Stephan K. Matthäi

Streaming current generation in two‐phase flow conditions

Self-potential (SP) signals that are generated under two-phase flow conditions could be used to study vadose zone dynamics and to monitor petroleum production. These streaming-potentials may also act as an error source in SP monitoring of vulcanological activity and in magnetotelluric studies. We propose a two-phase flow SP theory that predicts streaming currents as a function of the pore water velocity, the excess of charge in the pore water, and the porosity. The source currents that create the SP signals are given by the divergence of the streaming currents, and contributions are likely to be located at infiltration fronts, at the water table, or at geological boundaries. Our theory was implemented in a hydrogeological modeling code to calculate the SP distribution during primary drainage. Forward and inverse modeling of a well-calibrated 1D drainage experiment suggest that our theory can predict streaming potentials in the vadose zone.

Black-Oil Simulations for Three-Component - Three-Phase Flow in Fractured Porous Media

Discrete-fracture modeling and simulation of two-phase flow in realistic representations of fractured reservoirs can now be used for the design of IOR and EOR strategies. Thus far, however, discrete fracture simulators fail to include a third compressible gaseous phase. This hinders the investigation of the performance of gas-gravity drainage, water alternating gas injection, and blow-down in fractured reservoirs. Here we present a new numerical method that expands the capabilities of existing Black-Oil models for threecomponent – three-phase flow in three ways: (i) It utilizes a finite element - finite volume discretization generalized to unstructured hybrid element meshes. (ii) It employs higher-order accurate representations of the flux terms. (iii) Flash calculations are carried out with an improved equation of state allowing for a more realistic treatment of phase behavior. We illustrate the robustness of this numerical method in several applications. First, quasi-1D simulations are used to demonstrate grid convergence. Then, 2D discrete fracture models are employed to illustrate the impact of mesh quality on predicted production rates in discrete fracture models. Finally, the proposed method is used to simulate three-component – three-phase flow in a realistic 2D model of fractured limestone mapped in the Bristol Channel, U.K. and a 3D stochastically generated discrete fracture model.

Finite Element - Node-Centered Finite-Volume Two-Phase-Flow Experiments With Fractured Rock Represented by Unstructured Hybrid-Element Meshes

Fractured-reservoir relative permeability, water breakthrough, and recovery cannot be extrapolated from core samples, but computer simulations allow their quantification through the use of discrete fracture models at an intermediate scale. For this purpose, we represent intersecting naturally and stochastically generated fractures in massive or layered porous rock with an unstructured hybrid finite-element (FE) grid. We compute two-phase flow with an implicit FE/finite volume (FV) method (FE/FVM) to identify the emergent properties of this complex system. The results offer many important insights: Flow velocity varies by three to seven orders of magnitude and velocity spectra are multimodal, with significant overlaps between fractureand matrix-flow domains. Residual saturations greatly exceed those that were initially assigned to the rock matrix. Total mobility is low over a wide saturation range and is very sensitive to small saturation changes. When fractures dominate the flow, but fracture porosity is low (10 to 1%), gridblock average relative permeabilities, kr,avg, cross over during saturation changes of less than 1%. Such upscaled kr,avg yield a convex, highly dispersive fractionalflow function without a shock. Its shape cannot be matched with any conventional model, and a new formalism based on the fracture/matrix flux ratio is proposed. Spontaneous imbibition during waterflooding occurs only over a small fraction of the total fracture/matrix-interface area because water imbibes only a limited number of fractures. Yet in some of these, flow will be sufficiently fast for this process to enhance recovery significantly. We also observe that a rate dependence of recovery and water breakthrough occurs earlier in transient-state flow than in steady-state flow.

Numerical simulation of multi-phase fluid flow in structurally complex reservoirs

Abstract Realistic simulation of structurally complex reservoirs (SCR) is challenging in at least three ways: (1) geological structures must be represented and discretized accurately on vastly different length scales; (2) extreme ranges and discontinuous variations of material properties have to be associated with the discretized structures and accounted for in the computations; and (3) episodic, highly transient and often localized events such as well shut-in have to be resolved adequately within the overall production history, necessitating a highly adaptive resolution of time. To facilitate numerical experiments that elucidate the emergent properties, typical states and state transitions of SCRs, an application programmer interface (API) called complex systems modelling platform (CSMP++) has been engineered in ANSI/ISO C++. It implements a geometry and process-based SCR decomposition in space and time, and uses an algebraic multigrid solver (SAMG) for the spatio-temporal integration of the governing partial differential equations. This paper describes a new SCR simulation workflow including a two-phase fluid flow model that is compared with ECLIPSE in a single-fracture flow simulation. Geologically realistic application examples are presented for incompressible 2-phase flow, compressible 3-phase flow, and pressure-diffusion in a sector-scale model of a structurally complex reservoir.

Numerical simulation of water injection into layered fractured carbonate reservoir analogs

Water flooding of fractured reservoirs is risky because water breakthrough can occur early, leading to a prohibitively high water cut. In mixed or oil-wet carbonates, capillary drive is negligible or absent. For this scenario, we investigate fluid-pressure-driven displacement of oil by water in two-phase flow numerical models based on naturally fractured limestone beds mapped along the British Channel coast. These reservoir analogs are represented by unstructured finite-element grids with discrete representations of intersecting fractures. We solve the governing equations for slightly compressible two-phase flow with our original control-volume finite-element method. This permits the direct examination of displacement patterns in fractures and rock matrix.We find that the irreducible saturation in the fractured carbonate is much higher than the value prescribed to the rock matrix. The shape of water invasion fronts is highly sensitive to the viscosity ratio of oil and water. When the Brooks-Corey relative permeability model is applied to the rock matrix at a viscosity ratio of 1, the total mobility, t, is low at intermediate saturations. This stabilizes displacement fronts where a girdle of reduced t develops, but this effect disappears as the viscosity ratio increases.For an idealized model with a water-wet matrix, we have also evaluated the effect of countercurrent capillary-pressure–driven flow across fracture-matrix interfaces. The rate of this countercurrent imbibition scales with the specific fracture surface area and decays exponentially as intermediate saturation zones develop adjacent to the fractures. The resulting reduced t feeds back into the fluid-pressure-driven displacement process.

Is the Mount Isa copper deposit the product of forced brine convection in the footwall of a major reverse fault

Geochemical and mass-balance constraints in conjunction with stable isotope data in- dicate that the copper deposit of Mount Isa (Australia) formed by mixing of a reduced sulfur-rich fluid from overlying Mount Isa Group metasedimentary rocks with a copper- rich oxidized fluid entering a brecciated contact zone from underlying metabasalts. We have performed numerical simulations to test whether the deposit may have formed by forced fluid convection driven by progressive displacement on the Mount Isa fault zone, indicated by an ;200 8C offset in metamorphic grade. Results indicate that uplift of

Comparison of deterministic with stochastic fracture models in water-flooding numerical simulations

1 mm/yr induces regional fluid flow organizing into a stable, permeability-controlled cir- culation system. Far-field advection through the oxidized metabasalts is superimposed on smaller-scale convection in the metasedimentary rocks beneath the fault. As convection on the large scale gains momentum, the breccia progressively cools, consistent with min- eralogic and fluid-inclusion evolution. For realistic uplift rates, the measured silica en- richment in the orebody (

Numerical simulation of departures from radial drawdown in a faulted sandstone reservoir with joints and deformation bands

190 Mt SiO2) is achieved in ;1 m.y. Reduced and oxidized fluids mix at the proportions required for high-grade copper-iron sulfide precipitation, aided by rapid oscillations in the influx ratio of the two fluids into the most permeable and vigorously convecting orebody region.

The Influence of Fault Permeability on Single-Phase Fluid Flow Near Fault-Sand Intersections: Results from Steady-State High-Resolution Models of Pressure-Driven Fluid Flow

Determination of multiphase flow properties considering the variation of fracture patterns (i.e., number of fracture sets, their orientation, length distribution, spacing, and in-situ aperture) remains a key challenge in reservoirs. In reservoir engineering, one way is by studying outcrop analogs with comparable petrophysical properties and a similar geological history, and incorporating these data into model building, discretization, and numerical simulation. The limitation of directly incorporating attributes measured on outcrops is that this method is error prone because of postburial processes. Mineralized fracture (vein) attributes are good candidates to use as analogs for open fractures formed under in-situ conditions, to establish the relationship between fracture length and aperture and help to reveal the conditions at the time of their formation, and to quantify fracture-induced porosity in rock masses. Vein attributes determined from scan lines and window samples were combined to condition the stochastic generation of fractures using the discrete fracture network code FracMan. Comparison of water breakthrough time and oil saturation at breakthrough was then determined by applying a constant pressure gradient for each realization to simulate water-flooding numerical simulation using the combined finite element–finite volume method. The different stochastic realizations were compared with discrete fracture and matrix models, and we show how the uncertainty in these fracture attributes affects multiphase flow behavior in naturally fractured rocks. Uncertainty in quantifying these attributes has a profound impact for predicting the oil recovery and water breakthrough time based on limited information from boreholes.

Upscaling two-phase flow in naturally fractured reservoirs

Abstract Field measurements constrain the fluid flow characteristics of an analogue hydrocarbon reservoir in the faulted Entrada sandstone, Arches National Park, Utah. These data comprise maps of the geometry, inhomogeneous permeability, and porosity of fault zones, joints, and deformation bands in a region where two discontinuous normal faults overlap. Two-dimensional computer simulations of drainage of this analogue reservoir identify normal faults with highly permeable slip planes as the most important reservoir inhomogeneities. These faults compartmentalize fluid pressure over timespans greater than years while fluid can be drained on the kilometre scale along their highly permeable slip planes. Joints induce the second most important distortions of radial drawdown, influencing the timespans over which fault signatures are observed in pressure decline curves. The joints often extend to the boundaries of the reservoir. This also reduces the time before the rate of pressure decline accelerates due to boundary interaction. Zones of deformation bands less than 25 cm wide with a spacing ≥30 m have little effect on radial drawdown in our single phase fluid flow simulations. When drawdown spreads with time over the deformation structures in the analogue reservoir, the different structures simultaneously influence the change of pressure at the wellbore (pressure derivative). This temporal overlap prohibits an analysis of the effects of individual structures. Drawdown does not ‘recover’ to radial flow after an inhomogeneity is encountered.