US20160061025A1

US20160061025A1 - Method for determining downhole pressure

Info

Publication number: US20160061025A1
Application number: US14/804,681
Authority: US
Inventors: Maria Viktorovna Sidorova; Vyacheslav Pavlovich Pimenov; Bertrand Theuveny; Valery Vasilievich Shako
Original assignee: Schlumberger Technology Corp
Current assignee: Schlumberger Technology Corp
Priority date: 2014-08-28
Filing date: 2015-07-21
Publication date: 2016-03-03
Also published as: RU2569522C1

Abstract

A pressure in a wellbore and a temperature at least at one point of the wellbore are measured during wellbore testing. Transient profiles of temperature along the wellbore are determined and changes in a density of a downhole fluid and in a length of atubing when the wellbore is shut in are calculated. The pressure measurement results are corrected on the basis of the calculated changes in the density of the downhole fluid and in the length of the tubing.

Description

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to Russian Application No. 2014135163 filed Aug. 28, 2014, which is incorporated herein by reference in its entirety.

BACKGROUND

The disclosure relates to the field of studying oil and gas wells and is designed to correct results of pressure measurements in high-rate wells, performed during well tests.
At present, significant improvement in the accuracy and reliability of pressure sensors takes place. The pressure sensors have a resolution better than 0.01 psi and an absolute measurement accuracy of the order of 1 psi. This is especially significant in study of high-productive formations when rapid increase in a pressure is followed by very slow increase in the pressure for a long time. In this case, temperature variations which occur during a well test can change even the nature of pressure variation during the second—slow—stage: the pressure can decrease and not increase in a shut-in well.
Investigation of oil/gas formation properties by analyzing dynamics of pressure variation in a well at a change in the productivity of the well (including said change when the well is shut in) is called as Pressure Transient Analysis (PTA). The traditional techniques for processing data obtained in the PTA do not take into account a possible influence of non-isothermal effects and assume that a pressure sensor is at a fixed distance (50 to 100 m) from an upper boundary of a formation to be studied. Modern techniques for processing the PTA data (cf., Kuchuk F. J., Onur M., Hollaender F. Monograph series: Vol. 57. Pressure Transient Formation and Well Testing (1st ed.). ELSEVIER, 2010, pp. xv-xx, 23-26) comprise stimulating an inflow of a fluid from a formation, taking a sample and registering a flow rate and a pressure, preferably a bottom hole pressure. The PTA data is currently interpreted using analytical solutions of the piezoconductivity equation at various well completion schemes and various boundary conditions. The developed analytical techniques are applicable to fractured, layered, horizontally and radially composite formations. Numerical simulation techniques are used for even more complicated heterogeneous systems and multiphase flows. In the majority of cases, however, all analytical and numerical methods assume the flow of a fluid under isothermal conditions. With this, reduction in a pressure, as logged in some high-rate wells, shows that the traditional isothermal techniques for interpretation of measurement results are not applicable in such wells.

SUMMARY

The technical result provided by the invention is an enhanced accuracy of downhole pressure measurement due to taking non-isothermal effects into account.
In accordance with the method, a pressure in a wellbore and a temperature at least at one point of the wellbore are measured during wellbore testing. Then, transient profiles of temperature along the wellbore are determined during the wellbore testing and changes in a density of a downhole fluid and in a length of a tubing when the wellbore is shut in are calculated. The pressure measurement results are corrected on the basis of the calculated changes in the density of the downhole fluid and in the length of the tubing.
The transient profiles of the temperature along the wellbore are determined by measuring the temperature along the wellbore using a system of sensors distributed on the wellbore at different depths or by numerical or analytical simulating the temperature profile. If necessary, the continuous transient profiles of the temperature can be obtained by interpolating the measured temperatures.
The pressure is measured using at least one sensor disposed at a fixed depth within the wellbore.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure is illustrated by the drawings wherein:

FIG. 1 shows a comparison of the bottom hole pressure recovery dynamics during the wellbore shut-in under isothermal and non-isothermal conditions;

FIG. 2 shows simulated downhole temperatures at a depth of a sensor and at a surface during the wellbore testing;

FIG. 3 shown a simulated downhole pressure at the depth of a sensor and at the surface during the wellbore testing;

FIG. 4 shows non-stationary profiles of the temperature along the wellbore for a wellbore shut-in mode used for processing the PTA results;

FIG. 5 a shows change in an average temperature of a downhole fluid between a tubing anchorage point and a pressure sensor;

FIG. 5 b shows a density of the downhole fluid between the sensor and an upper boundary of a reservoir;

FIG. 5 c shows variation in a tubing length (the right graph) in time when the wellbore is shut in;

FIG. 6 shows a comparison of the bottom hole pressure recovery dynamics in an oil formation after production without and with taking non-isothermal effects into account.

DETAILED DESCRIPTION

A wellbore testing is divided into two periods: an inflow period and a pressure recovery period. In the first period, the wellbore is opened to operate at a constant or variable flow rate, wherein a downhole pressure drops. For a time depending upon targets of the wellbore testing, formation properties, a bottom-hole zone state, reservoir fluid properties, and a pressure draw-down, the wellbore is shut in, and the pressure is recovered up to its original value.
Pressure and temperature sensors are usually placed on a tubing approximately at a distance L₀=100 M above an upper boundary of a reservoir. Since a temperature of a fluid to be produced is essentially higher than an average temperature of overlying rocks, heating of rocks near the wellbore takes place. After shutting the wellbore in, a temperature in the vicinity of the borehole decreases, a fluid filling the wellbore is cooled down to a geothermal temperature, and an average temperature of said fluid decreases. Calculations show that the average temperature of the downhole fluid can decrease down to 30-40° C. in case of deep wells (4,000-6,000 m).
This circumstance can result in effects as follows:
1) a density of the fluid filling the wellbore in an interval between the pressure sensor and the reservoir increases;
2) a length of the tubing (anchored at the surface) changes and a position of the sensor relative to the reservoir changes.
Both said effects leads to reduction in measured pressure.
A pressure change related to a downhole temperature change can be calculated by the formula (1):
ΔP(t)=g·[ ρ (t)·(L ₀ +ΔL(t))− ρ(0)·L ₀], (1)
r
e ΔP(t) is a pressure change, Pa; ρ(t) is a downhole fluid density below the pressure sensor, kg/m³; ρ(0) is an average downhole fluid density below the pressure sensor immediately after shutting the well in, kg/m³; L₀is an initial position of the pressure sensor immediately after shutting the wellbore in, m; ΔL(t) is a change in a tubing length (from a surface anchorage point to the sensor) in the shut-in well, m; g is a gravity acceleration, m/s².
An increase of the fluid density below the pressure sensor is determined by a volumetric thermal expansion coefficient of the fluid, α_f, K⁻¹, and by a change in the average temperature of the fluid below the sensor in the shut-in well, ΔT(t), K:
ρ(t)= ρ(0)·(1−α_f ·ΔT(t)). (2)
A decrease in the tubing length, ΔL(t), and respective change in the sensor position is determined by a linear thermal expansion coefficient of the tubing, α_t, K⁻¹, and by a variation in a temperature profile through a depth (from an surface anchorage point to the sensor) in the shut-in well, m; g is a gravity acceleration, m/s². To determine the value ΔL(t), it is proposed to divide a distance between the tubing anchorage point and the pressure sensor into n equal sections and calculate a reduction in the tubing length by the formula (3):
$\begin{matrix} Δ L (t) = L_{0} \cdot α_{t} \cdot \frac{1}{n} \sum_{i = 1}^{n} (T_{oi} - T_{i} (t)), & (3) \end{matrix}$
r
e T_i(t) is a temperature of i^thsection at a time
t (i=1, . . . n) in the shut-in well,
; T_oia temperature of i^thsection immediately after shutting the wellbore in,
.
For quantitative estimations of both effects, it is necessary to know a dependency of the downhole fluid temperature upon the depth at different times after shutting the wellbore in. Transient (non-stationary) profiles of the downhole temperature should be measured during the wellbore testing or obtained as a result of the numerical or analytical simulation.
We propose to calculate a corrected downhole pressure value (from which the influence of the fluid density and tubing length variation is excluded) by a formula (4):
P _g _— _r(t)=P _g(t)+ΔP(t), (4)
where P_g(t) is a measured pressure, Pa, ΔP(t) is a correction taking an influence of temperature effects into account and being calculated by the formulae (1)-(3).
In case of high-productive formations, a pressure in a shut-in well rapidly increases up to short of an initial pressure. Hereupon, there is a long and slow increase in the pressure, and the temperature effects considered above can have an essential influence upon the dynamics of said increase. In some cases, the measured pressure can decrease in time.
FIG. 1 shows a comparison of the bottom hole pressure recovery dynamics during the wellbore shut-in under isothermal and non-isothermal conditions. The pressure recovery dynamics in an oil formation after production of oil at a flow rate of 2,000 m³/day for 20 hours is illustrated by a dashed line (Isothermal). This dependency was obtained by the Saphir module in the program Ecrin v4.30 using the option “Test Design” for a uniform formation having a length of 100 m, a permeability of 2 d at a well skin of 5 and an outer formation radius of 1,500 M. It was supposed that the temperature is constant in the formation and in the well.
A solid line (Non-isothermal) shows calculation results for the same wellbore testing but with taking the non-isothermal effects into account. It was supposed that the pressure sensor is on the tubing at a depth of 100 m above the upper boundary of the reservoir. According to the calculation, an average temperature of a fluid filling the tubing has been decreased by 37° C. during the pressure recovery, while a density of a fluid in the wellbore has been increased by 10 kg/m³.
The decrease in the average temperature of the downhole fluid in the shut-in wellbore in the present case is 37° C. The processing of the pressure curve (Non-isothermal) resulted from measurement by standard isothermal techniques in the shut-in wellbore at such a pressure change gives an incorrect formation model, its permeability and a well skin factor.
Thus, to exclude the influence of the thermal effects, it is necessary to correct the results of measuring the downhole pressure.
The possibility to correct the measured pressure using the method of the disclosure is shown by synthetic examples prepared using the numerical simulator T-Mix (Ramazanov, A. Sh., et al. Termogidravlicheskie issledovania v skvazhine dlya opredelenia parametrov priskvazhinnoi zony plasta i debitov mnogoplastovoi sistemy” (Thermohydrodynamic Studies In Well For Determining Parameters Of Formation Nearfield and Multilayered System Flow Rates), 2010, SPE 136256). It is a code allowing simulation of transient pressure and temperature distributions when a single-phase fluid flows in a formation and in a wellbore, said code being able to reproduce an arbitrary sequence of production operations in the wellbore: the production beginning, the flow rate variation, the wellbore shutting in, etc.
The transient pressure distribution in the formation is simulated using the Darcy filtration law for a cylindrical gas flow or a poorly-compressible liquid in a layered medium. The downhole pressure is calculated using the quasi-stationary law of conservation of momentum with taking into account a friction force, a gravity force, an acceleration, and an effect of a wellbore filled with a compressible fluid.
The transient formation temperature field is calculated taking into account the conductive and convective heat transfer, the adiabatic effect, and the Joule-Thomson effect. The transient thermal model of the wellbore takes into account the fluid mixing effect, the heat exchange between the well and surrounding rocks as well as the adiabatic effect and the fluid heating due to viscous friction forces.
According to the method described above, a transient temperature distribution along the wellbore is measured or simulated; adequacy of the simulation is controlled by matching of simulated transient pressure, temperature and flow rate with available measurement results of said quantities for the whole testing duration.
The temperature, the pressure, and the flow rate were calculated for values of parameters of the wellbore, the reservoir and the sequence of operations described above, using the numerical simulator T-Mix.
The simulation had the following parameters:
properties of the reservoir: homogeneous, the reservoir thickness—100 m; the initial reservoir pressure at the outer boundary of the radius of 1500 m was fixed to be 7,251.89 psi; the reservoir permeability—2 d; the temperature—120° C.; the well skin—5; the wellbore depth—4,000 m;
properties of the fluid: oil having the density of 800 kg/m³under formation conditions, thermal conductivity of 0.14 W/m/K, specific heat capacity of 2000 J/kg/K, viscosity of 1 cP, compressibility of 6.9×10⁻⁶psi⁻¹.
The sequence of production operations in the wellbore is as follows: circulation for 70 hrs; shut-in for 70 hrs; production at the flow rate of 2,000 M³per day for 20 hrs (70 to 90 hrs, FIG. 2, 3); shut-in for 30 hrs (90 to 120 hrs, FIG. 2, 3).
FIG. 2 shows the results of simulating the fluid temperature at the upper formation boundary (TOR), at the sensor depth (100 m above the formation) and at the surface. FIG. 3 shows the results of calculating the downhole pressure at the sensor depth (100 m above the formation). The calculation was carried out using the numerical simulator T-Mix through the wellbore testing time.
The second step is to obtain the transient downhole temperature profiles when the wellbore is shut in, said profiled being derived from numerical calculations using a model having input parameters that give the best match with available measurements. FIG. 4 shows the results of simulating the non-stationary temperature profiles along the wellbore for the wellbore shut-in mode used to process the GDS results (90 to 120 hrs).
The resulted transient (non-stationary) temperature profiles are used to calculate change in the downhole fluid density and the tubing length when the wellbore is shut in. The distance between the tubing anchorage point and the pressure sensor was divided into 78 equal sections. The average downhole fluid temperature change in time,
$Δ T_{t} = \frac{1}{n} \sum_{i = 1}^{n} (T_{oi} - T_{i} (t)),$
between the tubing anchorage point and the pressure sensor, the downhole fluid density variation between the sensor and the upper boundary of the reservoir, and the tubing length reduction in the shut-in wellbore were calculated by the formulae (2)
(3). The results of simulating the wellbore shut-in mode for 90 to 120 hr are shown in FIGS. 5 a, 5 b, and 5 c. The reduction in the average temperature of downhole fluid in the shut-in well was 37° C. in this case. The downhole fluid density between the pressure sensor and the formation has decreased by 10 kg/m³for the value α_f=1.5·10⁻³K⁻¹of the volumetric thermal expansion coefficient of the fluid. At the same time, the tubing length has reduced by 1.7 m for the value α_t=12·10⁻⁶K⁻¹of the linear thermal expansion coefficient of the tubing.
The final step is correction of the downhole pressure measurement results by the formula (4) taking into account the obtained results with respect to the downhole fluid density and the tubing length in order to exclude the influence of non-isothermal effects. FIG. 6 shows the pressure recovery dynamics in the oil formation after production, said dynamics corresponding to readings of the sensor arranged at 100 m above then upper formation boundary (the solid curve), and the calculation results for the same well study but with taking the influence of non-isothermal effects (the dashed curve).

Claims

1. A method for determining a downhole pressure, comprising:

measuring the pressure in the wellbore during the wellbore testing;

measuring a temperature at least at one point of the wellbore during the wellbore testing;

determining transient profiles of the temperature along the wellbore during the wellbore testing;

calculating changes in a density of a downhole fluid and in a length of a tubing when the wellbore is shut in; and

correcting the pressure measurement results on the basis of the calculated changes in the density of the downhole fluid and in the length of the tubing.

2. The method of claim 1, wherein the transient profiles of the temperature along the wellbore are determined by measuring the temperature along the wellbore using a system of sensors distributed on the wellbore at different depths.

3. The method of claim 2, wherein the transient profiles of the temperature along the wellbore are obtained by interpolating the measured temperatures.

4. The method of claim 1, wherein the transient profiles of the temperature along the wellbore are determined by numerical or analytical simulating the temperature profile.

5. The method of claim 1, wherein the pressure is measured by at least one sensor disposed at a fixed depth within the wellbore.