Dmitriy Silin

Predicting Relative-Permeability Curves Directly From Rock Images

The objective of this study is determination of relative per meability curves from an analysis of the pore space geometry. The main assumptions are that the capillary pressure determines the fluid distribution and the rock is water-wet. Maximal inscri bed spheres computations characterize the portion of the pore space occupied by each fluid at a given saturation. Numerical solution of the Stokes equations evaluates the pore-scale flow field, which is avera ged to estimate the permeability to each fluid. The computed r elative permeability curves are in good agreement with published data. The input for the proposed procedure can be either a computer tomography image of a sample of the rock of interest, or a computergenerated image based on depositional simulations. Partitioning of the entire domain into parts significantly improve s the convergence and makes feasible implementation of the computational procedure on a desktop computer. The stability of the results with respect to the choice of computational parameters makes the proposed method suitable for routine applications. The model admits generalizations relaxing the requirement of water wetness of the rock. This model can be applied to evaluate the evolution of the rock flow p roperties under deformation, damage, mineral dissolution and precipitation.

Water injection into a low-permeability rock. 1 : Hydrofracture growth

In this paper, we model water injection through a growing vertical hydrofracture penetrating a low-permeability reservoir. The results are useful in oilfield waterflood applications and in liquid waste disposal through reinjection. Using Duhamels principle, we extend the Gordeyev and Entov (1997) self-similar 2D solution of pressure diffusion from a growing fracture to the case of variable injection pressure. The flow of water injected into a low-permeability rock is almost perpendicular to the fracture for a time sufficiently long to be of practical interest. We revisit Carters model of 1D fluid injection (Howard and Fast, 1957) and extend it to the case of variable injection pressure. We express the cumulative injection through the injection pressure and effective fracture area. Maintaining fluid injection above a reasonable minimal value leads inevitably to fracture growth regardless of the injector design and the injection policy. The average rate of fracture growth can be predicted from early injection. A smart injection controller that can prevent rapid fracture growth is needed.

Frequency-dependent seismic reflection from a permeable boundary in a fractured reservoir

Summary The coefficients of normal reflection and transmission of a planar p-wave from a permeable boundary in a fractured reservoir are studied in low-frequency range. The coefficients are expressed as power series with respect to a small dimensionless parameter, which is the product of the reservoir fluid mobility and density, and the frequency of the signal. The coefficients of such series are functions of mechanical properties of the reservoir rock and fluid. The zero-order terms of the reflection and transmission coefficients have a form similar to the one derived from the classical theory, without accounting for fluid flow. There is a strong similarity to Gassmans effective medium model. The next power expansion term both for reflection and transmission coefficients is proportional to the square root of the small parameter described above. Unlike frequencydependent terms, the zero-order coefficient does not depend on the permeability contrast. The functional structure of the reflection and transmission coefficients provides opportunities for seismic inversion and suggests new seismic attributes.

Control Model of Water Injection Into a Layered Formation

Here we develop a new control model of water injection from a growing hydrofracture into a layered soft rock. We demonstrate that in transient flow, the optimal injection pressure depends not only on the instantaneous measurements, but also on the whole history of injection, growth of the hydrofracture, and the rock damage. Based on the new model, we design an optimal injection controller that manages the rate of water injection in accordance with hydrofracture growth and the formation properties. We conclude that maintaining the rate of water injection into a low-permeability rock above a reasonable minimum inevitably leads to hydrofracture growth, to establishment of steady-state flow between injectors and neighboring producers, or to a mixture of both. Analysis of field water injection rates and wellhead pressures leads us to believe that direct links between injectors and producers can be established at early stages of waterflood, especially if the injection policy is aggressive. Such links may develop in thin, highly permeable reservoir layers or may result from failure of the soft rock under stress exerted by injected water. These links may conduct a substantial part of injected water. Based on the field observations, we now consider a vertical hydrofracture in contact with a multilayer reservoir, where some layers have high permeability and quickly establish steady-state flow from an injector to neighboring producers. The main result of this paper is the development of an optimal injection controller for purely transient flow, and for mixed tran-sient/steady-state flow in a layered formation. The objective of the controller is to maintain the prescribed injection rate in the presence of hydrofracture growth and injector/producer linkage. The history of injection pressure and cumulative injection, along with estimates of the hydrofracture size, are the controller inputs. By analyzing these inputs, the controller outputs an optimal injection pressure for each injector. When designing the controller, we keep in mind that it can be used either offline as a smart adviser, or online in a fully automated regime. Because our controller is process model-based, the dynamics of actual injection rate and pressure can be used to estimate effective area of the hydrofracture and the extent of the rock damage. The latter can be passed to the controller as one of the inputs. Finally, a comparison of the estimated fracture area with independent measurements leads to an estimate of the fraction of injected water that flows directly to the neighboring producers …

Water Injection into a Low-Permeability Rock - 2: Control Model

In Part 1, we have demonstrated the inevitable growth of the fluid injection hydrofractures in low-permeability rocks. Thus, a smart controller that manages fluid injection in the presence of hydrofracture extension is highly desirable. Such a controller will be an essential part of automated waterflood project surveillance and control. Here we design an optimal injection controller using methods of optimal control theory. The controller inputs are the history of the injection pressure and the cumulative injection, along with the fracture size. The output parameter is the injection pressure and the control objective is the injection rate. We demonstrate that the optimal injection pressure depends not only on the instantaneous measurements, but it is determined by the whole history of the injection and of the fracture area growth. We show the controller robustness when the inputs are delayed and noisy and when the fracture undergoes abrupt extensions. Finally, we propose a procedure that allows estimation of the hydrofracture size at no additional cost.

Seismic Wave Reflection From a Permeable Layer: Low-Frequency Asymptotic Analysis

We study elastic wave propagation in a fluid-saturated porous medium. Low-frequency asymptotic analysis of Biot’s model of poroelasticity yields the wave velocity, attenuation, and wave number as power series with respect to a small dimensionless parameter. This parameter is the product of kinematic reservoir fluid mobility, imaginary unity, and the frequency of the signal. The simplified asymptotic relationships lead to explicit formulae for reflection and transmission coefficients for a planar wave crossing an interface between two permeable media. Theoretical calculations predict a peak of reflection from a thin highly-permeable lens in a low-frequency range. An explicit formula relates the resonance frequency to reservoir fluid mobility and reservoir thickness. The results have immediate practical implications for seismic modeling and attribute analysis.Copyright

Control of Fluid Injection into a Low-Permeability Rock - 1. Hydrofracture Growth

This paper deals with growth of injection hydrofractures in transient linear flow in a low permeability, soft rock. Seventeen waterflood injectors in Section 12 of the Middle Belridge diatomite, three steam injectors in Section 29 of the South Belridge diatomite, as well as forty four injectors in the Lost Hills I waterflood have been analyzed. The field data show that cumulative injection of water or steam scales with time to the power of 1, rather than ½ predicted from the theory of linear transient flow. In other words, at constant injection pressure, injection rate is remarkably constant. Therefore, either the injection hydrofractures grow with time, or the formation permeability increases with time, or both. A simple mass balance of hydrofracture growth during fluid injection, attributed to Carter, is corrected, extended to the case of variable injection pressure, and presented in a simplified form. The growth of fracture area at constant injection rate is expressed in terms of two easily measured field parameters, the early “injection slope” in linear transient flow, and the average injection rate. Carter’s fracture growth rate is further halved to account for the reservoir layer homogeneity parallel and perpendicular to the hydrofracture plane. The Carter theory predictions are then compared with the growth rate of hydrofracture area calculated independently for two steam injectors in Section 29. There is remarkable agreement between the modified Carter theory predictions and the independently estimated rates of growth of these two hydrofractures. We show that fluid injection above a reasonable minimum rate must lead to hydrofracture extension if injection pressure is bounded from above. Ultimately, fracture growth is inevitable, regardless of mechanical design of injection wells and injection policy. We also show that water injection leads to less severe formation damage and fracture extension than steam. By analyzing the thermal and pore stresses, we demonstrate that steam injection may lead to the creation of horizontal fractures, vertical fracture extension, and reservoir damage. Better control of steam injection is, therefore, a must. We address the optimal injection control strategy in Part 2 of this paper.

Waterflood Surveillance and Supervisory Control

A successful waterflood depends on the proper operation of individual wells in a pattern, on maintaining the balance between water injection and production over the entire project or field, and on preventing well failures. The problems with waterflood are further aggravated in tight rock, e.g., carbonate, chalk or diatomite, where injector-producer linkages, uncontrolled hydrofracture growth, and water breakthrough in thief layers are often encountered. For optimal operation of a waterflood, it is mandatory that field engineers routinely acquire, store and interpret huge amounts of data to identify potential problems and to address them quickly. The cost of an error can be extreme; failure of only one well may cost more than the entire surveillancecontroller system described here. As in preventive health care, it is important to diagnose the problems early and to apply the cure on time. Our solution is to design a multilevel, integrated system of surveillance and control, which acquires and processes waterflood data, and helps field personnel make optimal decisions. Our upper-end systems will rely on the satellite radar interferograms (InSAR) of surface displacement and the new revolutionary micro-electronic mechanical systems (MEMS) sensors. Many intermediate configurations are also possible. In the near future, the next generation of smart, reliable and cheap sensors will revolutionize field operations of small independents and majors alike. We think that the impact of the new technology on the independents will be proportionally larger.

Micromechanics of Hydrate Dissociation in Marine Sediments by Grain-Scale Simulations

We seek to quantify the impact of hydrate dissociation on the strength of hydrate-bearing sediments. Dissociation of gas-hydrates in marine sediments converts the solid hydrate structure into liquid water and gas. Together with the associated pore pressure increase, this process reduces the stiffness of the sediments, which may fracture or be fluidized. If sediment failure occurs, seafloor subsidence and landslides can severely damage offshore infrastructure. To evaluate the mechanical properties of a sediment sample, we simulate loading of a disordered pack of spherical grains by incremental displacements of its boundaries. The deformation is described as a sequence of equilibrium configurations. Each configuration is characterized by a minimum of the total potential energy. This minimum is computed using a modification of the conjugate gradient algorithm. We verify our model against published data from experiments on glass beads. Our simulations capture the nonlinear, path-dependent behavior of granular materials observed in experiments. Hydrates are modeled as load-bearing solid particles within the pores. To simulate the consequences of dissociation, we reduce the solid fraction by shrinking the hydrate grains. The effect of the associated excess pore pressure is modeled by isotropic compression of the solid grains, and reduction in macroscopic effective stress. Weakening of the sediment is quantified as a reduction of the effective elastic moduli.

Advanced Reservoir Imaging Using Frequency-Dependent Seismic Attributes

Our report concerning advanced imaging and interpretation technology includes the development of theory, the implementation of laboratory experiments and the verification of results using field data. We investigated a reflectivity model for porous fluid-saturated reservoirs and demonstrated that the frequency-dependent component of the reflection coefficient is asymptotically proportional to the reservoir fluid mobility. We also analyzed seismic data using different azimuths and offsets over physical models of fractures filled with air and water. By comparing our physical model synthetics to numerical data we have identified several diagnostic indicators for quantifying the fractures. Finally, we developed reflectivity transforms for predicting pore fluid and lithology using rock-property statistics from 500 reservoirs in both the shelf and deep-water Gulf of Mexico. With these transforms and seismic AVO gathers across the prospect and its down-dip water-equivalent reservoir, fluid saturation can be estimated without a calibration well that ties the seismic. Our research provides the important additional mechanisms to recognize, delineate, and validate new hydrocarbon reserves and assist in the development of producing fields.