A Multiple Interacting Continua method (MINC) is presented which is applicable for numerical simulation of heat and multi-phase fluid flow in multidimensional, fractured porous media. This method is a generalization of the double-porosity concept. The partitioning of the flow domain into computational volume elements is based on the criterion of approximate thermodynamic equilibrium at all times within each element. The thermodynamic conditions in the rock matrix are assumed to be primarily controlled by the distance from the fractures, which leads to the use of nested grid blocks. The MINC concept is implemented through the Integral Finite Difference (IFD) method. No analytical approximations are made for the coupling between the fracture and matrix continua. Instead, the transient flow of fluid and heat between matrix and fractures is treated by a numerical method. The geometric parameters needed in a simulation are preprocessed from a specification of fracture spacings and apertures, and the geometry of the matrix blocks. The MINC method is verified by comparison with the analytical solution of Warren and Root. Illustrative applications are given for several geothermal reservoir engineering problems.

/pdf/a-practical-method-for-modeling-fluid-and-heat-flow-in-1v3gozq01l.pdf

A practical method for modeling fluid and heat flow in fractured porous media

Vapor-dominated geothermal reservoirs produce saturated or superheated steam, and vertical pressure gradients are close to vapor static. These observations have been generally accepted as providing conclusive evidence that the liquid saturation must be rather small (<50%) in order that liquid may be nearly immobile. This conclusion ignores the crucial role of conductive heat transfer mechanisms in fractured reservoirs for vaporizing liquid flowing under two-phase conditions. We have developed a multiple interacting continuum method (MINC) for numerically simulating two-phase flow of a homogeneous fluid in a fractured porous medium. Application of this method to reservoir conditions representative of The Geysers, California, and results from an analytical approximation show that, for matrix permeability less than a critical value (≈2.5 to 5 microdarcies), the mass flux of water from the matrix to the fractures will be continuously vaporized by heat transported due to conduction. This gives rise to production of superheated steam even when the matrix has nearly full liquid saturation. Simple estimates also show that heat-driven steam/water counterflow can maintain a nearly vapor static vertical pressure profile in the presence of mobile liquid water in a reservoir with low vertical matrix permeability. The implication of these findings is that the fluid reserves of vapor-dominated geothermal reservoirs may be larger by a factor of about 2 than has generally been believed in the past.

/pdf/on-fluid-reserves-and-the-production-of-superheated-steam-3ky308zeo3.pdf

On fluid reserves and the production of superheated steam from fractured, vapor‐dominated geothermal reservoirs

/pdf/gminc-a-mesh-generator-for-flow-simulations-in-fractured-195pzb7fbh.pdf

Gminc - a mesh generator for flow simulations in fractured reservoirs

Analytical and numerical techniques are used to study nonisothermal flow of water and steam in idealized fractured porous media. We find that heat conduction in the rock matrix can substantially alter the flowing enthalpy in the fractures. Effects of matrix permeability and fracture spacing are demonstrated for production from and injection into vapor-dominated and liquid-dominated geothermal reservoirs.

/pdf/heat-transfer-in-fractured-geothermal-reservoirs-with-24gncp6vnk.pdf

Heat transfer in fractured geothermal reservoirs with boiling

Numerical simulation techniques are used to study the effects of noncondensable gases (CO/sub 2/) on geothermal reservoir behavior in the natural state and during exploitation. It is shown that the presence of CO/sub 2/ has a large effect on the thermodynamic conditions of a reservoir in the natural state, especially on temperature distributions and phase compositions. The gas will expand two-phase zones and increase gas saturations to enable flow of CO/sub 2/ through the system. During exploitation, the early pressure drop primarily results from ''degassing'' of the system. This process can cause a very rapid initial pressure drop, on the order of megapascals, depending on the initial partial pressure of CO/sub 2/. The flowing gas content from wells can provide information on in-place gas saturations and relative permeability curves that apply at a given geothermal resource. Site-specific studies are made for the gas-rich, two-phase reservoir at the Ohaaki geothermal field in New Zealand. A simple lumped-parameter model and a vertical column model are applied to the field data. The results obtained agree well with the natural thermodynamic state of the Ohaaki field (pressure and temperature profiles) and a partial pressure of 1.5 to 2.5 MPa (217 to 363 psi) ismore » calculated in the primary reservoirs. The models also agree reasonably well with field data obtained during exploitation of the field. The treatment of thermophysical properties of H/sub 2/O/CO/sub 2/ mixtures for different phase compositions is summarized.« less

/pdf/fluid-and-heat-flow-in-gas-rich-geothermal-reservoirs-1wcyshyfhc.pdf

Fluid and heat flow in gas-rich geothermal reservoirs

SHAFT79 (Simultaneous Heat And Fluid Transport) is an integrated finite difference program for computing two-phase non-isothermal flow in porous media. The principal application for which SHAFT79 is designed is in geothermal reservoir simulation. SHAFT79 solves the same equations as an earlier version, called SHAFT78, but uses much more efficient mathematical and numerical methods. The present SHAFT79 user's manual gives a brief account of equations and numerical methods and then describes in detail how to set up input decks for running the program. The application of SHAFT79 is illustrated by means of a few sample problems. (MHR)

/pdf/shaft79-user-s-manual-3nlqwx8b4c.pdf

SHAFT79 user's manual

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SHAFT79 user's manual