A method and system for calculating the original geological reserves of gas reservoirs

By plotting gas production curves and measuring formation pressure during gas well testing, the problem of excessively high pressure caused by failure to flow back fracturing fluid was solved, enabling the calculation of accurate geological reserves and pressure, improving data accuracy, and supporting gas well management.

CN117786274BActive Publication Date: 2026-06-30PETROCHINA CO LTD

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
PETROCHINA CO LTD
Filing Date
2022-09-22
Publication Date
2026-06-30

AI Technical Summary

Technical Problem

In existing technologies, if the fracturing fluid is not completely drained back, a liquid column forms in the wellbore, resulting in an overestimation of the measured formation pressure of the gas reservoir. This leads to an overestimation of the original geological reserves and affects the evaluation of dynamic reserves.

Method used

By calculating the daily gas and liquid production during wellhead testing, a single-well gas production curve is plotted to determine whether the well cleaning process has ended. After well cleaning, the formation pressure is measured for a period of stable production, and the actual original geological reserves are calculated using the material balance method.

Benefits of technology

Ensuring thorough cleaning of the wellbore prevents overestimation of actual pressure, provides accurate original geological reserves and formation pressure data, improves data accuracy, and supports precise evaluation of dynamic reserves and gas well production management in the later stages.

✦ Generated by Eureka AI based on patent content.

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Abstract

This invention discloses a method and system for calculating the original geological reserves of a gas reservoir, comprising the following steps: calculating the daily gas production and daily liquid production during wellhead testing; calculating the backflow rate of the liquid in the well based on the daily liquid production; determining whether the well cleaning process has ended based on the backflow rate of the liquid in the well; after the well cleaning process has ended and the gas well has been in stable production for a period of time, measuring the current formation pressure in the well and calculating the daily gas production at the wellhead during the stable production period; calculating the geological reserves under the current formation pressure; and calculating the original geological reserves based on the daily gas production at the wellhead during wellhead testing, the daily gas production at the wellhead during the stable production period, and the obtained geological reserves. This invention can calculate the true original geological reserves and the true formation pressure in the early stages of gas reservoir production, and the final data has higher accuracy, providing accurate data support for the evaluation of later dynamic reserves and the study of gas well production management.
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Description

Technical Field

[0001] This invention belongs to the field of natural gas development technology and relates to a method and system for calculating the original geological reserves of a gas reservoir. Background Technology

[0002] Accurately assessing the original geological reserves of a gas reservoir is fundamental to developing a gas reservoir development plan. Currently, the series of gas reservoirs discovered in the Kuqa foreland region are all ultra-deep, high-pressure fractured tight sandstone gas reservoirs. Due to their large burial depth, poor physical properties, and low matrix porosity and permeability, reservoir stimulation methods such as sand fracturing are generally required during the well testing phase to improve seepage capacity and increase single-well productivity. This often leads to inaccurate pressure readings during well testing, as fracturing fluid may not be completely flushed back, forming a liquid column within the wellbore due to gravity differentiation. This results in higher measured pressures than the original geological reserves, affecting subsequent dynamic reserve assessments and severely hindering gas reservoir development and management research. Summary of the Invention

[0003] The purpose of this invention is to solve the problem in existing technologies where incomplete drainage of fracturing fluid and other materials leads to the formation of liquid columns within the wellbore due to gravity separation. This results in overestimation of the measured formation pressure in the gas reservoir, leading to an overestimation of the original geological reserves, low early-stage production per unit pressure drop, and underestimation of dynamic reserves, thus affecting later dynamic reserve evaluation. The invention provides a method and system for calculating the original geological reserves of a gas reservoir. This method can calculate the true original geological reserves in the early stages of gas reservoir production, facilitating the later calculation of true dynamic reserves, and simultaneously calculating the true original formation pressure, providing accurate data support for later production management research.

[0004] To achieve the above objectives, the present invention employs the following technical solution:

[0005] A method for calculating the original geological reserves of a gas reservoir includes the following steps:

[0006] S1: Calculate the daily gas production and daily liquid production during the wellhead testing period, calculate the backflow rate of the liquid in the well based on the daily liquid production, and draw the gas production curve of the gas well.

[0007] S2: Determine whether the well cleaning process has ended based on the return flow rate of the fluid in the well and the gas production curve of the gas well.

[0008] S3: After the well cleaning process is completed and the gas well has been producing steadily for a period of time, measure the current formation pressure in the well and calculate the daily gas production at the wellhead during the stable production period.

[0009] S4: Calculate the geological reserves under the current formation pressure based on the current formation pressure;

[0010] S5: Calculate the original geological reserves based on the daily gas production at the wellhead during the oil testing period, the daily gas production at the wellhead during the stable production period, and the geological reserves obtained in S4.

[0011] A further improvement of the present invention is that:

[0012] In step S1, the method for calculating the well fluid backflow rate is as follows:

[0013] The daily liquid production during the oil trial period is summed to obtain the cumulative liquid output during the oil trial period.

[0014] Calculate the ratio f between the cumulative outflow volume and the total volume of fluid injected into the formation; f is the flowback rate.

[0015] Step S2 includes the following steps:

[0016] When the backflow rate is greater than 100%, and the daily gas production curve in the gas well production curve remains unchanged, and the oil pressure curve no longer rises, it indicates that the well cleaning process is over.

[0017] In step S3, the gas well maintains stable production for 15-30 days.

[0018] Step S4 includes the following steps:

[0019] The method for calculating the geological reserves under the current pressure is as follows:

[0020] Gc=0.01×Ag×h×Φ×Sg / Bg (1)

[0021] Among them, A g Indicates the oil-bearing area; h represents the effective thickness; Φ represents the effective porosity; S g Indicates oil saturation; B g This represents the volume coefficient.

[0022] The volume coefficient B g The calculation method is as follows:

[0023] B g =(P sc ×Z g ×T) / (P g ×T sc (2)

[0024] Among them, Z g P represents the deviation coefficient; sc T represents the standard surface pressure, and T represents the formation temperature; sc P represents the standard ground temperature. g This indicates the current measured formation pressure.

[0025] S5 includes the following steps:

[0026] The original geological reserves are obtained by adding the geological reserves under the current pressure obtained in step S4 to the cumulative gas production.

[0027] The cumulative gas production is the sum of the daily gas production during the oil trial period and the daily gas production during the stable production period.

[0028] It also includes the following steps:

[0029] Based on the original geological reserves obtained in step S5, the dynamic reserves are calculated using the material balance method.

[0030] The aforementioned material balance method is:

[0031] (P g / Z g )=(P i / Z i )×(1-G p / G i (3)

[0032] Among them, P g / Z g This indicates the current apparent formation pressure; P i / Z i G represents the original apparent formation pressure; p G represents the cumulative gas extraction volume; i Indicates the original geological reserves.

[0033] A system for calculating the original geological reserves of a gas reservoir includes a well fluid backflow rate calculation module, a well cleaning judgment module, a formation pressure measurement module, a geological reserve calculation module, and an original geological reserve calculation module.

[0034] The in-well fluid backflow rate calculation module is used to calculate the daily gas production and daily fluid production during wellhead testing, calculate the in-well fluid backflow rate based on the daily fluid production, and plot the gas production curve of a single gas well.

[0035] The well cleaning judgment module is used to determine whether the well cleaning process has ended based on the return flow rate of the fluid in the well and the gas production curve of a single gas well.

[0036] The formation pressure measurement module is used to measure the current formation pressure in the well after the well cleaning process is completed and the gas well has been in stable production for a period of time, and to calculate the daily gas production at the wellhead during the stable production period.

[0037] The geological reserves calculation module is used to calculate the geological reserves under the current formation pressure.

[0038] The original geological reserves calculation module is used to calculate the original geological reserves based on the daily gas production at the wellhead during the oil testing period, the daily gas production at the wellhead during the stable production period, and the geological reserves obtained from the geological reserves calculation module.

[0039] A system for calculating the original geological reserves of a gas reservoir, wherein the in-well fluid flowback rate calculation module is specifically used for:

[0040] The daily liquid production during the oil trial period is summed to obtain the cumulative liquid output during the oil trial period.

[0041] Calculate the ratio f between the cumulative outflow volume and the total volume of fluid injected into the formation; f is the flowback rate.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] This invention discloses a method for calculating the original geological reserves of a gas reservoir. During well testing, the flowback rate of the fluid in the well is calculated to ensure the well cleaning is completed. After well cleaning, and after a period of stable production, the current ground pressure is measured to avoid the formation of a liquid column in the wellbore, which could lead to an overestimation of the measured formation pressure and affect the subsequent calculation of geological reserves. After a period of stable production, the original geological reserves can be calculated from the gas production during well testing and the gas production during stable production. The method disclosed in this invention can calculate the true original geological reserves and the true formation pressure in the early stages of gas reservoir production, with higher data accuracy. This provides precise data support for the evaluation of later dynamic reserves and the study of gas well production management. Attached Figure Description

[0044] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a flowchart of the calculation process of the present invention;

[0046] Figure 2 This is a single-well gas production curve diagram of the present invention;

[0047] Figure 3 This is a schematic diagram of the PZ method in an embodiment of the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0049] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0050] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0051] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0052] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0053] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0054] The present invention will now be described in further detail with reference to the accompanying drawings:

[0055] See Figure 1 This invention discloses a method for calculating the original geological reserves of a gas reservoir, comprising the following steps:

[0056] Step 1: Calculate the backflow rate of fluid in the well.

[0057] First, the daily gas and liquid production during the well testing period are measured using wellhead metering equipment. The measured daily liquid production during well production is then summed to obtain the current cumulative produced liquid volume Ng. Finally, the ratio f between the cumulative produced liquid volume Ng and the total liquid volume injected into the formation is calculated.

[0058] That is, the flowback rate f = cumulative fluid production / total fluid injected into the formation;

[0059] Step 2: Determine if the well cleaning process is complete.

[0060] The well cleaning process ends when f > 100%.

[0061] Furthermore, in this embodiment of the invention, the well cleaning process is determined by generating a single-well gas production curve. When the well cleaning process is characterized by stable gas production and a slow, steady rise in pressure, it indicates that the well cleaning process is complete. (See [link to previous section]). Figure 2 .

[0062] Step 3: Calculate the formation pressure after well cleaning and a period of stable production.

[0063] After the well cleaning process is completed and the gas well is kept in stable production for a period of time, the current formation pressure P is measured. g ;

[0064] Furthermore, in this embodiment of the invention, when measuring the current pressure of the gas well, the measurement is performed by inserting a pressure gauge into the well.

[0065] Furthermore, in this embodiment of the invention, after well cleaning is completed, the period of stable production is 15-30 days.

[0066] Step 4: Calculate the geological reserves under the current pressure.

[0067] When the gas reservoir has a low level of recovery and has been in stable production for a period of time, the driving mechanism of the gas reservoir is still driven by the elastic expansion energy of the gas, and the influence of water bodies and other factors can be almost ignored.

[0068] At this point, the porosity Φ and gas saturation Sg of the gas reservoir remain almost unchanged. The geological reserves G under the current pressure can be calculated using the volumetric method reserve calculation formula. c :

[0069] Gc=0.01×Ag×h×Φ×Sg / Bg (1)

[0070] Where the reservoir temperature T remains constant under the original conditions, and in the formula, A g Indicates the oil-bearing area, in km² 2 h represents the effective thickness in meters (m); Φ represents the effective porosity; S g Indicates oil saturation; B g This represents the volume coefficient.

[0071] The volume coefficient B g The calculation method is as follows:

[0072] B g =(P sc ×Z g ×T) / (P g ×T sc (2)

[0073] In the formula, the deviation coefficient Z g This can be obtained from data in PVT experiments; P sc T represents the standard surface pressure, and T represents the formation temperature; sc P represents the standard ground temperature. g This indicates the current measured formation pressure.

[0074] Step 5: Calculate the original geological reserves based on geological reserves and cumulative gas production.

[0075] Calculate the geological reserves G under the current pressure. c back,

[0076] The total gas production during the oil testing period is obtained by summing the cumulative gas production during the oil testing period.

[0077] At the same time, after the well cleaning is completed, the gas production of the gas well during a period of stable production is summed to obtain the total gas production during the stable production stage;

[0078] The total gas production during the trial production period and the total gas production during the stable production phase are added together to obtain the cumulative gas production G. p ;

[0079] The cumulative gas extraction volume G obtained p And the geological reserves G obtained in step 4 c By adding them together, we can obtain the original geological reserves G. i ,Right now:

[0080] G i =G c +G p (4)

[0081] This invention also discloses a method for calculating the dynamic reserves of a gas reservoir:

[0082] After obtaining the original geological reserves based on step 5, the material balance method P / Z = Pi / Zi(1-Gp / G) can be used to calculate P on the original PZ method chart. i / Z i Value, that is:

[0083] (P g / Z g )=(Pi / Z i )×(1-G p / G i (3)

[0084] Based on formula (3), and then through (0, P) i / Z i ), (G p Equations are established between two points (P and Z) to calculate the dynamic reserves.

[0085] Among them, P g / Z g This indicates the current apparent formation pressure; P i / Z i G represents the original apparent formation pressure; p G represents the cumulative gas extraction volume; i Indicates the original geological reserves.

[0086] In this embodiment of the invention, the original formation pressure P i It was measured before the oil testing period.

[0087] This invention also discloses a system for calculating the original geological reserves of a gas reservoir, including a well fluid flowback rate calculation module, a well cleaning judgment module, a formation pressure measurement module, a geological reserve calculation module, and an original geological reserve calculation module.

[0088] The in-well fluid backflow rate calculation module is used to calculate the daily gas production and daily fluid production during wellhead testing, calculate the in-well fluid backflow rate based on the daily fluid production, and plot the gas production curve of a single gas well.

[0089] The well cleaning judgment module is used to determine whether the well cleaning process has ended based on the return flow rate of the fluid in the well and the gas production curve of a single gas well.

[0090] The formation pressure measurement module is used to measure the current formation pressure in the well after the well cleaning process is completed and the gas well has been in stable production for a period of time, and to calculate the daily gas production at the wellhead during the stable production period.

[0091] The geological reserves calculation module is used to calculate the geological reserves under the current formation pressure.

[0092] The original geological reserves calculation module is used to calculate the original geological reserves based on the daily gas production at the wellhead during the oil testing period, the daily gas production at the wellhead during the stable production period, and the geological reserves obtained from the geological reserves calculation module.

[0093] The in-well fluid flow rate calculation module is specifically used to: sum the daily fluid production during the oil testing period to obtain the cumulative fluid production during the oil testing period;

[0094] Calculate the ratio f between the cumulative outflow volume and the total volume of fluid injected into the formation; f is the flowback rate.

[0095] The method disclosed in this invention can calculate the true original geological reserves and the true formation pressure in the early stage of gas reservoir production, avoiding the phenomenon that the measured pressure is too high, which leads to the geological reserve calculation result being higher than the original geological reserves. The final data has higher accuracy, providing accurate data support for the evaluation of dynamic reserves and the research on gas well production management in the later stage.

[0096] This invention discloses a specific embodiment:

[0097] Specific data of the gas reservoir selected in this embodiment of the invention:

[0098] In Embodiment 1 of this invention, a data acquisition experiment was conducted using gas reservoir A as an example, wherein:

[0099] The effective area of ​​the gas reservoir is 19.65 km². 2 That is, the gas-bearing area is 19.65 km². 2 ,

[0100] The effective thickness is 23.6 μm, the effective porosity is 7.5%, and the gas saturation is 62.30%.

[0101] During the oil test, the formation pressure was measured to be 66.9 MPa, the deviation coefficient of PVT was 1.44, the P / Z value was 46.45, and the geological reserves were 15.944 billion cubic meters.

[0102] Three wells, A1, A2, and A3, are producing gas, with an average daily gas production of 150,000 cubic meters per well.

[0103] Well A1 was an exploratory well. After 185 days of trial production, wells A2 and A3 were put into production one after another.

[0104] Twenty days later, the flowback rate of wells A2 and A3 was >100% and the well cleaning phase was over. After 10 days of stable production, the cumulative production volume was 0.4151 billion cubic meters. The production volume of the three wells during the oil testing period was 0.0117 billion cubic meters.

[0105] At this point, a full reservoir pressure measurement was performed, and the actual measured pressure was 64.066 MPa, the formation temperature was 84℃ (183.2 K), and the PVT analysis showed a corresponding gas deviation coefficient of 1.418.

[0106] The standard ground temperature is 293.15 K, and the standard ground pressure is 0.101 MPa.

[0107] Based on the data obtained above, calculate the geological reserves of natural gas under the current pressure:

[0108]

[0109] Further, calculate the original geological reserves:

[0110] G i = G c +G p =153.9183 + 0.4268 = 154.3451 × 10 8 m 3

[0111] Further, calculate the Pi / Zi value:

[0112]

[0113] Furthermore, two sets of data points were marked on the PZ method chart to evaluate dynamic reserves;

[0114] Two sets of data were obtained:

[0115] One set is: the relationship between P / Z measured during the trial oil production period, P / Z measured after a period of production and cumulative output (0, 46.45), (0.4268, 45.18);

[0116] The other set consists of: the relationship between Pi / Zi calculated using the material balance method based on the calculated original geological reserves, and the measured P / Z after a period of production (0.45.31), (0.4268, 45.31), and the cumulative production (see [reference needed]). Figure 3 .

[0117] According to this embodiment, the fitting formula obtained from the pressure value measured during the oil test is y = -2.9931x + 46.458, which calculates the dynamic reserves to be 1.552 billion cubic meters and the original geological reserves to be 15.944 billion cubic meters.

[0118] The original geological reserves calculated in the embodiments of the present invention are 15.43451 billion cubic meters. The formula fitted by the PZ method is y = -0.2799x + 45.3, and the calculated dynamic reserves are 16.184 billion cubic meters, which are basically consistent with the geological reserves. It can be seen that the results calculated by the method disclosed in the fourteen examples of the present invention have high accuracy.

[0119] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the original geological reserves of a gas reservoir, characterized in that, Includes the following steps: S1: Calculate the daily gas production and daily liquid production during the wellhead testing period, calculate the backflow rate of the liquid in the well based on the daily liquid production, and draw the gas production curve of the gas well. S2: Determine whether the well cleaning process has ended based on the backflow rate of the fluid volume in the well and the gas production curve of the single well. S3: After the well cleaning process is completed and the gas well has been producing steadily for a period of time, measure the current formation pressure in the well and calculate the daily gas production at the wellhead during the stable production period. S4: Calculate the geological reserves under the current formation pressure based on the current formation pressure; S5: Calculate the original geological reserves based on the daily gas production at the wellhead during the oil testing period, the daily gas production at the wellhead during the stable production period, and the geological reserves obtained in S4. In step S1, the method for calculating the well fluid backflow rate is as follows: The daily liquid production during the oil trial period is summed to obtain the cumulative liquid output during the oil trial period. Calculate the ratio f between the cumulative fluid output and the total fluid injected into the formation; f is the backflow rate. Step S2 includes the following steps: When the backflow rate is greater than 100%, and the daily gas production curve in the gas well production curve remains unchanged, and the oil pressure curve no longer rises, it indicates that the well cleaning process is over. S5 includes the following steps: The original geological reserves are obtained by adding the geological reserves under the current pressure obtained in step S4 to the cumulative gas production. The cumulative gas production is the sum of the daily gas production during the oil trial period and the daily gas production during the stable production period.

2. The method for calculating the original geological reserves of a gas reservoir according to claim 1, characterized in that, In step S3, the gas well maintains stable production for 15-30 days.

3. The method for calculating the original geological reserves of a gas reservoir according to claim 1, characterized in that, Step S4 includes the following steps: The method for calculating the geological reserves under the current pressure is as follows: in, A g Indicates the oil-bearing area; h Indicates the effective thickness; Φ Indicates effective porosity; S g Indicates oil saturation; B g This represents the volume coefficient.

4. The method for calculating the original geological reserves of a gas reservoir according to claim 3, characterized in that, The volume coefficient B g The calculation method is as follows: in, Z g Indicates the deviation coefficient; P sc Indicates the standard ground pressure. T Indicates formation temperature; T sc P represents the standard ground temperature. g This indicates the current measured formation pressure.

5. The method for calculating the original geological reserves of a gas reservoir according to claim 1, characterized in that, It also includes the following steps: Based on the original geological reserves obtained in step S5, the dynamic reserves are calculated using the material balance method. The aforementioned material balance method is: in, P g / Z g This indicates the current apparent formation pressure; P i / Z i Indicates the original apparent formation pressure; G p This indicates the cumulative gas extraction volume; G i Indicates the original geological reserves.

6. A system for calculating the original geological reserves of a gas reservoir, characterized in that, The calculation method described in claim 1 includes a well fluid backflow rate calculation module, a well cleaning judgment module, a formation pressure measurement module, a geological reserve calculation module, and a raw geological reserve calculation module. The in-well fluid backflow rate calculation module is used to calculate the daily gas production and daily fluid production during wellhead testing, calculate the in-well fluid backflow rate based on the daily fluid production, and plot the gas production curve of a single gas well. The well cleaning judgment module is used to determine whether the well cleaning process has ended based on the backflow rate of the fluid in the well and the gas production curve of a single gas well. The formation pressure measurement module is used to measure the current formation pressure in the well after the well cleaning process is completed and the gas well has been in stable production for a period of time, and to calculate the daily gas production at the wellhead during the stable production period. The geological reserves calculation module is used to calculate the geological reserves under the current formation pressure. The original geological reserves calculation module is used to calculate the original geological reserves based on the daily gas production at the wellhead during the oil testing period, the daily gas production at the wellhead during the stable production period, and the geological reserves obtained from the geological reserves calculation module.

7. The system for calculating the original geological reserves of a gas reservoir according to claim 6, characterized in that, The in-well fluid backflow rate calculation module is specifically used for: The daily liquid production during the oil trial period is summed to obtain the cumulative liquid output during the oil trial period. Calculate the ratio f between the cumulative outflow volume and the total volume of liquid injected into the formation; f is the backflow rate.