparent slip correction. The geometric interpretation of the two slip correction methods revealed the possible reason for the difference of their performance. The slip corrected measurements were interpreted in the framework of the volume equalization principle.

General Anisotropic Effective Medium Theory for the Effective Permeability of Heterogeneous Reservoirs

One of the techniques to calculate the effective property of a heterogeneous medium is the effective medium theory. The present paper presents a general mathematical formulation for the effective medium approximation using a self-consistent choice of the effective permeability, to apply it to the case of a general anisotropic 2D medium and to the case of a 3D isotropic medium with randomly oriented ellipsoidal inclusions. The 2D results are compared with analytical results and with a homogenization technique with good result. The 3D correlations are used to derive percolation thresholds in two-phase systems with a large permeability contrast, which are compared to numerical results from the literature, also with good results.

The effective subsidence capacity concept: How to assure that subsidence in the Wadden Sea remains within defined limits?

Subsidence caused by extraction of hydrocarbons and solution salt mining is a sensitive issue in the Netherlands. An extensive legal, technical and organisational framework is in place to ensure a high probability that such subsidence will stay within predefined limits. The key question is: how much subsidence is acceptable and at which rate? And: how can it be reliably assured that (future) subsidence will stay within these limits? To address the issue for the Wadden Sea area, the concept of ‘effective subsidence capacity’ is used. To determine the ‘effective subsidence capacity’, the maximum volumetric rate of relative sea-level rise, that can be accommodated in the long term, without environmental harm, is established first. The volume of sediment that can be transported and deposited by nature into the tidal basin where the subsidence is expected, ultimately determines this ‘limit of acceptable average subsidence rate’. The capability of the tidal basins to ‘capture’ sediment over the lunar cycle period of 18.6 years is the overall rate-determining step. Effective subsidence capacity is then the maximum average subsidence rate available for planning of human activities. It is obtained by subtracting the subsidence volume rate ‘consumed’ by natural relative subsidence in the area (sealevel rise plus natural shallow compaction) from the total long-term acceptable subsidence volume rate limit. In the operational procedure for mining companies, six-years-average expectation values of subsidence rates are used to calculate the maximum allowable production rates. This is done under the provision that production will be reduced or halted if the expected or actual subsidence rate (natural + man induced) is likely to exceed the limit of acceptable subsidence. Monitoring and management schemes ensure that predicted (6-year average) and actual (18.6-year average) subsidence rates stay within the limit of acceptable subsidence rate and that no damage is caused to the protected nature. A GPS based early warning system is used for early detection of unexpected behaviour. In support of SSM (State Supervision of Mines, the government regulator), TNO-AGE (an independent government advisory group) applies an independent Bayesian statistical analysis of all data, as they become available, to calculate the probability of scenario’s under which future subsidence will exceed the defined limits. It is external to the operator’s annual measurement and control loop and ensures that preventive actions can be taken in time in case such scenarios emerge. Regular communication keeps the authorities and the general public informed on the use of the effective subsidence capacity to demonstrate that the actual average subsidence rate stays strictly within the defined bounds and that, from a scientific point of view, there is no reasonable doubt that damage to the tidal system will not occur now or in the future.

Inversion of double-difference measurements from optical leveling for the Groningen gas field

Hydrocarbon extraction leads to compaction of the gas reservoir, which is visible on the surface as subsidence. Subsidence measurements therefore give information on the hydrocarbon extraction and can thus be used to better estimate uncertain reservoir parameters. Normally, optical height difference measurements are taken between benchmarks, adjusted and tested to arrive at estimated height differences (or subsequently, heights relative to a reference benchmark) and are differenced between epochs to arrive at subsidence estimates. These can subsequently be used in inversions for reservoir parameters. We have designed, implemented and applied a new algorithm that uses measured optical height differences directly in the geophysical inversion. This eliminates the problems introduced by insufficient knowledge of the full covariance matrix of the subsidence estimates. The procedure was applied to invert for compaction of the Groningen gas reservoir in the Netherlands. We used a linear inversion procedure to update an existing reservoir compaction field. This yielded areas of increased and reduced compaction relative to the existing compaction field, which correspond with observed discrepancies in porosity and aquifer activity.

Applications of Harmonic Pulse Testing to Field Cases

Harmonic pulse testing is a well testing technique in which the injection or production rate is varied in a periodic way. The pressure response to the imposed rates, both in the pulser well and in the observer wells, can be analyzed in the frequency domain to evaluate the reservoir properties. The advantages of this type of test are that dedicated well testing surface equipment is not required and that the test can be performed during ongoing field operations. In an earlier study we demonstrated that the harmonic pulse testing methodology can be used to evaluate the effective permeability to hydrocarbons and the reservoir total compressibility even for such a heterogeneous case as in a water injection scenario. The analysis can be performed using a numerical simulator in the Fourier domain, by which heterogeneities can be explicitly taken into account. As time-stepping is not required in such a simulation, calculations are much faster than calculations in the time domain. In the present paper we report on the application of the methodology to two field cases. The first case is a gas storage reservoir, operated with a day-night injection-shut in scenario. Data analysis proved that the reservoir was homogeneous and that a minor fault identified by the seismic was not hindering hydraulic communication between the pulser and the observer wells. The second case is a set of harmonic test experiments on three groundwater wells, the details of which have been published earlier together with a first attempt to interpret the data. The previous analysis was based on the hypothesis of homogeneous formation, but could not consistently explain all the measurements. With our novel methodology it was possible to investigate the effects of heterogeneity and we demonstrated that the presence of a fault zone with reduced permeability may explain the observations.

Vaporization of fault water during seismic slip

Laboratory and numerical studies, as well as field observations, indicate that phase transitions of pore water might be an important process in large earthquakes. We present a model of the thermo-hydro-chemo-mechanical processes, including a two-phase mixture model to incorporate the phase transitions of pore water, occurring during fast slip (i.e., a natural earthquake) in order to investigate the effects of vaporization on the coseismic slip. Using parameters from typical natural faults, our modeling shows that vaporization can indeed occur at the shallow depths of an earthquake, irrespective of the wide variability of the parameters involved (sliding velocity, friction coefficient, gouge permeability and porosity, and shear-induced dilatancy). Due to the fast kinetics, water vaporization can cause a rapid slip weakening even when the hydrological conditions of the fault zone are not favorable for thermal pressurization, e.g., when permeability is high. At the same time, the latent heat associated with the phase transition causes the temperature rise in the slip zone to be buffered. Our parametric analyses reveal that the amount of frictional work is the principal factor controlling the onset and activity of vaporization and that it can easily be achieved in earthquakes. Our study shows that coseismic pore fluid vaporization might have played important roles at shallow depths of large earthquakes by enhancing slip weakening and buffering the temperature rise. The combined effects may provide an alternative explanation for the fact that low-temperature anomalies were measured in the slip zones at shallow depths of large earthquakes.

Joint History Matching of Well Data and Surface Subsidence Observations Using the Ensemble Kalman Filter: A Field Study

The number of reported applications of the Ensemble Kalman Filter (EnKF) for history matching reservoir models is increasing steadily for various reasons. Here, we report on exploiting the capability of EnKF to handle observations from different sources simultaneously. While traditionally only well data are matched, we use surface subsidence observations together with well data. Surface subsidence results from compaction of the reservoir rock through the mechanical response of the subsurface. Compaction is caused by decreasing pore pressures during reservoir depletion. Therefore, the subsidence data contains information about dynamic pressure distributions in the reservoir. The joint history matching of well data and surface subsidence observations was applied to the Roswinkel gas field. This field has been operated for 25 years, during which nine leveling campaigns generated a valuable data set of subsidence data. An important feature of the reservoir was the uncertainty about its compartmentalization, due to a large number of possibly sealing faults in the anticlinal structure. Therefore, instead of uncertain rock properties, fault transmissibilities were estimated in this study. In a previous study on Roswinkel, a compaction field was estimated by inverting subsidence measurements. The results indicated several sealing faults in the reservoir, dividing the field into different compartments with independent pressure histories. The post-inversion history match of production data, however, was unsatisfactory. We have now been able to show that estimating the driving parameters, in casu the fault transmissibilities in the reservoir, can be achieved in a consistent way with both production and surface subsidence data for a synthetic case. Furthermore, for the actual Roswinkel case, the joint history match clearly reveals the discreapancy between the data from both sources and the current reservoir simulation model. The joint history match of land surface movement data together with well production data is a success for EnKF as a flexible method for history matching. But more importantly, it demonstrates the potential of using complementary sources of information for improved reservoir characterization, and the possibility of estimating the driving parameters. Copyright 2011, Society of Petroleum Engineers.

Data Assimilation of PS-InSAR Movement Measurements Applied to the Bergermeer Gas Field

This paper reports a study on the use of satellite radar data to constrain the subsurface model parameters of the Bergermeer gas field. Using PSI (Persistent Scatterer InSAR) technology, ascending and descending data were applied in line-of-sight geometry, i.e., without first unravelling the horizontal and vertical components of the signal. The model parameters were constrained using an ensemble smoother with multiple data assimilation. A good match could be obtained with realistic values of the reservoir compaction coefficient and of the subsurface basement elastic modulus. For the aquifer parts that were depleted according to the reservoir simulation, the northern part indeed gave a reasonable value for the compaction coefficient. For the southern part the resulting compaction coefficient was around zero, indicating that the pressure depletion in this part of the aquifer was overestimated and that it was actually not connected to the reservoir. The study shows that it is feasible to use PSI surface movement data to obtain information about the reservoir and that the use of line-of-sight movements from both ascending and descending satellite passes adds an additional dimension to the data and an improved quality of the assimilation results.

A New Analytical Approximation for the Flow into a Well in a Finite Reservoir

A new approach is presented for the pressure calculation around a horizontal well or a partially penetrating vertical well in a finite height reservoir. The new method matches the asymptotic solutions close to- and far from the well. To this end, the reservoir is divided into two distinct volumes with ellipsoidal and elliptically cylindrical symmetry, respectively. Comparison with other techniques shows that the new expressions yield excellent results. The method is also applicable to reservoirs containing one elliptical, vertical or horizontal fracture, and can be used with account of a zone of altered permeability around the well or fracture due to formation damage or stimulation.

Frac-and-Pack Stimulation: Application, Design, and Field Experience

This paper discusses the criteria for selecting wells to be frac-and-packed. The authors show how systematic study of the inflow performance can be used to assess the potential of frac-and-packed wells, to identify the controlling factors, and to optimize design parameters. They also show that fracture conductivity is often the key to successful treatment. This conductivity depends largely on proppant size; formation permeability damage around the created fracture has less effect. Appropriate allowance needs to be made for flow restrictions caused by the presence of the perforations, partial penetration, and non-Darcy effects. They describe the application of the overpressure-calibrated hydraulic fracture model in frac-and-pack treatment design, and discuss some operational considerations with reference to field examples. The full potential of this promising new completion method can be achieved only if the design is tailored to the individual well. This demands high-quality input data, which can be obtained only from a calibration test. This paper presents their strategy for frac-and-pack design, drawing on examples from field experience. They also point out several areas that the industry needs to address, such as the sizing of proppant in soft formations and the interaction between fracturing fluids and resin in resin-coated proppant.