EP4680834A1

EP4680834A1 - Approximating spatial and temporal saturation and pressure of a carbon dioxide injection into an aquifer

Info

Publication number: EP4680834A1
Application number: EP24789302.7A
Authority: EP
Inventors: William Bailey; Peter Tilke
Original assignee: Services Petroliers Schlumberger SA; Schlumberger Technology BV
Current assignee: Services Petroliers Schlumberger SA; Schlumberger Technology BV
Priority date: 2023-04-11
Filing date: 2024-04-09
Publication date: 2026-01-21
Also published as: WO2024215646A1; US20240344451A1; EP4680834A4

Abstract

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.

Description

APPROXIMATING SPATIAL AND TEMPORAL SATURATION AND PRESSURE OF A CARBON DIOXIDE INJECTION INTO AN AQUIFER

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63/495404, filed on April 11, 2023, which is incorporated by reference herein.

BACKGROUND

[0002] 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 (“P_sat”) and CO2 carbon dioxide saturation (“Sco2”) are key inputs to any leaky well model.

[0003] 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. SUMMARY

[0004] 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.

[0005] 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.

[0006] 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. [0007] 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.

[0008] 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.

[0009] Both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the examples, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG. 1 is an illustration of an example model graphic for a CO2 aquifer injection.

[0011] FIG. 2 is an illustration of an example leaky wellbore and a visualization of corresponding model components.

[0012] FIG. 3 is an illustration of an example method for computing flow into an upper aquifer in a leaky well with a single flow path. [0013] FIG. 4 is an illustration of an example method for computing flow into an upper aquifer in a leaky well with multiple flow paths.

[0014] FIG. 5 is an illustration of an example well network template of a leaky well.

[0015] FIG. 6 is an illustration of an example system for computing flow into an upper aquifer in a leaky well.

DESCRIPTION OF THE EXAMPLES

[0016] 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.

[0017] 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.

[0018] FIG. 1 is an illustration of an example model 100 of a graphic network for a CO2 aquifer injection. The model 100 represents an aerial or birds-eye view of a drilling area and includes three types of nodes: injector nodes 110, abandoned well nodes 120, and pseudo-nodes 130. The injector nodes 110, illustrated by solid squares, represent locations where CO2 _IS injected. The abandoned well nodes 120, illustrated by open circles, represent locations of abandoned wells. Each pseudo-node 130, illustrated by solid circles, represents a 'junction' between the end of one or more edges 140 and the start of the next connecting edge 140, or edges, to an adjacent graphical edge. A pseudo-node 130 can, for example, demarcate a change in topology, a change in a reservoir property, a fault, or something else.

[0019] 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.

[0020] 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.

[0021] 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.

[0022] FIG. 2 is an illustration of an example leaky wellbore and a visualization of corresponding model components. The left side of FIG. 2 is a simple sketch of a leaky abandoned well, including a wellbore 202, casing 204, plug 206, and cement 208. The sketch also includes a main aquifer 212, an upper aquifer 214, and impermeable shale 210. The type of leak illustrated in FIG. 2 is a leak through the cement 208. In this case CO2 leaks into the cement 208 at the bottom of the wellbore 202 (possibly via a corroded casing 204). The CO2 then flows up the annular cement conduit 208 along the indicated leak path 214. The cement leak is used below in describing edge modeling. However, this is not meant to be limiting in any way. Edge modeling can be performed for any type of leak, such as a plug leak or a combination a of plug leak and a cement leak. Although only a cement leak is illustrated, other types of leaks and their respective modeling methods are described herein.

[0023] The right side of FIG. 2 includes a visual illustration of an edge model 220, which shows how an edge 140 is modeled. Example methods of edge modeling are discussed later herein regarding FIGS. 3 and 4. The edge model 220 defines the well. The edge model 220 shows various sub-edges 222, 224, 226, 228, each of which represents a different possible flow or computational need when modeling the edge 140. The edge model 220 includes a wellbore sub-edge 220 representing the wellbore 202, a cement sub-edge 222 that represents the cement 208, an equation of state (“EoS”) sub-edge 224 that represents the EoS of the well, and a temperature edge 226 that represents the temperature of the well. An EoS can be an expression or model relating the density of a fluid with its temperature and pressure. Some examples can include the GERG-2008 equation, the Peng-Robinson equation, the Soave-Redlich-Kwong equation, or any other suitable model. The temperature edge 226 represents a dedicated temperature model that can feed the EoS edge 224. Any suitable temperature model can be used.

[0024] 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.

[0025] 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).

[0026] 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 (“ID”) 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.

[0027] 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.

[0028] 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 (“pCCh”), may be either single phase pCCh = piiq or p_gas or p_sc (where subscript ' sc¹ denotes super-critical) or multiphase such that pCCh= aiiq. piiq. + (1 — CUiq.) Pgas.

[0029] 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.

[0030] FIG. 3 is an illustration of an example method for computing flow into an upper aquifer in a leaky well with a single flow path edge 140. References are made below to various elements of FIG. 2, which is an example visual representation of the method described below. Hereinafter, pressure of a segment 242 is represented by “P” and temperature of a segment 242 is represented by “T.” The following nomenclature is used: (P_n=a)b. The “P” indicates pressure, but a T is used to indicate temperature. The subscript “n=a” indicates the segment 242 when there are N segments 242 in total. For example, “n=l” refers to the bottom segment 242, and “n=N” refers to the top segment 242. The subscript “b,” when applicable, is replaced with an “in” or an “out” to refer to a pressure or temperature being an input or output, respectively. For example, (P_n=2)in refers to the input pressure (i.e., the pressure at the bottom) of the second segment 242. In the same manner, (TH-N)OUI refers to the output temperature (i.e., the temperature at the top) of the top segment 242. [0031] At stage 302, an initial pressure (P_n=i)in and initial temperature((T_n=i)in are defined. Using the nomenclature described above, (Pn-i)in and (T_n-i)in correspond to the pressure and temperature at the bottom of the bottom segment 242, assuming a vertical well. The (P_n=i)in and (T_n=i)in can come from measurements or can be manually input from simulation of the main aquifer 212.

[0032] 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 306 a 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 308 a 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) ”

[0033] 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 ((P_n=i)out). For example, the (Pn=i)in and (T_n=i)in are used as input for F(x) (as well as any other appropriate parameter inputs), and F(x) outputs the (Pn=i)out.

[0034] At stage 312, the (T_n=i)out is identified. In an example, (T_n=i)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 (T_n=i)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. [0035] 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 (P_n)out of the next segment 242. For example, the output pressure of the previous segment 242 (denoted by (Pn-i)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=i)out becomes (Pn=2)in. The same happens for any other applicable parameters, such as (T_n=i)out becoming (T_n=2)in. The method then returns to stage 310 where (P_n)out is calculated again. This cycle repeats until the F(x) has been computed for all segments 242.

[0036] 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.

[0037] FIG. 4 is an illustration of an example method for computing flow into an upper aquifer in a leaky well with multiple flow paths. References are made below to various elements of FIG. 2, which is an example visual representation of the method described below. The example method illustrated in FIG. 4 begins in much the same way as in FIG. 3. For example, at stage 402, the (P_n=i)in and (T_n=i)in are defined. At stage 404, based on the type of leak, either a W(x) function or a C(x) function is used based on the leak type. If the leak type is open channel, then at stage 406 a W(x) function is used. If the leak type is annular cement, then at stage 408 a C(x) function is used. Selecting the proper F(x) function at stages 406 and 408 also includes defining edges (denoted by “En”). “E” indicates the pressure of a sub-edge, such as sub-edges

222, 224, 226, or 228, “x” corresponds to the exact sub-edge, and “n” corresponds to the segment 242. As an example, E²²² corresponds to the pressure of the wellbore 202

(corresponding to the well sub-edge 222), and E²²⁴ corresponds to the pressure of the cement 208

(corresponding to the cement sub-edge 224).

[0038] At stage 410, the method can diverge depending on whether En is the same as

En-i . 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 AP_C. 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 x 10’¹⁴). Volumetric flowrate of the mixture, q_mix, 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.

[0039] 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., En En-i), then a corrected pressure ((Pi’i)in) is calculated by subtracting the pressure drop (AP_C) from (Pn)i_n. In other words, (P )in = (Pn)in - AP_C For completeness, all other parameters (denoted as x, which includes temperature) can be updated to conform with the new inlet pressure.

[0040] 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 ((P_n=i)out). For example, the (P_n=i)in and (T_n=i)in are used as input for F(x) (as well as any other appropriate parameter inputs), and F(x) outputs the (P_n=i)out.

[0041] At stage 416, the (Tn=i)out is identified. In an example, (Tn=i)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 (T_n=i)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.

[0042] 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-i)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 En En-i, the (P_n)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.

[0043] 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.

[0044] Any number of additional path-specific functions can be defined and added to the method of FIG. 4 if necessary. The choice of function can be a plurality of functions because a plurality of edges to denote a well can be specified. As an example, assume there are two annular casings and that at a specific location in the well, flow changes from the first annulus (nearest the open channel of the well) to the second annulus via a corroded outer casing. The presence of a second annular flow channel can be defined in the algorithm by adding an extra sub-edge to define this second annular channel, along with a revised/updated flow model for this channel.

[0045] FIG. 5 is an illustration of an example well network template 500 of a leaky well. The template 500 includes leaky well node 502, graphical edges 504, pseudo-nodes 506, and sink collectors 508. The topology of the template 500 is dictated by the configuration of graphical edges 504 and pseudo-nodes 506. Each pseudo-node 506 do not necessarily need to represent a natural change in aquifer geology. For example, a pseudo-node 506 can simply enable connections of graphical edges 504 that form the template configuration.

[0046] 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.

[0047] 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.

[0048] FIG. 6 is an illustration of an example system for computing flow into an upper aquifer in a leaky well. A server 610 includes an application 612 for modeling leaky wells. The server 610 can be a single server or a group of servers, including multiple servers implemented virtually across multiple computing platforms. In an example, the server 610 can be a web server that allows users to access the application 612 through a web browser 622 on a user device 620. For example, the server 610 can send a graphical user interface (“GUI”) to the user device 620, which can be a front-end interface of the application 612. The user device 620 can be one or more processor-based devices, such as a personal computer, tablet, or cell phone. The server 610 and user device 620 can exchange communications using any appropriate communication protocol, such as HyperText Transfer Protocol Secure (“HTTPS”) or Application Programming Interface (“API”) calls.

[0049] 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 FIG. 5.

[0050] 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.

Claims

WHAT IS CLAIMED IS:

1. A method for computing flow into an upper aquifer in a leaky well, comprising: receiving initial parameters for modeling a leak in a well, the parameters including an initial temperature and an initial pressure; dividing the well into multiple segments; calculating, using the initial parameters as first input parameters, first output parameters for a first segment, the first output parameters including a first output pressure; calculating, using the first output parameters as second input parameters, second output parameters for a second segment, the second output parameters including a second output pressure; and generating a model of the leak in the well by using an aggregation of the first output parameters and second output parameters.

2. The method of claim 1, further comprising rendering a graphic template of the well based on the model in a graphical user interface (“GUI”).

3. The method of claim 2, wherein the graphic template includes one or more pseudo-nodes that represent a change in a topology, a change in a reservoir property, or a fault.

4. The method of claim 3, the graphic template including edges connected to nodes representing the well and the one or more pseudo-nodes.

5. The method of claim 4, wherein each edge includes a first sub-edge representing a corresponding wellbore, a second sub-edge representing a corresponding cement annulus, a third sub-edge representing equation of state properties, and a fourth sub-edge representing temperature.

6. The method of claim 1, further comprising: determining that the first output pressure is not equal to an initial pressure for the second segment; responsive to the determination, calculating an estimated pressure drop; calculating, based on the first output pressure and the estimated pressure drop, a corrected pressure; and using the corrected pressure as a second input parameter when calculating the second output parameters.

7. The method of claim 1, wherein the first output parameters are calculated using a first algorithm corresponding to a first leak type, and the second output parameters are calculated using a second algorithm corresponding to a second leak type.

8. A non-transitory, computer-readable medium containing instructions that, when executed by a hardware-based processor, causes the processor to perform stages for computing flow into an upper aquifer in a leaky well, the stages comprising: receiving initial parameters for modeling a leak in a well, the parameters including an initial temperature and an initial pressure; dividing the well into multiple segments; calculating, using the initial parameters as first input parameters, first output parameters for a first segment, the first output parameters including a first output pressure; calculating, using the first output parameters as second input parameters, second output parameters for a second segment, the second output parameters including a second output pressure; and generating a model of the leak in the well by using an aggregation of the first output parameters and second output parameters.

9. The non-transitory, computer-readable medium of claim 8, the stages further comprising rendering a graphic template of the well based on the model in a graphical user interface (“GUI”).

10. The non-transitory, computer-readable medium of claim 9, wherein the graphic template includes one or more pseudo-nodes that represent a change in a topology, a change in a reservoir property, or a fault.

11. The non-transitory, computer-readable medium of claim 10, the graphic template including edges connected to nodes representing the well and the one or more pseudo-nodes.

12. The non-transitory, computer-readable medium of claim 11, wherein each edge includes a first sub-edge representing a corresponding wellbore, a second sub-edge representing a corresponding cement annulus, a third sub-edge representing equation of state properties, and a fourth sub-edge representing temperature.

13. The non-transitory, computer-readable medium of claim 8, the stages further comprising: determining that the first output pressure is not equal to an initial pressure for the second segment; responsive to the determination, calculating an estimated pressure drop; calculating, based on the first output pressure and the estimated pressure drop, a corrected pressure; and using the corrected pressure as a second input parameter when calculating the second output parameters.

14. The non-transitory, computer-readable medium of claim 8, wherein the first output parameters are calculated using a first algorithm corresponding to a first leak type, and the second output parameters are calculated using a second algorithm corresponding to a second leak type.

15. A system for computing flow into an upper aquifer in a leaky well, comprising: a memory storage including a non-transitory, computer-readable medium comprising instructions; and a hardware-based processor that executes the instructions to carry out stages comprising: receiving initial parameters for modeling a leak in a well, the parameters including an initial temperature and an initial pressure; dividing the well into multiple segments; calculating, using the initial parameters as first input parameters, first output parameters for a first segment, the first output parameters including a first output pressure; calculating, using the first output parameters as second input parameters, second output parameters for a second segment, the second output parameters including a second output pressure; and generating a model of the leak in the well by using an aggregation of the first output parameters and second output parameters.

16. The system of claim 15, the stages further comprising rendering a graphic template of the well based on the model in a graphical user interface (“GUI”).

17. The system of claim 16, wherein the graphic template includes one or more pseudo-nodes that represent a change in a topology, a change in a reservoir property, or a fault.

18. The system of claim 17, the graphic template including edges connected to nodes representing the well and the one or more pseudo-nodes.

19. The system of claim 18, wherein each edge includes a first sub-edge representing a corresponding wellbore, a second sub-edge representing a corresponding cement annulus, a third sub-edge representing equation of state properties, and a fourth sub-edge representing temperature.

20. The system of claim 15, the stages further comprising: determining that the first output pressure is not equal to an initial pressure for the second segment; responsive to the determination, calculating an estimated pressure drop; calculating, based on the first output pressure and the estimated pressure drop, a corrected pressure; and using the corrected pressure as a second input parameter when calculating the second output parameters.