SYSTEM AND METHOD TO TEST WELLS AT CONTINUOUSLY-VARYING PRODUCTION RATES

Information

  • Patent Application
  • 20240218788
  • Publication Number
    20240218788
  • Date Filed
    December 28, 2022
    2 years ago
  • Date Published
    July 04, 2024
    8 months ago
Abstract
A method includes: accessing databases storing pressure data of a reservoir at a downhole location, temporal production data of the reservoir, petrophysical parameters, and fluid properties; creating grids comprising sections during which respective segments of temporal production data are measured, wherein each of the respective segments of temporal production data is continuous within a corresponding section of the grids, and wherein the temporal production data comprise at least one discontinuity between two neighboring sections of the grid; based on the temporal production data, petrophysical parameters, and fluid properties, computing a superposition-time function over the sections, wherein the superposition-time function is free from the at least one discontinuity; constructing a plot of the pressure data versus the computed superposition-time function; and based on the plot of the pressure data, deriving characteristics of the reservoir such that the reservoir is monitored despite the at least one discontinuity in the temporal production data.
Description
TECHNICAL FIELD

This disclosure generally relates to petroleum reservoir engineering and reservoir characterization.


BACKGROUND

Well testing can involve the measurement of production rates and downhole pressures. Combining these measurements of production rate and pressure with fluid and petrophysical properties, diagnostic plots can be created.


SUMMARY

In one aspect, some implementations provide a computer-implemented method that includes: accessing one or more databases storing geo-exploration data associated with a reservoir, the geo-exploration data comprising: pressure data measured temporally of the reservoir at a downhole location inside a well of the reservoir, temporal production data of the reservoir through the well at surface conditions, petrophysical parameters of the reservoir, and fluid properties of the reservoir; creating temporal grids comprising sections during which respective segments of temporal production data are measured, wherein each of the respective segments of temporal production data is continuous within a corresponding section of the grids, and wherein the temporal production data comprise at least one discontinuity between two neighboring sections of the grid; based on, at least in part, the temporal production data, the petrophysical parameters of the reservoir, and the fluid properties of the reservoir, computing a superposition-time function over the sections, wherein the superposition-time function is free from the at least one discontinuity; constructing a plot of the pressure data versus the computed superposition-time function; and based on, at least in part, the plot of the pressure data, deriving characteristics of the reservoir such that the reservoir is monitored continuously despite the at least one discontinuity in the temporal production data.


Implementations may include one or more of the following features.


The characteristics of the reservoir may include: a transmissibility, a reservoir flow capacity, and a reservoir permeability. The method may further include: determining a slope of the pressure data being plotted versus the superposition-time function, wherein the slope encodes at least one of the characteristics of the reservoir. The method may further include: based on, at least in part, the determined slope, iteratively determining at least one of the characteristics of the reservoir.


The method may further include: computing a pressure derivative with respect to the computed superposition-time function. The method may further include: based on, at least in part, the log-log plot of pressure derivative versus elapsed time, the determined intercept, the derived characteristics of the reservoir, predicting a production rate of the reservoir beyond the temporal production data. The temporal production data may include: a production rate, and an injection rate.


In another aspect, some implementations provide a computer system comprising one or more hardware processors configured to perform operations of: accessing one or more databases storing geo-exploration data associated with a reservoir, the geo-exploration data comprising: pressure data measured temporally of the reservoir at a downhole location inside a well of the reservoir, temporal production data of the reservoir through the well at surface conditions, petrophysical parameters of the reservoir, and fluid properties of the reservoir; creating temporal grids comprising sections during which respective segments of temporal production data are measured, wherein each of the respective segments of temporal production data is continuous within a corresponding section of the grids, and wherein the temporal production data comprise at least one discontinuity between two neighboring sections of the grid; based on, at least in part, the temporal production data, the petrophysical parameters of the reservoir, and the fluid properties of the reservoir, computing a superposition-time function over the sections, wherein the superposition-time function is free from the at least one discontinuity; constructing a plot of the pressure data versus the computed superposition-time function; and based on, at least in part, the plot of the pressure data, deriving characteristics of the reservoir such that the reservoir is monitored continuously despite the at least one discontinuity in the temporal production data.


Implementations may include one or more of the following features.


The characteristics of the reservoir may include: a transmissibility, a reservoir flow capacity, and a reservoir permeability. The operations may further include: determining a slope of the pressure data being plotted versus the superposition-time function, wherein the slope encodes at least one of the characteristics of the reservoir. The operations may further include: based on, at least in part, the determined slope, iteratively determining at least one of the characteristics of the reservoir.


The operations may further include: computing a pressure derivative with respect to the computed superposition-time function. The operations may further include: based on, at least in part, the log-log plot of pressure derivative versus elapsed time, the determined intercept of pressure derivative, the derived characteristics of the reservoir, predicting a production rate of the reservoir beyond the temporal production data. The temporal production data may include: a production rate, and an injection rate.


In yet another aspect, some implementations provide a non-transitory computer-readable medium comprising software instructions which, when executed by a computer processor, causes the computer processor to perform operations of: accessing one or more databases storing geo-exploration data associated with a reservoir, the geo-exploration data comprising: pressure data measured temporally of the reservoir at a downhole location inside a well of the reservoir, temporal production data of the reservoir through the well at surface conditions, petrophysical parameters of the reservoir, and fluid properties of the reservoir; creating temporal grids comprising sections during which respective segments of temporal production data are measured, wherein each of the respective segments of temporal production data is continuous within a corresponding section of the grids, and wherein the temporal production data comprise at least one discontinuity between two neighboring sections of the grid; based on, at least in part, the temporal production data, the petrophysical parameters of the reservoir, and the fluid properties of the reservoir, computing a superposition-time function over the sections, wherein the superposition-time function is free from the at least one discontinuity; constructing a plot of the pressure data versus the computed superposition-time function; and based on, at least in part, the plot of the pressure data, deriving characteristics of the reservoir such that the reservoir is monitored continuously despite the at least one discontinuity in the temporal production data.


Implementations may include one or more of the following features.


The characteristics of the reservoir may include: a transmissibility, a reservoir flow capacity, and a reservoir permeability. The operations may further include: determining a slope of the pressure data being plotted versus the superposition-time function, wherein the slope encodes at least one of the characteristics of the reservoir. The operations may further include: based on, at least in part, the determined slope, iteratively determining at least one of the characteristics of the reservoir.


The operations may further include: computing a pressure derivative with respect to the computed superposition-time function. The operations may further include: based on, at least in part, the log-log plot of pressure derivative versus elapsed time, the determined intercept, the derived characteristics of the reservoir, predicting a production rate of the reservoir beyond the temporal production data. The temporal production data may include: a production rate, and an injection rate.


Implementations according to the present disclosure may be realized in computer implemented methods, hardware computing systems, and tangible computer readable media. For example, a system of one or more computers can be configured to perform particular actions by virtue of having software, firmware, hardware, or a combination of them installed on the system that in operation causes or cause the system to perform the actions. One or more computer programs can be configured to perform particular actions by virtue of including instructions that, when executed by data processing apparatus, cause the apparatus to perform the actions.


The details of one or more implementations of the subject matter of this specification are set forth in the description, the claims, and the accompanying drawings. Other features, aspects, and advantages of the subject matter will become apparent from the description, the claims, and the accompanying drawings.





DESCRIPTION OF DRAWINGS


FIG. 1 illustrates an example of a hardware configuration in a well test used by some implementations of the present disclosure.



FIG. 2 illustrates an example of a production-rate history of a producing well seen by some implementations of the present disclosure.



FIG. 3 is a flow chart illustrating an example according to some implementations of the present disclosure.



FIG. 4 shows an example of creating grids with sectionally-continuous functions according to some implementations of the present disclosure.



FIG. 5 is a flow chart illustrating another example according to some implementations of the present disclosure.



FIG. 6 shows an example of production-rate history as a function of elapsed time as analyzed by some implementations of the present disclosure.



FIG. 7 shows an example of the computed superposition-time functions according to some implementations of the present disclosure.



FIG. 8 shows an example of pressures calculated from the superposition-time functions as related to the elapsed time.



FIG. 9 shows an example of computed pressure derivative as related to superposition-time functions.



FIG. 10 shows an example of a log-log plot unifying flow and build-up periods according to some implementations of the present disclosure.



FIG. 11 is a block diagram illustrating an example of a computer system used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures, according to an implementation of the present disclosure.





Like reference numbers and designations in the various drawings indicate like elements.


DETAILED DESCRIPTION

The disclosed technology is directed to improved reservoir characterization based on measured production rates and downhole pressures. Some implementations of the present disclosure incorporate a rigorous methodology for analyzing continuously-varying pressure and production rates. These implementations can establish continuity of the superposition-time function and the pressure derivative over the flow and build-up periods of the recorded history. As a result, the implementations can generate continuous semi-log and log-log plots that are free from the discontinuities commonly seen in production history records of a reservoir at surface. The implementations can avert loss of data due to the end effects while keeping multiple flow and build-up periods by upholding the representation of the available pressure and rate data in the analysis. Moreover, the implementations can replace logarithmic approximations of the superposition-time function with accurate mathematical expressions, derived from the first principle. While some implementations emphasize the analysis of flow periods to accommodate the available accurate production-rate history, the implementations are equally applicable to enhance the analysis of build-up data.


By combining production rate, pressure, fluid and petrophysical properties, diagnostic plots can create a superposition-time function and log-log plots. From these plots, reservoir behaviors can be determined to ascertain if the infinite-acting radial flow has established. If so, in-situ reservoir properties such as transmissibility, flow capacity and effective permeability in the reservoir around the well can be determined. Although the downhole transient well pressure is tied to the rate of production at a given time, measured production rate has not been accurate and frequent, thus giving rise to discontinuities when gaps are created in neighboring records. In addition, the drawdown or flow analysis method with downhole pressure and detailed production rates of the prior art has not been reliable, which has caused the elevation of the build-up tests over the flow tests.


The pressure data can be analyzed during the shut-in period for estimating the reservoir properties because the data quality of pressure build-up is better during the shut-in period than it is during the flow period. The shut-in period refers to a temporary cease of production (i.e., shut-in a well). Existing analysis methods are thus inclined to compute the superposition-time function for the build-up data, which refer to the measurement data taken during a monotonous ramp up of pressure at the wellbore during the period of no-production through the wellbore. Conventional testing may have the well in a shut-in configuration which causes a loss of revenue for the lost oil production. Build-up tests by shutting-in the well has been practiced because detailed, accurate measurement of rates has been unavailable. Faced with the unavailability, operators tend to hold the rate steady (zero rate) and to record the pressure data in steady state for consistency and quality control. But the build-up test comes with a loss of production in the test well given its shut-in condition. Although some prior art have shown how build-up data can be analyzed, the focus of these prior art, however, are unrelated to the transient production rates.


Operationally, in a well, it can be difficult to hold the production rate steady so that the corresponding pressure data could be of good quality as in a build-up test. Although the pressure measurements can be accurate in such steady state conditions, the corresponding rate measurements have not been frequent and accurate in most cases. With the introduction of accurate rate measurements of multi-phase flow meters, it has become possible to have transient rates measured at surface in addition to the transient pressures measured downhole. While the implementations of the present disclosure are equally applicable to the data collected during both flow and build-up tests, the present disclosure emphasizes the capability of continuously-changing production rate and pressure data collected during the flow periods during which the rate and the pressure data can be recorded at the well location with high resolution.


The following summarized the symbols and nomenclature used by the present disclosure.

    • B Formation volume factor, bbl/STB
    • ct Total system compressibility, 1/psia
    • Ei(−z) Exponential integral function of (−z)
    • h Net pay thickness, ft
    • j An arbitrary node or grid in data set, 1≤j≤N
    • k Effective reservoir permeability, md
    • mj Slope in jth rate grid, STB/D/hr, Equation (1) [zero, positive or negative]
    • δmj Difference in slope in (j−1)th and jth rate grids, STB/D/hr, Equation (5)
    • N Number of grid points in production-rate history
    • p0 Initial or static reservoir pressure, psia
    • pw Downhole pressure at a given elapsed time, psia
    • p′ First-order derivative with respect to superposition-time function or well-test pressure derivative, psia
    • Δp Pressure drawdown at elapsed time, psia, Equation (6)
    • qN-1 (N−1)th rate in production history, STB/D
    • qj jth rate in production history, STB/D
    • δqj Spike or sharp rate change at Δtj, STB/D, Equation (4) [zero, positive or negative]
    • Δq Arbitrary rate-scaling factor applied on superposition-time function, STB/D
    • rw Wellbore radius, ft
    • Δt Current elapsed time, hr
    • Δtj jth point in elapsed time in data set, hr
    • T(Δt) Superposition-time function corresponding to elapsed time Δt, no unit, Equation (8)
    • T′ Truncated amount of superposition-time function in prior art at elapsed time, Δt, no unit, Equation (13)
    • Tj Superposition-time function corresponding to elapsed time Δtj, no unit
    • Tt Logarithmic approximation of superposition-time function corresponding to elapsed time, Δt, no unit, Equation (12)
    • α Rock-fluid parameter, cp/md-ft, defined in Equation (7)
    • γ Euler's constant, 0.5772156649
    • η Hydraulic diffusivity, md-psia/cp, defined in Equation (9)
    • μ Fluid viscosity, cp
    • ξ Impulse response, defined in Equation (10)
    • τ Local temporal abscissa or dummy variable, hr
    • ϕ Porosity, fraction
    • ψ Drawdown per unit downhole production rate, psia/bbl/D, defined in Equation (8)



FIG. 1 illustrates an example of a hardware configuration 100 in a well test used by some implementations of the present disclosure. In this hardware configuration 100, the transient pressure data is recorded at the gauge location downhole, while the multi-phase flow meter or a similar measurement device at surface gathers detailed flow rates with time. Additionally or alternatively, raw data out of the electrical submersible pump in an oil well can also be utilized to estimate detailed production rates. In both cases, the transient pressure and the corresponding transient rate are inter-dependent at a given time.


As illustrated, hardware configuration 100 includes a downhole pressure gauge 105 enclosed inside tubing 103. Reservoir fluid from the reservoir 102 enters the bottom section of the production casing 106 through the perforations 101. This fluid channels through the tubing which is isolated from the production casing with a packer 104. As the fluid passes by the pressure gauge 105, pressure is recorded downhole. The fluid then flows through casing 107 to the surface. After the production choke, the produced stream passes through a multi-phase flow meter 109 for the production-rate to be measured before the stream is routed to separator 110.


Prior art have attempted to utilize the detailed production rates in the analysis of the flow periods under variable production rates. However, the prior art are not capable of analyzing continuously-varying production rates for at least three reasons. First, approximating the production-rate history in a stair-step distribution can create a large number of flow periods with stair steps, which can hinder analysis using prior art. Second, each flow period that includes discontinuous superposition-time function, which would cause a loss of data at early- and late-times at each flow period, can result in uneven pressure-derivative profiles. Third, the superposition-time function is calculated with logarithmic approximations, which can cause a loss of accuracy at the early times of each flow period.


The inadequate capability of the prior art to handle a variable-rate production history makes the build-up test more attractive than the flow test. However, operators may not wish to lose production due to a build-up test, and would rather choose a flow test A flow test can be inherently subject to variable-rate of production because it is difficult to maintain the rate at a constant value. Implementations of the present disclosure may eliminate the shortcomings of the prior art, and allow for analyzing the transient pressure and rate data, both captured in high resolution. The implementations can account for the recorded production-rate history including the intermittent shut-in periods when computing the superposition-time function with the elapsed time. The implementations may introduce the superposition-time function to account for the varying rates while dealing with the constant-rate solution for pressure. As a result, a well can have the production history that includes natural variations. The disclosure follows the convention that any positive rates are considered production from the reservoir, and any negative rates are considered injection into the reservoir. As discussed in more detail below, the implementations can provide a new methodology for rigorous analysis of the pressure and the rate data.


The pressure history captured during a well test can be reliable for deployment of high-quality gauges. The implementations of the present disclosure aim at utilizing the corresponding continuously-varying production rates with the elapsed time. Faced with changing rates, implementations can employ the superposition-time function to build the pressure function based on a constant-rate solution for pressure. Notably, some intermittent shut-in periods can be present in the recorded production history. Capturing and representing the production rates, including the intermittent shut-in periods, with high fidelity can play a major role in the superposition-time function for analyzing the resulting transient pressure in response to the continuously-varying production rates. Some implementations of the present disclosure include a high fidelity reconstruction of the superposition-time function.


Referring to FIG. 2, showing a partial production-rate history 200 of the early part of an entire history, the changing rates are captured through N grids (e.g., from 0 to 9) in the entire history. As illustrated, each grid describes the rate linearly with elapsed time. For example, the jth grid (1≤j≤N) located between the nodes, Δtj-1 and Δtj, presents the rate variation with a slope of mj, appearing as a ramp. In some grids, the slope can be zero, replicating a constant rate of production as in a stair-step distribution. In other words, mj can be zero, positive or negative. There can be no limit to the number of grids that can be created to capture the entire production history as accurately as possible. In addition, at each node, the production rate can spike by a finite amount. For example, at Δtj, the production rate can spike from qj to {acute over (q)}j by δqj={acute over (q)}j−qj. At the jth node, δqj can be zero, positive or negative based on the given production-rate history. In other words, the entire production-rate history can be represented with a combination of ramps and stair steps.


Implementations may perform the computation of a unified superposition-time function, and the construction of the corresponding diagnostic plot encompassing all the flow and build-up periods in a sequence. In comparison, the prior art deal with separate drawdown and build-up superposition-time function plots, which leads to a loss of valuable test data due to the end effects. FIG. 3 is a flow chart 300 illustrating an example of a process according to some implementations of the present disclosure. This flow chart 300 shows an example in which the implementations can influence the ultimate production forecasts of reservoir simulators. The flow chart 300 starts (301) and obtains data (302) by obtaining detailed measured well pressure as a function of time, high-resolution production/injection rate as a function of time, petrophysical parameters, and fluid properties. Flow chart 300 may then construct a rigorous superposition-time function (303) which, as further discussed below, eventually impacts the forecasting of future production with a large simulation model. Flow chart 300 may then construct, using the rigorous superposition-time function, a log-log plot of the pressure derivative (304). Based on the log-log plot of pressure derivative, flow chart 300 may then compute reservoir parameters (305). Using the reservoir parameters, flow chart 300 may then build reservoir simulation (306). Based on the reservoir simulation, flow chart 300 may then forecast future production rates (307). Implementations may include building grids, and constructing the rigorous superposition-time function, as further explained below.


First, the implementations may build N grids (or grids with N−1 sections) in the entire production-rate history. FIG. 4 shows an example 400 of creating grids with sectionally-continuous rate functions according to some implementations of the present disclosure. FIG. 4 particularly shows a zoomed-in view of the jth grid with two consecutive nodes, namely, Δtj-1 and Δt1. In each grid, two features can characterize the rate change including, the rate spike at a node, and the rate variation in a straight line between the nodes. In other words, the rate variation within each grid section is continuous. The line joining the consecutive nodes should represent the production-rate variation between the nodes. The slope of the line joining these two consecutive nodes, Δtj and Δtj-1, in the jth grid can be expressed as










m
j

=



q
j

-


q
´


j
-
1





Δ


t
j


-

Δ


t

j
-
1









(
1
)







If the production rate is constant over a grid as in a traditionally-expressed, stair-step rate history, the corresponding value of mj is zero. In addition, n can also be either positive or negative depending on the rate variations in the given history—such grids appear as ramps in the production-rate history. Table 1 illustrates how the grids in terms of elapsed time and rates are oriented in a sequence for computations of the corresponding slope values.









TABLE 1







Organization of production rates in sequence.











Sequence of
Measured
Slope of Line Joining



Data Point(s)
Rates
Consecutive Nodes







Δt0
q0, {acute over (q)}0
m1



Δt1
q1, {acute over (q)}1
m2



Δt2
q2, {acute over (q)}2
m3



Δt3
q3, {acute over (q)}3
m4



Δt4
q4, {acute over (q)}4
m5



Δt5
q5, {acute over (q)}5
m6



Δt6
q6, {acute over (q)}6
m7



Δt7
q7, {acute over (q)}8
m8



Δt8
q8, {acute over (q)}8



Δt9
q9, {acute over (q)}9
m9










Referring to example 400 of FIG. 4, to observe the linear variation of the production rate, q, as a function of the local temporal abscissa, τ, is located between the nodes, Δtj-1 and Δtj-1. This linear variation of production rate can be expressed as:










q

(
τ
)

=



q
´


j
-
1


+


m
j


τ






(
2
)







The above equation (2) represents the production-rate variation in the jth grid, and is valid for Δtj-1≤τ≤Δtj. Additionally, at the nodes, the production rates can experience spikes, for example, by δqj-1 at Δtj-1, and δqj at Δtj. Such spikes can be zero, positive or negative depending on the given production-rate history. Existence of such positive or negative spikes can cause discontinuity between the two neighboring rate grids. Representing the production rate at each grid with a spike and a linear variation allows for the generality to capture how the actual production rate is recorded in the history. In the above manner, the entire production-rate history can be represented with sectionally-continuous functions. Having represented with sectionally-continuous functions, the continuously-varying production rates can be mathematically inducted into the superposition-time function. As the rate-data frequency is expected to be non-uniform, the grid sizes are expected be non-uniform. Thus, uniformity of grid sizes may not be a pre-requisite for this methodology to be applicable.


Second, the implementations may construct the superposition-time function for building the corresponding pressure function from the constant-rate solution for pressure due to the varying rates of production. In other words, the superposition-time function is a tool to convert the constant-rate equation for pressure into a multiple-rate equation for pressure. From the first principle of physics, a generalized, rigorous superposition-time function can be established as:










T

(

Δ

t

)

=


1

Δ

q







j
=
1

N


{


δ


q
j



ξ

(


Δ

t

-

Δ


t

j
-
1




)


+

δ


m
j





0


Δ

t

-

Δ


t

j
-
1







ξ

(
τ
)







}







(
3
)








where









δ


q
j


=




q
´

j

-

q
j


=



q
´

j

-

[



q
´


j
-
1


+


(

m
j

)



(


Δ


t
j


-

Δ


t

j
-
1




)



]







(
4
)













δ


m
j


=


m
j

-

m

j
-
1







(
5
)







A given value can be utilized as Δq, which acts as an arbitrary rate-scaling factor consistently for an entire analysis. A non-zero value of Δq does not impact the final results of an analysis. Note that τ is acting as a dummy variable which happens to be the local temporal abscissa. By definition of the superposition-time function, implementations may characterize the pressure drawdown or pressure change at the elapsed time as:










Δ


p

(

Δ

t

)


=



p
0

-


p
w

(

Δ

t

)


=

α

Δ

q

B


T

(

Δ

t

)







(
6
)








where








α
=


70.6
μ


k

h






(
7
)







To derive the superposition-time function in the infinite-acting radial flow, we bring in the exponential-integral solution for the drawdown per unit downhole production rate in the infinite-acting radial flow as:










ψ

(
τ
)

=



Δ


p

(
τ
)



q

B


=


α


ξ

(
τ
)


=

-

αEi

(

-


r
w
2


4

η

τ



)








(
8
)








where








η
=


2.63679
×
1


0

-
4



k


ϕ

μ


c
t







(
9
)







The impulse-response function, ξ(τ), can be derived from ψ(τ) in Equation (8) as:










ξ

(
τ
)

=



ψ

(
τ
)

α

=


-
E



i

(

-


r
w
2


4

η

τ



)







(
10
)







With the introduction of ξ(τ) by Equation (10), the radial superposition-time function in Equation (3) turns out to be:










T

(

Δ

t

)

=


-

1

Δ

q








j
=
1

N


[



{


δ


q
j


+


(

δ


m
j


)



(


Δ

t

-

Δ


t

j
-
1



+


r
w
2


4

η



)



}


E


i

(

-


r
w
2


4


η

(


Δ

t

-

Δ


t

j
-
1




)




)


+


(

δ


m
j


)



(

Δt
-

Δt

j
-
1



)


exp


(

-


r
w
2


4


η

(


Δ

t

-

Δ


t

j
-
1




)




)



]







(
11
)







Equation (11) can be an exact and rigorous solution, which does not suffer from the artifacts of approximations, especially at early times of a flow period. Also, the final evaluation of superposition-time function in Equation (11) requires the knowledge of the transmissibility value which is the one of the end products in the analysis. Such implicit nature of this equation requires an iterative scheme to solve for the superposition-time function. This matter will be discussed later. In comparison, conventional and traditional superposition-time function is a truncated version of the logarithmic approximation to the rigorous version for radial flow in Equation (11) as:











T
t

(

Δ

t

)

=


1

Δ

q







j
=
1

N


[



(


δ


q
j


+


(

δ


m
j


)



(


Δ

t

-

Δ


t

j
-
1




)



)


ln


(


Δ

t

-

Δ


t

j
-
1




)


-


(

δ


m
j


)



(


Δ

t

-

Δ


t

j
-
1




)



]







(
12
)







The truncated amount missing in the traditional superposition-time function of Equation (12) for can be expressed as:











T


(

Δ

t

)

=


-

1

Δ

q








j
=
1

N


[



(


δ


q
j


+


(

δ


m
j


)



(


Δ

t

-

Δ


t

j
-
1




)



)



{


ln


(


r
w
2


4

η


)


+
γ

}


+


(

δ


m
j


)



(


r
w
2


4

η


)



{


ln


(


r
w
2


4


η

(


Δ

t

-

Δ


t

j
-
1




)



)


+
γ
+
1

}



]







(
13
)







The truncated amount in the superposition-time function as presented in Equation (13) can cause the discontinuity in the presentation of the superposition-time function in the prior art. Notably, the rigorous version in Equation (11) is approximately equivalent to the sum total of the components of the superposition-time function, expressed in Equations (12) and (13), as shown below.










T

(

Δ

t

)

=



T
t

(

Δ

t

)

+


T


(

Δ

t

)






(
14
)







Rearranging Equation (6), the well pressure at Δt can be estimated from the known superposition-time function as:











p
w

(

Δ

t

)

=


p
0

-

α

Δ

q

B


T

(

Δ

t

)







(
15
)







Additionally, the well-test pressure derivative at the jth point is calculated with the superposition-time function as











p


(

T
j

)

=


(


d

p


d

T


)

j





(
16
)







where p′(Tj) or







(


d

p


d

T


)

j




is the first-order derivative at the jth point with respect to the superposition-time function. Notably, the well-test pressure derivative for a single-rate drawdown test may require the first-order elapsed-time derivative to be multiplied by the elapsed time (Δtj). However, for variable-rate tests, the first-order derivative of well pressure with respect to the superposition-time function equals the well-test pressure derivative because of the utilization superposition-time function, T(Δt), in place of the elapsed time. This is also true in single-rate tests when taken with respect to the superposition-time function.


From Equations (15) and (16), the derivative profile due to the infinite-acting radial flow will stabilize at a value as













"\[LeftBracketingBar]"


p




"\[RightBracketingBar]"


Stabilized

=

α

Δ

q

B





(
17
)







Equation (17) leads to extractions of transmissibility (hk/μ), reservoir flow capacity (kh), and reservoir permeability (k). Notably, the superposition-time function in Equation (11) may require the input of assumed transmissibility. Because of inter-related or implicit feature, some implementations of the present disclosure may incorporate an iterative technique to refine the output transmissibility. For example, the implementations may start with a seed value for the transmissibility, compute the superposition-time function based on the seed value, derive the slope which leads to a computed transmissibility, and iteratively update the superposition-time function and refine the estimated slope. Such an iterative scheme does not impact the raw (input) temporal pressure or rate data nor does it make any changes to the ongoing well operations if applicable. Rather, this iterative scheme refines the computed superposition-time function with each successive iteration. In some cases, an operator can define a level of tolerance for stopping the iteration process. For example, if any of the maximum difference in the superposition-time function values between the successive iterations at each rate node over the entire range of pressure and rate history is within 10−6, the iteration may be terminated. For these reasons, the final set of superposition-time function and the analysis results can be accepted as conclusive.



FIG. 5 is a flow chart 500 illustrating another example according to some implementations of the present disclosure. Flow chart 500 starts (501) and obtains data (502) by obtaining detailed measured well pressure as a function of time, high-resolution production/injection rate as a function of time, petrophysical parameters, and fluid properties.


Flow chart 500 may then create grids with sectionally-continuous functions in production-rate history (503). In one illustrative example, as tabulated in Table 2, the production-rate history records 30 production rates in 30 flow periods, each of 1-hour duration, followed by the build-up period of 1,000 hour. This illustrative example is also shown graphically in example 600 of FIG. 6, in which the production-rate history (e.g., production rate history) is shown as a function of elapsed time on the created grids.









TABLE 2







Production-rate history









Elapsed Time,
Measured Rates, STB/D










hour
qj
{acute over (q)}j












0
0
700


1
700
900


2
500
800


3
1,200
500


4
1,200
300


5
800
900


6
500
800


7
1,200
900


8
500
400


9
300
900


10
1,200
800


11
400
700


12
900
1,200


13
300
1,500


14
800
1,800


15
900
2,000


16
2,000
1,100


17
1,500
800


18
700
1,600


19
600
1,200


20
1,900
2,000


21
1,100
1,700


22
900
1,500


23
1,300
600


24
1,700
500


25
1,900
1,800


26
600
1,800


27
700
1,700


28
1,200
300


29
2,000
2,200


30
600
0


1030
0
1,000









In this example the grid is from 1 hour up to 30 hours of elapsed time during flow at variable rates. Subsequently, the record shows a 1,000 hours of shut-in that follows the flow periods. The first flow period of 1 hour is a constant rate of production at 700 STB/D (standard tank barrel per day). In this example, a total of 31 grids can be inserted, for example, to cover the 30-hour duration on each hourly segment. Implementations may create sub-grids or computational grids when more resolution is desired in the distribution of the calculated pressures. For example, finer, computational grids with sub-grids can visualize how the pressure builds up during 1,000 hours of shut-in. The number of sub-grids can be configured/adjusted to fit a flow or build-up period. However, the illustrative example is without sub-grids, and, as explained below, the superposition-time function and pressure are computed at each node of 31 grids.


Flow chart 500 may then compute a rigorous superposition-time function (504). The methodology described earlier in association with Equation (11) can be employed to calculate the superposition-time function, at each rate grid, by incorporating the given rate-time relationship. This calculation also incorporates input of rock and fluid properties, especially the transmissibility. Table 3 presents the rock and fluid properties in the reservoir. In some examples, Δq=1 STB/D. However, this arbitrary rate-scaling factor may not impact the ultimate results of an analysis.









TABLE 3







Rock and fluid properties










Property
Value














k, md
100



h, ft
40



ϕ, fraction
0.1



B, bbl/STB
1



μ, cp
1



ct, 1/psia
3.0e−6



rw, ft
0.354167



P0, psia
5,000











FIG. 7 shows an example 700 of the computed superposition-time function with the elapsed time according to some implementations of the present disclosure. As shown, the example 700 presents the computed superposition-time function, along with elapsed time, on log scales. With this superposition-time function, computation and construction of the pressure-derivative plot can follow.


Flow chart 500 may then construct pressure as a function of the elapsed time. For example, Equation (15) can be utilized to compute pressure at each node. FIG. 8 shows an example 800 of pressures, calculated from the superposition-time functions of FIG. 7, but presented with elapsed time. Notably, only one pressure point is visible after 1,000 hours of shut-in on the right-hand side of example 800.


Flow chart 500 may then present computed pressures with the superposition-time function (505). FIG. 9 shows an example 900 of the computed pressures, which demonstrates a straight-line or linear (with slope −αΔq B) relationship of pressure with the superposition-time function of FIG. 7. This observation is consistent with Equation (15).


Flow chart 500 may then compute well-test pressure derivative with Equation (16) (506). The analyst can utilize computed pressures or measured pressures from the field for computing the pressure derivatives. In general, the pressure derivative at each node demonstrates a clear trend of lines (e.g., a straight line) over entire temporal pressure and rate history. If the presentation of the nodal values is noisy, regression fittings of lines can be considered for analysis. Similarly, the pressure at each node demonstrates a clear trend of lines (e.g., a straight line) over entire temporal pressure and rate history. If the presentation of the nodal values is noisy, regression fittings of lines can be considered for analysis.


Flow chart 500 may further construct log-log plot of pressure derivative (507). FIG. 10 shows a unified log-log plot 1000 of the pressure change and the pressure derivative during flow of build-up periods. The analyst has an option to present an overlay of the two sets of log-log plots—one with computed pressure change and computed pressure derivatives, and another with measured pressure and measured pressure derivative of the field data. The closeness of such respective plots is utilized in determining the quality of the reservoir model by analysts. In this example of FIG. 10, the computed pressures with the computed superposition-time function have been utilized to compute the pressure derivatives. The appearance of pressure derivative in log-log plot 1000 shows that both drawdown and build-up derivatives have stabilized on the same transmissibility line to cause a fixed intercept value. Scattered pressure-change [defined by (p0−pw)] points may be referenced to the initial reservoir pressure, which is tied to the skin factor of the well. Generally, the pressure derivative at each node can demonstrate a clear trend of lines (e.g., a straight line) over entire temporal pressure and rate history. If the presentation of the nodal values is noisy, regression fittings of lines can be considered for analysis. The demonstrated trend of the pressure derivative implies the reservoir quality in terms of transmissibility, flow capacity or permeability. Equation (17) is utilized to estimate transmissibility from the value of the intercept of the pressure derivative in the log-log plot. By analyzing Equations (15) through (17), one can infer that the values on the straight line in FIG. 9 and the corresponding pressure derivative values in FIG. 10 are related. The single transmissibility line of pressure derivative of all flow and build-up periods in the log-log plot in FIG. 10 refers to the infinite-acting (e.g., no physical boundary has been felt within the elapsed time), homogeneous reservoir in this example. The prior art would have resulted in the appearance of pressure derivative as discontinuous lines of all flow and build-up periods.


Prior art, while reporting the advantage of pressure derivative for reservoir characterization with the emphasis of analyzing build-up test, acknowledged the problems of the end effect, which had plagued commercial software packages for computing well-test derivatives for reservoir characterization. The superposition-time function, as used by prior art techniques, is not adequate for dealing with continuously-varying production rate due to its emphasis on build-up data. In fact, these derivative profiles suffer from distortion at both ends due to segmented computations of the superposition-time function.


The implementations can overcome the persistent shortcomings of the superposition-time function in the prior art. The implementations can create a finite number of grids in production-rate history. Each node can have a spike in the rate, and each grid defines the rate variation linearly. This arrangement can describe the full production history with N ramps and/or stair steps. Such description can be readily absorbed in the newly-defined superposition-time function. A person skilled in the art can now construct the rigorous superposition-time function where the continuously-varying production rates have been addressed adequately. The implementations can correct the logarithmic approximations in the superposition-time function with the first principle to remove the numerical artifacts at the early times of individual flow periods. Moreover, the implementations have unified the superposition-time plot, and the corresponding log-log plot to cover the entire pressure and production history of the well. Such unification can save a substantial amount of valuable data from distortion or exclusion from the analysis and parameter extractions. Without a radical intervention as used in the implementations of the present disclosure, such developments would not have been possible. Indeed, no combination of the available techniques in the prior art could deliver the robustness of the implementations of the present disclosure. The numerical algorithms used by implementations of the present disclosure are directed towards accuracy and efficiency of computations through closed-form equations and logical flow charts for a given set of production-rate and pressure data. No combination of methods in the prior art could come close to the advancements demonstrated by implementations of the present disclosure.



FIG. 11 is a block diagram 1100 illustrating an example of a computer system 1100 (used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures, according to an implementation of the present disclosure. The illustrated computer 1102 is intended to encompass any computing device such as a server, desktop computer, laptop/notebook computer, wireless data port, smart phone, personal data assistant (PDA), tablet computing device, one or more processors within these devices, another computing device, or a combination of computing devices, including physical or virtual instances of the computing device, or a combination of physical or virtual instances of the computing device. Additionally, the computer 1102 can comprise a computer that includes an input device, such as a keypad, keyboard, touch screen, another input device, or a combination of input devices that can accept user information, and an output device that conveys information associated with the operation of the computer 1102, including digital data, visual, audio, another type of information, or a combination of types of information, on a graphical-type user interface (UI) (or GUI) or other UI.


The computer 1102 can serve in a role in a computer system as a client, network component, a server, a database or another persistency, another role, or a combination of roles for performing the subject matter described in the present disclosure. The illustrated computer 1102 is communicably coupled with a network 1130. In some implementations, one or more components of the computer 1102 can be configured to operate within an environment, including cloud-computing-based, local, global, another environment, or a combination of environments.


The computer 1102 is an electronic computing device operable to receive, transmit, process, store, or manage data and information associated with the described subject matter. According to some implementations, the computer 1102 can also include or be communicably coupled with a server, including an application server, e-mail server, web server, caching server, streaming data server, another server, or a combination of servers.


The computer 1102 can receive requests over network 1130 (for example, from a client software application executing on another computer 1102) and respond to the received requests by processing the received requests using a software application or a combination of software applications. In addition, requests can also be sent to the computer 1102 from internal users, external or third-parties, or other entities, individuals, systems, or computers.


Each of the components of the computer 1102 can communicate using a system bus 1103. In some implementations, any or all of the components of the computer 1102, including hardware, software, or a combination of hardware and software, can interface over the system bus 1103 using an application programming interface (API) 1112, a service layer 1113, or a combination of the API 1112 and service layer 1113. The API 1112 can include specifications for routines, data structures, and object classes. The API 1112 can be either computer-language independent or dependent and refer to a complete interface, a single function, or even a set of APIs. The service layer 1113 provides software services to the computer 1102 or other components (whether illustrated or not) that are communicably coupled to the computer 1102. The functionality of the computer 1102 can be accessible for all service consumers using this service layer. Software services, such as those provided by the service layer 1113, provide reusable, defined functionalities through a defined interface. For example, the interface can be software written in JAVA, C++, another computing language, or a combination of computing languages providing data in extensible markup language (XML) format, another format, or a combination of formats. While illustrated as an integrated component of the computer 1102, alternative implementations can illustrate the API 1112 or the service layer 1113 as stand-alone components in relation to other components of the computer 1102 or other components (whether illustrated or not) that are communicably coupled to the computer 1102. Moreover, any or all parts of the API 1112 or the service layer 1113 can be implemented as a child or a sub-module of another software module, enterprise application, or hardware module without departing from the scope of the present disclosure.


The computer 1102 includes an interface 1104. Although illustrated as a single interface 1104 in FIG. 11, two or more interfaces 1104 can be used according to particular needs, desires, or particular implementations of the computer 1102. The interface 1104 is used by the computer 1102 for communicating with another computing system (whether illustrated or not) that is communicatively linked to the network 1130 in a distributed environment. Generally, the interface 1104 is operable to communicate with the network 1130 and comprises logic encoded in software, hardware, or a combination of software and hardware. More specifically, the interface 1104 can comprise software supporting one or more communication protocols associated with communications such that the network 1130 or interface's hardware is operable to communicate physical signals within and outside of the illustrated computer 1102.


The computer 1102 includes a processor 1105. Although illustrated as a single processor 1105 in FIG. 11, two or more processors can be used according to particular needs, desires, or particular implementations of the computer 1102. Generally, the processor 1105 executes instructions and manipulates data to perform the operations of the computer 1102 and any algorithms, methods, functions, processes, flows, and procedures as described in the present disclosure.


The computer 1102 also includes a database 1106 that can hold data for the computer 1102, another component communicatively linked to the network 1130 (whether illustrated or not), or a combination of the computer 1102 and another component. For example, database 1106 can be an in-memory, conventional, or another type of database storing data consistent with the present disclosure. In some implementations, database 1106 can be a combination of two or more different database types (for example, a hybrid in-memory and conventional database) according to particular needs, desires, or particular implementations of the computer 1102 and the described functionality. Although illustrated as a single database 1106 in FIG. 11, two or more databases of similar or differing types can be used according to particular needs, desires, or particular implementations of the computer 1102 and the described functionality. While database 1106 is illustrated as an integral component of the computer 1102, in alternative implementations, database 1106 can be external to the computer 1102. As illustrated, the database 1106 holds data 1116 including, for example, input data from the production rate record (e.g., measured at gauge 105, multi-phase flow meter 109), as explained in more detail in association with FIGS. 1-10.


The computer 1102 also includes a memory 1107 that can hold data for the computer 1102, another component or components communicatively linked to the network 1130 (whether illustrated or not), or a combination of the computer 1102 and another component. Memory 1107 can store any data consistent with the present disclosure. In some implementations, memory 1107 can be a combination of two or more different types of memory (for example, a combination of semiconductor and magnetic storage) according to particular needs, desires, or particular implementations of the computer 1102 and the described functionality. Although illustrated as a single memory 1107 in FIG. 11, two or more memories 1107 or similar or differing types can be used according to particular needs, desires, or particular implementations of the computer 1102 and the described functionality. While memory 1107 is illustrated as an integral component of the computer 1102, in alternative implementations, memory 1107 can be external to the computer 1102.


The application 1108 is an algorithmic software engine providing functionality according to particular needs, desires, or particular implementations of the computer 1102, particularly with respect to functionality described in the present disclosure. For example, application 1108 can serve as one or more components, modules, or applications. Further, although illustrated as a single application 1108, the application 1108 can be implemented as multiple applications 1108 on the computer 1102. In addition, although illustrated as integral to the computer 1102, in alternative implementations, the application 1108 can be external to the computer 1102.


The computer 1102 can also include a power supply 1114. The power supply 1114 can include a rechargeable or non-rechargeable battery that can be configured to be either user- or non-user-replaceable. In some implementations, the power supply 1114 can include power-conversion or management circuits (including recharging, standby, or another power management functionality). In some implementations, the power-supply 1114 can include a power plug to allow the computer 1102 to be plugged into a wall socket or another power source to, for example, power the computer 1102 or recharge a rechargeable battery.


There can be any number of computers 1102 associated with, or external to, a computer system containing computer 1102, each computer 1102 communicating over network 1130. Further, the term “client,” “user,” or other appropriate terminology can be used interchangeably, as appropriate, without departing from the scope of the present disclosure. Moreover, the present disclosure contemplates that many users can use one computer 1102, or that one user can use multiple computers 1102.


Implementations of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Software implementations of the described subject matter can be implemented as one or more computer programs, that is, one or more modules of computer program instructions encoded on a tangible, non-transitory, computer-readable computer-storage medium for execution by, or to control the operation of, data processing apparatus. Alternatively, or additionally, the program instructions can be encoded in/on an artificially generated propagated signal, for example, a machine-generated electrical, optical, or electromagnetic signal that is generated to encode information for transmission to a receiver apparatus for execution by a data processing apparatus. The computer-storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of computer-storage mediums. Configuring one or more computers means that the one or more computers have installed hardware, firmware, or software (or combinations of hardware, firmware, and software) so that when the software is executed by the one or more computers, particular computing operations are performed.


The term “real-time,” “real time,” “realtime,” “real (fast) time (RFT),” “near(ly) real-time (NRT),” “quasi real-time,” or similar terms (as understood by one of ordinary skill in the art), means that an action and a response are temporally proximate such that an individual perceives the action and the response occurring substantially simultaneously. For example, the time difference for a response to display (or for an initiation of a display) of data following the individual's action to access the data can be less than 1 millisecond (ms), less than 1 second (s), or less than 5 s. While the requested data need not be displayed (or initiated for display) instantaneously, it is displayed (or initiated for display) without any intentional delay, taking into account processing limitations of a described computing system and time required to, for example, gather, accurately measure, analyze, process, store, or transmit the data.


The terms “data processing apparatus,” “computer,” or “electronic computer device” (or equivalent as understood by one of ordinary skill in the art) refer to data processing hardware and encompass all kinds of apparatus, devices, and machines for processing data, including by way of example, a programmable processor, a computer, or multiple processors or computers. The apparatus can also be, or further include special purpose logic circuitry, for example, a central processing unit (CPU), an FPGA (field programmable gate array), or an ASIC (application-specific integrated circuit). In some implementations, the data processing apparatus or special purpose logic circuitry (or a combination of the data processing apparatus or special purpose logic circuitry) can be hardware- or software-based (or a combination of both hardware- and software-based). The apparatus can optionally include code that creates an execution environment for computer programs, for example, code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of execution environments. The present disclosure contemplates the use of data processing apparatuses with an operating system of some type, for example LINUX, UNIX, WINDOWS, MAC OS, ANDROID, IOS, another operating system, or a combination of operating systems.


A computer program, which can also be referred to or described as a program, software, a software application, a unit, a module, a software module, a script, code, or other component can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it can be deployed in any form, including, for example, as a stand-alone program, module, component, or subroutine, for use in a computing environment. A computer program can, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, for example, one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, for example, files that store one or more modules, sub-programs, or portions of code. A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.


While portions of the programs illustrated in the various figures can be illustrated as individual components, such as units or modules, that implement described features and functionality using various objects, methods, or other processes, the programs can instead include a number of sub-units, sub-modules, third-party services, components, libraries, and other components, as appropriate. Conversely, the features and functionality of various components can be combined into single components, as appropriate. Thresholds used to make computational determinations can be statically, dynamically, or both statically and dynamically determined.


Described methods, processes, or logic flows represent one or more examples of functionality consistent with the present disclosure and are not intended to limit the disclosure to the described or illustrated implementations, but to be accorded the widest scope consistent with described principles and features. The described methods, processes, or logic flows can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output data. The methods, processes, or logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, for example, a CPU, an FPGA, or an ASIC.


Computers for the execution of a computer program can be based on general or special purpose microprocessors, both, or another type of CPU. Generally, a CPU will receive instructions and data from and write to a memory. The essential elements of a computer are a CPU, for performing or executing instructions, and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to, receive data from or transfer data to, or both, one or more mass storage devices for storing data, for example, magnetic, magneto-optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, for example, a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a global positioning system (GPS) receiver, or a portable memory storage device.


Non-transitory computer-readable media for storing computer program instructions and data can include all forms of media and memory devices, magnetic devices, magneto optical disks, and optical memory device. Memory devices include semiconductor memory devices, for example, random access memory (RAM), read-only memory (ROM), phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and flash memory devices. Magnetic devices include, for example, tape, cartridges, cassettes, internal/removable disks. Optical memory devices include, for example, digital video disc (DVD), CD-ROM, DVD+/−R, DVD-RAM, DVD-ROM, HD-DVD, and BLURAY, and other optical memory technologies. The memory can store various objects or data, including caches, classes, frameworks, applications, modules, backup data, jobs, web pages, web page templates, data structures, database tables, repositories storing dynamic information, or other appropriate information including any parameters, variables, algorithms, instructions, rules, constraints, or references. Additionally, the memory can include other appropriate data, such as logs, policies, security or access data, or reporting files. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.


To provide for interaction with a user, implementations of the subject matter described in this specification can be implemented on a computer having a display device, for example, a CRT (cathode ray tube), LCD (liquid crystal display), LED (Light Emitting Diode), or plasma monitor, for displaying information to the user and a keyboard and a pointing device, for example, a mouse, trackball, or trackpad by which the user can provide input to the computer. Input can also be provided to the computer using a touchscreen, such as a tablet computer surface with pressure sensitivity, a multi-touch screen using capacitive or electric sensing, or another type of touchscreen. Other types of devices can be used to interact with the user. For example, feedback provided to the user can be any form of sensory feedback. Input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with the user by sending documents to and receiving documents from a client computing device that is used by the user.


The term “graphical user interface,” or “GUI,” can be used in the singular or the plural to describe one or more graphical user interfaces and each of the displays of a particular graphical user interface. Therefore, a GUI can represent any graphical user interface, including but not limited to, a web browser, a touch screen, or a command line interface (CLI) that processes information and efficiently presents the information results to the user. In general, a GUI can include a plurality of user interface (UI) elements, some or all associated with a web browser, such as interactive fields, pull-down lists, and buttons. These and other UI elements can be related to or represent the functions of the web browser.


Implementations of the subject matter described in this specification can be implemented in a computing system that includes a back-end component, for example, as a data server, or that includes a middleware component, for example, an application server, or that includes a front-end component, for example, a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of wireline or wireless digital data communication (or a combination of data communication), for example, a communication network. Examples of communication networks include a local area network (LAN), a radio access network (RAN), a metropolitan area network (MAN), a wide area network (WAN), Worldwide Interoperability for Microwave Access (WIMAX), a wireless local area network (WLAN) using, for example, 802.11 a/b/g/n or 802.20 (or a combination of 802.11x and 802.20 or other protocols consistent with the present disclosure), all or a portion of the Internet, another communication network, or a combination of communication networks. The communication network can communicate with, for example, Internet Protocol (IP) packets, Frame Relay frames, Asynchronous Transfer Mode (ATM) cells, voice, video, data, or other information between networks addresses.


The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.


While this specification contains many specific implementation details, these should not be construed as limitations on the scope of what can be claimed, but rather as descriptions of features that can be specific to particular implementations. Certain features that are described in this specification in the context of separate implementations can also be implemented, in combination, in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations, separately, or in any sub-combination. Moreover, although previously described features can be described as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can, in some cases, be excised from the combination, and the claimed combination can be directed to a sub-combination or variation of a sub-combination.


Particular implementations of the subject matter have been described. Other implementations, alterations, and permutations of the described implementations are within the scope of the following claims as will be apparent to those skilled in the art. While operations are depicted in the drawings or claims in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed (some operations can be considered optional), to achieve desirable results. In certain circumstances, multitasking or parallel processing (or a combination of multitasking and parallel processing) can be advantageous and performed as deemed appropriate.


Moreover, the separation or integration of various system modules and components in the previously described implementations should not be understood as requiring such separation or integration in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.


Furthermore, any claimed implementation is considered to be applicable to at least a computer-implemented method; a non-transitory, computer-readable medium storing computer-readable instructions to perform the computer-implemented method; and a computer system comprising a computer memory interoperably coupled with a hardware processor configured to perform the computer-implemented method or the instructions stored on the non-transitory, computer-readable medium.

Claims
  • 1. A computer-implemented method comprising: accessing one or more databases storing geo-exploration data associated with a reservoir, the geo-exploration data comprising: pressure data measured temporally at a downhole location inside a well of the reservoir, temporal production data of the reservoir through the well and measured at a surface of the well, petrophysical parameters of the reservoir, and fluid properties of the reservoir;creating temporal grids comprising sections during which respective segments of temporal production data are measured, wherein each of the respective segments of temporal production data is continuous within a corresponding section of the grids, and wherein the temporal production data comprise at least one discontinuity between two neighboring sections of the grid;based on, at least in part, the temporal production data, the petrophysical parameters of the reservoir, and the fluid properties of the reservoir, computing a superposition-time function over the sections, wherein the superposition-time function is free from the at least one discontinuity;constructing a plot of the pressure data versus the computed superposition-time function; andbased on, at least in part, the plot of the pressure data, deriving characteristics of the reservoir such that the reservoir is monitored continuously despite the at least one discontinuity in the temporal production data.
  • 2. The computer-implemented method of claim 1, wherein the characteristics of the reservoir comprise: a transmissibility, a reservoir flow capacity, and a reservoir permeability.
  • 3. The computer-implemented method of claim 2, further comprising: determining a slope of the pressure data being plotted versus the superposition-time function, wherein the slope encodes at least one of the characteristics of the reservoir.
  • 4. The computer-implemented method of claim 3, further comprising: based on, at least in part, the determined slope, iteratively determining at least one of the characteristics of the reservoir.
  • 5. The computer-implemented method of claim 2, further comprising: computing a pressure derivative with respect to the computed superposition-time function, a log-log plot of pressure derivative, and an intercept of the pressure derivative plot, wherein the intercept encodes at least one of the characteristics of the reservoir.
  • 6. The computer-implemented method of claim 1, further comprising: based on, at least in part, the derived characteristics of the reservoir, predicting a production rate of the reservoir beyond the temporal production data.
  • 7. The computer-implemented method of claim 1, wherein the temporal production data comprise: a production rate, and an injection rate.
  • 8. A computer system comprising one or more hardware processors configured to perform operations of: accessing one or more databases storing geo-exploration data associated with a reservoir, the geo-exploration data comprising: pressure data measured temporally at a downhole location inside a well of the reservoir, temporal production data of the reservoir through the well and measured at a surface of the well, petrophysical parameters of the reservoir, and fluid properties of the reservoir;creating temporal grids comprising sections during which respective segments of temporal production data are measured, wherein each of the respective segments of temporal production data is continuous within a corresponding section of the grids, and wherein the temporal production data comprise at least one discontinuity between two neighboring sections of the grid;based on, at least in part, the temporal production data, the petrophysical parameters of the reservoir, and the fluid properties of the reservoir, computing a superposition-time function over the sections, wherein the superposition-time function is free from the at least one discontinuity;constructing a plot of the pressure data versus the computed superposition-time function; and
  • 9. The computer system of claim 8, wherein the characteristics of the reservoir comprise: a transmissibility, a reservoir flow capacity, and a reservoir permeability.
  • 10. The computer system of claim 9, wherein the operations further comprise: determining a slope of the pressure data being plotted versus the superposition-time function, wherein the slope encodes at least one of the characteristics of the reservoir.
  • 11. The computer system of claim 10, wherein the operations further comprise: based on, at least in part, the determined slope, iteratively determining at least one of the characteristics of the reservoir.
  • 12. The computer system of claim 9, wherein the operations further comprise: computing a pressure derivative with respect to the computed superposition-time function, a log-log plot of pressure derivative, and an intercept of the pressure derivative plot, wherein the intercept encodes at least one of the characteristics of the reservoir.
  • 13. The computer system of claim 8, wherein the operations further comprise: based on, at least in part, the derived characteristics of the reservoir, predicting a production rate of the reservoir beyond the temporal production data.
  • 14. The computer system of claim 8, wherein the temporal production data comprise: a production rate, and an injection rate.
  • 15. A non-transitory computer-readable medium comprising software instructions which, when executed by a computer processor, causes the computer processor to perform operations of: accessing one or more databases storing geo-exploration data associated with a reservoir, the geo-exploration data comprising: pressure data measured temporally at a downhole location inside a well of the reservoir, temporal production data of the reservoir through the well and measured at a surface of the well, petrophysical parameters of the reservoir, and fluid properties of the reservoir;creating temporal grids comprising sections during which respective segments of temporal production data are measured, wherein each of the respective segments of temporal production data is continuous within a corresponding section of the grids, and wherein the temporal production data comprise at least one discontinuity between two neighboring sections of the grid;based on, at least in part, the temporal production data, the petrophysical parameters of the reservoir, and the fluid properties of the reservoir, computing a superposition-time function over the sections, wherein the superposition-time function is free from the at least one discontinuity;constructing a plot of the pressure data versus the computed superposition-time function; andbased on, at least in part, the plot of the pressure data, deriving characteristics of the reservoir such that the reservoir is monitored continuously despite the at least one discontinuity in the temporal production data.
  • 16. The non-transitory computer-readable medium of claim 15, wherein the characteristics of the reservoir comprise: a transmissibility, a reservoir flow capacity, and a reservoir permeability.
  • 17. The non-transitory computer-readable medium of claim 16, wherein the operations further comprise: determining a slope of the pressure data being plotted versus the superposition-time function, wherein the slope encodes at least one of the characteristics of the reservoir.
  • 18. The non-transitory computer-readable medium of claim 17, wherein the operations further comprise: based on, at least in part, the determined slope, iteratively determining at least one of the characteristics of the reservoir.
  • 19. The non-transitory computer-readable medium of claim 17, wherein the operations further comprise: computing a pressure derivative with respect to the computed superposition-time function, a log-log plot of pressure derivative, and an intercept of the pressure derivative plot, wherein the intercept encodes at least one of the characteristics of the reservoir.
  • 20. The non-transitory computer-readable medium of claim 15, wherein the operations further comprise: based on, at least in part, the derived characteristics of the reservoir, predicting a production rate of the reservoir beyond the temporal production data, wherein the temporal production data comprise: a production rate, and an injection rate.