GB2590280A - Method for determining the flow profile and hydrodynamic parameters of reservoirs - Google Patents

Abstract

A method for determining the flow profile of a producing well and the hydrodynamic parameters of individual formations is used in geophysical surveys of producing wells and includes measuring the temperature Тf (1) and the bottomhole pressure рb (1) across the bore of a well in a quasisteady state, changing the flow rate to a given value, and remeasuring the temperature Тf (2) and the bottomhole pressure рb (2) across the bore of the well. Next, the formation pressure p1 ex and the productivity K1 are calculated, and the flow rate V1 of each lth formation is determined for each operating regime of the well by solving a system of algebraic equations (formula (I)), where εf1 is the effective Joule-Thomson coefficient, T1 ex is the average geothermal temperature according to the thickness of the formation, T ∨ f1 is the temperature of the flow at the lower boundary of the 1th formation, T ∧ f1 is the resulting temperature of the flow at the upper boundary of the 1th formation, С1 is the relationship of the volumetric heat capacity of the flow above the upper boundary of the 1th formation and the heat capacity of the incoming flow from said formation, Tci is the average temperature of the egress of fluid from the 1th formation, and Qi1 is the total flow rate of the 1th and all of the lower formations. The invention improves the accuracy and reliability of calculating the flow profile in a well.

Description

METHOD for DETERMINING THE FLOW PROFILE AND HYDRODYNAMIC PARAMETERS OF RESERVOIRS Scope The invention relates to oil and gas production industry and can be used in production well logging to determine flow (production) profile in terms of hydrodynamic performance of individual layers (their production rates and formation pressures) in multilayer reservoirs, and estimate the rate of additional inflow from the uninvestigated (inaccessible) lower target zone or from below the bottomhole as part of the known total well production rate.

Background art

There are known methods of determining flow profile and near-wellbore characteristics of a multilayer reservoir, RU2455482 C2, W02011081552 Al, US8701762B2 and some others, in which, after a well has been producing at a constant rate for a long time, its rate is changed, with bottomhole pressure being measured both before and after the rate change, and well fluid temperature variations in time at the top and bottom of the producing formations boundaries are recorded. Besides, a similar method of fluid flow profile determination in a multilayer reservoir by measuring several temperature profiles in the wellbore at different production rates with subsequent data interpretation assisted by computer simulations is proposed in W02010036599A2.

In all those methods, however, logging data are processed using simplified models of heat-and mass-transfer in reservoir pay zones without taking into account the thermal conductivity effects in the near-wellbore zone (See E.B. Chekalyuk, Oil Reservoir Thermodynamics, Nedra, M, 1965, pp. 63-68), and the temperature field formation process is either reduced to convective transfer of temperature variations due to the Joule-Thomson effect from the well drainage area to the bottomhole, or reservoir temperature perturbations are assumed to be inherently stationary. Such approximations are only acceptable in case of high specific fluid flow rates and extremely long well operation periods at each production rate.

Besides, the methods disclosed in RU2455482 C2 and W02010036599A2 use the formulas that describe stationary hydrodynamic processes under the approximation of the short-time pressure stabilization, while as a rule after switching the well to a new operating regime, the reservoir and near-wellbore zone pressures and wellbore flows normally stabilise within several hours or even days, and they cannot be considered as steady. Further on, if the far-field pressures of the reservoir units (at their external boundaries) are different, any changes in the bottomhole pressure or well production rates will inevitably result in redistribution of the fluid outflows and production rates from the reservoir units not taken into account by the known logging-data processing methods and models in use.

Estimation of the reservoir skin factor based on the method described in RU2455482 C2 does not seem to be realistic because it implicitly introduces the perturbed near-wellbore zone radius which is unknown a priori and cannot be determined by means of logging surveys. Furthermore, the specific rate of fluid flow towards the well also depends on the perturbed nearwellbore radius (in proportion to its square) and these two characteristics cannot be inferred simultaneously. The RU2455482 C2 method cannot be used even in the simplest case of an unperturbed near-wellbore zone with the zero skin factor.

Besides, the methods of logging data processing disclosed in RU2455482 C2 and W02010036599A2 are not generally applicable on the long-term scales because they do not take into account the effects of heat exchange with the reservoir top and bottom, which considerably affects the outflow fluid temperature, especially from thin reservoir units (less than 10 m thick).

In the method disclosed in W02011081552 Al the well production profile is determined by direct measurement of the sandface fluid temperature at the well bottom in transient flow conditions. However, in addition to the above-mentioned drawbacks, this method, being similar to the technique of the flow profile determination described in G.A Cheremensky's monograph (G.A. Cheremensky, The Applied Geothermics, L. Nedra, 1977, pp. 181-183), is based on the fact that the reservoir pressure or the drawdown, i.e. the difference between reservoir pressure and measured bottomhole pressure, are the known values.

A substantial drawback that is common for the considered that the flow profile is determined without concurrent estimation of the far-field reservoir-unit pressures (at the external reservoir boundaries) and possible variations of these important characteristics during the reservoir development are not taken into account.

Moreover, all these methods are based on the simplification assuming that Joule-Thomson coefficients are constant and identical in all reservoirs. At the same time, as shown by computational experiments in G.G. Kushtanova's monograph (G.G. Kushtanova Temperature Monitoring During Oil and Gas Field Development, Novoye Znaniye, 2003, pp. 63-65 and Figs. 2-14), the so-called effective 'non-stationary' Joule-Thomson coefficients that crucially depend on reservoir permeability and operating conditions should be used for correct interpretation of the logging data.

Disclosure of the invention

The objective to be attained by using the proposed method is to create a universal and unified approach to conducting geophysical logging surveys in producers and developing a generalised methodology for temperature data interpretation with the use of the effective 'non-stationary' Joule-Thomson coefficients depending on specific total flow rates and hydrodynamic characteristics of the reservoir units and durations of the well production regimes under consideration.

The technical result of the invention is a substantial expansion of the permissible conditions and enhanced accuracy and reliability of the inferred flow (production) profile in a well through determination of hydrodynamic characteristics of individual units (their productivities and formation pressures) in a multilayer reservoir.

Another technical result to be achieved by using the proposed invention is a more rigorous logging procedure and a more reliable logging data interpretation technique.

The claimed technical result is achieved due to the fact that the method of determining the producer's flow profile and hydrodynamic characteristics of the reservoir units includes temperature Tfil) and bottomhole pressure pb(1) measurements in the wellbore after the well has been producing for a long time at a known constant rate in a quasi-stationary regime; after this the rate is changed by a predetermined value for a period sufficient for the new quasi-stationary flow regime to set in, and then the wellbore temperature Ti(2) and bottomhole pressure pb(2) measurements are repeated. Whenever necessary and practicable, additional wellbore temperature and bottomhole pressure logging can be performed at different flow rates, and then reservoir pressure pcx and productivity IC are determined together with the flow rates Vi calculated for each layer / (1=1, 2,...L, where L is top layer number) at each production regime on the basis of the bottomhole pressure and temperature measurement data, with total production rates of the well being known for all logging regimes. This is done by solving the system of algebraic equations, starting from the topmost layer L (7= L, , 2, 1) as described in detail below in the Summary of the invention section.

(7/ (Pi/ -l'fl)= K, (pf -plq)(T( -rift+ Eft (plex -Pb!)), = K, (pr -mil), where Ellis the effective (non-stationary) Joule -Thomson coefficient; Tr -the average geothermal temperature across the /-th layer; Pit -the flowing temperature at the lower boundary of the /-th layer; TAIT -the resulting flowing temperature at the top of the /-th layer; -the ratio of the volumetric heat capacity of flow above the top of the /-th layer and that of the flow entering the well from the /-th layer; Ta-the mean mixing temperature of the fluid flow from the /-th layer; 0/ -the total cumulative flow rate of the /-th layer and all the underlying layers.

The set change of the total well production rate can amount up to 25-50% of the initial rate.

The time sufficient for a new quasi-stationary regime to set in may vary from 12 hours to 2-3 days.

To calculate a temperature profile and bottomhole pressure in the wellbore, a high-precision thermo-hydrodynamic simulator can be used.

This method, in addition to identification of the flow profile across the layers covered by the logging procedure allows also estimation of the total fluid flow rate from the lower non-surveyed (inaccessible) zone of the target formation, or from below the bottomhole (hold up depth) as the difference between the known (measured) total well production rate and the cumulative amount of the fluid inflow from the surveyed reservoir interval.

Using an advanced thermo-mechanical simulator which, in addition to convective heat transfer processes, can also simulate thermal conductivity phenomena and other thermohydrodynamic effects, considerably expands the range of applicability of the proposed method and, in comparison with the known methods, increases the reliability of flow profiling and hydrodynamic characteristics determination in individual layers due to a higher accuracy of predicting apparent 'non-stationary' Joule-Thomson coefficients.

A more rigorous logging procedure due to pre-designing of the experiment and higher reliability of resulting data interpretation also relies on an extensive use of advanced high-precision thermo-mechanical simulators that are capable to iteratively calculate thermophysical properties of complex multiphase flows in the near-wellbore zone of a multilayer reservoir and in a well, additionally taking into account the heterogeneity of rocks and productive reservoir units, transient effects and other specific features of thermo-hydrodynamic processes in productive formations, including heat exchange between the well, reservoir units and surrounding rocks.

The formulas given below support the validity of the proposed method and can be used for preliminary processing of logging data.

Essence of the invention The proposed method is based on determination of hydrodynamic properties of individual reservoir units (their productivities and far-field formation pressures) in a multilayer reservoir. The total number of layers L in the proposed method is not limited.

The data processing method proposed in this invention makes it possible to determine the flow profile VI VL through the reservoir units 1 = 1, 2, ... L where measurements have been taken and estimate the total residual rate of the fluid flow from the non-surveyed lower part of the target zone or from below the bottomhole (hold up depth) of the well.

Fig. 1 shows a schematic representation of a production well. Pressure and temperature logging data and results of their interpretation are also displayed.

The general approach to determining the flow profile in a production well is based on measuring wellbore temperature Tin and bottomhole pressure ph(1) at a constant known total volume flow rate QfI) at the top of the upper layer (see Fig. 1) after the well has been operating in quasi-stationary regime for a long time so that any subsequent temperature and pressure variations during logging surveys would be negligible.

Temperature measurements are taken with high-precision downhole pressure gauges placed inside the tubing or using fibre optic devices of compatible precision installed either inside or behind tubing string, or behind casing. Bottomhole pressure is measured with downhole pressure-recording gauges or using an indirect method that ensures the required accuracy.

After that, in case of the flow profile being determined in a vertical or deviated well, the flow rate is changed by a predetermined value (25-50% of the initial rate a) (I)) to 00(2) -value for a time period sufficient for a new quasi-stationary regime to set in (approximately from 12 hours to 2-3 days) and then temperature Ti2) and pressure pb(2) measurements along the wellbore are repeated (See Fig. 1).

Additional surveys in three or more operating regimes at different flow rates will increase the statistical validity of the data. Preferentially, if possible, the total well flow rate should be changed upward, to higher values, because this reduces the stabilisation time of thermohydrodynamic processes in the near-wellbore zone and increases the reliability of logging data and their interpretation.

In case the flow profile determination in a horizontal well passing through a single formation, it is sufficient to perform only one logging survey at the quasi-stationary production regime and then estimate the overall (average) far-field reservoir pressure in the well vicinity. Repeated measurements of temperature and pressure profiles in a horizontal well at another hydrodynamic regime can additionally increase accuracy of the flow profile determination and make it possible to account for possible reservoir pressure variations along the wellbore. However, it might take several months for a horizontal well to reach the new quasi-stationary thermo-hydrodynamic regime, and this substantially limits the practical applicability of such surveys.

The above-recommended variations of the total well flow rates within 25-50% of the initial well flow regime have been deduced according to the preliminary modelling results (G.G. Kushtanova. Temperature Monitoring in Oil and Gas Field Development; Novoye Znaniye, 2003, pp. 63-65, Figs. 2-14), which are based on a reliable estimation of effective non-stationary Joule-Thomson coefficients Eft with account of the well production history, thermophysical properties of each /-th reservoir unit and changes in its production rates. Minor changes in the total production rate will produce similar temperature logs with the difference between them being commensurable with the temperature measurement error. Conversely, major changes in the total production rate may result in substantial changes in reservoir hydrodynamic properties and misinterpretation of the logging data.

Operational stability of the well completion equipment is an important and necessary condition of the measurement procedures at all stages of the logging surveys; in case of tubing string installed in the well, the well bottomhole should be open across the pay zone with unidirectional, upward fluid flow, without cross-flows inside the wellbore.

To interpret the obtained logging data, the wellbore pressure and temperature measurements are processed at known total well flow rates for all logging regimes on the basis of sequential solution of the system of equations (1) -(3) given below to recurrently estimate: reservoir pressure pix; productivity K1; and inflow rates V/ for each /-th unit (/ = L,..., 2, 1) starting from the topmost layer L in all production regimes of the well.

The proposed procedure for calculating the flow profile and hydrodynamic properties (productivities and far-field formation pressures) of individual units in a multilayer reservoir accumulates the following well-known concepts of the reservoir thermo-hydromechanics.

In a quasi-stationary regime the flow rate V/ of each rth unit with formation pressure pr is determined by its productivity ICI = K (pier -Pb!). (1) The sandface fluid temperature within the layer is not constant and varies across its thickness according to the geothermal gradient changes and also due to heat exchange of the layer with the over-and underlying rocks. The average sandface fluid temperature Ta is given by the following formula: = itT + eft (pix -phi) , (2) where eft is the effective, non-stationary Joule-Thomson coefficient of the rth matrix layer, Tr is the geothermal temperature averaged over the thickness of the rth layer assumed to be the known geological characteristic of the reservoir, Phi is the measured bottomhole pressure at the depth of the rth layer.

The thermal mixing equation for the well flow with temperature Tifi measured at the lower boundary of the rth layer with the flow rate 171 determines the resulting flowing temperature TAfl measured at the top of this layer: CI 01(711 -PO= Vi(Ta -T11), 1 -1, 2, (3) In this formula a = -...+ VI is the total cumulative flow rate of the rth layer and all the underlying layers, G is the ratio of the volumetric heat capacity of flow above the top of the rth layer and that of the flow entering the well from the rth layer.

Generally, when temperature measurements are taken using high-precision temperature gauges or fibreopfics cable inside the wellbore (not behind casing), temperature Ta of the flow coming from the layer is unknown and the heat balance equation (3) alone is insufficient to process temperature logs and estimate flow rates VI.

Substituting relationships (1) and (2) into (3), we obtain the equation with respect to two target characteristics-formation pressure picx and productivity K, for each rth layer: G 0 (r rifl) K (19 P bl)(T le - + Eft p (EY -pm)), -Li... ,2, 1. (4) Combining equations (4) for all production regimes, k = 1, 2..., in which the logging surveys have been performed, we arrive at the system of algebraic equations (not less than two for each reservoir unit) from which pr-and IC-values are found, and, hence, the flow rates i(k) are also determined (see Equation (1)) for each k-th well-operation regime (see Fig. 1).

The procedure of recurrent calculation of the searched reservoir unit characteristics is carried out sequentially, starting from the top layer at at equal to the total well flow rate = 0o) and further at a-1 = a -k, / = 2, iteratively with account of the impact rendered by the flow rate change and temperature field transition in the well vicinity on the effective (non-stationary) Joule-Thomson coefficients cif and, possibly, heat capacity ratios C,.

The calculations can be done with the use of preliminarily compiled tables or nomograms for efi and CI as functions of inflow rates of reservoir units and durations of different well production regimes, e.g. by analogy with the tables and nomograms (G.G. Kushtanova, Temperature Monitoring in Oil and Gas Field Development, Novoye Znaniye, 2003, pp. 58-61, Tables 2.1-2.4, and Figs. 2-14).

A more effective approach to logging data processing on the basis of equations (1) -(4) could be the use of high-precision thermo-hydrodynamic simulators, e.g. commercial simulator TERMOSIM developed by TGT Oilfield Services, which can considerably expand the applicability scope of the proposed method and provide more accurate interpretation results by means of iterative calculations of the effective (non-stationary) Joule-Thomson coefficients and thermophysical properties of complex multiphase flows in the bottomhole zone of a multilayer reservoir and ensure a better fit of computer simulations to the logging data (measured temperature and pressure profiles).

An example of implementation of the above-described algorithm is shown in Fig. 1.

In the case under discussion the oil-producing well is targeting three reservoir units with different hydrodynamic properties and different far-field reservoir pressures. Relative heat capacities in case of homogeneous fluid are CI = 1. The thermo-hydrodynamic simulator was used to predict wellbore pressure and temperature profiles in two well-operation regimes. In the first regime, the well was flowing for three months at the total rate of 00(1) = 200 ms/day in reservoir conditions. The pressure and temperature logs are shown by blue curves. In the second test regime, the well was flowing for three days at the total rate 00(2) = 300 ms/day. Pressure and temperature logs are shown by pink curves.

The calculation of the reservoir unit characteristics and flow profile starts from the top third layer. The two coupled equations (4) are formulated at the known geothermal temperature of the unit 73ex = 88.81°C for two flow rates 03(1) = 200 m3/day and 03(2) = 300 m3/day (coinciding with the total well flow rates 000) and Q0(2)), corresponding to the measured bottomhole pressures pb3(1) = 23.73 MPa and pb3(2) = 20.95 MPa, and flowing temperatures at the unit bottom r(1)fi = 89.99°C, r(2)/3 = 90.35°C and at the unit top r(1)"3 = 90.35°C, r(2) = 90.73°C (See Fig. 1).

Equations (4) are solved iteratively with respect tom and K3, in combination with the inflow rates predictions according to relationship (1) and estimation of effective non-stationary Joule-Thomson coefficients, using nomograms or the simulator.

In the course of iterations, the effective non-stationary Joule-Thomson coefficients of the upper unit for each of the two well-operation regimes take the following different values: = 0.225°C/MPa, 6/3(2) = 0.210°C/MPa.

After excluding productivity IC3 from the two equations (4) written at the above-specified parameters, we arrive at a quadratic equation with respect to the far-field reservoir pressure p3ex in unit 3. In the case under consideration, only one of the two roots, i.e. p3ex = 31.61 MPa, has physical meaning because it is the only one that delivers a nonnegative value of the productivity, K3 = 15.42 m3/(MPa.day).

The respective flow rates of top layer estimated for the two logging regimes according to formula (1) are: 173(1) = 122 m3/day, LT3 (2) = 164 m3/day, and the flow profiles are shown in Fig. 1.

At the next step of logging data interpretation, the characteristics of the middle unit 2 are determined.

The total flow rates at the top of the 2-d layer are 02(1) = 03(1) -I73(1) = 78 m3/day and 02(2) = 3(2) -V3(2) = 136 m3/day in the first and second production regimes. Similar to the top layer, the two coupled equations (4) for unit 2 are formulated at the known geothermal temperature 72ex = 89.08°C for measured bottomhole pressures pb2(I) =23.89 MPa and pb2(2) = 21.12 MPa, and respective flowing temperatures P(1) = 89.99°C, T1(2)/2 = 90.29°C at the bottom and P(I)/2 = 90.02°C, r(2)/2. = 90.39°C at the top of the layer (see Fig. 1).

Equations (4) are solved iteratively with respect to p2' and K2 in combination with the inflow rates predictions according to relationship (1) and estimation of effective non-stationary Joule-Thomson coefficients, using nomograms or the simulator to finally deduce the following values: ej2(1) = 0.183°C/M Pa, ef2(2) = 0.167°C/M Pa, = 29.57 MPa, K2 = 6.75 NOW Pa-day), and obtain the flow rates: I/2") = 39 m3/day, V2 (2) = 58 m3/day, and the flow profile shown in Fig 1.

Evidently, the flow rates from the bottom unit 1 (see Fig. 1) follow directly from the mass-balance condition: 7/i(1) = Qo(1) -773(1) -V2(1) = 39 m3/day, I71(2) = Qo(2) -773(2) -V2(2) = 78 m3/day.

Additional calculations can be also used for estimation of the effective non-stationary Joule-Thomson coefficients for the bottom layer: efi (1) = 0.174°C/MPa, (2) _ n Efi -u.162 C/MPa together with the reservoir unit pressure and productivity: piex = 27.31 MPa, K1 = 12.55 m3/(MPa-day), In conclusion of the above analysis it should be emphasised that the calculated effective non-stationary Joule-Thomson coefficients for all three layers are essentially (more than two or three times) different from the marginal theoretical (thermodynamic) estimate of 0.545 °C/MPa, when the effects of thermal conductivity and convective heat transfer in the reservoir units are not taken into account.

In the course of the above-described stages of the proposed method, the following possible particular cases of its implementation should be additionally taken into consideration: -With reservoir unit pressures or productivities being known (or measured by other methods) for all units of a mulfilayer reservoir, it would be sufficient to perform the logging survey only at one quasi-stationary production regime and then estimate the unknown characteristics (reservoir-unit productivities or pressures); -In a horizontal well passing through a single reservoir formation it would be sufficient, as pointed out above, to perform only one logging survey at the quasi-stationary production regime and then estimate the overall (average) far-field reservoir pressure in the well vicinity.

Claims (4)

1. CLAIMS1. A method of determining production well flow profiles and hydrodynamic performance of reservoir pay zones, wherein: with reservoir pressures pfx or productivities K1 of all the reservoir units in the bottomhole being known, temperature Tin and bottomhole pressure ph(1) along the wellbore are measured after the well has been producing for a long time at a known constant rate at least in one quasi-stationary regime, then estimate unknown values of productivity K1 or reservoir pressure pier and determine the total flow rate VI of each /-th reservoir unit, or with reservoir pressures pr and productivities IC of all or part of the multilayer reservoir units in the well being unknown, temperature Tin and bottomhole pressure p1(1) along the wellbore are measured after the well has been producing for a long time in two quasi -stationary regimes at known and different total well flow rates, then estimate unknown values productivity IC and reservoir pressure pier and determine the total flow rate Tri of each /-th reservoir unit; whenever necessary and practicable, temperature and bottomhole pressure measurements along the wellbore are taken in more than two different quasi -stationary regimes at known and different total well flow rates, then estimate unknown values productivity IC and reservoir pressure pfx and determine the total flow rate Vi of each /-th reservoir unit; the reservoir unit pressures pier and productivities IC are deduced and total flow rates V/ are determined for each /-th unit (1=1, 2,...L, where L is top layer) in each production regime on the basis of the bottomhole pressure ph and temperature Tic measurement data, with total rates of the well in all logging regimes being known, by solving the system of algebraic equations (1) -(2), starting from the topmost layer L (1= L, ..., 2, 1).CIQI(ryi -rift) -K7 (plet -mil)(Tlex rill ± Eft (1) let -mil)), VI= KI(piex Pb!), 1 = L,. ., 2, 1 where Ell is the effective (non-stationary) Joule -Thomson coefficient; Tex the average geothermal temperature across the tth layer; rfl -the flowing temperature at the lower boundary of the /-th layer; rfl -the resulting flowing temperature at the top of the /-th layer; -the ratio of the volumetric heat capacity of flow above the top of the /-th layer and that of the flow entering the well from the /-th layer; T,-the mean mixing temperature of the fluid flow from the /-th layer; 0/ -the total cumulative flow rate of the /-th layer and all the underlying layers. phi-the measured bottomhole pressure at the depth of the layer!; -the top layer number.
2. 2. The method according to Claim 2, wherein the set value of the total well production rate variation is 25-50% of the initial rate.
3. 3. The method according to Claim 2, wherein the time sufficient to reach the new quasi-stationary regime ranges from 12 hours to 2-3 days.
4. 4. The method according to Claim 1, wherein a high-precision thermo-hydrodynamic simulator is additionally used to predict the temperature and bottomhole pressure profiles along the wellbore.