FAST SCREENING OF HYDRAULIC FRACTURE AND RESERVOIR MODELS CONDITIONED TO PRODUCTION DATA

Abstract

A method involves obtaining a measured drainage function for a well and obtaining a set of drainage models, wherein each drainage model includes a reservoir model and a fracture model. The method also includes, for each drainage model, forming a predicted drainage function based, at least in part, on the drainage model, and determining a misfit value based, at least in part, on the predicted drainage function and the measured drainage function. The method further includes determining a set of candidate drainage models based, at least in part, on the misfit value for each drainage model, wherein each candidate drainage model comprises a candidate reservoir model and a candidate fracture model.

Description

BACKGROUND

One of the great challenges in unconventional reservoir development is to quantify uncertainties in hydraulic fracture geometries and reservoir properties. The process to quantify uncertainties requires sampling hundreds of different hydraulic fracture (HF) and reservoir models (RM) and running thousands of flow simulations to check and calibrate against actual production data. As a result, one can select model combinations that match production data and eliminate those that do not. This workflow is very time consuming and computationally expensive due to the cost associated with the volume of sampling models and flow simulations. As a result, the process is typically not performed, risking optimal well spacing and field development planning.

To help overcome computational cost challenges, shortcuts have been introduced. Upscaling is a common approach to reduce the number of grid blocks in simulation models, which reduces the runtime for a single simulation run. However, upscaling tends to smooth out the geologic heterogeneities, reducing subsurface uncertainties. Ranking and selecting a few geologic models is also commonly employed to reduce the total number of simulations needed. Such a process is generally based on calculation of volumetric properties within an area of interest, which ignores heterogeneities that control effective drainage volumes and flow behavior (both of which change over time).

Understanding of the transient-drainage volume is essential for unconventional-reservoir and fracture assessment and optimization. To overcome this problem, a fast marching method (FMM) was developed to quantify connected reservoir volume in a given well for dynamic ranking of geologic models. FMM is a proxy method to capture the pressure-propagation in the reservoir with reasonable accuracy within seconds as compared to hours for multi-million cell geologic models. FMM has been applied to both conventional and unconventional reservoirs. One of the great challenges in unconventional reservoir development is to quantify uncertainties in hydraulic fracture geometries and reservoir properties. FMM alone does not address complexities and uncertainties in hydraulic fracture geometries, which are key performance drivers of any unconventional well. Further, FMM offers no ability to screen out unrealistic geologic models based on actual production performance of existing wells.

SUMMARY

This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter.

In one aspect, embodiments disclosed herein relate to a method, which may include obtaining a measured drainage function for a well and obtaining a set of drainage models, wherein each drainage model comprises a reservoir model and a fracture model. The method may also include, for each drainage model, forming a predicted drainage function based, at least in part, on the drainage model, and determining a misfit value based, at least in part, on the predicted drainage function and the measured drainage function. The method may further include determining a set of candidate drainage models based, at least in part, on the misfit value for each drainage model, wherein each candidate drainage model comprises a candidate reservoir model and a candidate fracture model.

In another aspect, embodiments disclosed herein relate to a non-transitory computer-readable medium storing instructions. The instructions, when executed on a processor, may comprise functionality for receiving a measured drainage function for a well and obtaining a set of drainage models, wherein each drainage model comprises a reservoir model and a fracture model. The instructions for each drainage model may comprise functionality for forming a predicted drainage function based, at least in part, on the drainage model, and determining a misfit value based, at least in part, on the predicted drainage function and the measured drainage function. The instructions may comprise further functionality for determining a set of candidate drainage models based, at least in part, on the misfit value for each drainage model, wherein each candidate drainage model comprises a candidate reservoir model and a candidate fracture model.

In yet another aspect, embodiments disclosed herein relate to a system. The system may include a well testing system, to determine a measured drainage function and a computer processor. The computer processor may be configured to receive a measured drainage function for a well and obtain a set of drainage models, wherein each drainage model comprises a reservoir model and a fracture model. The computer processor may also be configured to, for each drainage model. form a predicted drainage function based, at least in part, on the drainage model, and determine a misfit value based, at least in part, on the predicted drainage function and the measured drainage function. The computer processor may further be configured to determine a set of candidate drainage models based, at least in part, on the misfit value for each drainage model, wherein each candidate drainage model comprises a candidate reservoir model and a candidate fracture model. Other aspects and advantages of the claimed subject matter will be apparent from the following description and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

Specific embodiments of the disclosed technology will now be described in detail with reference to the accompanying figures. Like elements in the various figures are denoted by like reference numerals for consistency. The size and relative positions of elements in the drawings are not necessarily drawn to scale. For example, the shapes of various elements and angles are not necessarily drawn to scale, and some of these elements may be arbitrarily enlarged and positioned to improve drawing legibility. Further, the particular shapes of the elements as drawn are not necessarily intended to convey any information regarding the actual shape of the particular elements and have been solely selected for ease of recognition in the drawing.

FIG. 1 shows a system in accordance with one or more embodiments.

FIGS. 2A and 2B show systems in accordance with one or more embodiments.

FIG. 3 shows a hydraulic fracturing site in accordance with one or more embodiments.

FIG. 4 shows a computer system in accordance with one or more embodiments.

FIG. 5 shows a flowchart in accordance with one or more embodiments.

FIG. 6 shows a flowchart in accordance with one or more embodiments.

FIG. 7 shows a neural network in accordance with one or more embodiments.

DETAILED DESCRIPTION

In the following detailed description of embodiments of the disclosure, numerous specific details are set forth in order to provide a more thorough understanding of the disclosure. However, it will be apparent to one of ordinary skill in the art that the disclosure may be practiced without these specific details. In other instances, well-known features have not been described in detail to avoid unnecessarily complicating the description.

Throughout the application, ordinal numbers (e.g., first, second, third, etc.) may be used as an adjective for an element (i.e., any noun in the application). The use of ordinal numbers is not to imply or create any particular ordering of the elements nor to limit any element to being only a single element unless expressly disclosed, such as using the terms “before”, “after”, “single”, and other such terminology. Rather, the use of ordinal numbers is to distinguish between the elements. By way of an example, a first element is distinct from a second element, and the first element may encompass more than one element and succeed (or precede) the second element in an ordering of elements.

In the following description of FIGS. 1-7, any component described with regard to a figure, in various embodiments disclosed herein, may be equivalent to one or more like-named components described with regard to any other figure. For brevity, descriptions of these components will not be repeated with regard to each figure. Thus, each and every embodiment of the components of each figure is incorporated by reference and assumed to be optionally present within every other figure having one or more like-named components. Additionally, in accordance with various embodiments disclosed herein, any description of the components of a figure is to be interpreted as an optional embodiment which may be implemented in addition to, in conjunction with, or in place of the embodiments described with regard to a corresponding like-named component in any other figure.

It is to be understood that the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a seismic data set” includes reference to one or more of such seismic data set.

Terms such as “approximately,” “substantially,” etc., mean that the recited characteristic, parameter, or value need not be achieved exactly, but that deviations or variations, including for example, tolerances, measurement error, measurement accuracy limitations and other factors known to those of skill in the art, may occur in amounts that do not preclude the effect the characteristic was intended to provide.

It is to be understood that one or more of the steps shown in the flowcharts may be omitted, repeated, and/or performed in a different order than the order shown. Accordingly, the scope disclosed herein should not be considered limited to the specific arrangement of steps shown in the flowcharts.

Although multiple dependent claims are not introduced, it would be apparent to one of ordinary skill that the subject matter of the dependent claims of one or more embodiments may be combined with other dependent claims.

There exists a need for efficient and effective quantification of uncertainties and risks for unconventional reservoir development. Before any upscaling and expensive flow simulation studies, the real challenge is to reasonably identify combinations of hydraulic fracture and geologic models that are conditioned to actual well performances. There is currently no workflow which integrates historical production data into geologic models for hydraulically fractured wells without the needing to perform flow simulation. Such technology and workflow will not only enhance the quality of reservoir models and capture of inherent uncertainties and begin history matching studies on a better footing, but will also diminish computational burden with effective screening and ranking of hundreds of different fracture model and reservoir model combinations.

In one aspect, embodiments disclosed herein relate to a method of generating combinations of hydraulic fracture and geological or upscaled reservoir models which honor production data diagnostics in order to quantify uncertainties, screen out unrealistic models, and rank models. From the ranked models, a small given number may be selected for detailed flow simulation studies. In another aspect, embodiments herein relate to a workflow that combines diffusive time of flight (DTOF) based production data diagnostics with model based fast marching method (FMM) analysis for calculating pressure propagation.

FIG. 1 shows a schematic diagram in accordance with one or more embodiments. FIG. 1 illustrates a well environment (100) that includes a hydrocarbon reservoir (“reservoir”) (102) located in a subsurface hydrocarbon-bearing formation (“formation”) (104) and a well system (106). The hydrocarbon-bearing formation (104) may include a porous or fractured rock formation that resides underground, beneath the earth's surface (“surface”) (108). In the case of the well system (106) being a hydrocarbon well, the reservoir (102) may include a portion of the hydrocarbon-bearing formation (104). The hydrocarbon-bearing formation (104) and the reservoir (102) may include different layers of rock having varying characteristics, such as varying degrees of permeability and porosity. In the case of the well system (106) being operated as a production well, the well system (106) may facilitate the extraction of hydrocarbons (or “production”) from the reservoir (102).

In some embodiments, the well system (106) includes a wellbore (120), a well sub-surface system (122), a well surface system (124), and a well control system (“control system”) (126). In one or more embodiments, the wellbore (120) may be vertical. However, the wellbore (120) may also be horizontal or deviated without departing from the scope of this disclosure. The control system (126) may control various operations of the well system (106), such as well production operations, well completion operations, well maintenance operations, as well as reservoir operations including monitoring, assessment and development operations. In some embodiments, the control system (126) includes a computer that is the same as or similar to that of computer system (402) described below in FIG. 4 and the accompanying description.

The wellbore (120) may include a bore hole that extends from the surface (108) into a target zone of the hydrocarbon-bearing formation (104), such as the reservoir (102). An upper end of the wellbore (120), terminating at or near the surface (108), may be referred to as the “up-hole” end of the wellbore (120), and a lower end of the wellbore, terminating in the hydrocarbon-bearing formation (104), may be referred to as the “down-hole” end of the wellbore (120). The wellbore (120) may facilitate the circulation of drilling fluids during drilling operations, the flow of hydrocarbon production (“production”) (121) (e.g., oil and gas) from the reservoir (102) to the surface (108) during production operations, the injection of substances (e.g., water) into the hydrocarbon-bearing formation (104) or the reservoir (102) during injection operations, or the communication of monitoring devices (e.g., logging tools) into the hydrocarbon-bearing formation (104) or the reservoir (102) during monitoring operations (e.g., during in situ logging operations).

In some embodiments, during operation of the well system (106), the control system (126) collects and records wellhead data (140) for the well system (106). The wellhead data (140) may include, for example, a record of measurements of wellhead pressure (Pwh) (e.g., including flowing wellhead pressure), wellhead temperature (Twh) (e.g., including flowing wellhead temperature), wellhead production rate (Qwh) over some or all of the life of the well system (106), and water cut data. In some embodiments, the measurements are recorded in real-time, and are available for review or use within seconds, minutes or hours of the condition being sensed (e.g., the measurements are available within 1 hour of the condition being sensed). In such an embodiment, the wellhead data (140) may be referred to as “real-time” wellhead data (140). Real-time wellhead data (140) may enable an operator of the well system (106) to assess a relatively current state of the well system (106), and make real-time decisions regarding development of the well system (106) and the reservoir (102), such as on-demand adjustments in regulation of production flow from the well.

In some embodiments, the well surface system (124) includes a wellhead (130). The wellhead (130) may include a rigid structure installed at the “up-hole” end of the wellbore (120), at or near where the wellbore (120) terminates at the Earth's surface (108). The wellhead (130) may include structures for supporting (or “hanging”) casing and production tubing extending into the wellbore (120). Production (121) may flow through the wellhead (130), after exiting the wellbore (120) and the well sub-surface system (122), including, for example, the casing and the production tubing. In some embodiments, the well surface system (124) includes flow regulating devices that are operable to control the flow of substances into and out of the wellbore (120). For example, the well surface system (124) may include one or more production valves (132) that are operable to control the flow of production (121). For example, a production valve (132) may be fully opened to enable unrestricted flow of production (121) from the wellbore (120), the production valve (132) may be partially opened to partially restrict (or “throttle”) the flow of production (121) from the wellbore (120), and production valve (132) may be fully closed to fully restrict (or “cell”) the flow of production (121) from the wellbore (120), and through the well surface system (124).

Keeping with FIG. 1, in some embodiments, the well surface system (124) includes a surface sensing system (134). The surface sensing system (134) may include sensors for sensing characteristics of substances, including production (121), passing through or otherwise located in the well surface system (124). The characteristics may include, for example, pressure, temperature, and flow rate of production (121) flowing through the wellhead (130), or other conduits of the well surface system (124), after exiting the wellbore (120).

In some embodiments, the surface sensing system (134) includes a surface pressure sensor (136) operable to sense the pressure of production (151) flowing through the well surface system (124), after it exits the wellbore (120). The surface pressure sensor (136) may include, for example, a wellhead pressure sensor that senses a pressure of production (121) flowing through or otherwise located in the wellhead (130). In some embodiments, the surface sensing system (134) includes a surface temperature sensor (138) operable to sense the temperature of production (151) flowing through the well surface system (124) after it exits the wellbore (120). The surface temperature sensor (138) may include, for example, a wellhead temperature sensor that senses a temperature of production (121) flowing through or otherwise located in the wellhead (130), referred to as “wellhead temperature” (T_WH). In some embodiments, the surface sensing system (134) includes a flow rate sensor (139) operable to sense the flow rate of production (151) flowing through the well surface system (124), after it exits the wellbore (120). The flow rate sensor (139) may include hardware that senses a flow rate of production (121) (Q_WH) passing through the wellhead (130).

In some embodiments, the well system (106) includes a reservoir simulator (160). For example, the reservoir simulator (160) may include hardware and/or software with functionality for generating one or more reservoir models regarding the hydrocarbon-bearing formation (104) and/or performing one or more reservoir simulations. For example, the reservoir simulator (160) may store well logs and data regarding core samples for performing simulations. A reservoir simulator may further analyze the well log data, the core sample data, seismic data, and/or other types of data to generate and/or update the one or more reservoir models. While the reservoir simulator (160) is shown at a well site, embodiments are contemplated where reservoir simulators are located away from well sites. In some embodiments, the reservoir simulator (160) may include a computer system that is similar to the computer system (402) described below with regard to FIG. 4 and the accompanying description.

FIG. 2A shows a schematic diagram in accordance with one or more embodiments. FIG. 2A shows a geological region (200) that may include one or more hydrocarbon reservoir regions (e.g., reservoir region (230)) with various production wells (e.g., production well A (211), production well (212)). For example, a production well may be similar to the well system (106) described above in FIG. 1 and the accompanying description. Hydrocarbons, such as oil, gas, or a combination of both, may be produced from hydrocarbon reservoir through the production wells. The hydrocarbon may then transported to a primary processing facility, such as a gas-oil separation plant (“GOSP”) via surface pipelines (not shown) or stored in tanks (not shown) near the production wells for later transportation by tanker trucks.

Likewise, a reservoir region may also include one or more injection wells (e.g., injection well C (216)) that include functionality for enhancing production by one or more neighboring production wells. Production may be enhanced by injection fluid, such as water, from pumping systems (e.g., pumping system (250)) through the injection wells into the hydrocarbon reservoir. The injected fluid may be wastewater from a GOSP or drawn from nearby aquifers and may enhance production by increasing or maintaining the fluid pressure in the reservoir and/or by pushing the hydrocarbon through the hydrocarbon reservoir towards the production wells.

As shown in FIG. 2A, wells may be disposed in the reservoir region (230) above various subsurface layers (e.g., subsurface layer A (241), subsurface layer B (242)), which may include hydrocarbon deposits. In particular, production data and/or injection data may exist for a particular well, where production data may include data that describes production or production operations at a well, such as wellhead data (142) described in FIG. 1 and the accompanying description.

Pumping systems may pump fluid according to a schedule defined in a hydrocarbon reservoir production plan. Similarly, productions well may be produced at flow rates determined by the hydrocarbon reservoir production plan. In some cases, additional production and/or injection wells may be drilled according to the hydrocarbon reservoir production plan. The hydrocarbon reservoir production plan may be formed based on data about the reservoir, such as seismic data and well log data, and on production and injection data recorded over the lifetime of the hydrocarbon reservoir. A reservoir simulator (160) may use the reservoir data arranged on a reservoir grid model, production data, and injection data to predict the future performance of the reservoir, such as expected production rates, and to simulate various future scenarios. For example, the reservoir simulator (160) may predict the future production of a new production well drilled at a future data, or the effect on the production of all the production wells caused by increasing fluid injection rate at one or more injection wells. Further, the reservoir simulator may predict the reservoir pressure as a function of position within the reservoir and time. This information may be critical in understanding the behavior or condensate or wet gas reservoirs and understanding when oil condensate with form as the reservoir pressure falls. These scenarios may be used by reservoir engineers managing hydrocarbon to form the hydrocarbon reservoir production plan.

In accordance with one or more embodiments, FIG. 2B shows a reservoir grid model (290) that corresponds to the geological region (200) from FIG. 2A. More specifically, the reservoir grid model (290) includes grid cells (261) that may refer to a coarse grid cell (262) of a reservoir grid model as well as fine grid cells (263) that may refer to a subdivision of coarse grid cells (262) of the reservoir grid model (290). For example, if a coarse grid cell (262) may be of size 1×1, the fine grid cells (263) may be of sizes ½×½, ¼×¼, or ⅛×⅛. Grid cells (261), fine grid cells (263), and the coarse grid cells (262) may correspond to columns for multiple model layers (260) within the reservoir grid model (290). The grid cells (261), coarse grid cells (262) and fine grid cells (263) may or may not be cubic. Typically, the size of the grid cells in the horizontal directions and much greater than the size of the grid cells in the vertical direction.

Predicting the performance of a condensate or wet gas reservoir is of paramount interest for gas producers. Generally, reservoir simulators are used to predict the gas production rates from the wells. For a reliable prediction of the gas production rate, it is critical for the simulator to model the liquid drop-out process properly. To achieve this, reservoir simulators with capable of having a full description of the fluid composition and very fine grid cells around the wellbore may be required. The size of these very fine grid cells may be of the order of a few feet. As a result, the computation times required to complete the simulation may frequently be impractical.

In practice, models composed of coarse grid cells, with horizontal sizes on the order of hundreds of feet, may be used to simulate models covering the full reservoir and containing many wellbores. These models are computationally tractable but cannot accurately calculate low pressures and steep pressure gradients around the wellbores. Consequently, these models typically fail to simulate liquid drop-out around the wellbores accurately and consequently often over-predict gas production rates.

Turning now to FIG. 3, FIG. 3 shows a hydraulic fracturing site (300) undergoing a hydraulic fracturing operation in accordance with one or more embodiments. The particular hydraulic fracturing operation and hydraulic fracturing site (300) shown is for illustration purposes only. The scope of this disclosure is intended to encompass any type of hydraulic fracturing site (300) and hydraulic fracturing operation. In general, a hydraulic fracturing operation includes two separate operations: a perforation operation and a pumping operation. As such, FIG. 3 shows a hydraulic fracturing operation occurring on a first well (302) and a second well (304). The first well (302) is undergoing the perforation operation and the second well (304) is undergoing the pumping operation.

The first well (302) and the second well (304) are horizontal wells meaning that each well includes a vertical section and a lateral section. The lateral section is a section of the well that is drilled at least eighty degrees from vertical. The first well (302) is capped by a first frac tree (306) and the second well (304) is capped by a second frac tree (308). A frac tree (306, 308) is similar to a Christmas/production tree but is specifically installed for the hydraulic fracturing operation. Frac trees (306, 308) tend to have larger bores and higher-pressure ratings than a Christmas/production tree would have. Further, hydraulic fracturing operations require abrasive materials being pumped into the well at high pressures, so the frac tree (306, 308) is designed to handle a higher rate of erosion.

In accordance with one or more embodiments, the perforating operation includes installing a wireline blow out preventor (BOP) (310) onto the first frac tree (306). A wireline BOP (310) is similar to a drilling BOP; however, a wireline BOP (310) has seals designed to close around (or shear) wireline (312) rather than drill pipe. A lubricator (314) is connected to the opposite end of the wireline BOP (310). A lubricator (314) is a long, high-pressure pipe used to equalize between downhole pressure and atmosphere pressure in order to run downhole tools, such as a perforating gun (316), into the well.

When the perforating gun (316) reaches a predetermined depth, a message is sent along the wireline (312) to set the frac plug (318). After the frac plug (318) is set, another message is sent through the wireline (312) to detonate the explosives, as shown in FIG. 3. The explosives create perforations in the casing (326) and in the surrounding formation. There may be more than one set of explosives on a singular perforation gun (316), each detonated by a distinct message. Multiple sets of explosives are used to perforate different depths along the casing (326) for a singular stage. Further, the frac plug (318) may be set separately from the perforation operation without departing from the scope of the disclosure herein.

As explained above, FIG. 3 shows the second well (304) undergoing the pumping operation after the fourth stage perforating operation has already been performed and perforations are left behind in the casing (326) and the surrounding formation. A pumping operation includes pumping a frac fluid (328) into the perforations in order to propagate the perforations and create fractures (342) in the surrounding formation. The frac fluid (328) often comprises a certain percentage of water, proppant, and chemicals.

FIG. 3 also shows chemical storage containers (330), water storage containers (332), and proppant storage containers (334) located on the hydraulic fracturing site (300). Frac lines (336) and transport belts (not pictured) transport the chemicals, proppant, and water from the storage containers (330, 332, 334) into a frac blender (338). The frac blender (338) blends the water, chemicals, and proppant to become the frac fluid (328). The frac fluid (328) is transported to one or more frac pumps, often pump trucks (340), to be pumped through the second frac tree (308) into the second well (304). The frac fluid (328) is transported from the pump truck (340) to the second frac tree (308) using a plurality of frac lines (336). The fluid pressure propagates and creates the fractures (342) while the proppant props open the fractures (342) once the pressure is released.

Rate transient analysis (RTA) and pressure transient analysis (PTA) are methods used to characterize fracture and reservoir properties. Both RTA and PTA methods are based on simplifying assumptions which cannot provide a description of the evolving reservoir-drainage volume accessed from a hydraulically fractured well. Drainage volume refers to the volume of a reservoir drained by a well. However, unconventional reservoir and fracture assessment and optimization requires an understanding of the transient-drainage volume.

Some flow characteristics of unconventional wells may be interpreted using a diagnostic approach. In one or more embodiments, the approach may depend on the high-frequency asymptotic solution of the diffusivity equation in heterogeneous reservoirs. Such an approach may allow for the determination of well-drainage volume and instantaneous recovery ratio (IRR) directly from production data. As one skilled in the art will be aware, IRR refers to the ratio of produced volume to drainage volume.

In one or more embodiments, a diagnostic plot may feature DTOF (τ) on the horizontal axis and w(τ) on the vertical axis. In one or more embodiments, w(τ) refers to the derivative of pore volume (also known as drainage volume) with respect to DTOF and is defined by Equation 1:

$\begin{array}{cc}w\left(\tau \right)=\frac{{\mathrm{dV}}_p\left(\tau \right)}{d\tau },& \mathrm{Equation}1\end{array}$

where τ is the diffusive time of flight (DTOF) physically associated with the propagation of the peak of a pressure pulse for an impulse source and V_p is the pore volume at a given τ. In one or more embodiments, a w(τ) model may also be referred to as a drainage model.

The diagnostic plot may indicate different flow regimes and the specific DTOF value when fracture interference begins. Further, the diagnostic plot may capture high-resolution flow patterns which cannot be observed in traditional RTA and PTA analysis. The diagnostic plot may also capture varying flow types. For example, the diagnostic plot may reflect a linear flow period, a radial flow period, and a boundary-dominated pseudo steady state (PSS) flow period.

The diagnostic plot may also be used to calculate formation permeability (k) using Equation 2 and total fracture surface area (A_ƒ) using Equation 3:

$\begin{array}{cc}k=\frac{X_s^2}{4{\tau }_{\mathrm{Fl}}^2}\mathrm{\varphi \mu }{c}_t,& \mathrm{Equation}2\end{array}$ $\begin{array}{cc}{A}_f=\frac{{w\left(\tau \right)}_{\mathrm{LF}}}{\sqrt{\alpha }\varphi },& \mathrm{Equation}3\end{array}$

where X_s is fracture spacing, ϕ is porosity, μ is viscosity, τ_Fl is the time of flight representing the beginning of fracture interference, and c_t is formation compressibility. w(τ)_LF may be read from the linear flow period (406 of the diagnostic plot (400). α refers to diffusivity, which may be defined by Equation 4:

$\begin{array}{cc}\alpha =\frac{k}{\mathrm{\varphi \mu }{c}_t},& \mathrm{Equation}4\end{array}$

Stimulated rock volume may describe a sum of the drainage volume at the fracture interference and the distance the pressure penetrates beyond the fracture tips, which is equal to half of the fracture spacing. Stimulated rock volume may be defined by Equation 5:

$\begin{array}{cc}{V}_{\mathrm{SRV}}=V_{\mathrm{Fl}}+\varphi \mathrm{Lh}\frac{x_s}{2},& \mathrm{Equation}5\end{array}$

where L is the horizontal well length, h is the formation thickness, V_Fl is the drainage at the fracture interference, and x_s is the cluster spacing.

In one or more embodiments, utilizing the diagnostic plot allows for model-free analysis without assuming planar fractures, homogeneous formation properties, and specific flow regimes. Further, the diagnostic plot may capture high-resolution flow patterns which are not observed in traditional RTA and PTA analysis. The diagnostic plot may also allow for a comparison of productivity of different wells.

FMM has become popular in a range of applications as a method of speeding up modeling of unconventional oil and gas reservoirs. FMM is a computationally efficient method for calculating the pressure front propagation time on the basis of reservoir properties. FMM is based on solving the Eikonal equation by use of upwind finite-difference approximation. Further, pressure/front location can be calculated as a function of time without running any flow simulations. In one or more embodiments, pressure/front location may also be referred to as radius of investigation.

One particularly useful application of FMM is visualizing and analyzing evolution of drainage volumes for hydraulically fractured wells over time. For example, FMM allows for visualization of drainage volume over time. FMM considers heterogenous reservoir properties and variable hydraulic fracture geometries with a comparable ease to those in homogeneous cases. Further, since FMM requires no flow simulations or generation of streamlines and takes only a few seconds of computation time, FMM can be used for fine scale models within geomodelling platforms for many different types of rapid evaluations.

In order to calculate pressure front propagation, it is necessary to first calculate diffusive time of flight (DTOF). DTOF can be obtained by solving the Eikonal equation, which is derived from the diffusivity equation (Equation 4) and its asymptotic solution, which is represented in Equation 6, which can be solved using FMM:

$\begin{array}{cc}\nabla \tau \left(x\right)=\frac{1}{\sqrt{\alpha \left(x\right)}},& \mathrm{Equation}6\end{array}$

A homogeneous reservoir may refer to a reservoir with rock properties which do not change throughout the reservoir. A permeability plot shows permeability across the homogeneous reservoir. In one or more embodiments, permeability refers to a measure of a rock's ability to transmit fluids. For example, a reservoir with a high permeability may transmit fluids easily, while a reservoir with a low permeability may transmit fluids poorly. In a homogenous reservoir, permeability is consistent across the entire reservoir.

A DTOF plot corresponding to the permeability plot may be obtained. The DTOF plot may have the same x-axis and y-axis as the permeability plot. The DTOF plot shows the radial variance in DTOF around the wellbore, where areas close to the wellbore have a relatively low DTOF value and areas further from the wellbore have a high DTOF value.

In one or more embodiments, a heterogeneous reservoir may be a reservoir in which rock properties vary throughout the reservoir. A permeability plot may show a horizontal well, highlighting high permeability areas and low permeability areas. Comparing the permeability plot to the DTOF plot, high permeability areas correlate with low DTOF areas. In the same manner, low permeability areas correlate with high DTOF areas. In low permeability areas, the fluid within the reservoir may find an alternate route of lesser resistance through the reservoir. In other words, the fluid may travel around the low permeability area. As such, the DTOF may increase, creating a correlation between low permeability areas and high DTOF areas. Further, the DTOF plot may show low DTOF areas immediately surrounding the well.

Permeability and DTOF plots may also be obtained for a heterogeneous reservoir within a horizontal well with multi-stage hydraulic fractures. In such plots, the horizontal well is shown running through the center of the 3D permeability plot and 3D DTOF plot. A number of hydraulic fractures may be shown along the length of horizontal well in the permeability plot. In one or more embodiments, hydraulic fractures may be areas of infinite permeability. As such, hydraulic fractures are typically associated with low DTOF areas.

In one or more embodiments, DTOF can also be used to transform 3D flow equations from spatial coordinates to a 1D w(τ) coordinate system. Such a transformation may reduce flow simulation computation times by numerous orders of magnitude. In one or more embodiments, a plot may show circular pressure propagation fronts in a homogenous reservoir. In one or more embodiments, a wellbore may be located in the center of the circular pressure propagation. There may be a number of concentric circles surrounding the wellbore, where the radial distance between each of the concentric circles is equal. In one or more embodiments, the circular pressure propagation fronts may be described using radial coordinates. For example, the diffusivity equation for a homogeneous reservoir may be represented in Equation 7:

$\begin{array}{cc}\frac{k}{\mathrm{\varphi \mu }{c}_t}\frac{1}{2\pi \mathrm{rh}}\frac{\partial }{\partial r}\left(2\pi \mathrm{rh}\frac{\partial p}{\partial r}\right)=\frac{\partial p}{\partial t},& \mathrm{Equation}7\end{array}$

where ∂p/∂r refers to the pressure gradient, which can also be defined by Equation 8:

$\begin{array}{cc}\nabla p=\frac{\partial p}{\partial r}=\nabla \tau \frac{\partial p}{\partial r},& \mathrm{Equation}8\end{array}$

A heterogeneous reservoir may have uneven pressure propagation fronts. In contrast to the radial coordinates used to describe the homogeneous reservoir, a heterogeneous reservoir with uneven pressure propagation fronts may be described in DTOF-based spatial coordinates. The uneven characteristic of the pressure propagation fronts may be directly caused by spatial heterogeneity. In one or more embodiments, w(τ) may be used to transform the DTOF coordinates into a corresponding radial coordinate. The w(τ) function is defined as the derivative of drainage volume with respect to DTOF and physically indicates the surface area of the propagating pressure front. The w(τ) function may be equal to 2πrh for homogeneous radial flow. As such, Equation 7 may be transformed using w(τ) into Equation 9:

$\begin{array}{cc}\frac{1}{w\left(\tau \right)}\frac{\partial }{\partial \tau }\left(w\left(\tau \right)\frac{\partial p}{\partial \tau }\right)=\frac{\partial p}{\partial t},& \mathrm{Equation}9\end{array}$

In one or more embodiments, more complicated mathematical and physics modelling, such as multi-phase modelling, may be incorporated into the FMM analysis.

FIG. 4 depicts a block diagram of a computer system (402) used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures as described in this disclosure, according to one or more embodiments. The illustrated computer (402) is intended to encompass any computing device such as a server, desktop computer, laptop/notebook computer, wireless data port, smart phone, personal data assistant (PDA), tablet computing device, one or more processors within these devices, or any other suitable processing device, including both physical or virtual instances (or both) of the computing device. Additionally, the computer (402) may include a computer that includes an input device, such as a keypad, keyboard, touch screen, or other device that can accept user information, and an output device that conveys information associated with the operation of the computer (402), including digital data, visual, or audio information (or a combination of information), or a GUI.

The computer (402) can serve in a role as a client, network component, a server, a database or other persistency, or any other component (or a combination of roles) of a computer system for performing the subject matter described in the instant disclosure. The illustrated computer (402) is communicably coupled with a network (430). In some implementations, one or more components of the computer (402) may be configured to operate within environments, including cloud-computing-based, local, global, or other environment (or a combination of environments).

At a high level, the computer (402) is an electronic computing device operable to receive, transmit, process, store, or manage data and information associated with the described subject matter. According to some implementations, the computer (402) may also include or be communicably coupled with an application server, e-mail server, web server, caching server, streaming data server, business intelligence (BI) server, or other server (or a combination of servers).

The computer (402) can receive requests over network (430) from a client application (for example, executing on another computer (402)) and responding to the received requests by processing the said requests in an appropriate software application. In addition, requests may also be sent to the computer (402) from internal users (for example, from a command console or by other appropriate access method), external or third-parties, other automated applications, as well as any other appropriate entities, individuals, systems, or computers.

Each of the components of the computer (402) can communicate using a system bus (403). In some implementations, any or all of the components of the computer (402), both hardware or software (or a combination of hardware and software), may interface with each other or the interface (404) (or a combination of both) over the system bus (403) using an application programming interface (API) (412) or a service layer (413) (or a combination of the API (412) and service layer (413). The API (412) may include specifications for routines, data structures, and object classes. The API (412) may be either computer-language independent or dependent and refer to a complete interface, a single function, or even a set of APIs. The service layer (413) provides software services to the computer (402) or other components (whether or not illustrated) that are communicably coupled to the computer (402). The functionality of the computer (402) may be accessible for all service consumers using this service layer. Software services, such as those provided by the service layer (413), provide reusable, defined business functionalities through a defined interface. For example, the interface may be software written in JAVA, C++, or other suitable language providing data in extensible markup language (XML) format or another suitable format. While illustrated as an integrated component of the computer (402), alternative implementations may illustrate the API (412) or the service layer (413) as stand-alone components in relation to other components of the computer (402) or other components (whether or not illustrated) that are communicably coupled to the computer (402). Moreover, any or all parts of the API (412) or the service layer (413) may be implemented as child or sub-modules of another software module, enterprise application, or hardware module without departing from the scope of this disclosure.

The computer (402) includes an interface (404). Although illustrated as a single interface (404) in FIG. 4, two or more interfaces (404) may be used according to particular needs, desires, or particular implementations of the computer (402). The interface (404) is used by the computer (402) for communicating with other systems in a distributed environment that are connected to the network (430). Generally, the interface (404) includes logic encoded in software or hardware (or a combination of software and hardware) and operable to communicate with the network (430). More specifically, the interface (404) may include software supporting one or more communication protocols associated with communications such that the network (430) or interface's hardware is operable to communicate physical signals within and outside of the illustrated computer (402).

The computer (402) includes at least one computer processor (405). Although illustrated as a single computer processor (405) in FIG. 4, two or more processors may be used according to particular needs, desires, or particular implementations of the computer (402). Generally, the computer processor (405) executes instructions and manipulates data to perform the operations of the computer (402) and any machine learning networks, algorithms, methods, functions, processes, flows, and procedures as described in the instant disclosure.

The computer (402) also includes a memory (406) that holds data for the computer (402) or other components (or a combination of both) that can be connected to the network (430). For example, memory (406) can be a database storing data consistent with this disclosure. Although illustrated as a single memory (406) in FIG. 4, two or more memories may be used according to particular needs, desires, or particular implementations of the computer (402) and the described functionality. While memory (406) is illustrated as an integral component of the computer (402), in alternative implementations, memory (406) can be external to the computer (402).

The application (407) is an algorithmic software engine providing functionality according to particular needs, desires, or particular implementations of the computer (402), particularly with respect to functionality described in this disclosure. For example, application (407) can serve as one or more components, modules, applications, etc. Further, although illustrated as a single application (407), the application (407) may be implemented as multiple applications (407) on the computer (402). In addition, although illustrated as integral to the computer (402), in alternative implementations, the application (407) can be external to the computer (402).

There may be any number of computers (402) associated with, or external to, a computer system containing a computer (402), wherein each computer (402) communicates over network (430). Further, the term “client,” “user,” and other appropriate terminology may be used interchangeably as appropriate without departing from the scope of this disclosure. Moreover, this disclosure contemplates that many users may use one computer (402), or that one user may use multiple computers (402).

FIG. 5 depicts a flowchart in accordance with one or more embodiments. More specifically, FIG. 5 depicts a flowchart 500 of a method of screening of hydraulic fracture and reservoir models conditioned to production data. Further, one or more blocks in FIG. 5 may be performed by one or more components as described in FIGS. 1-4. While the various blocks in FIG. 5 are presented and described sequentially, one of ordinary skill in the art will appreciate that some or all of the blocks may be executed in different orders, may be combined, may be omitted, and some or all of the blocks may be executed in parallel. Furthermore, the blocks may be performed actively or passively.

Initially, in step S502, a well may be selected. In one or more embodiments, there may be one or more models for the well. There may also be a plurality of wells. Production data for the well may already have been gathered. In one or more embodiments, the production data may be filtered to remove any outliers or noise from the data set.

In step S504, a production based w(τ) may be calculated from the production data, which may or may not be filtered. This may include plotting w(τ) vs. τ, or by employing other production data analysis techniques. From the diagnostic plot, key parameters may be extracted. In one or more embodiments, the key parameters may include w(τ)_LF, time of flight at the onset of fracture interference (τ_Fl), and stimulated rock volume (SRV). In one or more embodiments, production based w(τ) may also be referred to as a measured drainage function.

In step S506, a model based w(τ) may be calculated. In one or more embodiments, a model for the well may be selected, where the model includes a fracture model and a reservoir model. The selected reservoir model may be converted to DTOF. In one or more embodiments, this may be accomplished by solving the Eikonal equation, as shown above in Equation 6. Further FMM can be run to calculate r contour lines originating from selected fracture models. In one or more embodiments, the key parameters may include w(τ)_LF, τ_Fl, and SRV.

In step S508, the reservoir model and fracture model may be conditioned to production data. In one or more embodiments, conditioning may involve changing fracture model characteristics, which can include half length, height, efficiency, and distribution. Changing fracture model characteristics may, in some embodiments, combine fracture model characteristics with certain uncertainty ranges with a distribution function. The distribution function may be, for example, a triangular, normal, or uniform distribution. However, the distribution function may be any type of distribution without departing from the scope of this disclosure. In one or more embodiments, a misfit value may refer to the difference between production based w(τ) and model based w(τ). The misfit value may be calculated and then iteratively minimized. A tolerance may be defined, where the tolerance is either a predetermined value or a given percentage of data points. In one or more embodiments, if the minimized misfit is greater than the tolerance, the fracture model and reservoir model combination may be discarded. For example, there may be some embodiments where the tolerance is set as 20% of the range of misfit values, such that any combination with a misfit value above 20% of the range may be discarded. In one or more embodiments, minimization of the misfit may be accomplished using a variety of different proxy modelling techniques including, but not limited to, machine learning.

As shown in step S510, steps S504-S508 may be repeated for all models in the selected well. Further, once all models for a particular well have been selected, Steps S502-S510 may be repeated for all wells with production data within the desired sample area, as shown in step S512.

Once all models in all wells have been analyzed, fracture model and reservoir model combinations may be ranked and screened, allowing for any unsuitable combinations to be discarded, as shown in step S514. Ranking criteria can, for example, be based on study objectives, which may include, but are not limited to, SRV and total fracture surface area (A_ƒ). All fracture and reservoir model combinations within an acceptable misfit range may be ranked in order to select a few model combinations to represent, for example, P10, P50, and P90 models for detailed and robust flow simulations. In one or more embodiments, P10, P50, and P90 models may refer to models which fall in the 10, 50, and 90 percentiles of the ranked model combinations, respectively.

FIG. 6 depicts a flowchart in accordance with one or more embodiments. More specifically, FIG. 6 depicts a flowchart 600 of a method of determining a set of drainage models based, at least in part, on a misfit value. More specifically, flowchart 600 depicts a more specific version of the generalized method depicted in flowchart 500. Further, one or more blocks in FIG. 6 may be performed by one or more components as described in FIGS. 1-4. While the various blocks in FIG. 6 are presented and described sequentially, one of ordinary skill in the art will appreciate that some or all of the blocks may be executed in different orders, may be combined, may be omitted, and some or all of the blocks may be executed in parallel. Furthermore, the blocks may be performed actively or passively.

Initially, in step S602, a set of drainage models may be obtained. The set of drainage models may exist for a given well, though there may be many wells within the desired sample area, each with one or more drainage models. Further, the given well may have production data already available. Each drainage model may include a reservoir model and a fracture model. In one or more embodiments, the fracture model may include a plurality of fracture models, where each fracture model describes one of a plurality of hydraulic fractures intersecting the well.

Next, for each drainage model, a predicted drainage function based, at least in part, on the drainage model may be formed in step S604. In one or more embodiments, the predicted drainage function may be defined as w(τ). Further, forming a predicted drainage function may include simulating a connected volume using a FMM solution to an eikonal equation.

In step S606, a measured drainage function may be obtained for the well. In one or more embodiments, the measured drainage function may be obtained by creating a DTOF plot based on well production data, and determining a w(τ) function from the plot, which may be referred to as the measured drainage function.

In step S608, a misfit value may be determined for each drainage model based, at least in part, on the predicted drainage function and the measured drainage function. In one or more embodiments, the misfit value may be determined by calculating the difference between the measured drainage function and the predicted drainage function.

In step S610, a set of candidate drainage models based, as least in part, on the misfit value for each drainage model may be determined. In one or more embodiments, determining the set of candidate drainage models may include comparing the misfit value of each drainage model with a tolerance value. In some embodiments, the tolerance value may be a predetermined value. In other embodiments, the tolerance value may be selected based on a range of the misfit values. In one or more embodiments, a preferred drainage model for each candidate model may be determined based on a reduction of the misfit value. The reduction of the misfit value may be caused by perturbing of the candidate fracture model. In one or more embodiments, reduction of the misfit value may be accomplished by applying a machine learning network.

In one or more embodiments, a full-physics pressure-transient/rate-transient simulation may be performed using the preferred drainage model. Further, performing a full-physics pressure-transient/rate-transient simulation may include determining an uncertainty for the drainage model.

The methods described in flowcharts 500 and 600 may be implemented functionally to determine a probabilistic range of hydraulic fracture geometries and spacing under different geologic scenarios. The methods may quickly generate production data constrained hydraulic fracture characteristics such as fracture half length, fracture height, fracture efficiency, and fracture geometry variations along a horizontal wellbore. The methods may also enable production data constrained dynamic ranking and selection of pessimistic, optimistic, and likely scenarios (P10, P90, and P50 scenarios, respectively) for detailed flow simulation studies. As such, utilizing the methods described in flowcharts 500 and 600 may reduce the time and effort needed for expensive history matching and uncertainty studies for unconventional reservoirs.

In one or more embodiments, a machine learning network may be applied in order to determine the preferred drainage model. Machine learning (ML), broadly defined, is the extraction of patterns and insights from data. The phrases “artificial intelligence”, “machine learning”, “deep learning”, and “pattern recognition” are often convoluted, interchanged, and used synonymously throughout the literature. This ambiguity arises because the field of “extracting patterns and insights from data” was developed simultaneously and disjointedly among a number of classical arts like mathematics, statistics, and computer science. For consistency, the term machine learning, or machine-learned, will be adopted herein and deep learning (DL) will refer to a subset of machine learning (ML) which deals with so-called “deep” models. For example, a deep model may be a neural network with one or more hidden layers. However, one skilled in the art will recognize that the concepts and methods detailed hereafter are not limited by this choice of nomenclature.

Machine-learned model types may include, but are not limited to, generalized linear models, Bayesian regression, random forests, and deep models such as neural networks, convolutional neural networks, and recurrent neural networks. Machine-learned model types, whether they are considered deep or not, are usually associated with additional “hyperparameters” which further describe the model. For example, hyperparameters providing further detail about a neural network may include, but are not limited to, the number of layers in the neural network, choice of activation functions, inclusion of batch normalization layers, and regularization strength. Commonly, in the literature, the selection of hyperparameters surrounding a model is referred to as selecting the model “architecture”. As such, a DL-based framework consists of methods and systems to transform data, or otherwise determine a quantity, which leverage at least one machine-learned model which may be considered deep. A DL-based framework may include methods and processes to select a machine-learned model type and associated architecture, evaluating said machine-learned model, and using the machine-learned model in a production setting (also known as deployment of the machine-learned model).

In one or more embodiments, the machine learning network may be a neural network. A diagram of a neural network is shown in FIG. 7. At a high level, a neural network (700) may be graphically depicted as being composed of nodes (702), where here any circle represents a node, and edges (704), shown here as directed lines. The nodes (702) may be grouped to form layers (705). FIG. 7 displays four layers (708, 710, 712, 714) of nodes (702) where the nodes (702) are grouped into columns, however, the grouping need not be as shown in FIG. 7. The edges (704) connect the nodes (702). Edges (704) may connect, or not connect, to any node(s) (702) regardless of which layer (705) the node(s) (702) is in. That is, the nodes (702) may be sparsely and residually connected. A neural network (700) will have at least two layers (705), where the first layer (708) is considered the “input layer” and the last layer (714) is the “output layer”. Any intermediate layer (710, 712) is usually described as a “hidden layer”. A neural network (700) may have zero or more hidden layers (710, 712) and a neural network (700) with at least one hidden layer (710, 712) may be described a “deep” neural network or a “deep learning method”. In general, a neural network (700) may have more than one node (702) in the output layer (714). In this case the neural network (700) may be referred to as a “multi-target” or “multi-output” network.

Nodes (702) and edges (704) carry additional associations. Namely, every edge is associated with a numerical value. The edge numerical values, or even the edges (704) themselves, are often referred to as “weights” or “parameters”. While training a neural network (700), numerical values are assigned to each edge (704). Additionally, every node (702) is associated with a numerical variable and an activation function. Activation functions are not limited to any functional class, but traditionally follow the form

$A=f\left(\sum _{i\in \left(\mathrm{incoming}\right)}\left[{\left(\mathrm{node}\mathrm{value}\right)}_i{\left(\mathrm{edge}\mathrm{value}\right)}_i\right]\right),$

where i is an index that spans the set of “incoming” nodes (702) and edges (704) and ƒ is a user-defined function. Incoming nodes (702) are those that, when viewed as a graph (as in FIG. 7), have directed arrows that point to the node (702) where the numerical value is being computed. Some functions for ƒ may include the linear function ƒ(x)=x, sigmoid function

$f\left(x\right)=\frac{1}{1+e^{-x}},$

and rectified linear unit (ReLU) function ƒ(x)=max(0, x), however, many additional functions are commonly employed. Every node (702) in a neural network (700) may have a different associated activation function. Often, as a shorthand, activation functions are described by the function ƒ by which it is composed. That is, an activation function composed of a linear function ƒ may simply be referred to as a linear activation function without undue ambiguity.

When the neural network (700) receives a network input (e.g., the final output of an LSTM), the network input is propagated through the network according to the activation functions and incoming node (702) values and edge (704) values to compute a value for each node (702). That is, the numerical value for each node (702) may change for each received input. Occasionally, nodes (702) are assigned fixed numerical values, such as the value of 1, that are not affected by the input or altered according to edge (704) values and activation functions. Fixed nodes (702) are often referred to as “biases” or “bias nodes” (706), displayed in FIG. 7 with a dashed circle.

In some implementations, the neural network (700) may contain specialized layers (705), such as a normalization layer, or additional connection procedures, like concatenation. One skilled in the art will appreciate that these alterations do not exceed the scope of this disclosure.

Embodiments of the present disclosure may provide at least one of the following advantages. In general, FMM and DTOF based diagnostic plot methods are used in separate and distinct environments, where FMM is a solely model based method and DTOF diagnostic plot is a production data-based model. The methods disclosed herein allow for the integration of two previously distinct methods for understanding unconventional reservoirs. Further, integration of two separate methods may force consistency in the individual analysis performed in both methods.

For example, reservoir model properties can be assumed and hydraulic fracture characteristics can be predicted using DTOF production data analysis. However, there may be a large range of uncertainty in understanding reservoir characteristics which may cast shadow on the reliability of results. On the other hand, FMM analysis may provide good estimates on drainage volumes, which may not necessarily be consistent with production data. The methods disclosed herein combine the strengths of both methods in a workflow to generate reservoir and hydraulic fracture model combinations that matches production response for a given well.

The methods disclosed herein allow for fast and effective integration of production data into unconventional reservoir models in order to produce ranked fracture model and reservoir model combinations. A ranked list of combinations allows for screening out of any unsuitable combinations, as well as for selection of a number of combinations for more detailed and expensive flow simulation and history matching studies. In one or more embodiments, selection of ranked combinations for detailed simulation studies may include selecting P10, P50, and P90 models. Screening out unsuitable combinations also reduces uncertainty in the various combinations, which can typically be large.

Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from this invention. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims.

Claims

1. A method, comprising:

obtaining a measured drainage function for a well;

obtaining a set of drainage models, wherein each drainage model comprises a reservoir model and a fracture model;

for each drainage model: forming a predicted drainage function based, at least in part, on the drainage model, and determining a misfit value based, at least in part, on the predicted drainage function and the measured drainage function; and

determining a set of candidate drainage models based, at least in part, on the misfit value for each drainage model, wherein each candidate drainage model comprises a candidate reservoir model and a candidate fracture model.

2. The method of claim 1, wherein forming a predicted drainage function comprises simulating a connected volume using a fast marching method solution to an eikonal equation.

3. The method of claim 1, further comprising determining, for each candidate model, a preferred drainage model based on a reduction of the misfit value caused by perturbing of the candidate fracture model.

4. The method of claim 3, further comprising performing full-physics pressure-transient/rate-transient simulation using the preferred drainage model.

5. The method of claim 1, wherein determining the set of candidate drainage models comprises comparing the misfit value of each drainage model with a tolerance value.

6. The method of claim 5, wherein the tolerance value is a predetermined value.

7. The method of claim 5, wherein the tolerance value is selected based on a range of the misfit values.

8. The method of claim 3, wherein determining, for each candidate model, a preferred drainage model based on a reduction of the misfit value comprises applying a machine learning network.

9. The method of claim 4, wherein performing full-physics pressure-transient/rate-transient simulation comprises determining an uncertainty for the drainage model.

10. The method of claim 1, wherein the fracture model comprises a plurality of fracture models each describing one of a plurality of hydraulic fractures intersecting the well.

11. The method of claim 1, wherein the well comprises one or more wells.

12. The method of claim 1, further comprising:

determining a spacing of hydraulic fractures in an adjacent well; and

generating hydraulic fractures at the spacing.

13. A non-transitory computer-readable medium storing instructions, the instructions, when executed on a processor, comprising functionality for:

receiving a measured drainage function for a well;

obtaining a set of drainage models, wherein each drainage model comprises a reservoir model and a fracture model;

for each drainage model: forming a predicted drainage function based, at least in part, on the drainage model, and determining a misfit value based, at least in part, on the predicted drainage function and the measured drainage function; and

determining a set of candidate drainage models based, at least in part, on the misfit value for each drainage model, wherein each candidate drainage model comprises a candidate reservoir model and a candidate fracture model.

14. The non-transitory computer-readable medium of claim 13, wherein forming a predicted drainage function comprises simulating a connected volume using a fast marching method solution to an eikonal equation.

15. The non-transitory computer-readable medium of claim 13, further comprising determining, for each candidate model, a preferred drainage model based on a reduction of the misfit value caused by perturbing of the candidate fracture model.

16. The non-transitory computer-readable medium of claim 15, further comprising performing full-physics pressure-transient/rate-transient simulation using the preferred drainage model.

17. A system, comprising:

a well testing system, to determine a measured drainage function; and

a computer processor, configured to: receive a measured drainage function for a well; obtain a set of drainage models, wherein each drainage model comprises a reservoir model and a fracture model; for each drainage model: form a predicted drainage function based, at least in part, on the drainage model, and determine a misfit value based, at least in part, on the predicted drainage function and the measured drainage function; and determine a set of candidate drainage models based, at least in part, on the misfit value for each drainage model, wherein each candidate drainage model comprises a candidate reservoir model and a candidate fracture model.

18. The system of claim 17, wherein the computer processor is further configured to:

determine a spacing of hydraulic fractures in an adjacent well; and

generate hydraulic fractures at the spacing.

19. The system of claim 17, wherein the computer processor is further configured to determine, for each candidate model, a preferred drainage model based on a reduction of the misfit value caused by perturbing of the candidate fracture model.

20. The system of claim 19, wherein the computer processor is further configured to perform full-physics pressure-transient/rate-transient simulation using the preferred drainage model.