CN106897544B - Method of modeling oil and gas production from fractured unconventional formations - Google Patents
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Abstract
A method of modeling hydrocarbon flow from a fractured unconventional reservoir wherein the formation has variability in stimulated reservoir properties caused by a multi-stage fracturing treatment. A chart is created that divides the formation into a plurality of closed production zones, each of which is in turn divided into a plurality of flow subsystems that extend between fractures in the formation. Production behavior is then calculated for each flow subsystem based on the geographic conditions and characteristics of the individual flow subsystem. Regional flows for each enclosed production region are determined by coupling the calculated production behaviors of the flow subsystems and are simulated by summing the regional flows. A template curve showing the simulated hydrocarbon flow at the selected time point may then be plotted.
Description
Technical Field
The present invention relates to a method of generating a hydrocarbon production curve from a geological formation, and more particularly provides a method of generating a hydrocarbon production curve from an unconventional hydrocarbon reservoir stimulated by multi-stage hydraulic fractures.
Background
There is a long history of technological development and innovation in the field of oil and gas exploration and exploitation. As a capital intensive business, the oil and gas recovery industry has many incentives to optimize and maximize production from a particular hydrocarbon-bearing formation. For example, unconventional reservoirs are reservoirs that are less permeable and require stimulation to achieve profitable production.
In producing hydrocarbons from unconventional geological formations such as shale, one common production optimization technique is to stimulate the reservoir by creating multiple hydraulic fractures along a multi-stage fractured horizontal well. This technique is commonly referred to as "hydraulic fracturing". The oil and gas production initiated in hydraulic fracturing schemes is the result of flow in the matrix, in the natural fracture network, and in the hydraulic fractures themselves.
There are a number of problems in modeling hydrocarbon production in fractured geologic formations with high heterogeneity. For example, in a multi-stage hydraulic fracturing process, many pre-existing natural fractures are reactivated. The hydraulic fractures and the active natural fractures constitute a hydraulic conductive flow network for oil and gas production. In other cases, unconventional formations along horizontal wells are known to be highly heterogeneous in petrophysical and geological properties. In such cases, the formation reacts differently at different fracturing stages, and the fracture network created along the horizontal well is also highly heterogeneous. The simulation method may be reliable only if these post-fracture unconventional formation heterogeneities are taken into account.
Many fracturing companies have also developed and used innovative fracturing techniques, including two representative techniques named under the simuldrac and ZIPPERFRAC brands. In the SIMULFRAC or ZIPPERFRAC process, two or more parallel horizontal wells are drilled and then drilled and fractured at alternating intervals along the wellbore. This creates a high density network of hydraulic fractures, and therefore, the stimulation volume that each hydraulic fracture can control is relatively reduced. The stimulation volume beyond the hydraulic fracture tip also becomes smaller and its internal flow may no longer behave like a linear flow. Existing modeling methods are not applicable if they assume that the flow beyond the fracture tip is linear.
Another complication is that the fluid flow mechanisms in unconventional reservoirs are quite complex compared to conventional formations. Darcy's law is often deficient in such reservoirs. In the production of certain unconventional gas reservoirs, gas diffusion occurs simultaneously with desorption. In addition, the high dependence of reservoir permeability on stress has been demonstrated by a number of tests. No method has been developed in any technical literature or methodology to fully incorporate all of these complex flow mechanisms into the modeling or evaluation of unconventional reservoir production.
Another problem associated with modeling or performing fracture treatments in unconventional formations is the difficulty associated with predicting or accurately simulating the likely production of the formation. Although complex analytical and numerical methods can be developed to represent fluid flow towards multi-stage fractured horizontal wells, these methods require high computational power, long computational time, and have certain difficulties in iterative applications. One of the main technical reasons for the difficulty in these calculations is the low matrix permeability.
The hydrocarbons produced from each stage of the fracture are primarily from the stimulated reservoir volume surrounding the hydraulic fracture, which provides the possibility of breaking down the reservoir into smaller portions. Methods from unconventional reservoir production based on rapid, simple and reliable studies to break down unconventional reservoirs into smaller fractions are believed to be highly desirable.
It would be highly desirable in the oil and gas production industry if a method of generating hydrocarbon production profiles from unconventional reservoirs stimulated by multiple hydraulic fractures could be created.
Disclosure of Invention
The present invention includes a method of modeling hydrocarbon flow from an unconventional fractured reservoir that has been multi-staged fractured. The present invention develops a prototype curve of hydrocarbon production from unconventional reservoirs stimulated by multi-stage fracturing. The prototype curve refers to a series of curves with time on the x-axis and production rate q/bottom hole pressure p/bottom hole pressure derivative on the y-axis for a particular reservoir condition. The template curves may help predict reservoir properties, fracture properties, and production trends by matching field production data.
In some embodiments, a method of modeling hydrocarbon flow from a fractured unconventional reservoir may include: collecting correlation data corresponding to unconventional reservoirs that have been subjected to multi-stage hydraulic fracturing, using the correlation data to model subsystem flows for each set of flow subsystems as a function of at least one set of reservoir properties assigned to the subsystem and the correlation data corresponding to the flow subsystems, modeling regional flows for each enclosed production region by coupling calculated subsystem flows for each flow subsystem within the enclosed production region, and/or modeling reservoir flows for unconventional reservoirs by coupling calculated regional flows for each set of enclosed production regions.
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To facilitate identification of the discussion of any particular element or act, the most significant digit or digits in a reference number refer to the reference number in which the element is first introduced.
FIG. 1 is a flow chart showing steps in one embodiment of the method of the present invention for modeling hydrocarbon flow from a fractured unconventional reservoir;
FIG. 2 is a flow chart of the method of FIG. 1 with the addition of the step of generating a prototype curve from the modeled reservoir production;
FIG. 3 is a flow chart of the method of FIG. 2, with the addition of the step of modifying a plurality of enclosed production areas once initially calculated;
FIG. 4 is a schematic illustration of an unconventional reservoir stimulated by multi-stage hydraulic fracturing;
FIG. 5 is a plan view of a streamline-type distribution in the unconventional reservoir of FIG. 4;
FIG. 6 shows the subdivision of the enclosed production area of FIG. 5 into a plurality of flow subsystems (area 1 of FIG. 5) in accordance with one embodiment of the present invention;
FIG. 7 shows an alternative embodiment of the subdivision of the enclosed production area of FIG. 5 into a plurality of flow subsystems (area 1 of FIG. 5) in accordance with the present invention;
FIG. 8 illustrates another embodiment of subdividing a closed production area into a plurality of flow subsystems in accordance with the present invention;
FIG. 9 illustrates another embodiment of subdividing a closed production area into a plurality of flow subsystems in accordance with the present invention;
FIG. 10 illustrates another embodiment of subdividing a closed production area into a plurality of flow subsystems in accordance with the present invention;
FIG. 11 illustrates another embodiment of subdividing a closed production area into a plurality of flow subsystems in accordance with the present invention;
FIG. 12 is a sample of a prototype curve made by the method of the present invention for modeling hydrocarbon flow from a fractured unconventional reservoir;
FIG. 13 illustrates one aspect of the subject matter of one embodiment of the present invention.
Detailed Description
The present invention is a method of modeling hydrocarbon flow from a fractured unconventional reservoir. An "unconventional reservoir" refers to a reservoir that is less permeable and requires stimulation to achieve profitable production. Multi-stage hydraulic fracturing techniques are commonly used to maximize the hydrocarbon recovery of oil and gas from such formations, and the template curves are useful simulation/modeling techniques for assessing the productivity of the hydrocarbon reservoir.
The prototype curve is a visualization tool for evaluating hydrocarbon production-it is a graph of time as the x-axis and production rate q/bottom hole pressure p/bottom hole pressure derivative for a particular reservoir condition as the y-axis. Typically, a plurality of template curves are generated based on adjustments to formation parameters. The template curves may help predict reservoir properties, fracture properties, and production trends by matching field production data.
As outlined herein, the present invention includes a method of modeling hydrocarbon flow from a fractured unconventional reservoir. Current techniques for hydrocarbon production simulation in fractured unconventional reservoirs are time consuming and less accurate than in some cases. The method of the present invention, which effectively deconstructs a particular unconventional reservoir into multiple enclosed production zones and multiple flow subsystems therein, each accommodating individual hydraulic fracture locations in the formation, provides related full template curves and more accurate results with greater efficiency and speed.
The method comprises the following steps:
fig. 1, to which reference is first made, is a flow chart showing the steps of the method of the present invention. As outlined herein, the present invention is a method of modeling hydrocarbon flow from a fractured unconventional reservoir-generating a template curve of hydrocarbon production parameters in the unconventional reservoir based on the simulation techniques outlined herein.
The first step in the method of the present invention for modeling hydrocarbon flow from a fractured unconventional reservoir is to collect relevant data corresponding to the unconventional reservoir that has been subjected to natural or artificial multi-stage hydraulic fracturing. This is shown at step 1-1. Relevant data that may be used in the present method include, but are not limited to, mine site data, production history, fracture treatment records, and microseismic activity. This relevant data will be used in the remainder of the method of modeling the flow from a fractured unconventional reservoir to provide an unconventional reservoir model, a production reservoir block, and the location and characteristics of hydraulic fractures used to determine reservoir flow.
After collecting the correlation data, the correlation data is used as the next step of the method for modeling the flow of hydrocarbons from a fractured unconventional reservoir-shown at step 1-2. The first element of this next step is to define a production reservoir block, which is the primary hydrocarbon production zone in the unconventional reservoir that needs to be simulated. Using the correlation data, the production reservoir block may be selected from the overall geology of the unconventional reservoir. In addition to selecting the overall shape and size of the production reservoir block, reservoir dimensions will also be determined as the length, width and height of the production reservoir block. The production reservoir volume and other calculations related to the reservoir flow may be calculated using the reservoir dimensions.
After defining the production reservoir block and determining reservoir dimensions, the hydraulic fracture location and fracture properties of each at least one hydraulic fracture within the production reservoir block will also be determined and reflected in the model of the production reservoir block. This is shown at steps 1-3. Hydraulic fracture location is an important parameter for the remainder of the method of the present invention for modeling hydrocarbon flow from a fractured unconventional reservoir because the production reservoir block will be divided into multiple closed production zones according to the hydraulic fracture location.
The production reservoir block is then subdivided into a plurality of closed production zones, shown at 1-4, according to the hydraulic fracture locations therein. Each enclosed production zone will typically contain at least one hydraulic fracture intact. Again, from the relevant data relating to the particular selected mine section (area) making up each enclosed production area, the area dimensions of each enclosed production area, i.e., the length, width and height of each such enclosed production area, will be determined. In simulating each enclosed production area, at least one hydraulic fracture therein may be located in the center of the enclosed production area, or may not be centered therein. The present invention covers both methods.
Each enclosed production zone will be divided into a plurality of flow subsystems according to its size, geology and at least one hydraulic fracture located therein. The division of each of the plurality of enclosed production areas into a plurality of flow subsystems is shown at steps 1-5. Effectively dividing each enclosed production area into a plurality of flow subsystems comprises: the closed production area is parsed into a granular set of sub-units, each of which is preferably capable of being accurately and quickly modeled from a production perspective, based on the granularity of the relevant data available and the conditions used therein for that purpose.
Each flow subsystem will then have at least one set of reservoir properties assigned to it at 1-6, which are additional parameters in addition to the dimensions and other available relevant data that can be used to determine the likely flow of hydrocarbons in that flow subsystem in a formula. A number of different types of reservoir properties may be associated with formation production and with the simulation and generation of a prototype curve involving unconventional reservoirs in which multiple hydraulic fractures are or have been employed. These include reservoir properties as well as fracture properties. The oil and gas reservoir properties mainly comprise matrix permeability k and porosity
Fracture properties refer to the properties of natural fractures and hydraulic fracturesWhich includes the crack permeability kFPorosity of crack
Crack thickness/width wfFracture compressibility cFAnd hydraulic fracture half length xf。
After the production reservoir block is defined and subdivided into a plurality of closed production zones each containing a plurality of flow subsystems, modeling of the actual production of hydrocarbons from the flow subsystems (shown at 1-7) can begin for subsequent coupling to produce a complete calculation of the reservoir hydrocarbon flow. For each flow subsystem, this is accomplished by first modeling the subsystem hydrocarbon flow according to at least one set of reservoir properties assigned to the associated flow subsystem. As will be appreciated by those skilled in the art, there are many methods that are capable of modeling the subsystem hydrocarbon flow, and all such methods are considered to be within the scope of the present invention. It is specifically contemplated that the subsystem hydrocarbon flows may be modeled by generating subsystem flow partial differential equations, which are partial differential equations like partial differential equations that may be coupled to adjacent flow subsystems in a set of grouped total area hydrocarbon flows, and the like. The subsystem flow partial differential equations may include at least one of linear flow equations, radial flow equations, or source/sink functions.
In embodiments where subsystem hydrocarbon flow is simulated by generating such subsystem flow partial differential equations, the subsystem flow partial differential equations may use available and relevant data and at least one set of reservoir properties assigned for the relevant flow subsystem. The same type of partial differential equations may be generated to model the subsystem hydrocarbon flow for each flow subsystem in a closed production zone or in a production reservoir block, or different types of subsystem flow partial differential equations may be used for different flow subsystems depending on the available parameters, geology, and characteristics of the assigned region that makes up the flow subsystem.
After modeling production from each flow subsystem, the next step of the method of the present invention is to model the expected zone hydrocarbon flows for each of the plurality of enclosed production zones (steps 1-8), which may be accomplished by summing the expected subsystem hydrocarbon flows for all flow subsystems in the enclosed production zone. When the expected sub-system flow of each flow sub-system in the enclosed production zone is represented by a sub-system flow partial differential equation, the zone flow can be modeled by coupling the sub-system flow partial differential equations. Those skilled in the geology and mathematics can understand how to accurately couple such sub-system flow partial differential equations to produce a rolling up model of the desired regional oil and gas flow, and all such methods are considered to be within the scope of the present invention. The zonal flow may be represented by another zonal flow partial differential equation or otherwise, and all such methods are also contemplated herein.
Finally, the reservoir flow may be simulated by summing the regional flows of each of the plurality of enclosed production regions in the production reservoir block (steps 1-9). This may again be achieved by a coupled zone flow partial differential equation representing the expected aggregate hydrocarbon flow from each flow subsystem in each of the plurality of enclosed production zones, or in other ways, and again all are considered to be within the scope of the present invention.
When each subsystem flow partial differential equation is a couplable partial differential equation, the solution to each subsystem flow partial differential equation can represent the production pressure and volumetric production rate of the corresponding flow subsystem. Similarly, when the zone flow is represented by couplable micro-zone flow partial differential equations, the solution to such zone flow partial differential equations can represent the production pressure and production flow rate of the respective enclosed production zone. If the reservoir flow is modeled as a coupled reservoir flow equation consisting of solutions to a plurality of regional flow partial differential equations, the solution to the reservoir flow equation represents the production pressure and production flow for the unconventional reservoir.
The method of fig. 1 may be improved by using modeled reservoir production to draw one or more prototype curves. After modeling the expected reservoir flow from the production reservoir block, as a production pressure and thus a volumetric production rate, one or more prototype curves may be generated using the reservoir flow in the following steps. The prototype curve may be generated at the level of a flow subsystem, an enclosed production area, or a production hydrocarbon reservoir block. The flowchart of fig. 2 illustrates an extension of the method of fig. 1, wherein the first nine steps are the same as the method of fig. 1, and one or more template curves are plotted and shown at steps 2-10.
A further modification of the basic method of the present invention of modeling hydrocarbon flow from a fractured unconventional reservoir of fig. 1 or 2 is shown in fig. 3. The method shown in fig. 3 differs from that of fig. 2 in that steps 3-5 are inserted after subdividing the production reservoir block into a plurality of closed production areas, showing manual or intervening modifications to at least one of the plurality of closed production areas after their initial determination or allocation. The remainder of the steps shown in fig. 3 are the same as the steps of the method embodiment of fig. 2, and steps 3-5 are inserted therein followed by a renumbering of the steps in order.
Modeling example:
having reviewed the method of modeling hydrocarbon flow from a fractured unconventional reservoir in terms of a high-level concept, we now wish to delineate the effect of the method itself and describe in more detail the development of the production reservoir block, the plurality of enclosed production zones and the plurality of flow subsystems for a particular unconventional reservoir.
Figure 4 shows an embodiment of an unconventional hydrocarbon reservoir that has been stimulated with multiple stages of hydraulic fracturing. In which a multi-stage fractured horizontal well is shown centrally. In this fig. 4, the production reservoir block refers to the primary hydrocarbon production zone in the unconventional reservoir that needs to be simulated. The reservoir length L in fig. 4 is equal to the horizontal length of the wellbore. The well spacing is selected as the width W. Typically, the target formation thickness serves as the height H. For the fractured horizontal well, each hydraulic fracture has half length xfAnd width wf. The number, location and spacing of hydraulic fractures are determined from the fracture treatment record. On the basis of the processing record,hydraulic fracturing is always done in multiple stages, each stage having multiple perforation clusters (perforation clusters s). Some embodiments assume one fracture per stage in calculating the number and spacing of fractures, while some embodiments may consider one fracture per perforation cluster. The number or grouping of the hydraulic fractures may vary and any method of achieving such variation is considered to be within the scope of the present invention.
The hydraulic fracture shown in fig. 4 is assumed to penetrate the target formation completely and therefore has the same height as reservoir height H. The fracture properties in any two hydraulic fractures may also be different.
Although stimulated reservoirs are complex, some methods may achieve rapid, simple, and reliable simulation of internal fluid flow. Figure 5 shows the streamline distribution during production for the stimulated production hydrocarbon reservoir block of figure 4. The streamlines represent snapshots of the transient flow field. For simplicity, the production reservoir block in fig. 5 is homogeneous and of a single porosity. Streamlines indicate that each hydraulic fracture controls a portion of the production reservoir block where fluid flows only towards the hydraulic fracture. The production reservoir block contains six closed production zones with fully closed outer boundaries, corresponding to the six hydraulic fractures in fig. 5. No fluid flows across these boundaries. Each enclosed production zone further contains four types of fluid flow. Since the flow distribution is symmetrical with respect to the wellbore, it is sufficient to study half of the production reservoir blocks to establish a reliable model. For example, referring to zone 1 of the formation shown in fig. 5, in the upper portion of zone 1, streamlines indicate that flow from the producing reservoir block in that zone converges toward the hydraulic fracture tip. On the left and right side of zone 1, the flow from both sides down to the hydraulic fracture is perpendicular to the fracture plane, and in the hydraulic fracture of zone 1, the internal flow moves towards the horizontal wellbore.
The complex fluid flow in stimulated production reservoir blocks can be reduced to several types of simple flows, which provides the basis of the present invention. The simple flow in the flow subsystem and the enclosed production area then gives a prototype curve of the entire production reservoir block. For the various types of simple flows in fig. 5, there is a mathematical solution in the laplace domain to describe the corresponding transient pressure/flow fields.
In the flow subsystem shown in fig. 6, the flow towards the fracture tip is shown according to the green's function method. At point a there is a line sink. The green's function of the line sink in the closed rectangular flow subsystem shown is calculated as follows:
wherein
p1DIs a dimensionless pressure in subsystem 1.1,
tDis a non-dimensional time, and is,
η1is the dimensionless reservoir diffusivity of subsystem 1.1,
q1Dis the dimensionless flow into the line sink at point A in subsystem 1.1, q1/Q。
And B is the formation volume factor.
Q、μ、Lr、ctAnd phi is the production rate, viscosity, length, compressibility and porosity, respectively, used as reference values in the dimensionless definition.
When using the radial equation, the embodiments herein assume that a radial reservoir with a Dietz form factor is equivalent to subsystem 1.1. FIG. 7 shows in dashed lines with a boundary rwAnd reIs given as radial subsystem 1.1. The radial flow equation for subsystem 1.1 in the Laplace domain is:
it has an outer boundary condition:
where s is the Laplace variable.
rDIs a dimensionless assumed radius, r/Lr。
The detailed description and solutions of radial flow equations and Green's functions in the Laplace domain are described in detail in various references including E.Stalgorova, L.Mattar, "Analytical Model for numerical Multi-fractional Composite Systems," SPE Reserve Evaluation & Engineering, SPE 162516 and S.Yao, F.Zeng, H.Liu, G.ZHao, "A Semi-Analytical Model for Multi-stage segmented well Wells," Journal of Hydrology 507: 201: 212. In designing multiple closed production zones for any unconventional reservoir, a closed boundary is typically placed at the center of two adjacent hydraulic fractures. However, the closed boundary may be off-center. The final dimensions of each enclosed production area are determined from the best match results.
Y in FIG. 6 or FIG. 7 in designing any closed production area flow subsystem1Is usually less than xf. When the Green function is applied, the position of point A is (0, y)1+ Δ y), the position of point B being (0, y)1). According to the best matching junctionDetermining y from the result1And the final value of Δ y.
In subsystems 1.2 and 1.3, the linear flow equations may describe fluid flow perpendicular to the hydraulic fracture planes C and D. For example, the linear subsystem flow partial differential equation for subsystem 1.2 is:
detailed descriptions and solutions of linear flow equations in the Laplace domain are described in detail in a number of references, including an SPE article: M.Brown, E.Ozkan, R.Raghavan, H.Kazemi "practical solutions for Pressure-transfer Response of Framed Horizontal Wells in Uncariational Shale Reservors", SPE Reserve Evaluation & Engineers SPE 12504.
In subsystem 1.4, the modified linear flow equation may describe the fluid flow inside the hydraulic fracture. The sub-system 1.4 connected to the wellbore has a sub-system flow partial differential equation:
wherein
FCDIs dimensionless fracture conductivity (k)FwF)/(kLr)
q2FAnd q is3FIs the flow into the hydraulic fracture from planes C and D.
qregion1Is the flow rate, q, through the exit zone 1 of the intersection of the hydraulic fracture with the horizontal wellboreregion1/Q。
Detailed descriptions and solutions of such linear equations in the laplace domain are described in detail in various references including l.larsen, t.m. here, "Pressure transfer Analysis of multifactual Horizontal Wells" SPE 28389. For initial conditions, the pressure is equal to the initial reservoir pressure in all flow subsystems.
After this operation of the individual flow subsystems, the next step in the method of modeling the flow of hydrocarbons from a fractured unconventional reservoir is to couple the solution to the subsystem flow partial differential equation for each of the plurality of flow subsystems in each of the closed production zones to derive a solution representing the zone flow partial differential equation for each of the closed zones. Reference is made to the embodiment shown for region 1. There are two cases when coupling subsystems 1.1 and 1.4. Pressure (x) at point B of 1.1 if Green's function is appliedB，yB) Is assumed to be equal to the pressure on the tip of the crack in 1.4. Furthermore, the collection rate at point a (sinkrate) at 1.1 is equal to the collection rate across the fracture tip. The coupling conditions become:
pressure and departure from inner boundary r in 1.1 if radial flow equation is applied in 1.1ewIs equal to those passing through the fracture tip in 1.4. The coupling conditions were:
the pressure values in 1.2 and 1.4 at the interface plane C are the same. Similar conditions apply to the interface plane D. The flow into plane C in 1.2 is equal to those leaving plane C in 1.4. Similarly, the flow into plane D in 1.3 is equal to those exiting plane D in 1.4. The coupling conditions were:
there is no interaction between subsystems 1.1, 1.2 and 1.3. At plane E, away fromThe flow of the hydraulic fracture is assumed to be equal to qregion1. The linear flow equations of the subsystem 1.4 can then be solved in the laplace domain under all the above-mentioned boundary and coupling conditions. The derived mathematical solution may give the transient pressure at plane E. Solutions for other regions can be derived in the same manner.
After coupling the sub-system flow partial differential equations into zone flow partial differential equations for each of the closed production zones, the next step in the method of modeling the flow from a fractured unconventional reservoir is to couple the zone flow partial differential equations for a plurality of closed production zones to obtain solutions for the entire production reservoir block. After coupling the sub-system flow partial differential equations into the zonal flow partial differential equations, the only unknown parameter in each zonal flow partial differential equation or solution is the flow rate q exiting the hydraulic fractureregion i(i ═ 1, 2 · · n, n is the number of hydraulic fractures). Since the hydraulic fractures are connected by the horizontal wellbore, the pressures at the ends of the hydraulic fractures are equal to each other. Furthermore, in mathematical modeling, horizontal wells are typically run at constant pressure or constant flow. By applying this additional condition, the method herein develops a system of n linear equations and solves analytically in the laplace domain. For example, a system of linear equations at constant production rate is similar to:
the solution of equation 8 gives the transient bottom hole pressure and the flow distribution along the horizontal borehole in the Laplace domain. The stepfest algorithm can convert values from the laplacian domain into the real time domain. In the Stehfest algorithm, the pressure becomes the real time domain as follows:
the Stehfest algorithm is described in detail in H.Stehfest, "scientific interrogation of Laplacetransorms", Communications of the ACM 13(1): 47-49. The invention selects a series of time points tDFind outCorresponding laplacian time points s, compute solutions at different time points and translate the results to real-time space according to equation 9. The final real-time solution is a series of bottom hole pressures/flows at different points in time. A template curve is generated from the pressure/flow vs. time data.
The true stimulated reservoir may be more complex in geology and behavior than shown in fig. 6 and 7-reservoir properties may change as the distance from the hydraulic fracture increases. Fig. 8-11 show several additional complex combinations of multiple flow subsystems in a closed production area.
Referring first to fig. 8, there are seven flow subsystems in a closed production area. The flow subsystem shown in this figure can simulate unconventional reservoirs where the reservoir properties gradually change throughout the production reservoir block. Each flow subsystem contains one type of simple flow and has independent reservoir properties. The radial flow moves through the flow subsystem 1.2 towards the flow subsystem 1.1. In the flow subsystem 1.1, the radial flow is directed towards the inner boundary rwGathering. The flow subsystem 1.3 contains linear flow. The flow subsystem 1.4 receives flow from the flow subsystem 1.3 and induces linear flow to the hydraulic fracture. Similarly, linear flow occurs in flow subsystems 1.5 and 1.6, and flow subsystem 1.7 has linear flow inside the hydraulic fracture. The control equations for these flow subsystems have been enumerated.
The coupling conditions for the subsystem flow partial differential equations based on the embodiment of fig. 8 are different from those outlined above. The coupling method shown in this context couples the subsystem flow partial differential equation of the flow subsystem 1.1 to the subsystem flow partial differential equation of the flow subsystem 1.2, primarily by equalizing the pressure and flow across the interface plane a. The subsystem flow partial differential equations of the flow subsystems 1.3 and 1.4 are coupled at the same pressure and flow across the interface plane B. The subsystem flow partial differential equations of the flow subsystems 1.5 and 1.6 are coupled with equal pressure and flow across the interface plane C. The sub-system flow partial differential equations of flow sub-system 1.7 are coupled with the sub-system flow partial differential equations of flow sub-systems 1.1, 1.4 and 1.6 by flow continuity across the fracture tip and plane D and E, respectively. The solution, or zone flow partial differential equation, is similar to the embodiment of fig. 6 and 7 when completed. The resulting template curves can also be matched and used to predict reservoir production.
Fig. 9 shows another different combination of flow subsystems in an enclosed production area. The enclosed production area of fig. 9 is divided into eight flow subsystems. Each flow subsystem in this figure has a simple fluid flow. In the flow subsystem 2.1, there is a line sink at the tip of the hydraulic fracture, and the green's function method describes the pressure field. The linear flow goes through the flow subsystem 2.2 to the flow subsystem 2.4. Likewise, the linear flow in the flow subsystem 2.3 enters the flow subsystem 2.6. The flow subsystems 2.4 and 2.5 take the flow from the adjacent flow subsystem and develop the internal linear flow. The flow subsystems 2.6 and 2.7 also have linear flow. For the flow subsystem 2.8, the hydraulic fracture receives flow from the surrounding flow subsystem and directs linear flow into the horizontal wellbore. The governing equations for fluid flow in the eight flow subsystems can be found from those in fig. 4 and 5.
The coupling conditions are different for different combinations of flow subsystems shown in fig. 9. The flow into the flow subsystem 2.4 is equal to the flow of the flow subsystem 2.2 perpendicular to the interface plane a. The flow into the flow subsystem 2.6 is equal to the flow of the flow subsystem 2.3 perpendicular to the interface plane B. The flow subsystems 2.4 and 2.5 are coupled with flow continuity across plane C. The flow subsystems 2.6 and 2.7 are also coupled based on flow continuity across plane D. The flow subsystem 2.8 is coupled with flow subsystems 2.1, 2.5 and 2.7 with flow continuity across the fracture tip, plane E and plane F, respectively. The solution is similar to fig. 4 and 5. The resulting prototype curve can be matched and predicted for reservoir production. Those skilled in the art will understand how to select appropriate coupling conditions and other elements of the associated differential equations, and the selection of appropriate conditions and equation elements are considered to be within the scope of the present invention.
A simulation of another complex unconventional reservoir is shown with reference to figure 10. As the unconventional reservoir becomes more complex in terms of fractures and flow, the methods herein of modeling the flow of hydrocarbons from a fractured unconventional reservoir simply divide the reservoir into a larger number of flow subsystems in a closed production area. Referring to FIG. 10, seven flow subsystems contain linear flow inside an unconventional reservoir, and three flow subsystems have radial flow towards the hydraulic fracture tip. In the embodiment of fig. 11, eleven flow subsystems have linear flow inside the reservoir and one flow subsystem has a line sink at the tip of the fracture. This means that the flow subsystem in the closed production area is not fixed. According to this approach, there are a large number of combinations of flow subsystems. Although the present invention has been described with respect to preferred embodiments, it is to be understood that various modifications and changes may be made without departing from the spirit and scope of the invention, as will be readily understood by those skilled in the art. Such modifications and variations are considered to be within the purview and scope of the claims appended hereto.
One advantage of the present invention is that heterogeneous reservoirs can be easily modeled. Heterogeneity is quite common for unconventional reservoirs. Reservoir properties around horizontal wellbores may vary significantly. To address the heterogeneity, the present invention assigns different reservoir properties to different flow subsystems. Any two flow subsystems may have different reservoir properties, whether or not the two subsystems are in the same region. For example, the flow subsystems 1.5 and 1.6 in FIG. 8 may have different reservoir properties, even though they are on the same side of the hydraulic fracture. Any two flow subsystems may likewise have different fracture properties. For example, the fracture permeability of zone 1 of fig. 5 may be different from the fracture permeability of zone 5.
Another advantage of the present invention is the ability to model dual pore reservoirs. Hydraulic fracturing can reactivate "dead" natural fractures, and a portion of the oil and gas reservoir may behave like a dual pore. A dual pore reservoir consists of two media: hydrocarbon reservoir matrix and natural fractures. Furthermore, such dual porosity characteristics may vary along a horizontal wellbore. In the present invention, any flow subsystem can be easily modified to a dual pore flow subsystem. This modification introduces two new parameters, a storable ratio ω to a flow capacity ratio λ, to characterize the natural fracture. The solution for a single pore flow subsystem is applicable to a dual pore flow subsystem with a modified laplace variable u, such as:
u＝sf(s)，…………………………………………………………(10.1)
a detailed description of this modification is given in J.E.Warren, P.J.root, "The Behavior of Natural Fratured Reservoirs", SPE Journal SPE 426 and O.A.de Swaan, "Analytical Solutions for determining Natural Fratured Reservoir properties by Well Testing", SPEjournal SPE 5346. Likewise, any two flow subsystems may have different dual pore parameters, whether or not the two flow subsystems are in the same enclosed production zone — typically by making the flow subsystems dual pore when they are closer to the hydraulic fracture.
Another advantage of the present invention is that complex flow mechanisms in shale gas oil and gas reservoirs are easily considered. Due to gas slippage, Knudsen diffusion, and stress sensitivity, in addition to inherent reservoir properties, reservoir matrix permeability becomes a function of reservoir pressure and gas properties: javadpour, "Nanopores and application durability of Gas Flowin Mudrocks (Shale and siltstone)", Journal of Canadian Petroleum Technology 48(8):16-21 and A.R.Bhand, P.B.Flemings, P.J.Polito, M.B.Cronin, S.L.Bryant, "Anisotopy and Stress Dependence of durability in the Bar Shale", Transport in Port Media108(2): 393-41. In addition, natural fractures and hydraulic fractures may become pressure sensitive during production:
kF＝kFif(pF)………………………………………………………(11)
the semi-analytical method can simulate the influence of the flow mechanism on oil and gas production. At an initial point in time, embodiments herein initialize the properties of the reservoir matrix and fractures in all flow subsystems. The pressure/flow field is then calculated for all flow subsystems. Reservoir matrix and fracture properties are updated according to the pressure/flow field. The updated properties are then used for the next time step calculation. This iterative process may continue until the last time step. In general, in the present invention, reservoir matrix and fracture properties may vary smoothly over time in each flow subsystem, and any two flow subsystems may have different properties. FIG. 13 (deleted) provides a flow chart summarizing the modeling scheme. The method is applied to basic combination and complex combination of the stream subsystems.
By applying this semi-analytical method, reservoir heterogeneity, diplopore and complex flow mechanisms can occur simultaneously in a closed production zone. For example, take region 1 in fig. 6. The flow subsystem 1.1 may be single pore. The flow subsystems 1.2 and 1.3 are dual pore and the internal natural fractures are stress sensitive. But the hydrocarbon reservoir matrix and fracture properties may be different in the flow sub-systems 1.2 and 1.3. For the flow subsystem 1.4, hydraulic fractures are stress sensitive. Gas slippage and knudsen diffusion play a role in the flow subsystems 1.1, 1.2 and 1.3. The summary is as follows: the enclosed production area may have a large number of combinations of flow subsystems, and each flow subsystem may have a large number of combinations of properties. Although the present invention has been described with respect to preferred embodiments, it will be understood that various modifications and changes may be made without departing from the spirit and scope of the invention.
The above solution is based on liquid oil and gas production. In order to use this solution and the template curve for gas flow, the dimensionless pressure should be expressed in terms of the real gas virtual pressure (pseudopressure). The definition of virtual pressure can be found in The references Al-Hussalny, R., Ramey Jr., H.J., Crawford, P.B, "The Flow of Real gases through Porous Media", Journal of Petroleum Technology18(5): 624-.
The prototype curve may be used to match and predict production of stimulated unconventional reservoirs. The prototype curves are grouped in the model according to the given reservoir and fracture properties of the various flow subsystems. Based on the known information, a set of stereotype curves can first be selected that fit the information. The master curve is placed over the submitted production data under the exact same coordinate system. If a template curve can best match the field data, the conditions behind the template curve represent unknown reservoir and hydraulic fracture properties. Trends in such a prototype curve also imply possible future production behavior. As much information as possible can be collected to reduce the time spent in matching and prediction. The boilerplate curve generated as described herein provides different models and scenarios that may be considered when reviewing or understanding potential reservoir production by the methods of the present invention.
Reservoir properties:
reservoir properties assigned to individual flow subsystems for purposes of simulating production of the reservoir include various types of reservoir properties. The reservoir property may be selected from a set of reservoir properties or a set of fracture properties.
Selected reservoir properties include matrix permeability and matrix porosity. The at least one set of reservoir properties assigned to each flow subsystem may also be selected from the group consisting of linear flow of the reservoir to the hydraulic fracture, flow towards the tip of the fracture, and flow within the hydraulic fracture. When fracture properties are used as reservoir properties assigned to a particular flow subsystem, these may include properties of natural fractures or hydraulic fractures, including fracture permeability, fracture porosity, fracture thickness/width, fracture stress sensitivity, and hydraulic fracture half-length.
The same reservoir properties may be assigned to one or more flow subsystems.
Study generated prototype curves:
based on the geometry of fig. 5, fig. 12 selects two generated prototype curves. In FIG. 12, the dotted line shows a prototype curve generated according to the method of the references S.Yao, F.Zeng, H.Liu, G.ZHao, "A Semi-analytical Model for Multi-stageFracted Horizontal Wells", Journal of Hydrology 507: 201-. The solid line shows the profile of the prototype according to the invention. For simplicity, the entire production reservoir block is assumed to be homogeneous here. Fig. 12 shows that both methods give almost the same results. However, the time to generate the prototype curves in the present invention is significantly shorter than the time used in the methods of the reference. The difference in calculation time becomes greater when more hydraulic fractures are included. The following is the time to calculate the prototype curve shown in fig. 12, which exhibits significant time benefits:
| calculating time of the invention | Calculated time of |
|
| 3 |
3 seconds | 19 |
| 6 hydraulic cracks | 5 seconds | 51 minutes |
| 12 hydraulic fractures | 8 seconds | 140 minutes |
The computation time also depends on the processing power of the computer. A better computer will further reduce the computation time. In general, the present invention provides a fast and reliable method of generating a stereotype curve for stimulated unconventional hydrocarbon reservoirs.
Computer software:
the method of the present invention can also be simplified to be implemented in a computer software program-indeed beyond the mathematical methods outlined herein, the computer software method of creating a stereotype curve according to the present invention is expected to be the most likely commercial embodiment of the present invention. Computer software developed to employ the methods of the present invention is to be considered and understood as included within the scope of the present invention.
The software of the present invention, as a non-transitory computer readable storage medium for a method for simulating hydrocarbon flow from a fractured unconventional hydrocarbon reservoir, includes instructions that, when executed by a computer, cause the computer to perform the following operations:
collecting correlation data corresponding to unconventional hydrocarbon reservoirs that have been subjected to multi-stage hydraulic fracturing;
using the correlation data:
defining a production reservoir block as a primary hydrocarbon production zone in the unconventional reservoir and calculating reservoir dimensions for the length, width and height of the production reservoir block; and
defining the location and characteristics of individual hydraulic fractures in the production reservoir block;
subdividing the production reservoir block into a plurality of closed production zones, each closed production zone having at least one hydraulic fracture therein, and calculating zone dimensions for the length, width and height of each closed production zone;
subdividing each enclosed production area into a plurality of flow subsystems; and
assigning at least one set of reservoir properties to each flow subsystem;
modeling subsystem hydrocarbon flows for each of the plurality of flow subsystems based on at least one set of reservoir properties assigned thereto and associated data corresponding to that flow subsystem;
modeling the regional oil and gas flow of each enclosed production region by coupling the calculated subsystem oil and gas flow of each flow subsystem in the enclosed production region; and
modeling reservoir flow for the unconventional reservoir by coupling the calculated regional flow for each of the plurality of closed production regions.
At its highest level, the software of the present invention is able to efficiently implement the computer-assisted execution of the method of modeling hydrocarbon flow from a fractured unconventional reservoir shown in fig. 1-3. In addition to the basic simulation of reservoir flow, a template curve can be drawn according to the results for use.
The parameter assignments and calculations performed by the software are as outlined above for the method of modeling hydrocarbon flow from a fractured unconventional reservoir.
Computer software of the present invention will be capable of developing couplable differential equations for performing embodiments of the method, including providing subsystem flow partial differential equations and zone flow partial differential equations that can be coupled to produce a solution representative of reservoir flow in the reservoir flow equations.
Figure 13 (deleted) illustrates one embodiment of the method of the present invention as performed in computer software.
Claims (46)
1. A method of modeling hydrocarbon flow from a fractured unconventional reservoir, the method comprising:
collecting correlation data corresponding to unconventional hydrocarbon reservoirs that have been subjected to multi-stage hydraulic fracturing;
using the correlation data:
defining a production reservoir block as a primary hydrocarbon production zone within the unconventional reservoir;
calculating reservoir dimensions of length, width and height of the production reservoir block; and
defining the location and characteristics of each hydraulic fracture within the production hydrocarbon reservoir block;
subdividing the production reservoir block into a plurality of closed production zones, each closed production zone containing at least one hydraulic fracture therein;
calculating the area size of the length, the width and the height of each closed production area;
subdividing each enclosed production area into a plurality of flow subsystems; and
assigning at least one set of reservoir properties to each flow subsystem;
relative to at least one selected point in time:
modeling subsystem hydrocarbon flow for each of the plurality of flow subsystems based on the at least one set of reservoir properties assigned to each flow subsystem and the associated data corresponding to that flow subsystem;
modeling the regional oil and gas flow for each enclosed production zone by coupling the calculated subsystem oil and gas flow for each flow subsystem within the enclosed production zone; and
reservoir flow of the unconventional reservoir is modeled by coupling the calculated regional flows coupled for each of the plurality of closed production regions.
2. The method of claim 1, wherein the subsystem hydrocarbon flow of at least one of the plurality of flow subsystems is modeled relative to a plurality of selected points in time, and further comprising the step of generating at least one template curve that displays the simulated subsystem hydrocarbon flow of the selected flow subsystem on one axis thereof and the associated selected point in time on another axis thereof.
3. The method of claim 1 wherein the regional hydrocarbon flow of at least one of the plurality of enclosed production regions is modeled relative to a plurality of selected points in time, and further comprising the step of generating at least one template curve that displays on one axis thereof the simulated regional hydrocarbon flow of the selected enclosed production region and on another axis thereof the associated selected points in time.
4. The method of claim 1, wherein reservoir flow is modeled relative to a plurality of selected points in time, and further comprising the step of generating at least one template curve showing simulated reservoir flow for the production reservoir block on one axis thereof and associated selected points in time on another axis thereof.
5. The method of claim 1 wherein the relevant data corresponding to the unconventional hydrocarbon reservoir is selected from the group consisting of mine site data, production history, fracture treatment records, and microseismic activity.
6. The method of claim 1, wherein the at least one set of reservoir properties assigned to the flow subsystem is selected from a set of reservoir properties or a set of fracture properties.
7. The method of claim 6, wherein the selected reservoir properties include matrix permeability and matrix porosity.
8. The method of claim 6, wherein the fracture properties are properties of hydraulic fractures and natural fractures.
9. The method of claim 8, wherein the selected fracture properties include fracture permeability, fracture porosity, fracture thickness/width, fracture stress sensitivity, and hydraulic fracture half-length.
10. The method of claim 1, wherein the subsystem hydrocarbon flow of each of the plurality of flow subsystems is modeled by generating partial differential subsystem flow partial differential equations representing determined hydrocarbon flows of the flow subsystems, whereby each subsystem flow partial differential equation can be coupled to the subsystem flow partial differential equations of the other flow subsystems within the respective closed production zone.
11. The method of claim 10 wherein the zone hydrocarbon flow of each enclosed production zone is modeled by coupling the subsystem flow partial differential equations of each of the plurality of flow subsystems within the enclosed production zone to produce partial differential zone flow partial differential equations whereby each zone flow partial differential equation can be coupled to the zone flow partial differential equations of the other enclosed production zones within the production hydrocarbon reservoir block.
12. The method of claim 11, wherein the reservoir flow is modeled by coupling zone flow partial differential equations for all of the plurality of enclosed production zones within the production reservoir block to produce reservoir flow equations.
13. The method of claim 12, wherein the result of the reservoir flow equation is an expected hydrocarbon production from the production reservoir block adjusted for unconventional geology and a plurality of fractures in the production reservoir block.
14. The method of claim 10, wherein the solution to each subsystem flow partial differential equation represents the production pressure and volumetric production rate of the corresponding flow subsystem.
15. The method of claim 11, wherein the solution to each zone flow partial differential equation represents the production pressure and volumetric production rate of the corresponding enclosed production zone.
16. The method of claim 12, wherein the solution to the reservoir flow equation represents production pressure and volumetric production rate of the unconventional reservoir.
17. The method of claim 1, wherein at least one hydraulic fracture in at least one enclosed production zone is located in the center of the enclosed production zone.
18. The method of claim 1, wherein at least one hydraulic fracture in at least one enclosed production zone is not located in the center of the enclosed production zone.
19. The method of claim 1, wherein the at least one set of reservoir properties assigned to each flow subsystem is selected from the group consisting of linear flow in the reservoir, linear flow of the reservoir to the hydraulic fracture, flow toward the tip of the fracture, and flow inside the hydraulic fracture.
20. The method of claim 19 wherein at least one set of reservoir properties assigned to each flow subsystem within the production reservoir block is the same.
21. The method of claim 19 wherein at least one set of reservoir properties assigned to each flow subsystem within the production reservoir block is different.
22. The method of claim 1, wherein each subsystem flow partial differential equation comprises at least one of a linear flow equation, a radial flow equation, or a source/sink function.
23. The method of claim 1, wherein a zone size of at least one enclosed production zone is modified from the initially calculated zone size based on the hydraulic fracture location and the correlation data.
24. A non-transitory computer-readable storage medium for a method of modeling hydrocarbon flow from a fractured unconventional reservoir, the computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to perform the operations of:
collecting correlation data corresponding to unconventional hydrocarbon reservoirs that have been subjected to multi-stage hydraulic fracturing;
using the correlation data:
the production reservoir block is defined as the primary hydrocarbon production zone in the unconventional reservoir,
calculating the length, width and height of the production oil and gas reservoir block; and
defining the location and characteristics of each hydraulic fracture within the production hydrocarbon reservoir block;
subdividing the production reservoir block into a plurality of closed production zones, each closed production zone containing at least one hydraulic fracture;
calculating the area size of the length, the width and the height of each closed production area;
subdividing each enclosed production area into a plurality of flow subsystems; and
assigning at least one set of reservoir properties to each flow subsystem;
relative to at least one selected point in time:
modeling subsystem hydrocarbon flow for each of the plurality of flow subsystems based on the at least one set of reservoir properties assigned to each flow subsystem and the associated data corresponding to that flow subsystem;
modeling the regional oil and gas flow for each enclosed production zone by coupling the calculated subsystem oil and gas flow for each flow subsystem within the enclosed production zone; and
the reservoir flow of the unconventional reservoir is modeled by coupling the calculated regional flow of each of the plurality of closed production regions.
25. The computer readable storage medium of claim 24, wherein the subsystem hydrocarbon flow of at least one of the plurality of flow subsystems is modeled relative to a plurality of selected time points, and wherein the instructions further cause the computer to generate at least one stereotype curve that displays the simulated subsystem hydrocarbon flow of the selected flow subsystem on one axis thereof and the associated selected time point on another axis thereof.
26. The computer readable storage medium of claim 24 wherein the regional hydrocarbon flow of at least one of the plurality of enclosed production regions is modeled relative to a plurality of selected time points, and wherein the instructions further cause the computer to generate at least one stereotype curve that displays the simulated regional hydrocarbon flow of the selected enclosed production region on one axis thereof and the associated selected time points on another axis thereof.
27. The computer readable storage medium of claim 24, wherein the regional hydrocarbon flow is modeled relative to a plurality of selected time points, and wherein the instructions further cause the computer to generate at least one stereotype curve that displays the simulated hydrocarbon flow for the production hydrocarbon reservoir block on one axis thereof and the associated selected time points on another axis thereof.
28. The computer readable storage medium of claim 24, wherein the relevant data corresponding to the unconventional hydrocarbon reservoir is selected from the group consisting of mine site data, production history, fracture treatment records, and microseismic activity.
29. The computer readable storage medium of claim 24, wherein the at least one set of reservoir properties assigned to the flow subsystem is selected from a set of reservoir properties or a set of fracture properties.
30. The computer readable storage medium of claim 29, wherein the selected reservoir properties include matrix permeability and matrix porosity.
31. The computer readable storage medium of claim 29, wherein the fracture properties are properties of hydraulic fractures and natural fractures.
32. The computer readable storage medium of claim 31, wherein the selected fracture properties include fracture permeability, fracture porosity, fracture thickness/width, fracture stress sensitivity, and hydraulic fracture half-length.
33. The computer readable storage medium of claim 24, wherein the subsystem oil and gas flow of each of the plurality of flow subsystems is modeled by generating partial differential subsystem flow partial differential equations representing determined oil and gas flows of the flow subsystems, whereby each subsystem flow partial differential equation can be coupled to the subsystem flow partial differential equations of the other flow subsystems within the respective closed production zone.
34. The computer readable storage medium of claim 33 wherein the zone hydrocarbon flow of each enclosed production zone is modeled by coupling the subsystem flow partial differential equations of each of the plurality of flow subsystems within the enclosed production zone to produce partial differential zone flow partial differential equations whereby each zone flow partial differential equation can be coupled to the zone flow partial differential equations of the other enclosed production zones within the production hydrocarbon reservoir block.
35. The computer readable storage medium of claim 34, wherein the reservoir flow is modeled by coupling the zone flow partial differential equations of all of the plurality of enclosed production zones within the production reservoir block to produce reservoir flow equations.
36. The computer readable storage medium of claim 35, wherein the result of the reservoir flow equation is an adjusted expected hydrocarbon production from the production reservoir block for unconventional geology and a plurality of fractures in the production reservoir block.
37. The computer readable storage medium of claim 33, wherein the solution to each subsystem flow partial differential equation represents the production pressure and volumetric production rate of the corresponding flow subsystem.
38. The computer readable storage medium of claim 34, wherein the solution to each zone flow partial differential equation represents the production pressure and volumetric production rate of the corresponding enclosed production zone.
39. The computer readable storage medium of claim 35, wherein the solution to the reservoir flow equation represents a production pressure and a volumetric production rate of the unconventional reservoir.
40. The computer readable storage medium of claim 24, wherein at least one hydraulic fracture in at least one enclosed production zone is located in the center of the enclosed production zone.
41. The computer readable storage medium of claim 24, wherein at least one hydraulic fracture in at least one enclosed production zone is not located in the center of the enclosed production zone.
42. The computer readable storage medium of claim 24, wherein the at least one set of reservoir properties assigned to each flow subsystem is selected from the group consisting of linear flow in the reservoir, linear flow of the reservoir to the hydraulic fracture, flow toward the tip of the fracture, and flow inside the hydraulic fracture.
43. The computer readable storage medium of claim 42, wherein at least one set of reservoir properties assigned to each flow subsystem within the production reservoir block are the same.
44. The computer readable storage medium of claim 42, wherein at least one set of reservoir properties assigned to each flow subsystem within the production reservoir block is different.
45. The computer readable storage medium of claim 24, wherein each subsystem flow partial differential equation comprises at least one of a linear flow equation, a radial flow equation, or a source/sink function.
46. The computer readable storage medium of claim 24, wherein a zone size of at least one enclosed production zone is modified from an initially calculated zone size based on the hydraulic fracture location and the correlation data.
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| CN106897544A (en) | 2017-06-27 |
| CA2914348A1 (en) | 2016-12-14 |
| CA2914348C (en) | 2018-03-06 |
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