The present disclosure is generally directed to method of modeling flow of gas within a reservoir.
Reservoir simulation tools may be used to optimize economics, forecast production, evaluate the effectiveness of fractures, evaluate/compare/contrast different well completion strategies, and determine reserves, according to K. H. Coats, in “Reservoir Simulation,” Petroleum Engineers Handbook, January 1998. Blackoil simulation involves determining solutions to a set of partial differential equations. Certain reservoir simulation tools solve a three-dimensional, three phase mass balance to model the reservoir. The three phases are typically oil, water, and gas. The process of modeling fluid flow in reservoir simulation tools may become more complex and encounter numerical stability challenges as the number of phases being computed increases.
Particular difficulties may arise in modeling gas extracted from low-permeability sandstone and shale formations. In such reservoirs, the gas may include both adsorbed gas, (e.g., gas that forms a molecular monolayer on the walls of solids in the reservoir) and free gas (e.g., gas that exists in openings within the reservoir, such as pores).
The gas can desorb from the solid matrix 106 or adsorb back onto the solid matrix 106 depending on conditions such as pressure and temperature. Often, blackoil equations assume that the reservoir 102 temperature is constant. With this assumption, the gas adsorption may be related to pressure by a “sorption isotherm.” According to A. C. Bumb and C. R. McKee, in “Gas-Well Testing in the Presence of Desorption for Coalbed Methane and Devonian Shale,” SPE 15227, SPE Formation Evaluation, March 1988, sorption in many reservoirs typically follows a Langmuir isotherm.
where V is the volume of gas currently adsorbed at pressure p, Vm is Langmuir's volume constant (typically measured in units of standard cubic feet per ton,
and pL is Langmuir's pressure (typically measured in units of pounds per square inch absolute, psia).
The Langmuir isotherm curve 200 may be considered to be analogous to a saturation curve and the gas content of the shale may be considered to equilibrate at a pressure when the gas content of the shale is equal to the gas content calculated using the Langmuir constants. Thus, the gas will desorb or adsorb to the solid matrix to achieve equilibrium. To illustrate, according to the Langmuir isotherm 200 shown in
while a gas reservoir at about 2000 psia may have a gas content of the rock that is about
Hence, if the pressure of the gas reservoir were reduced from about 4000 psia to about 2000 psia (e.g., by removing free gas), then about
of gas would be desorbed from the solid matrix.
The transport of the gas from the reservoir to a well may be considered to include a diffusion stage followed by Darcy flow. In the diffusion stage, a pressure gradient due to drawdown at the well causes gas to be desorbed from the solid matrix and to migrate through interconnected micro pores to a micro fracture network, such as the micro fracture network 104 shown in
Modeling reservoirs to account for adsorbed gas content is difficult or impossible with many reservoir simulators because typical reservoir simulators perform a mass balance calculation without taking into account a gas source term. One conventional approach to modeling such reservoirs has been the two phase approach. For example, Seidle et al. modeled gas desorption from coal as gas dissolved in immobile oil. The solution-gas ratio was calculated using the Langmuir isotherm constants. In this reservoir simulation, the solid matrix is modeled as oil, as shown in
However, there are several shortcomings to this two phase approach. With respect to vertical equilibrium, it is difficult to maintain the same value of gas saturation in the entire depth of the reservoir. If the well is fractured, the fractures are initialized with immobile oil. With respect to the three phase physics problem, inclusion of fracture treatment water cleanup in the model requires three phase physics and two transition zones. With respect to mesh resolution, to accurately capture the pressure transient behavior, often an extremely refined mesh may be required. Coupled with at least two phase physics, the simulation process may get very computationally expensive, and sometimes even prohibitively expensive.
In a particular embodiment, a method is disclosed that includes generating a representation of a gas reservoir, where the gas reservoir includes at least two phases of matter. The representation of the gas reservoir models the gas reservoir as a single phase. The method also includes modeling flow of gas within the gas reservoir using the representation.
In another embodiment, a method is disclosed that includes generating a representation of a gas reservoir, where the representation of the gas reservoir includes a proxy system compression factor to model free gas and gas desorption in the gas reservoir. The method also includes modeling flow of gas within the gas reservoir using the representation.
In another embodiment, a method is disclosed that includes generating a representation of a gas reservoir, where the representation of the gas reservoir includes a proxy gas compression factor to model free gas and gas desorption in the gas reservoir. The method also includes generating a modified viscosity curve that is adjusted for the proxy gas compression factor and modeling flow of gas within the gas reservoir using the representation.
In another embodiment, a computer-readable medium is disclosed. The computer-readable medium has processor instructions that are executable to cause a processor to generate a single phase representation of a gas reservoir, where the gas reservoir includes at least free gas and gas adsorbed to a solid substrate. Characteristics of the single phase representation of the gas reservoir are selected to account for the free gas and to account for the adsorbed gas with respect to particular gas reservoir conditions.
Various aspects, advantages, and features of the present disclosure will become apparent after review of the entire application, including the following sections: Brief Description of the Drawings, Detailed Description, and the Claims.
In various illustrative embodiments of the methods described herein (such as the method 400, the method 1200, the method 1400, and the method 1500) the representation that is generated may depend in part of the blackoil gas pseudo-component mass balance. The blackoil gas pseudo-component mass balance may be modified to include desorption as follows:
In Equation (1), ugx, ugy and ugz are components of the gas velocity vector, {right arrow over (ug)}, in the x, y and z directions, respectively, Bg is the formation volume factor, φ is the effective gas-filled porosity, and V is the volume of gas currently adsorbed at pressure p. In an illustrative embodiment, V is measured in units of
standard cubic feet per cubic foot. Dividing both sides of Equation (1) by ΔxΔyΔzΔt and taking the limits Δx→0, Δy→0, Δz→0, and Δt→0 gives:
Using Darcy's law that
where k is the reservoir permeability, μg is the gas viscosity, Pg is the gas phase pressure, ρg is the gas density, g is gravitational acceleration, and D is the gravitational potential, turns Equation (2) into:
Equation (3) is the diffusivity equation or the blackoil equation for the gas phase with a source term to account for desorption. Consider Equation (3) for an initial porosity φ1:
Consider Equation (3) for a modified porosity φ2 without the desorption term:
Subject to the constraint that
Equation (4) is equivalent to Equation (5). Solving the constraint equation gives:
φ2=φ1+VBg. (6)
The porosity satisfies φ=φr[1+cr(p−pr)]. The initial porosity φ1, the volume V of the gas at pressure p, and the formation volume factor Bg are all functions of pressure. If solutions are found for the modified porosity φ2 for all values of pressure, then a new set of pressure dependent porosity data may be generated that includes desorption. This is an example of a Pressure Dependent Porosity technique. Since the compressibility of the system cannot be negative, the gas compressibility should always exceed the pore volume compressibility at all pressures.
Consider Equation (3) for an initial gas viscosity μg1 and an initial formation volume factor Bg1, assuming that the hydrostatic head due to gas (the term with the gas density ρg factor) is negligible (e.g., where water is present hydrostatic head due to gas may be significantly less than hydrostatic head due to the water):
Consider Equation (7) for a modified gas viscosity μg2 and a modified formation volume factor Bg2 without desorption:
Subject to the two constraints
Equation (7) is equivalent to Equation (8). Solving the first constraint gives:
Solving the second constraint gives:
The initial formation volume factor Bg1, the initial gas viscosity μg1, and the volume V of the gas at pressure p are all functions of pressure. If solutions are found for the modified formation volume factor Bg2 and the modified gas viscosity μg2 for all values of the pressure, then a new set of pressure, volume, and temperature (PVT) data may be generated that includes desorption. This is an example of a Formation Volume Factor technique.
Both the Pressure Dependent Porosity technique and the Formation Volume Factor technique include desorption into a single phase blackoil gas mass balance. The compressibility of the gas or the pore volume may be modified to account for the pressure dependent desorption term. The Formation Volume Factor technique assumes the hydrostatic head of gas is negligible. This assumption is more applicable in a gas-water model. The Pressure Dependent Porosity technique may be used for single phase gas cases.
Various illustrative embodiments of the methods described herein (such as the method 400, the method 1200, the method 1400, and the method 1500) allow for accurate modeling of shale gas systems using existing blackoil reservoir simulators, such as the Resolve reservoir modeling software available from Object Reservoir, Inc. of Houston, Tex. The Resolve reservoir modeling software combines static and dynamic data. The Resolve reservoir modeling software also merges geology, geophysical, and engineering technology that allows near-real-time drilling, completion, and stimulation decisions. For example, shale gas reservoirs are typically extremely low permeability and effective fracture treatment may be important to economic success. In the Resolve reservoir modeling software permeability and fracture design are co-dependent and a real-time integrated modeling approach may improve ultimate recovery. The Resolve reservoir modeling software uses the finite element method with adaptive meshing capability that can conform to reservoir geometries and automatically scale to the resolution that is useful. Using a true unstructured 3-D mesh gives a combination of speed and realism that may not be available in other tools.
In extremely low permeability reservoirs, adequate numerical resolution around a fracture face may be required to capture the non-linear pressure profile. To complicate the problem, desorption is also pressure dependent. Numerical solutions to partial differential equations, such as Equation (3), may be subject to mathematical convergence problems with increased resolution. In various illustrative embodiments of the methods described herein (such as the method 400, the method 1200, the method 1400, and the method 1500), mesh or grids may be in the inch-scale around a fracture to converge shale gas simulations. This level of refinement, without manual re-gridding, is available using the Resolve reservoir modeling software. Particular embodiments of the methods described herein (such as the method 400, the method 1200, the method 1400, and the method 1500) may provide an order of magnitude increase in computational speed with respect to multi-phase gas reservoir modeling. The single phase desorption approach disclosed in particular embodiments herein may be usefully coupled with the unstructured mesh technology that offers extreme localized numerical resolution to capture the transport of gas in shales, for example.
Referring to
The representation of the gas reservoir 412 may be used to model flow of gas within the reservoir 412 and via tubing 418 of a well to surface production facilities 402. The representation of the gas reservoir 412 may be bounded by a reservoir boundary 414 defining a region in which the finite element mesh resides. The representation of the gas reservoir 412 may model vertical wells 408, horizontal wells 410, or any combination thereof. Additionally, either the vertical wells 408 or the horizontal wells 410 may include hydraulic fractures. For example, the horizontal wells 410 may include transverse hydraulic fractures. The representation of the gas reservoir 412 may also model one or more planned or proposed wells, such as a potential vertical well with a hydraulic fracture 416.
By using the method 400, high fidelity reservoir models may be simulated with much less computation and with greater computational stability than traditionally used formulations in tight gas reservoirs, while maintaining comparable accuracy. In addition, by using the method 400, an efficient and computationally inexpensive methodology may be provided to model the transport of gas in gas reservoirs, such as shale reservoirs. Further, by using the method 400, modeling techniques are made available that reduce the number of phases and the computational complexity, resulting in significant reductions in the run-times of the models and greater flexibility in the types of reservoirs that can be successfully modeled.
Referring to
Referring to
Referring to
Referring to
Referring to
Referring to
Referring to
Referring to
The method 1200 may include, at 1212, generating a modified viscosity curve 1214 that is adjusted for a proxy compressibility factor. The flow of gas within the gas reservoir may be modeled based on the modified viscosity curve. The method 1200 may include, at 1216, determining adsorption data related to a relationship between gas adsorbed to a substrate in the gas reservoir and pressure. In a particular embodiment, the adsorption data may include Langmuir isotherm data. In a particular embodiment, the substrate may include tar. In another particular embodiment, the substrate may include porous media with adsorbed gas. For example, the porous media may include shale, coal, another porous media, or any combination thereof. The method 1200 may include, at 1218, determining free gas data associated with gas stored in void spaces of the gas reservoir. The method 1200 may include, at 1220, combining the adsorption data and the free gas data to model the flow of gas within the gas reservoir with respect to particular reservoir conditions.
Referring to
In a particular embodiment, the representation of the gas reservoir 1204 may include a proxy porosity factor 1306, as discussed above with reference to Equations 3-6. The proxy porosity factor 1306 may account for gas desorption and free gas in the gas reservoir and modeling the flow of gas within the gas reservoir using the representation 1204 may include, at 1310, modeling desorption of gas and compressible Darcy flow within the gas reservoir.
In another particular embodiment, the representation of the gas reservoir 1204 may include a water phase 1308 and modeling the flow of gas within the gas reservoir may include, at 1312, modeling a coupled flow of water and gas within the gas reservoir.
Referring to
In another particular embodiment, the proxy system compression factor 1406 may include a proxy gas compression factor 1416 of the gas of the gas reservoir. In another particular embodiment, the proxy system compression factor 1406 may include a proxy water compression factor 1418 of a water phase of the gas reservoir.
The representation 1404 of the gas reservoir may include an unstructured mesh 1410. The unstructured mesh 1410 may correspond to geometric features of the gas reservoir. Further, the representation 1404 of the gas reservoir may include a plurality of numeric expressions 1412 associated with the unstructured mesh. The numerical expressions 1412 may be descriptive of flow in the gas reservoir.
The method 1400 also includes modeling flow of gas within the gas reservoir using the representation 1404. The method 1400 may also include, at 1420, estimating the production of gas, the production of water, and the production of liquid condensates from the gas reservoir over time, based at least partially on the representation. In a particular embodiment, the method 1400 includes, at 1422, forecasting economic information related to the gas reservoir based at least partially on the representation.
Referring to
The method 1500 may include, at 1512, modeling movement of liquids within the gas reservoir based at least partially on the representation 1504. The method 1500 may include, at 1514, modeling pressure fields within the gas reservoir based at least partially on the representation 1504. The method 1500 may include, at 1516, modeling subsidence related to the gas reservoir based at least partially on the representation 1504. The method 1500 may include, at 1518, forecasting performance of the gas reservoir based at least partially on the representation 1504.
In a particular embodiment, a computer-readable medium may be provided. The computer-readable medium may have processor instructions that are executable to cause a processor to generate a single phase representation of a gas reservoir. The gas reservoir may include at least free gas and gas adsorbed to a solid substrate. Characteristics of the single phase representation of the gas reservoir may be selected to account for the free gas and to account for the adsorbed gas with respect to particular gas reservoir conditions. The solid substrate may include porous media. For example, the porous media may include shale or coal.
The computer-readable medium may include instructions executable by the processor to model flow of gas within the gas reservoir based at least partially on the single phase representation. The computer-readable medium may also include instructions executable by the processor to estimate production of gas, production of water, and production of liquid condensates from the gas reservoir over time based at least partially on the single phase representation. The computer-readable medium may also include instructions executable by the processor to forecast economic information related to the gas reservoir based at least partially on the single phase representation.
Referring to
plotted against time (days) is indicated at 1608. The reservoir and well data for this simulation are as follows: reservoir area=640 acres, centered horizontal well length=2000 ft, isotropic permeability=0.1 mD (milliDarcy), gas effective porosity=0.0405,
Langmuir pressure=914.9 psia, residual water saturation=0, gas gravity=0.7, and layer thickness=100 ft.
The methods described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disk, a removable disk, a compact disk read-only memory (CD-ROM), or any other form of computer readable storage medium. An exemplary storage medium is coupled to the processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an application-specific integrated circuit (ASIC). The ASIC may reside in a computing device or a user terminal. In the alternative, the processor and the storage medium may reside as discrete components in a computing device or user terminal.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the disclosed embodiments. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the scope of the disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope possible consistent with the principles and novel features as defined by the following claims.