WATER INVASION-ORIENTED DYNAMIC PRODUCTION ALLOCATION METHOD FOR WATER-BEARING CARBONATITE GAS RESERVOIR

Abstract

The present disclosure provides a water invasion-oriented dynamic production allocation method for a water-bearing carbonatite gas reservoir, and belongs to the technical field of oil and gas field development. The problem that water breakthrough of a single well is too early due to uneven water invasion of an existing water-bearing carbonatite gas reservoir is solved. According to the technical scheme, on the basis of an original gas well production allocation scheme of a water-bearing carbonatite gas reservoir, the average water invasion rate of the reservoir is calculated as a stability reference of water invasion rates throughout the production period. A new water invasion-oriented production allocation method is designed from two aspects of stability of water invasion and uniformity of water invasion driving; and meanwhile, a reasonable production allocation range is predicted through a traditional deliverability equation, and a water invasion-oriented dynamic production allocation mathematical model is established.

Claims

1. A water invasion-oriented dynamic production allocation method for a water-bearing carbonatite gas reservoir, comprising the following steps: according to a water invasion rate during a production period, calculating an average water invasion rate W.sub.e as a water invasion reference value; by comparing stability of water invasion rates under different production allocation schemes, selecting an optimal single well production allocation scheme, which specifically comprises: based on a deliverability equation from a formation to a wellbore, and upper and lower limits of a laminar coefficient A and a turbulence coefficient B, calculating flux of formation water flowing into the wellbore according to a formation pressure and a flowing bottomhole pressure during the production period, and selecting j single well production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j; based on a numerical simulation method, determining water invasion rates U.sub.1, U.sub.2, U.sub.3, . . . , U.sub.j corresponding to different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j; according to the water invasion reference value W.sub.e obtained, comparing water invasion rates U.sub.1, U.sub.2, U.sub.3, . . . , U.sub.j corresponding to different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j, and determining a deviation between the water invasion rate corresponding to each production allocation scheme and the water invasion reference value by average deviation calculation, wherein the stability deviation of water invasion rates is expressed as: $\sigma =\underset{i=1}{\overset{t}{.Math.}}.Math.U_j-{\stackrel{\_}{W}}_e.Math./t\times 100\%$ wherein σ.sub.j denotes a stability deviation of a water invasion rate corresponding to a jth production allocation scheme, in unit of %; U.sub.j denotes a water invasion rate corresponding to a jth production allocation scheme, in unit of m.sup.3/d; W.sub.e denotes a water invasion reference value, in unit of m.sup.3/d; and t denotes cumulative producing days, in unit of d; and comparing stability deviations σ.sub.1, σ.sub.2, σ.sub.3, . . . , σ.sub.j of water invasion rates corresponding to different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j to seek a minimum stability deviation minσ.sub.j of water invasion rates; by comparing uniformity of water invasion driving under different production allocation schemes, selecting an optimal single well production allocation scheme, which specifically comprises: based on a numerical simulation method, determining water invasion rates in direction a, b, . . . , f at moment i corresponding to different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j; based on the water invasion reference value W.sub.e obtained in combination with the water invasion rates in direction a, b, . . . , f, determining, by average deviation calculation, a deviation between the water invasion reference value and the water invasion rates in direction a, b, . . . , f throughout the production period for indicating the uniformity of water invasion driving, wherein the uniformity deviation of water invasion driving is expressed as: ${\delta }_{\mathrm{direction}}=\stackrel{t}{\underset{i=1}{.Math.}}.Math.D_{\mathrm{direction}}-\stackrel{\_}{W_e}.Math./t\times 100\%$ wherein δ.sub.direction denotes a uniformity deviation of water invasion driving in a certain direction, in unit of %; and D.sub.direction denotes a water invasion rate in a certain direction, in unit of m.sup.3/d; aiming at different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j, calculating uniformity deviations δ.sub.a, δ.sub.b, . . . , δ.sub.f of water invasion driving in a single direction of direction a, b, . . . , f throughout the production period, and then calculating an average value of the uniformity deviation of water invasion driving in each single direction corresponding to each production allocation scheme as uniformity deviations δ.sub.1, δ.sub.2, δ.sub.3, . . . , δ.sub.j of water invasion driving corresponding to production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j; and comparing stability deviations δ.sub.1, δ.sub.2, δ.sub.3, . . . , δ.sub.j of water invasion driving under different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j to seek a minimum stability deviation minδ.sub.j of water invasion driving; and establishing a water invasion-oriented dynamic production allocation mathematical model, wherein the water invasion-oriented dynamic production allocation mathematical model is expressed as follows: $\{\begin{array}{c}{P}_R^2-P_{\mathrm{wf}}^2=A{q}_{\mathrm{production}\mathrm{allocation}}+{\mathrm{Bq}}_{\mathrm{production}\mathrm{allocation}}^2\\ S_{\mathrm{optimal}}={\left({\sigma }_j+{\delta }_j\right)}_{\min }\end{array}$ wherein S.sub.optimal denotes a comprehensive deviation of an optimal production allocation scheme q.sub.j, in unit of %.

2. The water invasion-oriented dynamic production allocation method for a water-bearing carbonatite gas reservoir according to claim 1, wherein the deliverability equation is P.sub.R.sup.2−P.sub.wf.sup.2=Aq.sub.production allocation+Bq.sub.production allocation.sup.2, wherein P.sub.R denotes a formation pressure during a production period, in unit of MPa; P.sub.wf denotes a flowing bottomhole pressure, in unit of MPa; q.sub.production allocation denotes a stable production rate during normal production after pilot production, in unit of 10.sup.4 m.sup.3/d; and .sub.A denotes a laminar coefficient, and .sub.B denotes a turbulence coefficient.

3. The water invasion-oriented dynamic production allocation method for a water-bearing carbonatite gas reservoir according to claim 1, wherein the numerical simulation method refers to a process of simulating different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j by Eclipse software to obtain corresponding water invasion rates, respectively.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] FIG. 1 is a technical route of a method according to the present disclosure.

[0027] FIG. 2 is a historical fitting curve established for daily water production of a single well.

[0028] FIG. 3 is a historical fitting curve established for daily gas production of a single well.

[0029] FIG. 4 is a curve showing the comparison between daily gas production under a new production allocation method and daily gas production in actual situations.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] The present the number is further described below with reference to the accompanying drawings and embodiments.

[0031] The present disclosure provides a water invasion-oriented dynamic production allocation method for a water-bearing carbonatite gas reservoir. As shown in the technical route in FIG. 1, the method includes the following steps:

[0032] first, according to a water invasion rate during a production period, calculating an average water invasion rate w, as a water invasion reference value;

[0033] second, by comparing stability of water invasion rates under different production allocation schemes, selecting an optimal single well production allocation scheme;

[0034] third, by comparing uniformity of water invasion driving under different production allocation schemes, selecting an optimal single well production allocation scheme; and

[0035] fourth, by considering a deliverability equation, stability of water invasion rates and uniformity of water invasion driving, establishing a water invasion-oriented dynamic production allocation mathematical model, where the water invasion-oriented dynamic production allocation mathematical model selects a distribution allocation range on the basis of the deliverability equation, and seeks the minimum value of the sum of the stability deviation of water invasion rates and the uniformity deviation of water invasion driving under different production allocation schemes by considering the stability water invasion rates and the uniformity of water invasion driving, so as to select an optimal production allocation scheme to address the influence of water invasion on production allocation in a water-bearing carbonatite gas reservoir, optimal production allocation is obtained after comprehensive consideration, and the water invasion-oriented dynamic production allocation mathematical model is expressed as follows:

[00004]$\{\begin{array}{c}{P}_R^2-P_{\mathrm{wf}}^2=A{q}_{\mathrm{production}\mathrm{allocation}}+{\mathrm{Bq}}_{\mathrm{production}\mathrm{allocation}}^2\\ S_{\mathrm{optimal}}={\left({\sigma }_j+{\delta }_j\right)}_{\min }\end{array};$

[0036] where P.sub.R denotes a formation pressure during a production period, in unit of MPa; P.sub.wf denotes a flowing bottomhole pressure, in unit of MPa; q.sub.production allocation denotes a stable production rate during normal production after pilot production, in unit of 10.sup.4 m.sup.3/d; σ denotes a stability deviation of a water invasion rate, in unit of %; δ denotes a uniformity deviation of water invasion driving in a certain direction, in unit of %; q.sub.j denotes a theoretical value of an optimal parameter of the production allocation scheme, in unit of 10.sup.4 m.sup.3/d; and A denotes a laminar coefficient, and B denotes a turbulence coefficient.

[0037] Furthermore, by comparing stability of water invasion rates under different production allocation schemes, select an optimal single well production allocation scheme, which specifically includes:

[0038] first, based on a deliverability equation from a formation to a wellbore, and upper and lower limits of a laminar coefficient A and a turbulence coefficient B, calculating flux of formation water flowing into the wellbore according to a formation pressure and a flowing bottomhole pressure during the production period, and selecting j single well production allocation schemes q.sub.1, q.sub.2, q.sub.3, q.sub.1;

[0039] where the deliverability equation is P.sub.R.sup.2−P.sub.wf.sup.2=Aq.sub.production allocation+Bq.sub.production allocation.sup.2;

[0040] second, based on a numerical simulation method, determining water invasion rates U.sub.1, U.sub.2, U.sub.3, . . . , U.sub.1 corresponding to different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j;

[0041] third, according to the water invasion reference value W.sub.e obtained, comparing water invasion rates U.sub.1, U.sub.2, U.sub.3, . . . , U.sub.j corresponding to different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j, and determining a deviation between the water invasion rate corresponding to each production allocation scheme and the water invasion reference value by average deviation calculation, where the stability deviation of water invasion rates is expressed as:

[00005]$\sigma =\underset{i=1}{\overset{t}{.Math.}}.Math.U_j-{\stackrel{\_}{W}}_e.Math./t\times 100\%$

[0042] where U.sub.j denotes a water invasion rate corresponding to a jth production allocation scheme, in unit of m.sup.3/d; W.sub.e denotes a water invasion reference value, in unit of m.sup.3/d; and t denotes cumulative producing days, in unit of d; and

[0043] fourth, comparing stability deviations σ.sub.1, σ.sub.2, σ.sub.3, . . . , σ.sub.j of water invasion rates corresponding to different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j to seek a minimum stability deviation minσ.sub.j of water invasion rates, where at this time, the corresponding q.sub.j is the optimal allocation scheme considering the stability of water invasion rates;

[0044] Furthermore, by comparing uniformity of water invasion driving under different production allocation schemes, selecting an optimal single well production allocation scheme, which specifically includes:

[0045] first, based on a numerical simulation method, determining water invasion rates in direction a, b, . . . , f at moment i corresponding to different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j;

[0046] second, based on the water invasion reference value W.sub.e obtained in combination with the water invasion rates in direction a, b, . . . , f, determining, by average deviation calculation, a deviation between the water invasion reference value and the water invasion rates in direction a, b, . . . , f throughout the production period for indicating the uniformity of water invasion driving, where the uniformity deviation of water invasion driving is expressed as:

[00006]${\delta }_{\mathrm{direction}}=\stackrel{t}{\underset{i=1}{.Math.}}.Math.D_{\mathrm{direction}}-\stackrel{\_}{W_e}.Math./t\times 100\%$

[0047] where δ.sub.direction denotes a uniformity deviation of water invasion driving in a certain direction, in unit of %; and D.sub.direction denotes a water invasion rate in a certain direction, in unit of m.sup.3/d;

[0048] third, aiming at different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j, calculating uniformity deviations δ.sub.a, δ.sub.b, . . . , δ.sub.f of water invasion driving in a single direction of direction a, b, f throughout the production period, and then calculating an average value of the uniformity deviation of water invasion driving in each single direction corresponding to each production allocation scheme as uniformity deviations δ.sub.1, δ.sub.2, δ.sub.3, . . . , δ.sub.j of water invasion driving corresponding to production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j; and

[0049] fourth, comparing uniformity deviations δ.sub.1, δ.sub.2, δ.sub.3, . . . , δ.sub.j of water invasion driving under different production allocation schemes q.sub.1, q.sub.2, q.sub.3, . . . , q.sub.j to seek a minimum uniformity deviation min δ.sub.j of water invasion driving, where at this time, the corresponding q.sub.j is regarded as the optimal production allocation value with the uniformity of water invasion driving considered.

[0050] For example, well X103 of a carbonatite gas reservoir located in Sichuan Basin was put into production on Dec. 6, 2012. In November 2015, by testing, water invasion occurred in the gas well, followed by production decline. On Jul. 21, 2017, water breakthrough occurred in the gas well. Taking this well as an example, a single well-based numerical simulation is done, and the history fitting is carried out, as shown in FIG. 2 and FIG. 3. The historical fitting curve and error distribution result show that a high fitting accuracy, and the established single well-based numerical simulation model can effectively characterize the production performance of the well X103.

[0051] If the original production plan remains effective after water invasion occurs, the cumulative gas production of well X103 is 5.18×10.sup.8 m.sup.3. If a new water invasion-oriented production allocation method is adopted, as shown in FIG. 4, the cumulative gas production of gas well X103 is 5.99×10.sup.8 m.sup.3 under the prediction of single well-based numerical simulation, which is 15.53% higher than that under the original production allocation scheme. This production allocation method can basically realize the rational utilization of formation water energy, effectively improve the recovery of single gas well, which provides theoretical guidance for the development of water-bearing gas reservoir in an oil field.