Patent Application
20240344451
In the context of injecting carbon dioxide (“CO2”) into aquifers, abandoned wells in the region of interest must be analyzed to ensure that they are properly sealed and not leaking any potentially harmful materials into nearby aquifers, including upper aquifers. One issue facing regulators and operators when analyzing this is the accuracy of the current solutions. Reliability of these predictions is critical when coupling the asset to leaky wells as pressure (“Psat”) and CO2 carbon dioxide saturation (“SCO2”) are key inputs to any leaky well model.
One problem with current modeling and simulation solutions is that they are either too simple (thereby reducing accuracy and reliability) or they have long run-times and require a large number of input data. The latter is the case with detailed finite difference simulators, such as E300 or INTERSECT. Current methods are not amenable to a rapid solution of the large number of geological realizations likely with automated geological modeling and other such tools. There is a need for a rapid solver that requires minimal input data and one that is coupled with leaky wells, which is something that current rigorous finite difference models cannot do easily. Thus, a requirement for a rapid, yet reliable, simulator that can ingest a large number of geological realizations and couple this with existing abandoned/orphaned wells remains.
Examples described herein include systems and methods for approximating spatial and temporal saturation and pressure of a carbon dioxide injection project into an aquifer. In an example, the well is divided into segments for modeling purposes. The well includes various graphical edges representing different properties of the well, such as pressure, temperature, the wellbore, the cement, and the casing.
A user can input known parameters into a graphical user interface (“GUI”). These initial parameters include the geological properties of the region of interest (“ROI”), and known properties and parameters of the wells and their uncertainties. The initial injection well parameters correspond to the bottom of the bottom segment of the well. An application inputs the initial parameters into one or more modeling algorithms that output values corresponding to properties of the well at the top of the corresponding segment. The output values are used as inputs for the next segment of the well. This continues until the properties of all segments have been calculated.
The application aggregates the output values to generate a model of the well. The application can render a graphic of the well and surrounding area in a GUI. The graphic can include the modeled well and any neighboring abandoned wells as nodes. The graphic can also include pseudo-nodes. Psuedo-nodes represent natural changes, such as a change in topology, a change in a reservoir property, a fault, or something else. The nodes and pseudo-nodes are connected by edges that represent an approximated flow of oil and water in a porous media. In other words, each edge is a model of part of the reservoir and represents the average reservoir properties affecting the hydraulic relationship between the associated leaky wells, neighboring wells, and pseudo-nodes.
A user provides initial input parameters for the bottom of a first segment, including an initial temperature and pressure. The initial parameters are used as input in an algorithm corresponding to the leak type. The algorithm outputs new property parameters corresponding to the top of the first segment. The new parameters are used as inputs in the algorithm in the next highest segment. This continues until all segments have been calculated. The outputs are aggregated and presented in a graphical template that includes edges representative of the output properties that connect nodes representing the well and surrounding wells and features.
The examples summarized above can each be incorporated into a non-transitory, computer-readable medium having instructions that, when executed by a processor associated with a computing device, cause the processor to perform the stages described. Additionally, the example methods summarized above can each be implemented in a system including, for example, a memory storage and a computing device having a processor that executes instructions to carry out the stages described.
Both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the examples, as claimed.
Reference will now be made in detail to the present examples, including examples illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts.
Systems and methods are described herein for approximating spatial and temporal saturation and pressure of a carbon dioxide injection into an aquifer. In an example, the well is divided into segments for modeling purposes. A user provides initial input parameters for the bottom of a first segment, including an initial temperature and pressure. The initial parameters are used as input in an algorithm corresponding to the leak type. The algorithm outputs new property parameters corresponding to the top of the first segment. The new parameters are used as inputs in the algorithm in the next highest segment. This continues until all segments have been calculated. The outputs are aggregated and presented in a graphical template that includes edges representative of the output properties that connect nodes representing the well and surrounding wells and features.
The edges 140 represent an approximated flow of oil and water in a porous media. In other words, each edge 140 is a model of part of the reservoir and represents the average reservoir properties affecting the hydraulic relationship between the associated injector 110 and pseudo-node 130. While a graphical edge 140 has units of length, each edge 140 is simply an “enabler”, or a geometrical construct that can accommodate almost any calculation (with any units). For example, the open conduit in an orphan well can be represented by one dedicated edge 140 to compute friction and head loss by a user-specified flow model.
Edges 140 can be depicted in different formats to illustrate different aspects of a segment. For example, the edge 140a is depicted as a dashed line. In one example, this can indicate that the simulation is performed over shorter edge length. Alternatively, the gaps in the dashed line can be representative of pseudo-nodes. The edges 140 can include CO2 segments 150 that represent CO2 plumes from CO2 injected at an injection site. The CO2 segments 150 simulate the CO2 migration in a primary aquifer.
Using an analogy to describe the model 100, the pseudo-nodes 130 can be thought of as traffic lights collecting the CO2 entering the node 130 from the exit(s) of the connecting edge(s) 140 while ensuring correct flow allocation (and mass) with the entrance to the next connecting edge(s) 140. The pseudo-node 130 ensures the correct split (or allocation) of CO2 of the localized system. For example, if the pseudo-node 130 has just one edge 140 entering it and one exiting, the pseudo-node 130 acts like a stop light at a pedestrian crossing on a single road. If, however, the pseudo-node 130 has multiple edges 130 entering and/or multiple edges 130 exiting, then the pseudo-node 130 ensures mass balance and the proper flow allocation.
The right side of
The sub-edges 222, 224, 226, 228 are merely exemplary and not meant to be limiting in any way. More, fewer, and/or different sub-edges can be used when modeling an edge 140. For example, for a cement leak, the well-bore edge 222 may not be needed. For a plug leak, the cement edge 224 may not be needed.
When modeling an edge 140, the edge 140 can be divided into segments 242. Each segment 242 represents a portion of a length L 240 that corresponds to the distance between the main aquifer 212 and the upper aquifer 214. The degree of segmentation of the edge 140 can be user defined, but a default segmentation can be used initially, such as 100 feet. Segmenting the edge 140 can avoid potential inaccuracies caused by large changes in pressure (due to hydrostatic head and friction) along with temperature changes that can occur by assuming single fluid properties over the entire length conduit path (L 240).
In an example, when modeling the edge 140, the behavior long the edge 140 at each segment 242 can be modeled in a one-dimensional (“1D”) simulator. The behavior of each segment 242 can be aggregated to obtain the behavior of the entire edge 140. A model 220 can include sub-edges for whichever possible flow or computational needs are required for the modeling technique.
When modeling a segment 242, the temperature sub-edge 228 is first considered in order to ensure correct CO2 phase. The temperature sub-edge 228 represents temperature and considers geometry and configuration of the wellbore 202, casing 204, cement annulus 208, and surrounding rock formation 210. If flow rates are low, a temperature profile of the well can be computed using previously known data. For example, such data may be collected during drilling operations and stored in a look-up table. This can save on run-time overhead.
The temperature profile can be inputted into an EoS equation represented by the EoS sub-edge 226. Initial pressure (at the bottom of the edge 140 in the main aquifer 212) comes from simulation or measurements. Subsequent pressures are computed as functions of the EoS as this may affect hydrostatic head as CO2 density (“ρCO2”), may be either single phase ρCO2=ρliq. Or ρgas Or ρsc (where subscript ‘sc’ denotes super-critical) or multiphase such that ρCO2=αliq. ρliq.+(1−αliq.) ρgas.
Because the EoS depends on both temperature and pressure, the EoS for a segment 242 can be calculated using the pressure from the previous segment 242 (i.e., the segment 242 below). This correctly accounts for hydrostatic head.
At stage 302, an initial pressure (Pn=1)in and initial temperature ((Tn=1)in are defined. Using the nomenclature described above, (Pn=1)in and (Tn=1)in correspond to the pressure and temperature at the bottom of the bottom segment 242, assuming a vertical well. The (Pn=1)in and (Tn=1)in can come from measurements or can be manually input from simulation of the main aquifer 212.
At stage 304, based on the type of leak, either an open channel function (“W(x)”) or an annular cement function (“C(x)”) can be used based on the leak type. For example, if the leak type is open channel, then at stage 306a W(x) is used. Any suitable single-or multiphase flow model can be used, such as a unified gas/liquid drift-flux model. If the leak type is annular cement, then at stage 308a C(x) function is used. If a reliable C(x) function is not available, a user-defined correlation based on experimental data can be used. Regardless of the function type, the function used for modeling the edge 140 is referred to hereinafter as “F(x).”
The method then proceeds in a cycle of stages 310, 312, 314, 316, and 320 for each segment 242. For example, at stage 310, the F(x) is calculated for the bottom segment 242 of the well to obtain the pressure at the top of the bottom segment 242 ((Pn=1)out). For example, the (Pn=1)in and (Tn=1)in are used as input for F(x) (as well as any other appropriate parameter inputs), and F(x) outputs the (Pn=1)out.
At stage 312, the (Tn=1)out is identified. In an example, (Tn=1)out can be identified using a separate temperature model. For example, if flow rates are low, a temperature profile of the well from previously known data can be used to identify (Tn=1)out. At stage 314, the n value is increased by one (denoted by n=n+1). This represents moving up to the next highest segment 242 for the next calculation.
At stage 316, if the new n is greater N (denoted by n>N), indicating that the last calculation was for the top segment 242 of the well, then the method proceeds to stage 318 where the modeling of the edge 140 is complete. However, if n is not greater than N, then the method proceeds to stage 320 where new parameters are identified for calculating the (Pn)out of the next segment 242. For example, the output pressure of the previous segment 242 (denoted by (Pn-1)out) is used as in the input pressure ((Pn)in) for the next segment 242. As an example, when moving from the bottom segment 242 to the next highest segment 242, ((Pn=1)out becomes (Pn=2)in. The same happens for any other applicable parameters, such as (Tn=1)out becoming (Tn=2)in. The method then returns to stage 310 where (Pn)out is calculated again. This cycle repeats until the F(x) has been computed for all segments 242.
The outputs of F(x) can be aggregated, along with the other parameters, to create a model of the whole well. If a leaky well intersects more than one upper aquifer 214, one can account of the amount of CO2 flowing into the first upper aquifer encountered and continue with the calculation (with a reduced volume) to the next point of leakage in the next aquifer, and so on.
At stage 410, the method can diverge depending on whether Enx is the same as En-1x. In other words, if there is a change of primary flow path sub-edge between segments 242, then an additional pressure drop must be considered at stage 412. Such a pressure drop is denoted as ΔPc. This pressure drop is analogous to loss through a constriction (like a nozzle). The general relationship used for such a loss is shown in Table 1 below:
In the equation in Table 1, Cu′ is a units conversion factor (for field units, Cu′=2.892×10−14). Volumetric flowrate of the mixture, qmix, is stated in ft3/d; inlet pressure, Pin, is stated in psi and Ac (the area of the constriction) is stated in ft2. The discharge coefficient is defaulted to Cv=0:85, but this can vary. Typically, for a known device (i.e., valve, nozzle), this is obtained through experimental studies and provided by the vendor. For a corroded hole in the casing, however, one can only but estimate this value. But, for simplicity Cv≈0:85 can be a suitable default.
When the inlet pressure of a sub-edge (e.g., the pressure of the well 202, casing 204, or cement 208) not identical to the outlet pressure of the previous edge (i.e., Enx≠En-1x), then a corrected pressure ((Pn′)in) is calculated by subtracting the pressure drop (ΔPc) from (Pn)in. In other words, (Pn′)in=(Pn)in−ΔPc. For completeness, all other parameters (denoted as x, which includes temperature) can be updated to conform with the new inlet pressure.
At stage 414, the F(x) function is calculated for the bottom segment 242 of the well to obtain the pressure at the top of the bottom segment 242 ((Pn=1)out). For example, the (Pn=1)in and (Tn=1)in are used as input for F(x) (as well as any other appropriate parameter inputs), and F(x) outputs the (Pn=1)out.
At stage 416, the (Tn=1)out is identified. In an example, (Tn=1)out can be identified using a separate temperature model. For example, if flow rates are low, a temperature profile of the well from previously known data can be used to identify (Tn=1)out. At stage 418, the n value is increased by one (denoted by n=n+1). This represents moving up to the next highest segment 242 for the next calculation.
At stage 418, if the new n is greater N (denoted by n>N), indicating that the last calculation was for the top segment 242 of the well, then the method proceeds to stage 422 where the modeling of the edge 140 is complete. However, if n is not greater than N, then the method proceeds to stage 424 where new parameters are identified for calculating the (Pn)out of the next segment 242. For example, the output pressure of the previous segment 242 (denoted by (Pn-1)out is used as in the input pressure (Pn)in for the next segment 242. For a leaky well with multiple leaky types, the F(x) used at stage 414 can vary between cycle iterations based on the type of leak occurring at the particular segment 242 being calculated. Whenever Enx≠En-1x, the (Pn)in can be modified at stage 412 using the pressure drop equation. This cycle repeats until the F(x) has been computed for all segments 242.
The outputs of F(x) can be aggregated, along with the other parameters, to create a model of the whole well. If a leaky well intersects more than one upper aquifer 214, one can account of the amount of CO2 flowing into the first upper aquifer encountered and continue with the calculation (with a reduced volume) to the next point of leakage in the next aquifer, and so on.
Any number of additional path-specific functions can be defined and added to the method of
The sink collectors 508 help ensure that all CO2 that may leak into the template 500 is accounted for. This node type is a mere sink, with large volume, that ensures any CO2“overflow” is fully collected and recorded. If a template is sufficiently large (each edge 504 has a natural volume as a function of the underlying flow model) then the sink collectors 508 do not come into play. However, if there is overflow (the template is “filled” with CO2), then the sink collectors 508 fully account for this and the volumes leaked into each upper aquifer 202 is properly recorded during modeling calculations. Such information can be used for regulatory purposes, for example. The template 500 should be sufficiently large and robust enough to accommodate all the CO2 that may enter these upper aquifers 202, and over a long period of time.
One advantage of deploying such a template approach is that tens, or even hundreds, of potentially leaky wells can be coupled to the main aquifer in simple and rapid manner.
The application 612 can model leaks of abandoned wells into upper aquifers using well data 614 and inputs provided by a user from the user device 620. For example, a user can designate the parameters for modeling an abandoned well and any nearby abandoned wells. The parameters can include data relating to concrete, casings, pressure, temperature, well segments, and so on. The application 612 can receive the user parameters and input them into one or more modeling algorithms. The application 612 can then present the output in a meaningful way, like as a template, such as the well network template 500 illustrated in
Other examples of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the examples disclosed herein. Though some of the described methods have been presented as a series of steps, it should be appreciated that one or more steps can occur simultaneously, in an overlapping fashion, or in a different order. The order of steps presented are only illustrative of the possibilities and those steps can be executed or performed in any suitable fashion. Moreover, the various features of the examples described here are not mutually exclusive. Rather any feature of any example described here can be incorporated into any other suitable example. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
This application claims priority to U.S. Provisional Patent Application No. 63/495,404, filed on Apr. 11, 2023, which is incorporated by reference herein.
| Number | Date | Country | |
|---|---|---|---|
| 63495404 | Apr 2023 | US |
