CN106897544B - Method of modeling oil and gas production from fractured unconventional formations - Google Patents

Abstract

A method of modeling hydrocarbon flow from a fractured unconventional oil and gas reservoir in which the formation has variability in stimulated reservoir properties caused by multi-stage fracturing treatments. A diagram is produced that divides the formation into a plurality of enclosed production areas, each of which is in turn divided into a plurality of fluid subsystems extending between fractures in the formation. The production behavior is then calculated for each flow subsystem based on the geography and characteristics of the individual flow subsystem. Regional oil and gas flows for each enclosed production area are determined by coupling the calculated production behavior of the flow subsystem, and the reservoir oil and gas flows are modeled by summing the regional oil and gas flows. A template curve showing the simulated oil flow at the selected point in time can then be drawn.

Description

Methods for modeling oil and gas production from fractured unconventional formations

technical field

The present invention relates to methods of generating oil and gas production curves from sets of geological formations, and more particularly provides methods of generating oil and gas production curves from unconventional oil and gas reservoirs stimulated by multi-stage hydraulic fractures.

Background technique

Technology development and innovation in the field of oil and gas exploration and production has a long history. As a capital-intensive industry, the oil and gas extraction industry has many incentives to optimize and maximize production from specific hydrocarbon-bearing formations. For example, unconventional oil and gas reservoirs are those that are less permeable and require stimulation to produce profitably.

When producing oil and gas from unconventional geological formations such as shale, a common production optimization technique is to create multiple hydraulic fractures along a multistage fracturing horizontal well to stimulate the reservoir. This technique is commonly referred to as "fracturing". Oil and gas production induced in a hydraulic fracturing program is the result of flow in the matrix, in the natural fracture network, and in the hydraulic fractures themselves.

There are many problems in modeling oil and gas production in fractured geological formations with high heterogeneity. For example, during multi-stage hydraulic fracturing, many pre-existing natural fractures are reactivated. Hydraulic fractures and active natural fractures constitute the hydraulically 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. Modelling methods are likely to be reliable only if the heterogeneity of these post-fractured unconventional formations is taken into account.

Many fracturing companies have also developed and used innovative fracturing technologies, including two representative technologies under the SIMULFRAC and ZIPPERFRAC brands. In the SIMULFRAC or ZIPPERFRAC method, two or more parallel horizontal wells are drilled and subsequently drilled and fractured at alternating intervals along the wellbore. This produces a high-density hydraulic fracture network and, therefore, a relatively low stimulus volume that can be controlled by each hydraulic fracture. The stimulus volume beyond the hydraulic fracture tip also becomes smaller, and its internal flow may no longer behave like a linear flow. Existing modeling methods cannot be applied if they assume linear flow beyond the fracture tip.

Another complication is that the fluid flow mechanisms in unconventional reservoirs are quite complex compared to conventional formations. Darcy's law is often flawed in such reservoirs. In the production of some unconventional gas reservoirs, gas diffusion and desorption occur simultaneously. In addition, the high dependence of reservoir permeability on stress has been confirmed by many experiments. No method has been developed in any technical literature or methodology to fully incorporate all these complex flow mechanisms into the modeling or evaluation of unconventional reservoir production.

Another problem associated with the modeling or execution of fracture treatments in unconventional formations is the difficulty associated with predicting or accurately simulating the likely production of the formation. Although sophisticated 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 difficulties in iterative applications. One of the main technical reasons for the difficulties in these calculations is the low matrix permeability.

The oil and gas produced from fractures at all levels mainly comes from the stimulated reservoir volume around hydraulic fractures, which provides the possibility to break down the oil and gas reservoir into smaller parts. A method for fast, simple and reliable study of production from unconventional oil and gas reservoirs based on the decomposition of unconventional oil and gas reservoirs into smaller parts is believed to be very popular.

It would be very desirable in the oil and gas production industry to be able to create a method for generating model curves of oil and gas production from unconventional reservoirs stimulated by multi-level hydraulic fractures.

SUMMARY OF THE INVENTION

The present invention includes a method of modeling oil flow from an unconventionally fractured oil and gas reservoir that has been subjected to multiple fracturing. The present invention develops a model curve for oil and gas production from unconventional oil and gas reservoirs stimulated by multi-stage fracturing. A template 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 given reservoir condition. Template curves can 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 oil and gas reservoir may include collecting correlation data corresponding to an unconventional oil and gas reservoir that has been subjected to multi-stage hydraulic fracturing, using the correlation Data, modeling the oil and gas flow of the subsystems of each group of fluid subsystems according to at least one set of oil and gas reservoir properties assigned to the subsystem and the relevant data corresponding to the fluid subsystem, by coupling the calculation of each fluid subsystem in the closed production area Model the regional oil and gas flow of each enclosed production area by using the derived subsystem oil flow, and/or model the oil and gas reservoir oil and gas flow of the unconventional reservoir by coupling the calculated regional oil and gas flow of each group of enclosed production areas.

Description of drawings

To easily identify the discussion of any particular element or act, the most prominent digit in a reference number refers to the reference number when the element is first introduced.

1 is a flow chart showing steps in one embodiment of a 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 template curve from modeled oil and gas reservoir production;

Figure 3 is a flow diagram of the method of Figure 2 with the addition of the step of modifying a plurality of enclosed production areas once initially calculated;

Figure 4 is a schematic diagram of an unconventional oil and gas reservoir stimulated by multi-stage hydraulic fracturing;

Figure 5 is a plan view of a streamlined distribution in the unconventional oil and gas reservoir of Figure 4;

Figure 6 shows the subdivision of the enclosed production area of Figure 5 into multiple flow subsystems (area 1 of Figure 5) in accordance with one embodiment of the present invention;

Fig. 7 shows an alternative embodiment of subdividing the enclosed production area of Fig. 5 into multiple flow subsystems (area 1 of Fig. 5) in accordance with the present invention;

Figure 8 illustrates another embodiment of subdividing a closed production area into multiple flow subsystems in accordance with the present invention;

Figure 9 illustrates another embodiment of the subdivision of a closed production area into multiple flow subsystems in accordance with the present invention;

Figure 10 illustrates another embodiment of the subdivision of an enclosed production area into multiple flow subsystems in accordance with the present invention;

Figure 11 illustrates another embodiment of the subdivision of a closed production area into multiple flow subsystems in accordance with the present invention;

12 is a sample of a template curve produced by the method of the present invention for modeling hydrocarbon flow from a fractured unconventional reservoir;

Figure 13 shows an aspect of the subject matter of an embodiment of the present invention.

Detailed ways

The present invention is a method of modeling hydrocarbon flow from a fractured unconventional reservoir. "Unconventional reservoirs" are those with low permeability that require stimulation to produce profitably. Multistage hydraulic fracturing techniques are often used to maximize oil and gas recovery from oil and gas from such formations, and template curves are a useful simulation/modeling technique for evaluating reservoir productivity.

A template curve is a visualization tool for evaluating oil and gas production—it is a graph with time as the x-axis and production rate q/bottom hole pressure p/bottom hole pressure derivative as the y-axis for a particular reservoir condition. Typically, multiple template curves are generated based on adjustments to formation parameters. Template curves can 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 modeling oil and gas production in fractured unconventional oil and gas reservoirs are time consuming and not as accurate in some cases. The method of the present invention (effectively deconstructing a given unconventional oil and gas reservoir into multiple enclosed production regions and multiple flow subsystems therein, each accommodating individual hydraulic fracture locations in the formation) provides greater efficiency and speed associated full template curves and more accurate results.

Method overview:

Figure 1, to which reference is first made, is a flow chart illustrating 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 template curves of hydrocarbon production parameters in unconventional reservoirs based on the modeling techniques outlined herein.

The first step in the method of the present invention for modeling oil flow from a fractured unconventional oil and gas reservoir is to collect relevant data corresponding to an unconventional oil and gas reservoir that has been subjected to natural or artificial multi-stage hydraulic fracturing. This is shown at step 1-1. Relevant data that can be used in this 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 for modeling hydrocarbon flow from fractured unconventional reservoirs to provide unconventional reservoir models, producing reservoir blocks, and hydraulics for determining reservoir hydrocarbon flow Location and characteristics of cracks.

After the relevant data is collected, the relevant data is used for the next step in the method of modeling hydrocarbon flow from a fractured unconventional reservoir - shown at steps 1-2. The first element of this next step is to define the producing reservoir block, which is the primary oil and gas producing area in the unconventional reservoir that needs to be modeled. Using this correlation data, the producing reservoir block can be selected from the overall geology of the unconventional reservoir. In addition to selecting the overall shape and size of the producing reservoir block, the reservoir dimensions will be determined as the length, width and height of the producing reservoir block. The producing reservoir block volume and other calculations involving hydrocarbon gas flow from the reservoir can be calculated using the reservoir dimensions.

After defining the producing oil and gas reservoir block and determining the size of the oil and gas reservoir, the respective hydraulic fracture locations and fracture properties of at least one hydraulic fracture in the producing oil and gas reservoir block are also determined and reflected in the model of the producing oil and gas reservoir block. This is shown at steps 1-3. The hydraulic fracture location is an important parameter for the remainder of the method of the present invention to model oil flow from a fractured unconventional reservoir, as the producing reservoir block will be divided into multiple enclosed production areas based on the hydraulic fracture location .

The producing reservoir block is then subdivided into closed producing areas - shown at 1-4 - based on the location of the hydraulic fractures therein. Each closed production area will generally contain at least one complete hydraulic fracture. Again, the area dimensions of each enclosed production area - ie the length, width and height of each such enclosed production area, will be determined from the relevant data relating to the particular selected areas that make up each enclosed production area. When simulating each closed production area, at least one of the hydraulic fractures may be located in the center of the closed production area, or may not be centered therein. The present invention covers both methods.

Each enclosed production area will be divided into multiple flow subsystems based on its size, geology and at least one hydraulic fracture located therein. The division of multiple enclosed production areas into multiple flow subsystems is shown at steps 1-5. Effectively dividing each enclosed production area into multiple flow subsystems involves resolving the enclosed production area into a granular set of subunits, each of which is It is best to be able to model accurately and quickly from a production perspective.

裂缝性质指的是天然裂缝和水力裂缝的性质，其包括裂缝渗透率k_F、裂缝孔隙率

裂缝厚度/宽度w_f、裂缝压缩率c_F和水力裂缝半长度x_f。Then at 1-6, each fluidics subsystem will then have at least one set of reservoir properties assigned to it, in addition to size and other available relevant data that can be used to formulate the likely hydrocarbon flows in that fluidics subsystem additional parameters. A number of different types of reservoir properties can be correlated with formation production and with the modeling and generation of template curves involving unconventional reservoirs where multistage hydraulic fracturing will be or has been employed. These include reservoir properties as well as fracture properties. The properties of oil and gas reservoirs mainly include matrix permeability k and porosity

Fracture properties refer to the properties of natural fractures and hydraulic fractures, including fracture permeability k _F , fracture porosity

Fracture thickness/width w _f , fracture compressibility c _F and hydraulic fracture half length x _f .

After the producing oil and gas reservoir block has been defined and subdivided into multiple enclosed production areas, each containing multiple flow subsystems, modeling of the actual production of oil and gas from each of the flow subsystems (shown in 1-7 ) for subsequent coupling to produce a complete calculation of reservoir hydrocarbon flow. For each flow subsystem, this is accomplished by first modeling the oil flow for that subsystem according to at least one set of reservoir properties assigned to the associated flow subsystem. As those skilled in the art will appreciate, there are many ways in which the oil flow of this subsystem can be modeled, and all such methods are considered to be within the scope of the present invention. It is specifically envisaged that this subsystem oil flow can be modeled by generating subsystem flow partial differential equations that can be coupled to adjacent flow subsystems in a set of grouped total area oil flow etc. A partial differential equation similar to a partial differential equation. 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 the subsystem flow partial differential equations are generated by generating such subsystem flow partial differential equations, the subsystem flow partial differential equations may use available and relevant correlation data and at least one set of oil and gas reservoirs assigned to the relevant flow subsystems nature. The same type of partial differential equations can be generated to model the sub-system oil flow of each fluidic subsystem in an enclosed production area or in a producing reservoir block, or according to the parameters available to the assigned area that make up the fluidic subsystem, Geological conditions and properties, different types of subsystem flow partial differential equations are used for different flow subsystems.

After modeling the production from the various flow subsystems, the next step of the method of the present invention is to model the expected regional oil flow for each of the plurality of enclosed production areas (steps 1-8), which can be achieved by This is accomplished by summing the expected subsystem oil flows for all flow subsystems in the enclosed production area. When the expected subsystem oil flow of each fluid subsystem in the enclosed production area is represented by the subsystem flow partial differential equations, the region oil flow can be simulated/modeled by coupling the subsystem flow partial differential equations. Those skilled in the fields of geology and mathematics can understand how to precisely couple such subsystem flow partial differential equations to produce rolled up models of oil and gas flow in the desired region, and all such methods are also considered to be within the scope of the present invention. Inside. The regional oil flow can be represented by another regional flow partial differential equation or in other ways, all such methods are also considered herein.

Finally, the oil and gas reservoir oil flow can be modeled by summing the regional oil and gas flow of each of the plurality of enclosed production regions in the producing oil and gas reservoir block (steps 1-9). This can again be accomplished by coupling regional flow partial differential equations representing the flow from the plurality of enclosed production regions, and all again considered to be within the scope of the present invention, or in other ways. Expected concentrated oil flow for each flow subsystem in each zone.

When the flow partial differential equations of each subsystem are coupleable partial differential equations, the solutions of the flow partial differential equations of each subsystem can represent the production pressure and volume production rate of the corresponding flow subsystem. Similarly, when the oil flow in the region is represented by a differential regional flow partial differential equation that can be coupled, the solution of such regional flow partial differential equation can represent the production pressure and production flow in the corresponding enclosed production region. If the reservoir oil flow is modeled as a coupled reservoir flow equation consisting of solutions of multiple regional flow partial differential equations, the solution of the reservoir flow equation represents the production pressure and production flow of the unconventional reservoir.

The method of FIG. 1 can be improved by drawing one or more template curves using modeled reservoir production. After modeling the expected reservoir gas flow from the producing reservoir block, one or more template curves can be generated using the reservoir gas flow in the following steps as production pressure and thus volumetric production rate. Template curves can be generated at the level of flow subsystems, closed producing areas, or producing reservoir blocks. The flow chart of FIG. 2 shows an extension of the method of FIG. 1, wherein the first nine steps are the same as the method of FIG. 1, and the drawing of one or more template curves is shown at steps 2-10.

A further modification of the basic method of the present invention of Figure 1 or Figure 2 for modeling hydrocarbon flow from a fractured unconventional reservoir is shown in Figure 3 . The method shown in Figure 3 differs from Figure 2 in that steps 3-5 are inserted after the subdivision of the producing reservoir block into multiple enclosed production areas, showing that after the initial identification or assignment of multiple enclosed production areas Manual or interventional modification of at least one of the plurality of enclosed production areas. The remainder of the steps shown in Figure 3 are identical to the steps of the method embodiment of Figure 2, and the steps have been renumbered sequentially after steps 3-5 have been inserted therein.

Modeling example:

Having reviewed, at a high-level, conceptual level, an approach to modeling hydrocarbon flow from a fractured unconventional reservoir, we now wish to characterize the effect of the approach itself and describe in more detail what is described for specific unconventional reservoir development. A production oil and gas reservoir block, the plurality of enclosed production areas, and the plurality of fluidic subsystems are produced.

Figure 4 shows one embodiment of an unconventional oil and gas reservoir that has been stimulated with multi-stage hydraulic fracturing. A multi-stage fractured horizontal well is shown in the center. In this Figure 4, the producing oil and gas reservoir block refers to the main oil and gas producing area in the unconventional oil and gas reservoir that needs to be modeled. The reservoir length L in Figure 4 is equal to the horizontal length of the wellbore. Well spacing is chosen as width W. Typically, the target formation thickness acts as the height H. For this fractured horizontal well, each hydraulic fracture has a half length x _f and a width w _f . The number, location, and spacing of hydraulic fractures are determined from the fracturing treatment records. According to treatment records, hydraulic fracturing is always done in multiple stages, each stage having multiple perforation clusters (perforation clusters). Some embodiments take one fracture per stage when calculating fracture number and spacing, 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 fractures shown in Figure 4 are assumed to penetrate the target formation completely and thus have the same height as the reservoir height H. The fracture properties in any two hydraulic fractures can also be different.

Despite the complexity of stimulated oil and gas reservoirs, certain methods enable fast, simple, and reliable modeling of internal fluid flow. FIG. 5 shows the streamline distribution during production for the stimulated producing reservoir block in FIG. 4 . Streamlines represent snapshots of the transient flow field. For simplicity, the producing reservoir blocks in Figure 5 are homogeneous and single porosity. The streamlines indicate that each hydraulic fracture controls a portion of the producing reservoir block where fluid flows only towards the hydraulic fracture. Corresponding to the six hydraulic fractures in Fig. 5, the producing oil and gas reservoir block contains six closed production areas with fully enclosed outer boundaries. There is no fluid flow across these boundaries. Each enclosed production area further contains four types of fluid flows. Since the flow distribution is symmetric with respect to the wellbore, it is sufficient to study half of the producing reservoir blocks to develop a reliable model. Referring, for example, to Region 1 of the formation shown in Figure 5, in the upper portion of Region 1, the streamlines show that the flow from the producing reservoir block in this region is converging towards the hydraulic fracture tip. On the left and right sides 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 producing oil and gas reservoir blocks can be reduced to several types of simple flows, which provide the basis of the present invention. The simple flow in the fluidic subsystem and the enclosed production area then gives a template curve for the entire producing reservoir block. For the various types of simple flows in Figure 5, mathematical solutions exist in the Laplace domain to describe the corresponding transient pressure/flow fields.

Region 1 of Figure 5 is divided into four flow subsystems. Each fluidic subsystem contains one type of simple fluid flow (arrows show fluid direction), and these fluidic subsystems each have independent reservoir properties. Figures 6 and 7 show two samples of the flow subsystem of Region 1 in Figure 5.

In the flow subsystem shown in Figure 6, the flow towards the fracture tip is shown according to the Green's function method. There is a line sink at point A. The Green's function of the sink in the shown closed rectangular flow subsystem is calculated as follows:

in

p _1D is the dimensionless pressure in subsystem 1.1,

t _D is the dimensionless time,

η ₁ is the dimensionless reservoir diffusivity of subsystem 1.1,

q _1D is the dimensionless flow into the sink at point A in subsystem 1.1, q ₁ /Q.

B is the formation volume factor.

Q, μ, L _r , _ct and φ are production rate, viscosity, length, compressibility and porosity, respectively, which are used as reference values in the dimensionless definition.

When using the radial equation, the embodiments herein assume a radial reservoir with a Dietz shape factor equivalent to Subsystem 1.1. Figure 7 shows a hypothetical radial subsystem 1.1 with boundaries r _w and r _e in dashed lines. The radial flow equation for subsystem 1.1 in the Laplace domain is:

It has outer boundary conditions:

where s is the Laplace variable.

r _D is the dimensionless hypothetical radius, r/L _r .

Detailed descriptions and solutions of radial flow equations and Green's functions in the Laplace domain are described in detail in several references including E. Stalgorova, L. Mattar "Analytical Model for Unconventional Multifractured Composite Systems", SPE Reservoir Evaluation & Engineering, SPE 162516 and S. Yao, F. Zeng, H. Liu, G. Zhao, "A Semi-analytical Model for Multi-stage Fractured Horizontal Wells", Journal of Hydrology 507:201-212. When designing multiple closed production areas for any unconventional reservoir, the closed boundary is usually placed at the center of two adjacent hydraulic fractures. However, closed boundaries can also be off-center. The final size of each closed production area is determined based on the best match.

When designing flow subsystems for any enclosed production area, y ₁ in Figure 6 or Figure 7 is typically less than x _f . When the Green's function is applied, the position of point A is (0, y ₁ +Δy) and the position of point B is (0, y ₁ ). The final values of y ₁ and Δy are determined according to the best matching result.

In subsystems 1.2 and 1.3, the linear flow equations can describe the 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:

A detailed description and solution of linear flow equations in the Laplace domain is detailed in several references, including an SPE paper: M. Brown, E. Ozkan, R. Raghavan, H. Kazemi "Practical Solutions for Pressure-Transient Response of Fractured Horizontal Wells in Unconventional Shale Reservoirs", SPE Reservoir Evaluation & Engineers SPE12504.

In Subsystem 1.4, the modified linear flow equation can describe the fluid flow inside the hydraulic fracture. Subsystem 1.4 connected to the wellbore has a partial differential equation for the flow of the subsystem:

in

F _CD is dimensionless fracture conductivity, (k _F w _F )/(kL _r )

q _2F and q _3F are the flows from planes C and D into the hydraulic fracture.

q _region1 is the flow out of region 1 through the intersection of the hydraulic fracture and the horizontal wellbore, q _region1 /Q.

A detailed description and solution of such linear equations in the Laplace domain is detailed in several references including L. Larsen, T.M. Herge, "Pressure Transient Analysis of Multifractured Horizontal Wells" SPE 28389. For initial conditions, the pressure is equal to the initial reservoir pressure in all flow subsystems.

Following this work on individual fluidic subsystems, the next step in the method of modeling oil flow from a fractured unconventional reservoir is to model each of the plurality of fluidic subsystems in each enclosed production area Coupling the solution with the subsystem flow partial differential equation to derive the solution, representing the regional flow partial differential equation for each enclosed region. Reference is made to the example shown for area 1 . There are two situations when coupling subsystems 1.1 and 1.4. The pressure at point B in 1.1 (x _B , y _B ) is assumed to be equal to the pressure at the fracture tip in 1.4 if the Green's function is applied. Furthermore, the sinkrate at point A of 1.1 is equal to the sinkrate across the fracture tip. The coupling condition becomes:

If the radial flow equation is applied in 1.1, the pressure and flow rate leaving the internal boundary _rew in 1.1 are equal to those across the fracture tip in 1.4. The coupling conditions are:

The pressure values in 1.2 and 1.4 at interface plane C are the same. Similar conditions apply to the interface plane D. The flows entering plane C in 1.2 are equal to those leaving plane C in 1.4. Similarly, the flows entering plane D in 1.3 are equal to those leaving plane D in 1.4. The coupling conditions are:

There is no interaction between subsystems 1.1, 1.2 and 1.3. At plane E, the flow out of the hydraulic fracture is assumed to be equal to q _region1 . The linear flow equations for subsystem 1.4 can then be solved in the Laplace domain under all the above boundary and coupling conditions. The derived mathematical solution can give the transient pressure at plane E. Solutions for other regions can be derived in the same way.

After coupling the subsystem flow partial differential equations into regional flow partial differential equations for each enclosed production area, the next step in the approach to modeling hydrocarbon flow from a fractured unconventional reservoir is to couple multiple enclosed production areas Flow partial differential equations in this region to obtain solutions for the entire producing reservoir block. After coupling the subsystem flow partial differential equations into regional flow partial differential equations, the only unknown parameter in each regional flow partial differential equation or solution is the flow rate q _{region i} (i=1, 2...n , n is the number of hydraulic fractures). Since the hydraulic fractures are connected by a horizontal wellbore, the pressures at the ends of the hydraulic fractures are equal to each other. Also, in mathematical modeling, horizontal wells typically operate at constant pressure or constant flow. By applying this additional condition, the method in this paper develops a system of n linear equations and solves it analytically in the Laplace domain. For example, a system of linear equations at constant production rate looks like:

The solution of Equation 8 gives the transient bottom hole pressure and flow distribution along the horizontal wellbore in the Laplace domain. The Stehfest algorithm can convert values from the Laplace domain to 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, "Numerical Inversion of LaplaceTransforms", Communications of the ACM 13(1):47-49. The present invention selects a series of time points t _D , finds the corresponding Laplacian time points s, calculates solutions at different time points, and transforms the results into real-time space according to Equation 9. The final real-time solution is a series of bottom hole pressure/flow at various points in time. Generate template curves from pressure/flow vs. time data.

A true stimulated reservoir may be more complex in geology and behavior than shown in Figures 6 and 7—reservoir properties may change as the distance from the hydraulic fracture increases. Figures 8-11 illustrate several additional complex combinations of multiple flow subsystems in an enclosed production area.

Referring first to Figure 8, there are seven flow subsystems in an enclosed production area. The flow subsystem shown in this figure can simulate unconventional reservoirs with progressively changing reservoir properties throughout the producing reservoir block. Each flow subsystem contains one type of simple flow and has independent reservoir properties. The radial flow moves towards the flow subsystem 1.1 through the flow subsystem 1.2. In the flow subsystem 1.1, the radial flow converges towards the inner boundary r _w . Flow subsystem 1.3 contains linear flow. The flow subsystem 1.4 receives the 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 governing equations for these flow subsystems have been enumerated.

The coupling conditions of the sub-system flow partial differential equations based on the embodiment of FIG. 8 differ from those outlined above. The coupling method shown in this context couples the subsystem flow partial differential equations of fluidic subsystem 1.1 to the subsystem flow partial differential equations of fluidic subsystem 1.2 primarily by equalizing the pressure and flow across the interface plane A. Subsystem flow partial differential equations for coupled flow subsystems 1.3 and 1.4 at the same pressure and flow across interface plane B. Coupling the sub-system flow partial differential equations of flow sub-systems 1.5 and 1.6 with equal pressure and flow across the interface plane C. The subsystem flow partial differential equations of fluid subsystem 1.7 are coupled with the subsystem flow partial differential equations of fluid subsystems 1.1, 1.4, and 1.6 by flow continuity across the fracture tip and planes D and E, respectively. This solution scheme, or area flow partial differential equation, is similar to the embodiments of Figures 6 and 7 when completed. The resulting template curves can also be matched to predict reservoir production.

Figure 9 shows another different combination of flow subsystems in a closed production area. The enclosed production area of Figure 9 is divided into eight flow subsystems. Each fluid subsystem in this figure has a simple fluid flow. In Fluid Subsystem 2.1, there are line sinks on the tip of hydraulic fractures, 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 flow subsystem 2.3 enters flow subsystem 2.6. Flow subsystems 2.4 and 2.5 obtain flows from adjacent flow subsystems and develop internal linear flows. Flow subsystems 2.6 and 2.7 also have linear flow. For 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 fluid subsystems can be found from those in Figures 4 and 5.

The coupling conditions are different for the different combinations of flow subsystems shown in Figure 9. The flow into the flow subsystem 2.4 is equal to the flow normal to the interface plane A of the flow subsystem 2.2. The flow into the flow subsystem 2.6 is equal to the flow perpendicular to the interface plane B of the flow subsystem 2.3. Flow subsystems 2.4 and 2.5 are coupled under flow continuity across plane C. Flow subsystems 2.6 and 2.7 are also coupled based on flow continuity across plane D. Flow subsystem 2.8 is coupled with flow subsystems 2.1, 2.5 and 2.7 using flow continuity across the fracture tip, plane E and plane F, respectively. The solution scheme is similar to Figures 4 and 5. The resulting template curves 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 included within the scope of the present invention.

Referring to Figure 10, a simulation of another complex unconventional oil and gas reservoir is shown. As the unconventional reservoir becomes more complex in terms of fractures and flow, the method in this paper to model the oil flow from a fractured unconventional reservoir simply divides the reservoir into larger areas in closed producing areas number of flow subsystems. Referring to Figure 10, seven flow subsystems contain linear flow inside the unconventional reservoir, and three flow subsystems have radial flow toward the hydraulic fracture tip. In the embodiment of Figure 11, eleven flow subsystems have linear flow inside the reservoir and one flow subsystem has line sinks at the fracture tips. This means that the flow subsystem in a closed production area is not stationary. According to this approach, there are a large number of combinations of flow subsystems. Although the present invention has been described in terms of preferred embodiments, it is to be understood that various modifications and changes can be made without departing from the spirit and scope of the invention, as those skilled in the art will readily understand. Such modifications and variations are considered to be within the purview and scope of the appended claims.

One advantage of the present invention is that heterogeneous hydrocarbon reservoirs can be easily modeled. Heterogeneity is fairly common in unconventional reservoirs. Reservoir properties around a horizontal wellbore can change significantly. To address heterogeneity, the present invention assigns different reservoir properties to different flow subsystems. Any two fluid subsystems can have different reservoir properties, whether or not the two subsystems are in the same region. For example, flow subsystems 1.5 and 1.6 in Figure 8 may have different reservoir properties, even though they are on the same side of a hydraulic fracture. Any two fluidic systems can likewise have different fracture properties. For example, the fracture permeability of region 1 of FIG. 5 may be different from the fracture permeability of region 5 .

Another advantage of the present invention is the ability to model dual-porosity oil and gas reservoirs. Hydraulic fracturing can reactivate "dead" natural fractures, and a portion of the reservoir may behave like a double porosity. Dual-porosity reservoirs consist of two media: reservoir matrix and natural fractures. Furthermore, this dual porosity characteristic may vary along the horizontal wellbore. In the present invention, any fluidic system can be easily modified into a dual-pore fluidic system. This modification introduces two new parameters - the storability ratio ω and the flow capacity ratio λ - to characterize natural fractures. 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 Naturally Fractured Reservoirs", SPE Journal SPE 426 and O.A. de Swaan, "Analytical Solutions for Determining Naturally Fractured reservoir properties by Well Testing", SPEJournal SPE 5346 . Also, any two fluidic systems can have different dual pore parameters, whether or not the two fluidic systems are in the same closed production area - usually by making the fluidic system dual when the fluidic system is closer to the hydraulic fracture porosity.

Another advantage of the present invention is that it is easy to account for the complex flow mechanisms in shale gas reservoirs. In addition to inherent reservoir properties, reservoir matrix permeability becomes a function of reservoir pressure and gas properties due to gas slippage, Knudsen diffusion, and stress sensitivity: F. Javadpour, "Nanopores and Apparent Permeability of Gas Flowin Mudrocks (shale Mudrocks) and siltstone)”, Journal of Canadian Petroleum Technology 48(8):16-21 and A.R. Bhandari, P.B. Flemings, P.J. Polito, M.B. Cronin, S.L. Bryant, “Anisotropy and Stress Dependence of Permeability in the Barnett Shale”, Transport in Porous Media108(2):393-41. Additionally, natural and hydraulic fractures can become pressure sensitive during production:

k _F = k _Fi f(p _F )…………………………………………………………(11)

The semi-analytical method of the present invention can simulate the influence of the above 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 fluid systems. The pressure/flow fields are then calculated for all flow subsystems. Reservoir matrix and fracture properties are updated based on this pressure/flow field. Subsequently, the updated properties are used for the next time step calculation. This iterative process can continue until the final time step. In general, in the present invention, reservoir matrix and fracture properties can vary smoothly over time in each fluid subsystem, and any two fluid subsystems can have different properties. Figure 13 (deleted) provides a flowchart summarizing this modeling approach. The method is applied to basic and complex combinations of flow subsystems.

By applying this semi-analytical approach, reservoir heterogeneity, dual porosity, and complex flow mechanisms can occur simultaneously in a closed producing area. For example, take area 1 in FIG. 6 . The fluidic subsystem 1.1 may be single pore. Fluidic systems 1.2 and 1.3 are dual porous and the internal natural fractures are stress sensitive. However, reservoir matrix and fracture properties can be different in fluid subsystems 1.2 and 1.3. For fluid subsystem 1.4, hydraulic fractures are stress sensitive. Gas slippage and Knudsen diffusion play a role in flow subsystems 1.1, 1.2 and 1.3. The summary is as follows: A closed production area can have a large number of combinations of flow subsystems, and each of them can have a large number of combinations of properties. Although the present invention has been described in terms of preferred embodiments, it should be understood that various modifications and changes can be made without departing from the spirit and scope of the invention.

The solutions above are based on liquid oil and gas production. In order to use this solution and template curve for gas flow, the dimensionless pressure should be expressed in terms of real gas pseudopressure. The definition of virtual pressure can be found in reference Al-Hussainy, R., Ramey Jr., H.J., Crawford, P.B, "The Flow of Real Gases Through Porous Media", Journal of Petroleum Technology 18(5):624-636.

Template curves can be used to match and predict production from stimulated unconventional reservoirs. The template curves are grouped in the model according to the given reservoir and fracture properties for each fluid subsystem. Based on known information, a set of template curves that conform to that information can be selected first. Place the template curve above the submitted production data in the exact same coordinate system. If a template curve best matches the field data, the conditions behind the template curve represent unknown reservoir and hydraulic fracture properties. Trends in such template curves also imply possible future production behavior. As much information as possible can be collected to reduce the time spent in matching and prediction. Template curves generated as described herein provide different models and scenarios to consider when examining or understanding potential reservoir production by the method of the present invention.

Reservoir properties:

Reservoir properties assigned to individual flow subsystems for modeling reservoir production include various types of reservoir properties. The reservoir properties 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 the respective flow subsystems may also be selected from linear flow of the reservoir to the hydraulic fracture, flow toward the fracture tip, and flow within the hydraulic fracture. When fracture properties are used as reservoir properties assigned to a particular fluid subsystem, these can 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 property can be assigned to one or more flow subsystems.

Study the generated sample curve:

Based on the geometry of Figure 5, Figure 12 selects two generated template curves. In Figure 12, the dashed line shows the method according to reference S. Yao, F. Zeng, H. Liu, G. Zhao, "A Semi-analytical Model for Multi-stage Fractured Horizontal Wells", Journal of Hydrology 507:201-212 Generated template curve. The solid line shows a model curve based on the present invention. For simplicity, the entire producing reservoir block is assumed to be homogeneous here. Figure 12 shows that both methods give almost identical results. However, the time to generate the template curve in the present invention is significantly shorter than that of the method of the reference. The difference in calculation time becomes larger when more hydraulic fractures are included. Below is the time to compute the template curve shown in Figure 12, which exhibits significant time benefits:

Calculation time of the present invention Calculation time for the reference method 3 hydraulic cracks 3 seconds 19 minutes 6 hydraulic cracks 5 seconds 51 minutes 12 hydraulic fractures 8 seconds 140 minutes

Computation time also depends on the processing power of the computer. Better computers will further reduce computing time. In general, the present invention provides a fast and reliable method for generating template curves for stimulated unconventional oil and gas reservoirs.

computer software:

The method of the present invention can also be simplified to be implemented in a computer software program - in fact beyond the mathematical methods outlined herein, establishing a computer software method to provide template curves 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 considered and understood to be 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 of simulating hydrocarbon flow from a fractured unconventional oil and gas reservoir, the computer readable storage medium comprising instructions that, when executed by a computer, cause The computer does the following:

Collect relevant data corresponding to unconventional oil and gas reservoirs that have been subjected to multi-stage hydraulic fracturing;

Use this relevant data:

Defining a production reservoir block that is the primary oil and gas producing area in the unconventional oil and gas reservoir, and calculating reservoir dimensions for the length, width and height of the production reservoir block; and

Defining the location and properties of the hydraulic fractures in the producing reservoir block;

subdividing the producing oil and gas reservoir block into a plurality of enclosed production areas, each enclosed production area containing at least one hydraulic fracture therein, and calculating the area dimensions of the length, width and height of each enclosed production area;

subdivide each closed production area into multiple flow subsystems; and

assigning at least one set of reservoir properties to each fluid subsystem;

modeling the subsystem oil flow of each of the plurality of flow subsystems based on at least one set of oil and gas reservoir properties assigned thereto and associated data corresponding to the flow subsystem;

modeling the regional oil flow of each enclosed production area by coupling the calculated subsystem oil flow of the various flow subsystems in the enclosed production area; and

The reservoir oil and gas flow of the unconventional oil and gas reservoir is modeled by coupling the calculated regional oil and gas flow of each of the plurality of enclosed production regions.

The software of the present invention, at its highest level, is capable of effectively implementing the computer-aided implementation of the method shown in FIGS. 1-3 for modeling hydrocarbon flow from a fractured unconventional reservoir. In addition to the basic simulation of oil and gas flow in oil and gas reservoirs, template curves can be drawn from 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.

The computer software of the present invention will enable the development of couplable differential equations for performing embodiments of the method, including providing subsystem flow partial differential equations and regional flow partial differential equations, which can be coupled to produce hydrocarbons representing the hydrocarbons in the reservoir flow equations Reservoir gas flow solution.

Figure 13 (deleted) illustrates one embodiment of the method of the invention implemented in computer software.

Claims (46)

1. A method of modeling hydrocarbon flow from a fractured unconventional oil and gas reservoir, the method comprising: collecting relevant data corresponding to unconventional oil and gas reservoirs that have been subjected to multi-stage hydraulic fracturing; Using the relevant data: Defining producing oil and gas reservoir blocks as major oil and gas producing areas within the unconventional oil and gas reservoir; calculating reservoir dimensions for the length, width and height of the producing reservoir block; and defining the location and characteristics of each hydraulic fracture within the producing reservoir block; subdividing the producing oil and gas reservoir block into a plurality of enclosed production areas, each enclosed production area containing at least one hydraulic fracture; Calculate area dimensions for the length, width and height of each enclosed production area; subdivide each closed production area into multiple flow subsystems; and assigning at least one set of reservoir properties to each fluid subsystem; Relative to at least one selected point in time: modeling the subsystem oil flow of each of the plurality of fluidic subsystems based on at least one set of reservoir properties assigned to each fluidic subsystem and associated data corresponding to the fluidic subsystem; modeling the regional oil flow of each enclosed production area by coupling the calculated subsystem oil flow of each of the flow subsystems within the enclosed production area; and The reservoir hydrocarbon flow of the unconventional reservoir is modeled by coupling the calculated regional hydrocarbon flow coupled to each of the plurality of enclosed production regions. 2. The method of claim 1, wherein subsystem oil flow of at least one of the plurality of flow subsystems is modeled relative to a plurality of selected points in time, and the method further comprises the step of generating at least one template curve , the template curve displays the simulated subsystem oil flow of the selected flow subsystem on one axis and the associated selected time point on the other axis. 3. The method of claim 1, wherein the regional oil flow of at least one of the plurality of enclosed production areas is modeled relative to a plurality of selected time points, and the method further comprises the step of generating at least one template curve, The template curve displays the simulated regional oil flow of the selected enclosed production area on one axis and the associated selected time point on the other axis. 4. The method of claim 1, wherein the reservoir gas flow is modeled relative to a plurality of selected time points, and the method further comprises the step of generating at least one template curve on one axis thereof A simulated reservoir hydrocarbon flow for the producing reservoir block is displayed and the associated selected time point is displayed on the other axis thereof. 5. The method of claim 1, wherein the relevant data corresponding to the unconventional oil and gas reservoir is selected from the group consisting of field 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 fluid 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 a subset of each fluidic subsystem of the plurality of fluidic subsystems is calculated by generating a partial molecular system flow partial differential equation representing the determined oil flow of the fluidic subsystem. The system oil flow is modeled whereby each subsystem flow partial differential equation can be coupled to the subsystem flow partial differential equations of other flow subsystems within the corresponding enclosed production area. 11. The method of claim 10, wherein each flow partial differential equation is generated by coupling a subsystem flow partial differential equation of each of the plurality of flow subsystems within the enclosed production region to generate a partial differential region flow partial differential equation. The regional flow partial differential equations of each enclosed production area are modeled, whereby each regional flow partial differential equation can be coupled to the regional flow partial differential equations of other enclosed production areas within the producing oil and gas reservoir block. 12. The method of claim 11, wherein the reservoir gas flow is modeled by coupling regional flow partial differential equations for all of the plurality of enclosed production areas within the producing reservoir block to produce a reservoir flow equation. 13. The method of claim 12, wherein the result of the reservoir flow equation is an expectation from the production reservoir block adjusted for unconventional geology and a plurality of fractures in the production reservoir block oil and gas production. 14. The method of claim 10, wherein the solution of 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 the partial differential equation of flow for each zone represents the production pressure and volumetric production rate of the corresponding enclosed production zone. 16. The method of claim 12, wherein the solution of the reservoir flow equation represents the 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 area is located in the center of the enclosed production area. 18. The method of claim 1, wherein at least one hydraulic fracture in at least one enclosed production area is not located in the center of the enclosed production area. 19. The method of claim 1, wherein the at least one set of reservoir properties assigned to each fluid subsystem is selected from the group consisting of linear flow in the reservoir, linear flow of the reservoir to hydraulic fractures, flow toward fracture tips, and hydraulic fractures internal flow. 20. The method of claim 19, wherein the at least one set of reservoir properties assigned to each fluidics subsystem within the producing reservoir block is the same. 21. The method of claim 19, wherein at least one set of reservoir properties assigned to each fluid subsystem within the producing 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 the 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 associated data. 24. A non-transitory computer-readable storage medium for a method for modeling hydrocarbon flow from a fractured unconventional oil and gas reservoir, the computer-readable storage medium comprising instructions that, when executed by a computer causes the computer to do the following: Collect relevant data corresponding to unconventional oil and gas reservoirs that have been subjected to multi-stage hydraulic fracturing; Using the relevant data: Define the producing oil and gas reservoir block as the main oil and gas producing area in the unconventional oil and gas reservoir, Calculate the reservoir dimensions for the length, width and height of the producing reservoir block; and Defining the location and characteristics of each hydraulic fracture within the producing reservoir block; subdividing the producing oil and gas reservoir block into a plurality of enclosed production areas, each enclosed production area containing at least one hydraulic fracture; Calculate area dimensions for the length, width and height of each enclosed production area; subdivide each closed production area into multiple flow subsystems; and assigning at least one set of reservoir properties to each fluid subsystem; Relative to at least one selected point in time: modeling the subsystem oil flow of each of the plurality of fluidic subsystems based on at least one set of reservoir properties assigned to each fluidic subsystem and associated data corresponding to the fluidic subsystem; modeling the regional oil flow for each enclosed production area by coupling the calculated subsystem oil flow of each fluid subsystem within the enclosed production area; and The reservoir oil and gas flow of the unconventional reservoir is modeled by coupling the calculated regional oil and gas flow for each of the plurality of enclosed production regions. 25. The computer-readable storage medium of claim 24, wherein the subsystem oil flow of at least one of the plurality of flow subsystems is modeled relative to a plurality of selected points in time, and wherein the instructions further cause the computer to At least one template curve is generated that displays the simulated subsystem oil flow of the selected flow subsystem on one axis thereof and the associated selected time point on the other axis. 26. The computer-readable storage medium of claim 24, wherein the regional hydrocarbon flow of at least one of the plurality of enclosed production areas is modeled relative to a plurality of selected points in time, and wherein the instructions further cause the computer to generate At least one template curve showing the simulated regional oil flow of the selected enclosed production area on one axis and the associated selected time point on the other axis. 27. The computer-readable storage medium of claim 24, wherein the regional oil flow is modeled relative to a plurality of selected points in time, and wherein the instructions further cause the computer to generate at least one template curve, the template curve The simulated reservoir hydrocarbon flow of the producing reservoir block is displayed on one axis thereof and the associated selected time point is displayed on the other axis thereof. 28. The computer-readable storage medium of claim 24, wherein the relevant data corresponding to the unconventional oil and gas reservoir is selected from the group consisting of mine 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 fluid 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 hydrocarbon 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 each flow in the plurality of fluidic subsystems is calculated by generating a partial molecular system flow partial differential equation representing the determined oil flow of the fluidic subsystem The subsystem oil flow of the subsystems is modeled so that each subsystem flow partial differential equation can be coupled to the subsystem flow partial differential equations of the other flow subsystems within the corresponding closed production area. 34. The computer-readable storage medium of claim 33, wherein the partial differential region flow partial differential is generated by coupling a subsystem flow partial differential equation of each of the plurality of flow subsystems within the enclosed production area equations to model the regional oil flow of each enclosed production area, whereby each regional flow partial differential equation can be coupled to the regional flow partial differential equations of other enclosed production areas within the producing oil and gas reservoir block. 35. The computer-readable storage medium of claim 34, wherein the oil and gas reservoir is determined by coupling regional flow partial differential equations of all of the plurality of enclosed production areas within the producing oil and gas reservoir block to generate a reservoir flow equation. flow modeling. 36. The computer-readable storage medium of claim 35, wherein the result of the reservoir flow equation is from the production reservoir adjusted for unconventional geology and a plurality of fractures in the production reservoir block Expected oil and gas production in the block. 37. The computer-readable storage medium of claim 33, wherein the solution of 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 of 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 of the reservoir flow equation represents the production pressure and 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 area is located in the center of the enclosed production area. 41. The computer readable storage medium of claim 24, wherein the at least one hydraulic fracture in at least one enclosed production area is not located in the center of the enclosed production area. 42. The computer-readable storage medium of claim 24, wherein the at least one set of reservoir properties assigned to each fluidics subsystem is selected from the group consisting of linear flow in the reservoir, linear flow of the reservoir toward a hydraulic fracture, and linear flow toward the fracture tip. Flow and flow inside hydraulic fractures. 43. The computer-readable storage medium of claim 42, wherein the at least one set of reservoir properties assigned to each flow subsystem within the producing reservoir block is the same. 44. The computer-readable storage medium of claim 42, wherein the at least one set of reservoir properties assigned to each flow subsystem within the producing 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 an area size of at least one enclosed production area is modified from an initially calculated area size based on the hydraulic fracture location and the associated data.

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