# Patent application title: METHOD FOR DETERMINING AN INFLOW PROFILE OF MULTILAYER RESERVOIR FLUIDS IN A WELLBORE

##
Inventors:
Valery Vasilievich Shako (Domodedovo, RU)
Valery Vasilievich Shako (Domodedovo, RU)
Vyacheslav Pavlovich Pimenov (Moscow, RU)
Vyacheslav Pavlovich Pimenov (Moscow, RU)
Bertrand Theuveny (Moscow, RU)
Maria Viktorovna Sidorova (Moscow, RU)

IPC8 Class: AE21B4700FI

USPC Class:
16625001

Class name: Wells processes with indicating, testing, measuring or locating

Publication date: 2015-02-26

Patent application number: 20150053398

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## Abstract:

Methods for determining an inflow profile of multilayer reservoir fluids
in a wellbore are described herein. A bottom-hole zone is cooled before
well perforation. Then, the wellbore is perforated, and a flow
temperature is measured in the wellbore above each perforation zone. A
production rate of each productive layer is determined taking into
account thicknesses of the perforation zones and using results of
temperature measurements acquired in a period between an end of an
initial production stage characterized by strong impact of a volume of
the wellbore and quick flow temperature changes in the wellbore, and a
time when the bottom-hole zone cooling effect on the temperature
measurements becomes insignificant.## Claims:

**1.**A method for determining an inflow profile of multilayer reservoir fluids in a wellbore comprising: cooling of a bottom-hole zone, perforating the wellbore, measuring flow temperature in the wellbore above each perforation zone, and determining a production rate of each productive layer taking into account thicknesses of the perforation zones and using results of temperature measurements acquired between (i) an end of an initial production stage and (ii) a time starting from which the bottom-hole zone cooling effect on the temperature measurements becomes insignificant.

**2.**The method of claim 1, wherein the bottom-hole zone is cooled by drilling.

**3.**The method of claim 1, wherein the bottom-hole zone is cooled by well circulation.

**4.**The method of claim 1, wherein the flow temperature in the wellbore is measured by sensors installed on a tubing string used for perforation above the each perforation zone.

**5.**The method of claim 1, wherein for determining the production rates of the productive layers, temperature measurement results are used, which are acquired within an interval of 1 to 10 hours after the start of production.

**6.**The method of claim 1, wherein starting from a second perforation zone relative production rates of perforation zones Y

_{n}, n=2, 3, . . . m are calculated successively upward by means of minimization according to: S ( Y n ) = i F ( Y n , t i ) 2 min ##EQU00020## where Y n = Q n Q 1 + Q 2 + + Q n , ##EQU00021## (n=2, 3, . . . m) is the production rate of each perforation zone, F ( Y n , t ) = Y n - T n - 1 , a ( t ) - T n , a ( t ) T n - 1 , a ( t ) - T 1 a [ a n t ] a n = q n q 1 = h 1 h n Y n ( 1 - Y 2 ) ( 1 - Y 3 ) ( 1 - Y n ) , ##EQU00022## h

^{n}(n=1, 2, . . . m) is a thickness of a n perforation zone, T

_{n,a}(t) is a flow temperature measured in the wellbore above the n perforation zone, t

_{i}is time moments equally distributed within the interval t

_{1}<t<t

_{2}, where t

_{1}is the end time of the initial production stage, t

_{2}is the time starting from which the bottom-hole zone cooling effect on the temperature measurements becomes insignificant, a number of the time moments in the interval t

_{1}<t<t

_{2}is equal to a number of temperature measurements, and the production rates Q

_{n}(n=2, 3, . . . m) of the perforation zones are determined formulas according to: Q 1 = Q 1 + Y 2 1 - Y 2 + Y 3 ( 1 - Y 2 ) ( 1 - Y 3 ) + + Y m ( 1 - Y 2 ) ( 1 - Y 3 ) ( 1 - Y m ) ##EQU00023## Q 2 = Q 1 Y 2 1 - Y 2 ##EQU

**00023.**2## Q 3 = Q 1 Y 3 ( 1 - Y 2 ) ( 1 - Y 3 ) ##EQU

**00023.**3## Q n = Q 1 Y n ( 1 - Y 2 ) ( 1 - Y 3 ) ( 1 - Y n ) ##EQU

**00023.**4## where Q is a total volumetric wellbore production rate.

**7.**The method of claim 1, wherein wellbore flow temperature is additionally measured under each perforation zone, and F(Y

_{n}, t) is determined according to: F ( Y n , t ) = Y n - T n , b ( t ) - T n , a ( t ) T n , b ( t ) - T 1 , a [ a n t ] ##EQU00024## where T

_{n,b}(t) and T

_{n,a}(t) are temperatures measured in the wellbore below and above the n perforation zone.

**8.**The method of claim 1, wherein pressure is additionally measured in the wellbore below all perforation zones and an inverse task is solved using a numerical simulation with such numerical model parameters selected which ensure matching of measured and calculated temperature-time dependencies, and the measured wellbore pressure is applied as a boundary condition for simulation of pressure and temperature fields in the production layers.

## Description:

**CROSS**-REFERENCE TO RELATED APPLICATION

**[0001]**This application claims priority to Russian Application No. 2013139149 filed Aug. 23, 2013, which is incorporated herein by reference in its entirety.

**TECHNICAL FIELD**

**[0002]**The disclosure relates to the field of geophysical exploration of oil and gas wells, namely to determining a profile of fluid inflow to a wellbore from producing layers of multilayer reservoirs.

**BACKGROUND**

**[0003]**Typically, when estimating production rates of individual producing layers based on temperature data, temperature is measured along a wellbore under quasi-steady production conditions and formation temperature near the wellbore is supposed to be close to a temperature of the undisturbed formation. It is assumed that rocks temperature near the wellbore is equal to the undisturbed rock mass temperature. A production rate of a producing layer is usually determined from flow temperature measured below and above the layer and from temperature of a fluid flowing from the formation into the wellbore (see, for example, Hill, A.D., 2002. Production Logging--Theoretical and Interpretive Elements. SPE Monograph Series).

**[0004]**Traditional methods to determine an inflow profile based on temperature data apply the following simplifying assumptions: a quasi-steady-state fluid flow in the wellbore, a Joule-Thomson effect constant, and a temperature of rocks near the wellbore is determined by an undisturbed geotherm.

**[0005]**These assumptions are not valid if temperature in the wellbore is measured at the initial production stage immediately after perforation. In the first turn, the assumption about the temperature of rocks near the wellbore is wrong. As a rule, during perforation, the temperature near the wellbore is significantly less than the temperature of undisturbed rocks. This is due to cooling effects of previous technological operations in the well: well drilling and circulation.

**[0006]**RU Patent No. 2474687 describes a method to determine the fluids inflow profile in multilayer wells based on results of measuring temperatures in the well immediately after perforation when temperature of rocks near the well is reduced due to previous technological operations (well drilling and circulation). According to this method, production rates of individual layers are calculated based on temperature rates of change measured in the wellbore. A theoretical basis for this method is a linear dependence established between the produced fluid temperature change rate and a formation specific production rate, which assumes cooling of a bottom-hole formation zone and a shut-in between the fluid circulation in the wellbore and perforation.

**[0007]**A disadvantage of this method is a relatively short period of production, when this linear dependence between the temperature change rate and production rate is retained, which can restrict applicability of this method to determine the inflow profile and a need to measure the temperature change rate in the well before its perforation, which increases a probable error and imposes additional restrictions on the perforation schedule.

**SUMMARY**

**[0008]**The disclosure provides improved accuracy and reliability of determining an inflow profile in a multilayer wellbore at an initial production stage immediately after the wellbore perforation. In this case, there is no need for a shut-in between well circulation and perforation and it is not required to measure temperature change rate in the wellbore before its perforation.

**[0009]**The method comprises cooling of a bottom-hole zone before perforation of a wellbore. Then the wellbore is perforated, and the flow temperature is measured in the wellbore above each perforation zone. A production rate of each pay zone is determined taking into account thicknesses of the perforation zones and using the results of temperature measurements acquired between the end of an initial production stage characterized by strong impact of a volume of the wellbore and quick flow temperature changes in the wellbore, and a time when the bottom-hole zone cooling impact on the temperature measurements becomes insignificant.

**[0010]**The bottom-hole zone can be cooled by drilling or well circulation.

**[0011]**The flow temperature in the wellbore is measured by means of sensors installed on a tubing string used for the perforation, above each perforation zone.

**[0012]**Starting from a second perforation zone relative production rates of the perforation zones Y

_{n}, n=2, 3, . . . m are calculated, successively upward, by means of minimization

**S**( Y n ) = i F ( Y n , t i ) 2 min ##EQU00001##

**where**

**Y n**= Q n Q 1 + Q 2 + + Q n , ##EQU00002##

**Q**

_{n}(n=2, 3, . . . m) are the production rates of the perforation zones

**F**( Y n , t ) = Y n - T n - 1 , a - T n , a ( t ) T n - 1 , a ( t ) - T 1 , a [ a n t ] ##EQU00003## a n = q n q 1 = h 1 h n Y n ( 1 - Y 2 ) ( 1 - Y 3 ) ( 1 - Y n ) , ##EQU00003.2##

**h**

_{n}(n=1, 2, . . . m) is a thickness of a n perforation zone, T

_{n,a}(t) is a flow temperature measured in the wellbore above the n perforation zone, t

_{i}is time moments equally distributed within an interval t

_{1}<t<t

_{2}, where t

_{1}is the end time of the initial production stage characterized by strong impact of a volume of the wellbore and quick flow temperature changes in the wellbore, t

_{2}is a time when the bottom-hole zone cooling impact on the temperature measurements becomes insignificant; a number of the time moments within this interval is equal to a number of the temperature measurements.

**[0013]**The production rates Q

_{n}(n=2, 3, . . . m) of the perforation zones are determined by formulas:

**Q**1 = Q 1 + Y 2 1 - Y 2 + Y 3 ( 1 - Y 2 ) ( 1 - Y 3 ) + + Y m ( 1 - Y 2 ) ( 1 - Y 3 ) ( 1 - Y m ) ##EQU00004## Q 2 = Q 1 Y 2 1 - Y 2 ##EQU00004.2## Q 3 = Q 1 Y 3 ( 1 - Y 2 ) ( 1 - Y 3 ) ##EQU00004.3## Q n = Q 1 Y n ( 1 - Y 2 ) ( 1 - Y 3 ) ( 1 - Y n ) ##EQU00004.4##

**where Q is a total volumetric well production rate**.

**[0014]**According to one of the embodiments of the disclosure, the wellbore flow temperature T

_{n}b(t) is measured under each perforation zone, with F(Y

_{n}, t) determined as follows:

**F**( Y n , t ) = Y n - T n , b ( t ) - T n , a ( t ) T n , b ( t ) - T 1 , a [ a n t ] ##EQU00005##

**[0015]**According to another embodiments of the disclosure n, pressure is additionally measured in the wellbore, below all perforation zones; and to solve an inverse task, a numerical simulation is used with such numerical model parameters which ensure coincidence of measured and calculated temperature-time dependencies; the measured wellbore pressure is applied as a boundary condition for simulation of pressure and temperature fields in the productive layers.

**[0016]**To determine the production rates of the productive layers, temperature measurement results are used, which are acquired preferably within an interval of 1 to 10 hours after start of production.

**BRIEF DESCRIPTION OF DRAWINGS**

**[0017]**The disclosure is illustrated by drawings where:

**[0018]**FIG. 1 shows a scheme of a wellbore with two perforation zone and three temperature sensors;

**[0019]**FIG. 2a shows calculated radial temperature distributions after the well circulation and shut-in period;

**[0020]**FIG. 2b shows calculated temperatures of fluids produced from layers with different specific production rates (full lines) and a temperature of a layer with a high flow rate after scaling of the timescale (markers);

**[0021]**FIG. 3 and FIG. 4 show calculated temperatures for various values of layer permeability;

**[0022]**FIG. 5 and FIG. 6 show dependencies of mis-ties on the formation relative production rate for various values of formation permeability;

**[0023]**FIG. 7a shows calculated temperatures with normal noise CKO=0.1 K. Option k

_{1}=100 mD, k

_{2}=30 mD;

**[0024]**FIG. 7b shows dependence of mis-tie S on value Y

_{2}. Solution Y

_{2}min=0.2;

**[0025]**FIG. 8a shows calculated temperatures with normal noise CKO=0.1 K. Option k1=30 mD, k2=100 mD;

**[0026]**FIG. 8b shows dependence of mis-tie S on value Y

_{2}. Solution Y

_{2}min=0.69;

**[0027]**FIG. 9a shows values of selected permeability to solve an inverse task. Option k

_{1}=100 mD, k

_{2}=30 mD;

**[0028]**FIG. 9b shows specified temperatures and temperatures calculated when solving the inverse task. k

_{1}=96 mD, k

_{2}=29 mD, Y

_{2}≈0.23;

**[0029]**FIG. 10a shows values of selected permeability to solve the inverse task. Option k

_{1}=30 mD, k

_{2}=100 mD;

**[0030]**FIG. 10b shows specified temperatures and temperatures calculated when solving the inverse task. k

_{1}=29 mD, k

_{2}=96 mD, Y

_{2}≈0.75.

**DETAILED DESCRIPTION**

**[0031]**The proposed method can be applied in conditions of typical perforation with a tubing string.

**[0032]**Normally, a bottom-hole zone is cooled during a well drilling. If drilling was completed recently (several days before perforation), special cleanout of the wellbore is not required. If the wellbore was drilled a long time ago, special cleanout may be performed before the perforation, which ensures significant (by 5-10° C. and over) decrease in temperature of rocks near the wellbore as compared with the undisturbed rock temperature.

**[0033]**The proposed method uses the fact that an initial radial distribution of temperature is approximately the same in all productive layers under consideration T≈T

_{0}(r).

**[0034]**This assumption is valid if:

**(a) the productive layers are close to each other (at a distance of 30-50 m); and (b) all productive layers have approximately the same thermal properties.**

**[0035]**After start of production, the radial temperature profile in a reservoir and a temperature of fluid flowing to the wellbore from the formation are mainly determined by convection heat transfer (1):

**ρ r c r ∂ T ∂ t - ρ f c f V ( r ) ∂ T ∂ r = 0 ( 1 ) ##EQU00006##**

**where**

**V**= q 2 π r ( 2 ) ##EQU00007##

**is a fluid filtration rate**, q [m

^{3}/m/s] is a production rate per 1 m of perforation zone, ρ

_{fc}

_{f}is a fluid volumetric heat capacity, ρ

_{rc}

_{r}=φρ

_{fc}

_{f}+(1-φ)ρ

_{m}- c

_{m}is a volumetric heat capacity of the fluid saturated reservoir, ρ

_{mc}

_{m}is a volumetric heat capacity of rock matrix, φ is reservoir porosity, and r is a distance to an axis of the wellbore.

**[0036]**Equation (1) does not take into account impact of conductive heat transfer, Joule-Thomson effect, and adiabatic effect. Negligible impact of conductive heat transfer in the inflow zone for typical specific production rates was demonstrated by means of detailed numeric simulation. Relative impact of Joule-Thomson and adiabatic effects is determined by pressure differential between the reservoir and the wellbore and by typical decrease of temperature in the bottom-hole area. Since pressure differentials at the initial production stage are normally insignificant (10-30 bar), and the reservoir cooling reaches 10 K and over, these effects may be neglected in the first approximation. The inflow profile can be determined more accurately based on transient temperature logging data by means of numerical simulation (see below).

**[0037]**Solution of equation (1) is as follows:

**T**( r , t ) = T 0 ( r 2 + χ π q t ) , ( 3 ) ##EQU00008##

**where**

**χ = c f ρ f ρ r c r , ##EQU00009##**

**T**

_{0}(r) is a radial distribution of temperature in the reservoir before start of production, and q is a specific production rate of the reservoir.

**[0038]**From (3), a temperature-time dependence expression follows for the fluid flowing into the wellbore:

**T in**( t ) = T 0 ( r w 2 + π q t ) , ( 4 ) ##EQU00010##

**where r**

_{w}is a radius of the wellbore.

**[0039]**Let us consider a wellbore with two productive layers (FIG. 1). Temperatures of fluids flowing from different layers with specific production rates q

_{1}and q

_{2}are as follows (respectively):

**T in**, 1 ( t ) = T 0 ( r w 2 + π q 1 t ) ##EQU00011## and ##EQU00011.2## T in , 2 ( t ) = T 0 ( r w 2 + π q 2 t ) ##EQU00011.3##

**[0040]**It is obvious that temperature T

_{in},2(t) can be written as

**T in**, 2 ( t ) = T 0 ( r w 2 + π q 1 t q 2 q 1 ) or T in , 2 ( t ) = T in , 1 ( a 2 t ) where : ( 5 ) a 2 = q 2 q 1 = h 1 h 2 Y 2 1 - Y 2 ; ( 6 ) ##EQU00012##

**[0041]**According to formula (6), a relative production rate of an upper productive layer Y

_{2}can be found by selecting such a scaling factor `a

_{2}` that will provide coincidence of time-dependent temperatures of fluids flowing from different productive layers.

**[0042]**This is illustrated (FIG. 2) by results of numerical calculations made by means of software COMSOL MULTIPHYSICS 3.5®. Calculated radial distributions of temperatures after the well circulation (24 hours of circulation at initial rock temperature of 100° C. and circulating fluid temperature of 50° C. (the dotted curve), and its shut-in for 24 hours (solid curve)) are shown on FIG. 2a. A thin solid curve on FIG. 2b shows calculated temperature of fluid flowing into the wellbore at a production rate q (q=10 m

^{3}/m/day). A thick solid line matches a production rate 2q. Markers that actually coincide with the thin curve show a result of twofold time-based expansion for the curve matching the flow rate of 2q.

**[0043]**Formulas (5) and (6) enable to find production rates of individual perforation zones, if all time dependent temperatures are measured for fluids flowing to the wellbore from different layers. In practice, only a wellbore flow temperature is measured. A temperature measured above a lower perforation zone is approximately equal to a temperature of fluid flowing from the lower zone, but for all other zones, temperature T

_{in}is normally unknown.

**[0044]**The disclosure proposes the following method to solve the problem.

**[0045]**Let us consider a case when temperature sensors are installed on a tubing above and below each perforation zone (FIG. 1).

**[0046]**In this case, relative production rates of productive layers can be approximately determined by means of the stationary energy conservation law that expresses a balance of thermal energy coming into the inflow zone and energy leaving this zone:

**ρcQ**

_{1}T

_{2},b+ρcQ

_{2}T

_{in},2=ρc(Q

_{1}+Q

_{2})T.- sub.2,a (7)

**where**ρc is a fluid volumetric conductivity.

**[0047]**Since we consider transient processes and wellbore fluid temperature varies with time, using this equation is not entirely correct; however, as the below calculations demonstrate, it can be used for an approximate solution of the problem.

**[0048]**From equation (7) the formula follows for a relative production rate of an upper layer Y

_{2}:

**Y**2 = T 2 , b - T 2 , a T 2 , b - T in , 2 ( 8 ) ##EQU00013##

**[0049]**Taking into account that

**T**

_{1},a(t)≈T

_{in},1(t)

**and using formula**(5)

**T**

_{in},2(t)=T

_{in},1(a

_{2}t)≈T

_{1},a(a

_{2}t)

**we find an equation for the unknown value Y**

_{2}:

**F**( Y 2 , t ) = 0 where : ( 9 ) F ( Y 2 , t ) = Y 2 - T 2 , b ( t ) - T 2 , a ( t ) T 2 , b ( t ) - T 1 , a [ a 2 ( Y 2 ) t ] ( 10 ) ##EQU00014##

**[0050]**It is essential that this equation does not include an unknown temperature of produced fluid T

_{in2}(t) and an unknown temperature of undisturbed rocks T

_{f}. The unknown value Y

_{2}is determined solely by results of wellbore temperature measurements: T

_{1},a, T

_{2},b, T

_{2},a

**[0051]**If a distance between layers is short (about 10 m), then, as calculations demonstrate T

_{2},b(t)≈T

_{1},a(t), equation (10) will look as follows:

**F**( Y 2 , t ) = Y 2 - T 1 , a ( t ) - T 2 , a ( t ) T 1 , a ( t ) - T 1 , a [ a 2 ( Y 2 ) t ] ( 11 ) ##EQU00015##

**[0052]**A relative production rate of the upper layer can be found by equation (9) for any fixed time moment `t`; however not all time moments are equivalent.

**[0053]**At short times (t<t

_{1}), the wellbore volume which is not considered by the simplified model described above can significantly impact the calculation results. Besides, at the initial stage, the wellbore fluid temperature quickly changes in the perforation zone and using stationary energy equation (7) can result in significant errors in determination of relative production rates of the layers.

**[0054]**At long times (t>t

_{2}), when the bottom-hole zone cooling effect ceases and the fluid flowing to the wellbore heats the near wellbore rocks actually to the reservoir temperature, Joule-Thomson and geotherm effects become more significant. Both of these effects are not taken into account in the above simplified model, which may result in errors in determination of the inflow profile. Therefore, when the above simplified model is used, data acquired at relatively short times t<t

_{2}is used.

**[0055]**Values T

_{1a}, T

_{2}b and T

_{2a}are measured with a certain error. This error is connected with sensors and measurement method errors. In reality, calculation formula (10) includes bulk flow temperatures while the sensor measures a temperature in a certain flow point and there is some temperature distribution along the flow cross-section. Therefore, to reduce impacts of various factors on results of the inflow profile determination, it is expedient to use all data acquired within time interval t

_{1}<t<t

_{2}.

**[0056]**It is proposed to find value Y

_{2}by minimization of function S (Y

_{2}) (11), which is calculated as a sum of squared mis-ties for all time moments in the interval t

_{1}<t<t

_{2}, for which measured temperatures are available:

**S**(Y

_{2})=ΣF(Y

_{2},t

_{i})

^{2}min (11)

**[0057]**The proposed method to determine the inflow profile was tested in several typical synthetic instances. It was shown, that values t

_{1}=1/2 hours and t

_{2}=8/10 hours ensure a satisfactory accuracy of the inverse task solution.

**[0058]**The described above method to determine the inflow profile for two productive layers is easily generalized and can be used for arbitrary number m of layers.

**[0059]**Starting from the second perforation zone relative production rates of perforation zones Y

_{n}, n=2, 3, . . . m are calculated, successively upward, by means of minimization

**S**( Y n ) = i F ( Y n , t i ) 2 min ( 12 ) ##EQU00016##

**where**

**Y n**= Q n Q 1 + Q 2 + + Q n , ##EQU00017##

**Q**

_{n}(n=2, 3, . . . m) are production rates of perforation zones

**F**( Y n , t ) = Y n - T n - 1 , a ( t ) - T n , a ( t ) T n - 1 , a ( t ) - T 1 a [ a n t ] ( 13 ) a n = q n q 1 = h 1 h n Y n ( 1 - Y 2 ) ( 1 - Y 3 ) ( 1 - Y n ) , ( 14 ) ##EQU00018##

**h**

_{n}(n=1, 2, . . . m) is a thickness of a n perforation zone, T

_{n,a}(t) is the fluid temperature measured in the wellbore above the n perforation zone, t

_{i}is time moments equally distributed within interval t

_{1}<t<t

_{2}, t

_{1}is the end time of the initial production stage characterized by strong impact of the volume of the wellbore and quick fluid temperature changes in the wellbore, t

_{2}is a time when the bottom-hole zone cooling effect on the temperature measurements becomes insignificant (of the same order that Joule-Thomson and geotherm effects); besides, a number of time moments in this interval is equal to a number of temperature measurements.

**[0060]**Production rates (n=2, 3, . . . m) of perforation zones are determined by formulas:

**Q**1 = Q 1 + Y 2 1 - Y 2 + Y 3 ( 1 - Y 2 ) ( 1 - Y 3 ) + + Y m ( 1 - Y 2 ) ( 1 - Y 3 ) ( 1 - Y m ) Q 2 = Q 1 Y 2 1 - Y 2 Q 3 = Q 1 Y 3 ( 1 - Y 2 ) ( 1 - Y 3 ) Q n = Q 1 Y n ( 1 - Y 2 ) ( 1 - Y 3 ) ( 1 - Y n ) ( 15 ) ##EQU00019##

**where Q is a total volumetric well production rate**.

**[0061]**Production rates of individual productive layers determined by means of formulas (12)-(15) can be considered as an approximate solution of the problem. In some instances, when the above conditions of the analytical model applicability are violated, an error in determination of individual production rates can reach 10-20% and more (see below).

**[0062]**A possibility to determine the inflow profile using the proposed method was demonstrated based on synthetic test cases that were generated by means of the transient numerical model of associated processes of heat and mass transfer in the layers and the wellbore. The model functionality enables simulate arbitrary alternation of various processes: well circulation, shut-in, production, and fluid injection. The wellbore numerical model was tested for many years on analytical solutions, using commercial simulators (COMSOL® and ECLIPSE®) and was successfully applied for simulation and interpretation of complicated field cases.

**[0063]**For verification of the proposed method to determine production rates of individual productive layers by means of the numerical model, the following sequence of technological operations in the wellbore was simulated:

**1. Well circulation for 24 hours. The wellbore circulating fluid temperature at a depth is assumed 100° C., undisturbed rock temperature is 123° C. 2. Shut-in for 24 hours. This stage is not obligatory for using the proposed method but as a rule there is a certain time interval between the well circulation and perforation. 3. Wellbore perforation and oil production for 24 hours with a total production rate of 100 m**

^{3}/day.

**[0064]**Thickness of perforation zones is h

_{1}=h

_{2}=10 m, distance between these zones is 10 m.

**[0065]**Two cases of formation permeability values were considered (skin factor was taken equal to zero):

**k**

_{1}=100 mD,k

_{2}=30 mD(Y≈0.25) (1)

**k**

_{1}=30 mD,k

_{2}=100 mD(Y≈0.75). (2)

**[0066]**In brackets are relative production rates for the upper zone in the cases under consideration.

**[0067]**FIGS. 3, 4 show calculated temperatures T

_{1},a, T

_{2},b, T

_{2},a, and T

_{in},2 for these options. Temperature T

_{1},a is equal to a flow temperature in the point which is 1 m above the upper boundary of the perforation zone, T

_{2},b-1 m below the lower boundary of the perforation zone. It is seen that in this case a difference between the temperatures T

_{1},a and T

_{2},b is very low since the well production rate is rather high, the layers are close to each other, and fluid energy losses to the surrounding rock are insignificant. This means that in this case, there is no need in a temperature sensor below the upper formation (T

_{2},b), and formula (11) can be used for function F (Y

_{2},t).

**[0068]**Calculations show that in all cases, mis-tie S (Y

_{2}) (11) can be calculated for a time interval of 3 to 7 hours. FIG. 5 shows that in case No. 1, mis-tie S (Y

_{2}) has a single minimum at Y

_{2}≈0.233. This value is very close to the accurate solution Y

_{2}=0.25 (error ˜7%). In case No. 2 (FIG. 6) mis-tie S (Y

_{2}) also has a single minimum at Y

_{2}min=0.68 (error ˜9%).

**[0069]**FIGS. 7, 8 show that the proposed method to determine the inflow profile is resistant to random errors of wellbore temperature measurements. Solution of inverse tasks by using noisy temperature data (with a standard deviation of 0.1 K) produces practically the same result as with using the initial data.

**[0070]**In some cases, accuracy of the proposed method to determine the inflow profile based on temperature data can be insufficient. It can be connected with violation of conditions that were used to derive calculation formulas. For example, with long distances between layers, initial radial distributions of temperature in the layers will be different, geothermal gradient will have a significant impact; with high pressure differentials between a layer and the wellbore, Joule-Thomson effect may not be neglected; with low-value times of observations, wellbore volume impact may not be neglected, etc.

**[0071]**In these cases, to improve accuracy of the inflow profile determination, it is possible, for solution of the inverse task, to use numerical simulation and to select such parameters of the numerical model, which would ensure agreement of measured and calculated time-temperature dependencies. However, the wellbore measured pressure not used above, can be used as a boundary condition for simulation of pressure and temperature fields in pay zones.

**[0072]**FIGS. 9, 10 illustrate application of this method to determine the inflow profile. For the above two synthetic cases, permeability values of two productive layers were selected automatically, to ensure coincidence of measured and calculated temperatures. Permeability values acquired while applying the simplified model were used as initial approximations. Based on FIG. 9, 10, it is seen that practically full agreement of temperatures was obtained after about 150 solutions of the direct task. Obtained values of permeability and flow rates actually match the target ones:

**k**

_{1}=96 mD,k

_{2}=29 mD(Y

_{2}≈0.23). (1)

**Target values**: k

_{1}=100 mD, k

_{2}=30 mD (Y

_{2}=0.25)

**k**

_{1}=29 mD,k

_{2}=96 mD(Y

_{2}≈0.75). (2)

**Target values**: k

_{1}=30 mD, k

_{2}=100 mD (Y

_{2}=0.75)

**[0073]**In this case, two parameters of permeability values were selected while solving the inverse task. Numerical experiments show that a single-value solution of the inverse task can be obtained with an increased number of selected parameters to 6 and more. In particular, along with permeability of individual formations, their skin factors can also be determined.

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