Patent Description:
<CIT> describes a method for geological formation analysis comprising collecting time-lapsed well-based measurement data from a first borehole in a geological formation over a measurement time period and collecting time-lapsed electromagnetic (EM) cross-well measurement data via a plurality of spaced-apart second boreholes in the geological formation over the measurement time period. The method further includes determining simulated changes to a hydrocarbon resource in the geological formation over the measurement time period based upon a geological model using a processor, and using the processor to determine if the simulated changes are within an error threshold of the time-lapsed well-based measurement data and the time-lapsed cross-well EM measurement data. If the simulated changes are not within the error threshold, then the geological model may be updated.

The present invention resides in a method for modeling a subterranean formation as defined in claim <NUM>.

The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the description of the invention and the appended claims, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term "and/or" as used herein refers to and encompasses any possible combinations of one or more of the associated listed items. It will be further understood that the terms "includes," "including," "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. Further, as used herein, the term "if" may be construed to mean "when" or "upon" or "in response to determining" or "in response to detecting," depending on the context.

<FIG> illustrate simplified, schematic views of oilfield <NUM> having subterranean formation <NUM> containing reservoir <NUM> therein in accordance with implementations of various technologies and techniques described herein. <FIG> illustrates a survey operation being performed by a survey tool, such as seismic truck <NUM>, to measure properties of the subterranean formation. The survey operation is a seismic survey operation for producing sound vibrations. In <FIG>, one such sound vibration, e.g., sound vibration <NUM> generated by source <NUM>, reflects off horizons <NUM> in earth formation <NUM>. A set of sound vibrations is received by sensors, such as geophone-receivers <NUM>, situated on the earth's surface. The data received <NUM> is provided as input data to a computer <NUM> of a seismic truck <NUM>, and responsive to the input data, computer <NUM> generates seismic data output <NUM>. This seismic data output may be stored, transmitted or further processed as desired, for example, by data reduction.

<FIG> illustrates a drilling operation being performed by drilling tools <NUM> suspended by rig <NUM> and advanced into subterranean formations <NUM> to form wellbore <NUM>. Mud pit <NUM> is used to draw drilling mud into the drilling tools via flow line <NUM> for circulating drilling mud down through the drilling tools, then up wellbore <NUM> and back to the surface. The drilling mud is typically filtered and returned to the mud pit. A circulating system may be used for storing, controlling, or filtering the flowing drilling mud. The drilling tools are advanced into subterranean formations <NUM> to reach reservoir <NUM>. Each well may target one or more reservoirs. The drilling tools are adapted for measuring downhole properties using logging while drilling tools. The logging while drilling tools may also be adapted for taking core sample <NUM> as shown.

Typically, the wellbore is drilled according to a drilling plan that is established prior to drilling. The drilling plan typically sets forth equipment, pressures, trajectories and/or other parameters that define the drilling process for the wellsite. The drilling operation may then be performed according to the drilling plan. However, as information is gathered, the drilling operation may need to deviate from the drilling plan. Additionally, as drilling or other operations are performed, the subsurface conditions may change. The earth model may also need adjustment as new information is collected.

Surface unit <NUM> may include transceiver <NUM> to allow communications between surface unit <NUM> and various portions of the oilfield <NUM> or other locations. Surface unit <NUM> may also be provided with or functionally connected to one or more controllers (not shown) for actuating mechanisms at oilfield <NUM>. Surface unit <NUM> may then send command signals to oilfield <NUM> in response to data received. Surface unit <NUM> may receive commands via transceiver <NUM> or may itself execute commands to the controller. A processor may be provided to analyze the data (locally or remotely), make the decisions and/or actuate the controller. In this manner, oilfield <NUM> may be selectively adjusted based on the data collected. This technique may be used to optimize (or improve) portions of the field operation, such as controlling drilling, weight on bit, pump rates, or other parameters. These adjustments may be made automatically based on computer protocol, and/or manually by an operator. In some cases, well plans may be adjusted to select optimum (or improved) operating conditions, or to avoid problems.

As shown, the sensor (S) may be positioned in production tool <NUM> or associated equipment, such as Christmas tree <NUM>, gathering network <NUM>, surface facility <NUM>, and/or the production facility, to measure fluid parameters, such as fluid composition, flow rates, pressures, temperatures, and/or other parameters of the production operation.

Data plots <NUM>-<NUM> are examples of static data plots that may be generated by data acquisition tools <NUM>-<NUM>, respectively; however, it should be understood that data plots <NUM>-<NUM> may also be data plots that are updated in real time. These measurements may be analyzed to better define the properties of the formation(s) and/or determine the accuracy of the measurements and/or for checking for errors. The plots of each of the respective measurements may be aligned and scaled for comparison and verification of the properties.

Static data plot <NUM> is a seismic two-way response over a period of time. Static plot <NUM> is core sample data measured from a core sample of the formation <NUM>. The core sample may be used to provide data, such as a graph of the density, porosity, permeability, or some other physical property of the core sample over the length of the core. Tests for density and viscosity may be performed on the fluids in the core at varying pressures and temperatures. Static data plot <NUM> is a logging trace that typically provides a resistivity or other measurement of the formation at various depths.

A production decline curve or graph <NUM> is a dynamic data plot of the fluid flow rate over time. The production decline curve typically provides the production rate as a function of time. As the fluid flows through the wellbore, measurements are taken of fluid properties, such as flow rates, pressures, composition, etc..

While a specific subterranean formation with specific geological structures is depicted, it will be appreciated that oilfield <NUM> may contain a variety of geological structures and/or formations, sometimes having extreme complexity. In some locations, typically below the water line, fluid may occupy pore spaces of the formations. Each of the measurement devices may be used to measure properties of the formations and/or its geological features. While each acquisition tool is shown as being in specific locations in oilfield <NUM>, it will be appreciated that one or more types of measurement may be taken at one or more locations across one or more fields or other locations for comparison and/or analysis.

The data collected from various sources, such as the data acquisition tools of <FIG>, may then be processed and/or evaluated. Typically, seismic data displayed in static data plot <NUM> from data acquisition tool <NUM> is used by a geophysicist to determine characteristics of the subterranean formations and features. The core data shown in static plot <NUM> and/or log data from well log <NUM> are typically used by a geologist to determine various characteristics of the subterranean formation. The production data from graph <NUM> is typically used by the reservoir engineer to determine fluid flow reservoir characteristics. The data analyzed by the geologist, geophysicist and the reservoir engineer may be analyzed using modeling techniques.

<FIG> illustrates an oilfield <NUM> for performing production operations in accordance with implementations of various technologies and techniques described herein. As shown, the oilfield has a plurality of wellsites <NUM> operatively connected to central processing facility <NUM>. The oilfield configuration of <FIG> is not intended to limit the scope of the oilfield application system. Part, or all, of the oilfield may be on land and/or sea. Also, while a single oilfield with a single processing facility and a plurality of wellsites is depicted, any combination of one or more oilfields, one or more processing facilities and one or more wellsites may be present.

Attention is now directed to <FIG>, which illustrates a side view of a marine-based survey <NUM> of a subterranean subsurface <NUM> in accordance with one or more implementations of various techniques described herein. Subsurface <NUM> includes seafloor surface <NUM>. Seismic sources <NUM> may include marine sources such as vibroseis or airguns, which may propagate seismic waves <NUM> (e.g., energy signals) into the Earth over an extended period of time or at a nearly instantaneous energy provided by impulsive sources. The seismic waves may be propagated by marine sources as a frequency sweep signal. For example, marine sources of the vibroseis type may initially emit a seismic wave at a low frequency (e.g., <NUM>) and increase the seismic wave to a high frequency (e.g., <NUM>-<NUM>) over time.

The component(s) of the seismic waves <NUM> may be reflected and converted by seafloor surface <NUM> (i.e., reflector), and seismic wave reflections <NUM> may be received by a plurality of seismic receivers <NUM>. Seismic receivers <NUM> may be disposed on a plurality of streamers (i.e., streamer array <NUM>). The seismic receivers <NUM> may generate electrical signals representative of the received seismic wave reflections <NUM>. The electrical signals may be embedded with information regarding the subsurface <NUM> and captured as a record of seismic data.

In one implementation, seismic wave reflections <NUM> may travel upward and reach the water/air interface at the water surface <NUM>, a portion of reflections <NUM> may then reflect downward again (i.e., sea-surface ghost waves <NUM>) and be received by the plurality of seismic receivers <NUM>. The sea-surface ghost waves <NUM> may be referred to as surface multiples. The point on the water surface <NUM> at which the wave is reflected downward is generally referred to as the downward reflection point.

The electrical signals may be transmitted to a vessel <NUM> via transmission cables, wireless communication or the like. The vessel <NUM> may then transmit the electrical signals to a data processing center. Alternatively, the vessel <NUM> may include an onboard computer capable of processing the electrical signals (i.e., seismic data). Those skilled in the art having the benefit of this disclosure will appreciate that this illustration is highly idealized. For instance, surveys may be of formations deep beneath the surface. The formations may typically include multiple reflectors, some of which may include dipping events, and may generate multiple reflections (including wave conversion) for receipt by the seismic receivers <NUM>. In one implementation, the seismic data may be processed to generate a seismic image of the subsurface <NUM>.

Marine seismic acquisition systems tow each streamer in streamer array <NUM> at the same depth (e.g., <NUM>-<NUM>). However, marine based survey <NUM> may tow each streamer in streamer array <NUM> at different depths such that seismic data may be acquired and processed in a manner that avoids the effects of destructive interference due to sea-surface ghost waves. For instance, marine-based survey <NUM> of <FIG> illustrates eight streamers towed by vessel <NUM> at eight different depths. The depth of each streamer may be controlled and maintained using the birds disposed on each streamer.

Waterflood is a field development scheme used for secondary recovery of hydrocarbons. Successfully managing a waterflood scheme relies on reservoir characterization that uses a variety of subsurface measurements and the integration of these measurements into a reservoir model.

Electrical resistivity is a tool in formation evaluation of oil and gas reservoirs. For example, electrical resistivity is used in downhole logging to locate and analyze reservoir rocks, to perform fluid dynamics, and design well completions. Reservoir models may be used to map fluid flow to exploit the reservoir. Fluid saturation away from the well may be useful to help generate reservoir models. Measuring or determining fluid saturation may be achieved by integrating a deep investigation of resistivity with the reservoir models.

Measuring or determining fluid saturation may be accomplished by applying tools that are sensitive to an inter-well (i.e., between two or more wells) environment. One of these tools is inductive deep-look electromagnetics (EM) or cross-well EM. Cross-well EM is an induction-based tomography technology that inductively measures the inter-well resistivity between two or more wells. This technology, particularly useful for tracking water and steam floods or mapping residual saturation, is also used to enhance sweep efficiency, identify bypassed pay, and predict fluid-related issues such as water breakthrough.

Cross-well EM/seismic analysis techniques may provide results in inter-well space at high resolution. Thus, uncertainty in reservoir models in the inter-well space can be reduced by integrating them with cross-well EM/seismic data. While cross-well seismic techniques are specifically applicable in environments where the density difference between the fluids is large enough for seismic techniques to detect, EM may be useful in oil-water environments where the density difference between the fluids is not large enough for seismic techniques to detect. Therefore, calibrating reservoir models with cross-well EM data may reduce uncertainty in fluid system reservoirs.

The present disclosure integrates streamlines with deep-look EM data/analysis to better determine the flowpath of the injected fluid, thus also determining the flowpath of resident fluids. The streamlines generated may be revised until a reasonable match of streamlines with deep-look EM is achieved. Once a close match between the two is achieved, a dynamic model can be used to determine the effectiveness of waterflooding and further design multiple scenarios of field development, such as enhanced oil recovery (EOR) implementation, infill well planning, etc..

As the original energy of a reservoir depletes with production, and the reservoir is no longer able to support the production of hydrocarbons up to the surface, even with an artificial lift, secondary recovery mechanisms are employed to continue the production. One method of restoring and maintaining reservoir energy is to inject water into the reservoir. This is known as waterflooding. However, waterflooding has its own challenges related to design, execution, and surveillance. The success of a waterflooding project may depend upon a well-planned and well-executed program of surveillance and monitoring. At one time, waterflood surveillance included aspects of reservoir performance, but with the application of the reservoir management approach, the industry's focus shifted to include wells, facilities, operating conditions, etc. in surveillance programs. There are various surveillance factors to be considered for a successful waterflood process, including precise reservoir analysis. A detailed reservoir analysis may facilitate accurate waterflood monitoring and real-time decisions to modify the ongoing waterflood for economic development of the field.

From the aspect of reservoir analysis, there may be two ways of monitoring a waterflood: locally, which is restricted to the small part of the field close to the injectors, and globally, which operates at the field level and incorporates the full-field performance of the waterflood. The local methods of monitoring a waterflood include data acquisition approaches such as deep-look time-lapse cross-well EM and tracers. The global methods for understanding, analyzing, planning, and predicting waterflood development include modeling approaches such as tank models, fractional-flow models, or simulation models. One example of these modeling approaches includes or otherwise involves streamline simulation. Both of these methods (i.e., local and global) have limitations that affect the accuracy of waterflood surveillance and cause uncertainty during field development. However, the two methods may complement each other, if combined in a logical manner, to generate an accurate waterflood surveillance scheme. The present disclosure describes an approach that uses a combination of local and global methods of waterflood surveillance (e.g., deep-look time-lapse cross-well EM as an example of local methods and streamline simulation as an example of global methods) and explains how a logical workflow to combine these two methods can generate a strong water surveillance scheme.

As mentioned above, streamline simulation may be used for hydrocarbon reservoir simulation. A streamline may be considered to be a line that is tangential to the local velocity field at a given instant of time. Streamline-based flow simulation differentiates itself from cell-based simulation techniques, such as finite-differences and finite-elements, in that phase saturations and components are transported along a flow-based grid defined by streamlines (or streamtubes) rather than moved from cell-to-cell. The objective is to capture how injected reservoir volumes (e.g., water) displace resident reservoir volumes, which may aid in understanding waterflood management. Streamline simulation encompasses multiple assumptions (e.g., capillary pressure effects are not considered, lift curves are used for reporting, limited well management capability, etc.) and does not have as wide an application as finite difference simulations. However, a waterflood in an oil-water fluid system is a case where streamline simulation can be applied.

Waterflood management at a full-field level has been studied through two approaches: static allocation by analytical methods, and sensitivities in numerical simulation. Whereas analytical methods largely provide results of injection behavior, water influx, and fluid movement at a time-step and not over time, finite difference simulations use large amounts of computational time for such sensitivities and have a limitation on resolution (e.g., cell-size) to maintain a reasonable simulation time. Therefore, streamline simulation is a tool to monitor and improve large waterfloods at a full-field level because it provides an efficient method to model and predict detailed fluid movement.

There is, however, a limitation in full-field modeling approaches that limits their use as a method for waterflood management. This limitation is common to streamline simulation as well. The streamlines generated are largely dependent on the modeled geology of the field, and because the geology between the wells is uncertain (e.g., mostly modeled either based on statistical methods or deterministic methods), there is inherent uncertainty in the generated streamlines. This uncertainty can have widespread impacts on the waterflood development program of the field and hence the project economics. Streamlines, if validated, can help in mitigating an uncertainty existing in today's reservoir analysis methodology (e.g., uncertainty in flow paths between wells) and thus help an operator prepare an appropriate large-scale waterflood development plan or EOR development of a brownfield (e.g., subsequently with the development of streamlines to handle more than <NUM>-phase black oil cases).

As mentioned above, cross-well EM is an induction-based tomography technology that measures the inter-well resistivity between two or more wells. The data acquisition strategy involves moving (e.g., raising and lowering) a transmitter in one well and measuring the transmitted signals in a second well with a stationary receiver array. After a specified depth interval is logged in the first and/or second wells, the transmitter and/or the receiver(s) is/are moved to a new depth, and the process is repeated until the logging interval is covered by both the transmitter and the receiver(s). A data point may include stacking a monochromatic sine wave a plurality (e.g., hundreds or thousands) of times. An entire data set may include about <NUM>-<NUM> separate receiver positions covering the depth range of interest, so a string of receivers may be used to reduce the data acquisition time. Capturing an entire data set may take from about <NUM> to <NUM> hours depending on the tools available, the well conditions, and the well separation. Therefore, a comprehensive workflow incorporating streamline simulation and cross-well EM may address the uncertainty in waterflood surveillance and aid in subsequent field development.

<FIG> illustrates a flowchart of a method <NUM> for modelling a subterranean formation, according to an embodiment.

The method <NUM> may include measuring or receiving data representing (or collected from) a subterranean formation, as at <NUM>. The data may be or include (e.g., time-lapse) cross-well EM data. The cross-well EM data may be in the form of superposed primary and secondary electric fields between two or more wells. An example of this is shown in <FIG>, which illustrates a schematic view of cross-well electromagnetic (EM) data acquisition.

As shown in <FIG>, a first well <NUM> and a second well <NUM> are formed in a subterranean formation <NUM>. The first well <NUM> may have a transmitter <NUM> positioned therein. The transmitter <NUM> may be configured to transmit EM signals <NUM> into the subterranean formation <NUM>. The transmitter <NUM> may be raised and lowered to a plurality of different depths within the first well <NUM> (e.g., by a cable <NUM>) to transmit the EM signals <NUM> at/from the plurality of different depths.

The second well <NUM> may have one or more receivers positioned therein. As shown, four receivers 522A-522D are axially-adjacent to one another with respect to a central longitudinal axis through the second well <NUM>. Thus, the receivers 522A-522D may be positioned at a plurality of different depths within the second well <NUM>. The receivers 522A-522D may receive/measure the EM signals <NUM> transmitted from the transmitter <NUM>. The receivers 522A-522D may be raised and lowered to a plurality of different depths within the second well <NUM> (e.g., by a cable <NUM>) to receive/measure the EM signals <NUM> at the plurality of different depths.

Returning to <FIG>, the method <NUM> may also include processing the data (e.g., the cross-well EM data) to produce a resistivity profile of the subterranean formation, as at <NUM>. More particularly, the amplitude of the EM signals <NUM> received/measured by the receivers 522A-522D may be processed using tomographic inversion to produce a resistivity profile of the subterranean formation <NUM> in a two-dimensional (2D) section (also referred to as a 2D plane) between the first and second wells <NUM>, <NUM>. There may be an inherent uncertainty in the inversion of the cross-well EM data to resistivity. In at least one embodiment, a seismic-petrophysics calibration may be used to reduce the uncertainty in the inversion.

The derived resistivity information may be used to calibrate one or more static geo-cellular model(s) and dynamic reservoir model(s), as described below. In addition, the reduction in uncertainty of reservoir characterization and fluid saturation mapping may become more robust if the cross-well EM data is acquired in a time-lapse manner, across one or more well groups in the field.

The method <NUM> may also include determining a static model of the subterranean formation based at least partially upon the resistivity profile, as at <NUM>. More particularly, this may include determining, calibrating, and/or estimating a porosity distribution in a static GCM based at least partially upon the resistivity profile derived from the cross-well EM data between the wells <NUM>, <NUM>. Two techniques are described below to estimate the porosity and saturation along the 2D section between the wells <NUM>, <NUM>. A more detailed description of static GCM calibration is described below with respect to <FIG>.

PJI exploits the outcomes from amplitude-versus-offset (AVO) seismic inversion (e.g., acoustic impedance) and cross-well EM inversion (e.g., electrical resistivity) to delineate the reservoir behavior in the seismic domain and the EM domain. Such geophysical properties are combined through a rock physics framework and jointly inverted to provide a quantitative description of the reservoir properties in terms of rock and fluid properties (e.g., porosity and fluid content). PJI supports the reservoir characterization through a robust petrophysical model that makes use of the complementary information contained in the multi-physics dataset such as cross-well and seismic AVO.

<FIG> illustrates a schematic view of a two-stage PJI workflow <NUM>: from a well-log scale <NUM> to a reservoir scale <NUM>, according to an embodiment. The two-stage workflow <NUM> is based on a rock cross properties paradigm. First, a rock physics model is calibrated from the available well logs applying PJI to the acoustic impedance (AI) and deep resistivity logs. Second, the rock model is used to relate the reservoir's elastic and electrical properties (e.g., seismic and cross-well inversion derived) directly to underlying lithology and fluid properties with related uncertainties in terms of a-posteriori standard deviation.

In embodiments where the gathered seismic data has higher angles (e.g., ><NUM> degrees) with respect to a horizontal surface (e.g., a mean sea level can be considered a reference) that capture the AVO signature and a reliable acoustic impedance, a Vp/Vs ratio and/or a density can be derived within the seismic resolution. As used herein, Vp represents primary wave velocity, and Vs represents secondary wave velocity. These attributes can be used in equations governing a multi-attribute rock physics transform or a stochastic joint porosity saturation inversion to estimate porosity. The variable(s) in the equations involving hydrocarbons and water density may be obtained from a pressure-volume-temperature (PVT) laboratory analysis, and matrix density may be obtained from core analysis and/or well logs.

<FIG> illustrates a schematic view of a calibrator <NUM>, according to an embodiment. To validate the geological model with porosity distribution derived from cross-well EM data, the calibrator <NUM> may be used. The calibrator <NUM> works on evolutionary computation methodology of evolution strategy to minimize the root mean square error (RMSE) between the cross-well EM derived property and reservoir model property. To validate porosity, the calibrator <NUM> may change the global population of porosity in the geological model (e.g., by varying geostatistical population methods, variogram parameters, facies-biasing of porosity, well log upscaling, etc.) to match with the porosity derived from the cross-well EM data. The number of realizations of the static model for calibrating may be dependent upon the level of complexity and total acreage of the field under study. Once the RMSE between the two porosities in the 2D section is less than a predetermined amount, a group of models below a threshold RMSE are selected for dynamic model calibration. The porosity from the GCM is an input to derive the porosity in the 2D section from the cross-well resistivity. Thus, there is a high chance that the derived cross-well porosity may have a bias towards GCM porosity, particularly if the derivation is a single-step process. Therefore, an iterative process of porosity derivation may be used to avoid/reduce the bias of cross-well EM derived porosity on the GCM porosity.

<FIG> illustrates a graph <NUM> showing variables varied to calibrate the RMSE, according to an embodiment. More particularly, the graph <NUM> shows the variogram parameters used to geo-statistically populate a property (e.g., porosity) in a 3D reservoir model. These parameters may be derived from data analysis of well logs, and any change in these parameters may change the entire distribution of a property, essentially generating a new realization of 3D reservoir model. <FIG> illustrates a graph <NUM> showing a fitness calibration, according to an embodiment. More particularly, the graph <NUM> shows a threshold <NUM> and a plurality of GCMs <NUM> that have a RMSE below the threshold <NUM>.

Returning to <FIG>, the method <NUM> may also include determining a dynamic model of the subterranean formation based at least partially upon one or more of the static (e.g., GCM) models, as at <NUM>. More particularly, this may include determining, calibrating, and/or estimating a fluid (e.g., water or gas) saturation in a dynamic reservoir model based at least partially upon the resistivity profile derived from the cross-well EM data between the wells <NUM>, <NUM> and/or the static GCM (from <NUM>). For example, the dynamic reservoir model may be determined or calibrated based at least partially upon the one or more static (e.g., GCM) models <NUM> that have a RMSE below the threshold <NUM> (in <FIG>).

The dynamic reservoir model may be determined or calibrated against water saturation that is determined based at least partially upon the resistivity obtained from time lapse-cross-well EM data. The group of static GCM models <NUM> may be calibrated to match the cross-well EM derived water saturation (e.g., using the calibrator <NUM>). At each time step where actual cross-well EM data has been acquired, the water saturation from the dynamic reservoir model may be regressed using the calibrator <NUM> until it closely matches with the water saturation calculated from cross-well EM data. The calibrator <NUM> may change the parameters in the dynamic reservoir model that affect fluid-flow for each flow-unit to match with the water saturation derived from time-lapse cross-well EM data. Streamline simulation becomes an effective simulation technique in this workflow because it reduces the timeline of calibration (e.g., through quick simulations) with a high-resolution solution (e.g., on a fine-scale model). A more detailed description of dynamic model calibration (e.g., saturation calibration) is described below with respect to <FIG>.

The reasoning behind selecting a plurality of static GCMs <NUM> for dynamic model calibration, instead of the one model with least RMSE, is to improve the possibility of achieving the most accurate calibrated model for water saturation.

The two-level (e.g., static and dynamic) calibration ensures that the uncertainty is sequentially reduced and the final dynamic reservoir model approaches a unique solution. The result of the calibration workflow is a calibrated geological and dynamic model, with reduced uncertainty and enhanced predictability.

A practical application of the method <NUM> includes determining whether to waterflood (or gasflood) the subterranean formation based at least partially upon the static GCM model and/or the dynamic model, as at <NUM>. For example, a user may be able to design one or more scenarios of field development, such as EOR implementation, infill well planning, etc. Thus, the user may decide whether to inject fluid (e.g., water) into an injection well (e.g., the first well <NUM>). The fluid may displace hydrocarbons (e.g., oil) in the subterranean formation <NUM> to one or more production wells (e.g., the second well <NUM>), where the hydrocarbons may be recovered. In another embodiment, this may include performing the physical action of waterflooding (or gasflooding) the subterranean formation <NUM>.

<FIG> illustrates a schematic view of a method <NUM> for iteratively determining or calibrating porosity in a static geo-cellular model (GCM), according to an embodiment. The method <NUM> may include measuring or receiving cross-well EM data representing a subterranean formation, as at <NUM>. This may be similar to <NUM> above. The method <NUM> may also include processing the cross-well EM data (e.g., using tomographic inversion) to produce a resistivity profile of the subterranean formation between the wells, as at <NUM>. This may be similar to <NUM> above. The method <NUM> may also include determining or calibrating a porosity (e.g., in a 2D section) in the subterranean formation between the wells based at least partially upon the resistivity profile, as at <NUM>. In one embodiment, the porosity may be determined or calibrated using joint EM and seismic rock property inversion, which is described in "technique one" above. In another embodiment, the porosity may be determined or calibrated using seismic inversion and extended elastic inversion, which is described in "technique two" above.

The method <NUM> may also include building or receiving a first static GCM of the subterranean formation, as at <NUM>. The first static GCM may be built using well logs calibrated with core data, well tests, formation tests, etc. The first static GCM may also or instead be built using seismic data to derive horizons, faults, and trends for a 3D population of geological properties. The method <NUM> may also include determining or calibrating a porosity of the first static GCM, as at <NUM>. As shown, in at least one embodiment, the porosity of the first static GCM may be used to help determine the resistivity profile. The method <NUM> may also include determining (e.g., extracting) the porosity in a 2D section of the first static GCM, as at <NUM>.

The method <NUM> may also include varying one or more parameters of the first static GCM to vary the porosity in the (e.g., 2D section of the) first static GCM, thereby producing a second (e.g., updated) GCM, as at <NUM>. The parameters may be or include variogram parameters (e.g., nugget, sill, range, seed number, etc.), geostatistical population parameters, facies-biasing (of porosity) parameters, well log upscaling parameters, or the like. The porosity in the 2D section of the first static GCM may be varied to vary (e.g., reduce) the RMSE between the 2D section of the first static GCM (from <NUM> and/or <NUM>) and the 2D section based at least partially upon the resistivity profile (from <NUM>). In other words, the porosity in the 2D section of the first static GCM (from <NUM> and/or <NUM>) may be varied to more closely match the porosity in the 2D section based at least partially upon the resistivity profile (from <NUM>). In at least one embodiment, at least a portion of <NUM> may be performed using the calibrator <NUM> in <FIG>.

As mentioned above, this produces the second static GCM, which may loop back to <NUM> for another iteration. The next iteration may be directed to the same 2D section (e.g., the same depth in the subterranean formation) or to a different 2D section (e.g., a different depth). Thus, a plurality of static GCMs may be produced by the plurality of iterations. The method <NUM> may also include selecting one or more of the plurality of static GCMs with a RMSE below a predetermined threshold, as at <NUM>. An example of this is shown in <FIG> and described above. The selected static GCMs may be used in the dynamic data calibration described below with respect to <FIG>.

<FIG> illustrates a schematic view of a method <NUM> for iteratively determining water saturation calibration in a dynamic reservoir model, according to an embodiment. The method <NUM> may include measuring or receiving time-lapse cross-well EM data representing a subterranean formation, as at <NUM>. This may be similar to <NUM> and/or <NUM> above. The method <NUM> may also include processing the time-lapse cross-well EM data (e.g., using tomographic inversion) to produce a resistivity profile of the subterranean formation between the wells, as at <NUM>. This may be similar to <NUM> and/or <NUM> above. The method <NUM> may also include determining or calibrating a fluid (e.g., water) saturation (e.g., in a 2D section) in the subterranean formation between the wells based at least partially upon the resistivity profile, as at <NUM>.

The method <NUM> may also include building or receiving a first dynamic reservoir model of the subterranean formation, as at <NUM>. The first dynamic reservoir model may be built using, or otherwise based at least partially upon, the selected static GCMs (from <NUM>). The method <NUM> may also include determining or calibrating a water saturation of the first dynamic reservoir model, as at <NUM>. The method <NUM> may also include determining (e.g., extracting) the water saturation in a 2D section of the first dynamic reservoir model, as at <NUM>.

The method <NUM> may also include varying one or more parameters of the first dynamic reservoir model to vary the water saturation in the (e.g., 2D section of the) first dynamic reservoir model, thereby producing a second (e.g., updated) dynamic reservoir model, as at <NUM>. The parameters may be or include fluid flow parameters such as relative permeability endpoints, corey constants, and saturation-height function, etc. The water saturation in the 2D section of the first dynamic reservoir model may be varied to vary (e.g., reduce) the RMSE between the 2D section of the first dynamic reservoir model (from <NUM> and/or <NUM>) and the 2D section based at least partially upon the resistivity profile (from <NUM>). In other words, the water saturation in the 2D section of the first dynamic reservoir model (from <NUM> and/or <NUM>) may be varied to more closely match the water saturation in the 2D section based at least partially upon the resistivity profile (from <NUM>). In at least one embodiment, at least a portion of <NUM> may be performed using the calibrator <NUM> in <FIG>.

As mentioned above, this produces the second dynamic reservoir model, which may loop back to <NUM> for another iteration. The next iteration may be directed to the same 2D section (e.g., the same depth in the subterranean formation) or to a different 2D section (e.g., a different depth). Thus, a plurality of dynamic reservoir models may be produced. In at least one embodiment, the different iterations may be performed, and the different dynamic reservoir models may be produced, using streamline simulation, which may reduce the timeline of calibration through quick simulations with high resolution (e.g., on a fine-scale model).

The method <NUM> may also include selecting one or more of the plurality of dynamic reservoir models with a RMSE below a predetermined threshold, as at <NUM>. This is similar to the process shown in <FIG> above. As describe above with respect to <NUM>, the selected dynamic reservoir models may be used for the practical application of determining whether to waterflood the subterranean formation to recover hydrocarbons. This may include specific details related to which wells to inject, the type of fluid to inject, the pressure of the injected fluid, the flow rate of the injected fluid, the volume of the fluid to be injected, the recovery techniques, or a combination thereof.

The methods discussed above along with the technologies involved provide an opportunity to recalibrate the 3D numerical models to the best available data. However, it becomes more pertinent to understand the importance of selecting the right candidate wells, for carrying out the acquisition, so that the maximum potential of the methods may be realized. Although the methodology of selecting the right candidate wells may depend on various techno-economic considerations of a field development plan (FDP), certain guidelines can be followed to design the acquisition, to improve the reservoir characterization, as described below.

The methods may be applicable fields in the development phase. One of the plans in a development scenario is drilling infill wells to exploit bypassed/left-over oil pockets. Such planned infill wells, if falling under a favorable aspect ratio with any existing cased well or any other planned infill well, can form a candidate for cross-well acquisition. If multiple such pairs are available, the pair falling in the most heterogenous part of the reservoir may be selected for acquisition. Such a selection may ensure that most of the rock and fluid properties are tuned for the entire reservoir.

A reservoir under pressure maintenance through water flooding, may have several potential areas where new infill production/injection wells may be planned to drill. One possible candidate for the acquisition may be a new infill producer and an existing injector pair with a favorable aspect ratio. Furthermore, if this pair can be identified in the most heterogenous part of the reservoir, it may be an added benefit, as it may help in a better mapping of the water front movement across various heterogenous layers along with characterizing the reservoir facies distribution. For a waterflood scenario, deep look cross-well EM acquisition becomes more suitable, as EM is applicable in cases of resistivity contrast.

In a gas flood scenario, cross-well seismic acquisition technology may be better suited, as the density differences in the in-situ fluids would be prominent and can be mapped seismically. The methods described above may tune the rock/fluid parameters and thus improve the characterization in the full-field and not locally at the candidate wells. So, the acquisition may not be planned to introduce local improvements in characterization.

The foregoing methods scale the cross-well EM results to a full-field level. The process of calibration using evolution strategy may be fully-automated, which makes determining the RMSE quicker and more effective than conventional methods. Use of streamlines technology may enhance the scalability of application to fine grid GCMs, with fast simulation run-times, which may be helpful to quickly calibrate the dynamic models for water saturation. The methods may achieve a better predictive model fit for waterflood surveillance, particularly in aging reservoirs.

In some embodiments, any of the methods of the present disclosure may be executed by a computing system. <FIG> illustrates an example of such a computing system <NUM>, in accordance with some embodiments. The computing system <NUM> may include a computer or computer system 1101A, which may be an individual computer system 1101A or an arrangement of distributed computer systems. The computer system 1101A includes one or more analysis module(s) <NUM> configured to perform various tasks according to some embodiments, such as one or more methods disclosed herein. To perform these various tasks, the analysis module <NUM> executes independently, or in coordination with, one or more processors <NUM>, which is (or are) connected to one or more storage media <NUM>. The processor(s) <NUM> is (or are) also connected to a network interface <NUM> to allow the computer system 1101A to communicate over a data network <NUM> with one or more additional computer systems and/or computing systems, such as 1101B, 1101C, and/or 1101D (note that computer systems 1101B, 1101C and/or 1101D may or may not share the same architecture as computer system 1101A, and may be located in different physical locations, e.g., computer systems 1101A and 1101B may be located in a processing facility, while in communication with one or more computer systems such as 1101C and/or 1101D that are located in one or more data centers, and/or located in varying countries on different continents).

The storage media <NUM> can be implemented as one or more computer-readable or machine-readable storage media. Note that while in the example embodiment of <FIG> storage media <NUM> is depicted as within computer system 1101A, in some embodiments, storage media <NUM> may be distributed within and/or across multiple internal and/or external enclosures of computing system 1101A and/or additional computing systems. Storage media <NUM> may include one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories, magnetic disks such as fixed, floppy and removable disks, other magnetic media including tape, optical media such as compact disks (CDs) or digital video disks (DVDs), BLURAY® disks, or other types of optical storage, or other types of storage devices. Note that the instructions discussed above can be provided on one computer-readable or machine-readable storage medium, or alternatively, can be provided on multiple computer-readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media is (are) considered to be part of an article (or article of manufacture). The storage medium or media can be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions can be downloaded over a network for execution.

In some embodiments, computing system <NUM> contains one or more waterflood surveillance modeling module(s) <NUM> that may perform at least a portion of one or more of the method(s) <NUM>, <NUM>, <NUM> described above. It should be appreciated that computing system <NUM> is only one example of a computing system, and that computing system <NUM> may have more or fewer components than shown, may combine additional components not depicted in the example embodiment of <FIG>, and/or computing system <NUM> may have a different configuration or arrangement of the components depicted in <FIG>. The various components shown in <FIG> may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits.

Geologic interpretations, models and/or other interpretation aids may be refined in an iterative fashion; this concept is applicable to embodiments of the present methods discussed herein. This can include use of feedback loops executed on an algorithmic basis, such as at a computing device (e.g., computing system <NUM>, <FIG>), and/or through manual control by a user who may make determinations regarding whether a given step, action, template, model, or set of curves has become sufficiently accurate for the evaluation of the subsurface three-dimensional geologic formation under consideration.

Claim 1:
A method (<NUM>) for modeling a subterranean formation, comprising:
measuring or receiving (<NUM>) cross-well electromagnetic data representing a subterranean formation;
producing (<NUM>) a resistivity profile of the subterranean formation based at least partially upon the cross-well electromagnetic data;
determining (<NUM>) a static model of the subterranean formation based at least partially upon the resistivity profile, wherein the static model comprises a static geo-cellular model and
wherein determining the static model comprises calibrating a porosity (<NUM>) in the static model, by reducing an error between the porosity in the static geo-cellular model and a porosity derived from the cross-well electromagnetic data;
determining (<NUM>) a dynamic model of the subterranean formation based at least partially upon the static model;
determining (<NUM>) whether to waterflood or gasflood the subterranean formation based at least partially upon the static model and/or the dynamic model; and
building or updating a three-dimensional (3D) reservoir model of the subterranean formation for use in operations to waterflood the subterranean formation.