Dmitry B. Silin

Seismic low-frequency effects in monitoring fluid-saturated reservoirs

There is a complex relationship between seismic attributes, including the frequency dependence of reflections and fluid saturation in a reservoir. Observations in both laboratory and field data indicate that reflections from a fluid-saturated layer have an increased amplitude and delayed traveltime at low frequencies, when compared with reflections from a gas-saturated layer. Comparison of laboratory-modeling results with a diffusive-viscous-theory model show that low (<5) values of the quality factor Q can explain the observations of frequency dependence. At the field scale, conventional processing of time-lapse VSP data found minimal changes in seismic response of a gas-storage reservoir when the reservoir fluid changed from gas to water. Lowfrequency analysis found significant seismic-reflectionattribute variation in the range of 15‐50 Hz. The field observations agree with effects seen in laboratory data and predicted by the diffusive-viscous theory. One explanation is that very low values of Q are the result of internal diffusive losses caused by fluid flow. This explanation needs further theoretical investigation. The frequencydependent amplitude and phase-reflection properties presented in this paper can be used for detecting and monitoring fluid-saturated layers.

The Mathematical Model of Non-Equilibrium Effects in Water-Oil Displacement

Forced oil-water displacement and spontaneous countercurrent imbibition are crucial mechanisms of secondary oil recovery. The classical mathematical models of these phenomena are based on the fundamental assumption that in both these unsteady flows a local phase equilibrium is reached in the vicinity of every point. Thus, the water and oil flows are locally redistributed over their flow paths similarly to steady flows. This assumption allowed the investigators to further assume that the relative phase permeabilities and the capillary pressure are universal functions of the local water saturation, which can be obtained from steady-state flow experiments. The last assumption leads to a mathematical model consisting of a closed system of equations for fluid flow properties (velocity, pressure) and water saturation. This model is currently used as a basis for predictions of water-oil displacement with numerical simulations. However, at the water front in the water-oil displacement, as well as in capillary imbibition, the characteristic times of both processes are comparable with the times of redistribution of flow paths between oil and water. Therefore, the nonequilibrium effects should be taken into account. We present here a refined and extended mathematical model for the nonequilibrium two-phase (e.g., water-oil) flows. The basic problem formulation as well as the more specific equations are given, and the results of comparison with experiments are presented and discussed.

Robust Determination of the Pore Space Morphology in Sedimentary Rocks

This approach to study the morphology (shapes and connectivity) of sedimentary-rock pore space is based on fundamental concepts of mathematical morphology. An efficient and stable algorithm is proposed that distinguishes between the pore bodies and pore throats and establishes their respective volumes and connectivity.

The Mathematical Model of Nonequilibrium Effects in Water-Oil Displacement

Forced oil-water displacement and spontaneous countercurrent imbibition are the crucial mechanisms of secondary oil recovery. Classical mathematical models of both these unsteady flows are based on the fundamental assumption of local phase equilibrium. Thus, the water and oil flows are assumed to be locally distributed over their flow paths similarly to steady flows. This assumption allows one to further assume that the relative phase permeabilities and the capillary pressure are universal functions of the local water saturation, which can be obtained from steady-state flow experiments. The last assumption leads to a mathematical model consisting of a closed system of equations for fluid flow properties (velocity, pressure) and water saturation. This model is currently used as a basis for numerical predictions of wateroil displacement. However, at the water front in the water-oil displacement, as well as in capillary imbibition, the characteristic times of both processes are, in general, comparable with the times of redistribution of flow paths between oil and water. Therefore, the nonequilibrium effects should be taken into account. We present here a refined and extended mathematical model for the nonequilibrium two-phase (e.g., water-oil) flows. The basic problem formulation, as well as the more specific equations, are given, and the results of comparison with an experiment are presented and discussed.

Direct Prediction of the Absolute Permeability of Unconsolidated and Consolidated Reservoir Rock

A procedure of estimating the absolute rock permeability directly from a microscopic 3D rock image has been developed. Both computer-tomography and computergenerated images of reconstructed reservoir rock samples can be used as input. A physics-based depositional model serves to reconstruct natural sedimentary rock, and generate 3D images of the pore space at an arbitrary resolution. This model provides a detailed microstructure of the rock, and makes it possible to calculate the steady state velocity field in the single-phase fluid flow. In particular, using our model, one can analyze unconsolidated rocks whose micro-tomographic images cannot be obtained. The lattice-Boltzmann method is used to simulate viscous fluid flow in the pore space of natural and computer-generated sandstone samples. Therefore, the permeability is calculated directly from the sample images without converting them into a pore network or solving Stokes’ equation of creeping flow. We have studied the effect of compaction and various styles of cementation on the microstructure and permeability of reservoir rock. The calculated permeability is compared with the Kozeny-Carman formula and experimental data. Introduction The quantitative prediction of the continuum flow descriptors of porous media, such as the absolute permeability, the relative permeabilities, the capillary pressures, the formation resistivity, etc., is essential in earth sciences and – in particular – in petroleum engineering. Usually, the theoretical prediction of the absolute rock permeability is performed in two steps: (1) A model of the rock microstructure is formulated, and (2) a discretized field equation, such as Poisson’s or Stokes’ equation, is numerically solved on this model. Rock flow properties cannot be predicted without an accurate 3D representation of the rock microstructure. Several approaches have been proposed to reconstruct the 3D microstructures of natural rock: (1) Experimental; (2) Statistical; and (3) Processor physics-based. The experimental approach is necessary, but it is timeconsuming, expensive, and not applicable to damaged core material or drill cuttings. As an alternative, computerbased rock models have become increasingly attractive, because of their low cost and high speed, as well as the ability to overcome the present resolution constraints of experiment. Quantitative comparisons between computergenerated and microtomographic rock images have shown that the process-based models reproduce the 3D geometry of natural sedimentary rock much better than the stochastic models. The process-based models are also superior in their predictions of the pore space connectivity and, thus, the rock permeability. In this paper, we obtain the virtual samples of reservoir rock by applying the physics-based reconstruction procedure introduced in Refs. The essence of our approach is to build virtual samples of real sedimentary rock by (a) simulating the dynamic geological processes of grain sedimentation and compaction, (b) modeling the result of diagenesis, and (c) reproducing the mechanical behavior of 2 G. JIN, T. W. PATZEK AND D. B. SILIN SPE 90084 the simulated rock. In particular, our method accounts for the translations and rotations of rock grains during their settling and compaction. Once the detailed microstructure of a reservoir rock sample is obtained, it is possible to derive the macroscopic flow properties of this sample by, for example, solving numerically the continuum flow equations governing the fluid transport, or using the pore-network models. The numerical solution of the continuum flow equations can be extraordinarily challenging when all the details of the stunningly complex 3D rock microstructure are accounted for. The steady-state solution of Poiseuille’s flow on a disordered network of cylindrical ducts is easy to obtain, but the proper extraction of a pore network from a microscopic, 3D rock image is exceedingly difficult and non-unique, even if we neglect errors introduced by image processing and interpretation, and concentrate purely on rock geometry. In recent years, the lattice-Boltzmann method (LBM) has progressed into an established numerical scheme for simulating fluid flow and modeling fluid physics. This method relies on solving discrete kinetic equations for the flow of fluid particles, and it recovers the macroscopic continuity and momentum equations for an incompressible fluid in the double asymptotic limit of small Knudsen and Mach numbers. One of the most advertised advantages of LBM is its flexibility in handling complex flow geometries. The intricacies associated with the complicated boundary conditions can easily be handled in terms of particle reflections and bounces at solid sites. In principle, LBM is suitable for simulations of hydrodynamic flow in any domain. However, its “simple” treatment of complex geometries makes it particularly useful in the simulation of single-phase flow in porous media, see, e.g., Refs. In this paper, we apply LBM to model the viscous flow of a single fluid in the pore space of imaged and reconstructed samples of sedimentary rock. The absolute rock permeability is derived directly from the simulated velocity field. First, a simple rock, consisting of identical spherical grains, is used to validate our LB model for single-phase fluid flow. By combining the rock compaction model with the fluid flow simulation, the permeability is evaluated at different stresses. The results of these simulations are compared with the Kozeny-Carman formula and available experimental data. Second, beginning with an unconsolidated non-uniform grain packing, we study the influence of diagenesis on the rock microstructure and, thus, on the absolute permeability. The relation between the permeability, porosity, and diagenetic alteration is studied by depositing increasing amounts of cement on grain surfaces. Models of porous media In general, sedimentary rock formation process is classified into three stages. First, detrital rock fragments (grains) are deposited from flowing air or water to form an unconsolidated grain packing. Second, the packing is buried and compacted by the overburden rock. Third, flow Fig. 1— An unconsolidated random packing of 9111 identical grains after gravity sedimentation. The grain diamater is d = 3 mm. The arrow shows the direction of compaction. Fig. 2— An unconsolidated random packing of 14000 grains after gravity sedimentation. The grain diameters are uniformly distributed between dmin = 0.14 mm and dmax = 0.26 mm. of warm water causes dissolution, transport, and nucleation of different rock minerals. These coupled, complex physico-chemical processes, which take place in the buried sediments, are called diagenesis. Diagenetic alterations cement a grain packing into solid rock, simultaneously modifying the pore space geometry and connectivity. An efficient method of modeling the fundamental geological processes of rock formation is described in Refs. Here, we only describe the reconstructed rock samples and the discretized images of their pore space, on which we perform the LB simulations of viscous fluid flow. Unconsolidated grain packings. Two computergenerated unconsolidated random grain packings after gravity-driven sedimentation are shown in Fig. 1 and Fig. 2. These two packings have already reached gravity SPE 90084 DIRECT PREDICTION OF ABSOLUTE PERMEABILITY OF UNCONSOLIDATED AND CONSOLIDATED. . . 3 Fig. 3— The pore space in a 2 cm× 2 cm× 2 cm sub-volume (x ∈ [2.0, 4.0] cm, y ∈ [2.0, 4.0] cm, and z ∈ [1.0, 3.0] cm) of the grain packing in Fig. 1. The voxel resolution is 200 microns and the porosity is about 41.9%. equilibrium. Their dimensions are 6 cm×6 cm×6.6 cm in Fig. 1 and 5 mm×5 mm×4.6 mm in Fig. 2. Different grain size distributions are used in the packings: The uniform grain size d = 3 mm in Fig. 1 is used to match numerically the experiments by Wyllie and Gregory, and a uniform grain size distribution bounded by dmin = 0.14 mm and dmax = 0.26 mm in Fig. 2 is used to model Fontainebleau sandstone. For the purpose of fluid flow simulation, each sample is discretized into a three-dimensional array of identical small cubes, called voxels. We use the convention that a voxel is an element of the pore space if its center is in the pore space. Otherwise, it is an element of the solid skeleton. In order to eliminate or reduce the image generation boundary effects, only a fixed volume in the middle part of both grain packings is selected for discretization: x ∈ [2.0, 4.0] cm, y ∈ [2.0, 4.0] cm, and z ∈ [1.0, 3.0] cm in Fig. 1 and x ∈ [2.0, 3.0] mm, y ∈ [2.0, 3.0] mm, and z ∈ [2.0, 3.0] mm in Fig. 2. The orientation of the Cartesian coordinate system used in this analysis is shown in Fig. 1. The discretized images of the pore space in the central parts of both grain packings are shown in Fig. 3 and Fig. 4. The voxel resolutions of 200 microns and 10 microns, respectively, will be used in the analysis of these packings. The initial voxel-based porosity (the ratio of the number of voxels in the void space to the total number of voxels) of is 41.9% in Fig. 3 and 40.4% in Fig. 4. Consolidated grain packings. Compaction and cementation processes modify the microstructure of the initial grain packing. Fig. 5 displays the pore space of the central 1 mm×1 mm×1 mm sub-volume of the compacted grain packing, obtained after the packing in Fig. 2 was compacted uniaxially in the z-direction to reduce the bulk volume by 18.8%. So, the voxel-based porosity of this volume is now 28.5%. Comparing this image with the image before compaction, see Fig. 4, one observes that compaction causes some grain interpenetration, and large pores beFig. 4— The pore space in a 1 mm × 1 mm × 1 mm subvolume (x, y, z ∈ [2.0, 3.0] mm)of the grain packing in Fig. 2. The voxel resolution is 10 microns and the porosity is about 40.4%. Fig. 5— The pore space in a 1 mm×1 mm×1 mm sub-volume (x, y, z ∈ [2.0, 3.0] mm) of

Using frequency‐dependent seismic attributes in imaging of a fractured reservoir zone

Author(s): Goloshubin, Gennady; Silin, Dmitry | Abstract: Normal reflection from a fractured reservoir is analyzed using frequency-dependent seismic attributes. Processing of 3D low-frequency seismic data from a West-Siberian reservoir produced an accurate delineation of the fracturedhydrocarbon-bearing zones. P-wave propagation, reflection and transmission at an impermeable interface between elastic and dual-porosity poroelastic media is investigated. It is obtained that the reflection and transmission coefficients are functions of the frequency. At low frequencies, their frequency-dependent components are asymptotically proportional to the square root of the product of frequency reservoir fluid mobility and fluid density.

Pressure diffusion waves in porous media

Pressure diffusion wave in porous rocks are under consideration. The pressure diffusion mechanism can provide an explanation of the high attenuation of low-frequency signals in fluid-saturated rocks. Both single and dual porosity models are considered. In either case, the attenuation coefficient is a function of the frequency.

Oil Deposits in Diatomites: A New Challenge for Subterranean Mechanics

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the authors(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. Illus- trations may not be copied. The abstract should contain conspicuous acknowledgement of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-214-952-9435. Abstract Because of their size and difficulties with oil recovery, the oil-bearing diatomite formations attract now special at- tention worldwide. For example, the giant diatomaceous oil fields in California, Lost Hills and Belridge, contain some 10 billion barrels of oil in place. Diatomaceous strata have peculiar geological structure: as a result of the cyclic deposition, the diatomite rocks are layered across width scales ranging from tens of meters to sub-millimeter. The diatomite rock is very fragile and its fracture toughness is low: the inter-layer boundaries are weakly connected and ready to part when the fluid pressure changes. When intact, the diatomite has porosity of 50-70% and is al- most impermeable (0.1-1 md). Oil production from the diatomites was always difficult and started only 30 years ago after the introduction of hydrofracturing. The scan- ning electron microscopy images of the diatomite rock re- veal a disordered microstructure with little grain interlock- ing and cementation. Therefore, fluid flow through the diatomite starts only after changes of the rock microstruc- ture. The hydrofractures are not single vertical cracks, but are complex, multiply connected regions of damaged rock. The current models of fluid-rock systems, e.g., Refs., 1, 3, 19 cannot capture the dramatic rearrangements of the diatomite microstructure caused by fluid withdrawal and injection, and have little predictive capability. In particular, these models cannot capture the intense rock damage during hydrofracturing, followed by the nonequi- librium countercurrent imbibition with the ensuing rock damage and hysteretic effects. To understand and predict reservoir behavior in the diatomite and limit well failures, a new micromechanical approach has been developed.

Lost Hills Field Trial - Incorporating New Technology for Reservoir Management

This paper will discuss how Chevron U.S.A. Inc., a ChevronTexaco Company (ChevronTexaco), is implementing a field trial that will use research developed software integrated with Supervisory Control and Data Acquisition (SCADA) on injection wells, in conjunction with satellite images to measure ground elevation changes, to perform realtime reservoir management in the Lost Hills Field. Implementation of a new software control model to restrict hydrofracture growth in water injection wells is being field tested. 1 Synthetic Aperture Radar Interferograms (InSAR) are being obtained on an approximately 60-day interval to determine subsidence rates and will be used as an input variable for pattern voidage calculations. Incorporating new and innovative technologies is helping ChevronTexaco produce a very unique and challenging diatomite reservoir.

Monitoring Waterflood Operations: Hall Method Revisited

Hall’s method is a simple tool used to evaluate performance of water injection wells. It is based on the assumption of steadystate radial flow. Besides historical injection pressures and rates, Hall’s method requires information about the mean ambient reservoir pressure, e p . In addition, it is assumed that the equivalent radius, e r , of the reservoir domain influenced by the well is constant during the observation period. Neither e p nor e r are available from direct measurement. Here we modify and extend Hall’s plot analysis, calling it slope analysis. Our modification relies on the analysis of the variations of slope of the cumulative injection pressure versus cumulative injection volume. In particular, our slope analysis produces an estimate of the mean ambient reservoir pressure, and requires only the injection pressures and rates. Such data are routinely collected in the course of a waterflood. Note that the slope analysis method requires no interruptions of regular field operations. The proposed slope analysis method has been verified with the numerically generated pressure and rate data, and tested in the field. In both cases it proved to be accurate, efficient, and simple. The obtained ambient reservoir pressure estimate can be used to correct the Hall plot analysis or to map the average reservoir pressure over several patterns or an entire waterflood project. Such maps can then be used to develop an efficient waterflood policy, which will help to arrest subsidence and improve oil recovery.