Estimating Reservoir Properties from Falloff Tests Conducted with Thermally-Sensitive Injection Fluids

This disclosure relates generally to exploration seismology and, more specifically, to reservoir characterization through injection-falloff well test interpretation.

Reservoir characterization enables realization of rock and fluid properties of the subsurface. It provides an understanding of the subsurface, which is used in developing, monitoring, and managing reservoirs and optimizing production from the reservoirs. Of great significance to reservoir characterization is well testing because of its access to an extended volume of the reservoir and detection of the dynamic properties of the flow system. Conventional well test interpretation, however, inherently assumes a wellhead temperature at or near standard condition. As a result, naive pressure transient analysis of injection-falloff tests conducted with a thermally-sensitive injection fluid may yield misleading results.

The following detailed description describes methods and systems for estimating reservoir properties from falloff tests conducted with thermally sensitive injection fluids. Various modifications, alterations, and permutations of the disclosed implementations can be made and will be readily apparent to those of ordinary skill in the art. Further, the general principles defined may be applied to other implementations and applications, without departing from the scope of the disclosure. In some instances, details unnecessary to obtain an understanding of the described subject matter may be omitted so as to not obscure one or more described implementations with unnecessary detail since such details are within the skill of one of ordinary skill in the art. The present disclosure is not intended to be limited to the described or illustrated implementations. Furthermore, the present disclosure is to be accorded the widest scope consistent with the described principles and features.

Pressure transient analysis (PTA) refers to the analysis of pressure changes over time, such as pressure changes associated with variations in the well flow rate of a fluid. In examples, a limited amount of fluid is injected into a well of a host reservoir being tested and the pressure at the host reservoir monitored over time. The well is shut in and the pressure monitored while the fluid within the host reservoir equilibrates. The analysis of these pressure changes can provide information on the size and shape of the host reservoir as well as its ability to produce fluids.

A falloff test analysis is a type of PTA that includes the measurement and analysis of pressure data taken after an injection well is shut in. During such a test, wellhead pressure rises during injection. After shut-in of the well, the pressure declines and can be measured at the surface, and the bottomhole pressures are determined by summing pressures from the hydrostatic column to the wellhead pressure. During conventional falloff tests, the effects of temperature variations on the injection fluid is small and negligible. PTA, therefore, proceeds under an assumption that the wellhead temperature is equal to or near a predefined temperature, such as 60° F. As such, PTA analysis applies straightforwardly in conventional falloff tests because the surface flow rate is easily converted to its bottom-hole equivalent using the fluid's pressure-volume-temperature (PVT) correlation or laboratory measurements. For falloff tests involving the injection of thermally-sensitive fluids (e.g. CO2 and N2), where the wellhead temperature is substantially different than 60° F., deducing the correct bottom-hole flow rate cannot be done using assumptions for a conventional PTA.

The present techniques enable estimating reservoir properties from falloff tests conducted with thermally sensitive injection fluids. In some embodiments, the estimated fluid, rock, and reservoir properties include a bottom-hole flow rate, a total compressibility, and a total mobility. The estimated reservoir properties are used to reliably and accurately characterize a reservoir. A thermally sensitive injection fluid is introduced into a well opened at bottom-hole to a host reservoir, followed by a shut-in of the well during an injection-falloff test. The thermally sensitive injection fluid is introduced into the well at a prescribed injection rate. A bottom-hole pressure and a bottom-hole temperature are measured during the test. In examples, the bottom-hole pressure and temperature at the bottom-hole are obtained using downhole gauges; the bottom-hole density of the injection fluid is computed at the pressure and temperature conditions. A mass rate of the injection fluid is determined based on, at least in part, a wellhead density and wellhead flow rate. The mass rate and bottom-hole density are used to determine a bottom-hole flow rate corresponding to the wellhead flow rate. The bottom-hole flow rate, together with the measured bottom-hole pressure, are used to characterize the reservoir. In examples, the reservoir is characterized by determining a size of the reservoir, a shape of the reservoir, an ability of the reservoir to produce fluids, or any combinations thereof based on, at least in part, the bottom-hole flow rate and the bottom-hole pressure.

The subject matter described in this disclosure can be implemented to realize one or more of the following advantages. The disclosed estimation of reservoir properties generates accurate reservoir properties at a reduced computational cost compared to existing solutions. In particular, the quality of the estimated reservoir properties is at least similar to or exceeds the quality of reservoir properties generated using existing solutions that are more computationally expensive. Additionally, the disclosed techniques correct inaccuracies in existing solutions, which fail to incorporate the response of thermally sensitive injection fluids to temperatures that differ from standard, predefined temperatures used in existing solutions. Further, the present techniques enable a determination of bottom-hole flow rates where direct measurements are unavailable. For example, direct measurements are unavailable when the cost of downhole gauges is prohibitively expensive. Additionally, direct measurements are unavailable when the subsurface does not allow for the installation of downhole gauges. Other advantages will be apparent to those of ordinary skill in the art.

shows a pressure transient analysis (PTA) workflow. In the example of, the particular PTA executed byis an injection falloff test analysis. An injection-falloff test is a controlled operation conducted by injecting fluid through a well opened at bottom-hole to the host reservoir, followed by a well shut-in. Wellhead flow rate and pressure are recorded during the entire sequence of injection and shut-in periods. In some embodiments, permanent downhole gauges are used to capture bottom-hole pressure measurements. However, due to operational and/or economic reasons, flow rates are mostly measured at the wellhead where, for typical injection fluids, the temperature is in the neighborhood of standard temperature (60° F.). For pressure transient analysis (PTA) purposes, the wellhead injection rate is converted to its bottom-hole equivalent. This conversion is straightforward because it is underpinned by a fluid model which relates bottom-hole temperature to a standard temperature (60° F.). Challenges arise when the injection fluid is thermally-sensitive and injection is performed at temperatures substantially different than the standard temperature (e.g. injection of liquid CO2 and liquid N2). In examples, a thermally-sensitive fluid is a fluid whose properties change significantly in response to small temperature variations. For example, a thermally-sensitive fluid experiences significant Joule-Thomson cooling/heating effects as it (the fluid) expands adiabatically, leading to tangible variations in its temperature.

For ease of explanation, falloff tests where temperatures are substantially different than the standard temperature of 60° F. are referred to as atypical. Direct use of the wellhead flow rate in PTA of atypical tests suffers serious errors. In some embodiments, the present techniques accurately convert the surface flow rates of thermally-sensitive fluids to bottom-hole for use in PTA-driven reservoir characterization.

The following nomenclature is used herein:

Referring again to, at blockinput data is obtained. In examples, input data includes wellhead flow rate, wellhead pressure, wellhead temperature, bottom-hole pressure, bottom-hole temperature, fluid model, or any combinations thereof. At block, the input data is quality checked. Quality checking includes, for example, removing anomalies and noise. A number of quality checks performed on the transient data include, but are not limited to: ensuring all datasets are synchronized to enhance log-log diagnostics; confirming that the datasets track each other in a physical sense (e.g. confirming that increasing injection rate corresponds to rising bottom-hole pressure and vice versa); outliers and noise are removed from the dataset, otherwise they may skew analysis; and data density is managed by trimming/filtering the datasets smartly, such that pertinent features of the data are preserved and computing efficiency is improved. In examples, quality checking the inputs includes synchronizing the rate and pressure data, especially across the flow periods targeted for analysis. In examples, pressure and temperature data are synchronized or aligned with respect to time to resolve misalignments, possibly due to instrument drifts and/or inadvertent human errors. The data is synchronized either manually or by using algorithms which recognize and time-match falloff segments of the pressure/temperature data with the shut-in (zero-rate) segments of the injection rate data.

Note that the transient data, including pressure and temperature, have both wellhead and bottom-hole measurements except the flow rate which is reported at wellhead. To pursue transient analysis, bottom-hole flow rate is deduced from the wellhead flow rate provided at block. At block, flow events are selected for analysis. For an injector well, a flow event is a distinct portion of the well-test data describing a period when the well was either opened for injection (during which time pressure rises) or shut in (during which time pressure declines). The reverse is true for a producer well: a flow event corresponds to either a production period (during which time pressure drops) or a shut-in period (during when time pressure builds up).

In examples, a fluid property model supplied either as correlations or laboratory data is used to perform flow rate conversion from the surface flow rate to the bottom-hole flow rate. For example, in the early phase of exploration well testing, fluid samples are collected and analyzed in a laboratory to determine the behavior of the fluid with changing pressure, given the reservoir temperature. The output is a table of fluid properties (including, formation volume factor, density, compressibility, viscosity, etc.) over the pressure range expected during the reservoir flow. In examples, fluid models, in the form of correlations, are fitted to the table of laboratory data. For example, the correlations relate the fluid properties over the pressure range expected during the reservoir flow.

At block, a diagnostic log-log plot is generated using the bottom-hole flow rate. Once the conversion is accomplished, a diagnosis of the events of interest (preferably falloffs) is performed using the log-log plot. All things being equal, results from the diagnosis should be consistent across all the selected flow events. In examples, flow regimes are identified and well/reservoir parameters are estimated.

The fluid model, such as the fluid model at blockincludes a Formation Volume Factor (B) and a Solubility Ratio (R). The Formation Volume Factor (B) relates the volume a given mass of fluid occupies at surface (V) to the volume it occupies at bottom-hole (V) through the following expression:

In terms of density (ρ), Eq. (1) is the same as

In multiphase flow scenarios, if one fluid phase possesses the tendency to dissolve or be dissolved in another fluid phase, then a solubility Ratio (R) is also specified. This is given by the following expression:

Vis the volume of the dissolved fluid (component c) and Vis the volume of the dissolving fluid (phase p), both measured at standard conditions (sc). In industry parlance, this ratio is called solution gas-oil ratio for oil dissolving gas, and volatilized oil-gas ratio for gas vaporizing oil.

A fluid model relates reservoir temperature to standard temperature across the pressure variations encountered in a reservoir-well flow. It works well for transient analysis of typical well tests because their wellhead temperature condition is at or near standard. For atypical tests, direct use of the fluid model is insufficient because the wellhead temperature may be far-removed from standard temperature. Hence, corrections are made to the flow rate conversion to account for the deviation in surface temperature condition.

In some embodiments, the flow rate conversion includes both thermally sensitive and insensitive fluids and also addresses both single-phase and multiphase flow scenarios.shows a conversion of a surface flow rate to an equivalent bottom-hole flow rate. It utilizes the principle of mass conservation to translate flow rate from one thermodynamic state to another.

In the example of, wellhead flow rate (q) () is combined with wellhead density (ρ) () to estimate the mass rate of fluid injected (). Note that the wellhead density is obtained from the fluid model, read at wellhead pressure and temperature condition. When flow in the wellbore is fully developed and steady, assuming no extraneous event removes or adds fluid to the wellbore, fluid material is conserved. Hence, the obtained mass rate () is used together with bottom-hole density (ρ) () to obtain the bottom-hole flow rate (q) (). The attendant bottom-hole density (ρ) () is obtained from the fluid model anchored on bottom-hole pressure and temperature condition.

As shown, the conversion of a surface flow rate to an equivalent bottom-hole flow rate ultimately yields a bottom-hole flow rate given by

The conversion of a surface flow rate to an equivalent bottom-hole flow for single-phase flows is as follows. The densities in Eq. (4) are related to a standard condition as shown in Eq. (5),

In examples, the standard condition is a pressure and temperature condition generally accepted for comparison of fluid properties at the surface, especially for regulatory purposes in the oil and gas industry. For example, 14.7 psia and 60° F. are the set pressure and temperature points, respectively, of the standard condition.

The ratios of densities on the right-hand side of Eq. (5) corresponds to formation volume factor as reported in Eq. (2). This means that bottom-hole flow rate can be computed as

Note that the divisor (B) first translates the wellhead flow rate (q) to standard condition; then the multiplier (B) relates the resultant to bottom-hole condition. If the wellhead temperature equals standard temperature, then wellhead formation volume factor is B=1, simplifying Eq. (6) to

The expression in Eq. (7) translates wellhead rate to bottom-hole rate, provided that wellhead temperature is standard. Eq. (6) generalizes over arbitrary wellhead temperatures.

The conversion of a surface flow rate to an equivalent bottom-hole flow for multiphase flows is as follows. Eq. (6) is valid for single-phase flow. If, however, three mutually insoluble fluids (say oil, gas and water) are flowing, the total bottom-hole rate is the linear combination of the fluids' individual bottom-hole rate. That is,

If the fluids are soluble, then their solubility is accounted for in the total rate estimation. For a gas-oil-water flow system, for instance, where: (1) oil and gas are mutually soluble; (2) gas is soluble in water; and (3) water is insoluble in both gas and oil; the total subsurface rate is given by:

Note that Eq. (9) reduces to (8) if the solubility terms are zero, implying mutually insoluble fluids.

The total subsurface rate (q) given by Eq. (9) can be converted to surface rate (q) by introducing the formation volume factor (B) of the reference fluid phase (the primary reservoir fluid phase). That is,

Substituting Eq. (10) into (9), the formula for equivalent total rate becomes

The above rate conversion expressions have a firm theoretical underpinning; the proof is described with respect to.shows a source in a flow domain Ω bounded by a surface Γ.is an arbitrary domain Ω of a porous medium bounded by the surface Γ. Conservation of mass in an elemental volume of Ω for each fluid phase (oil, gas, or water) is expressed as:

The first term describes the spatial dynamics of fluid flow, the second term indicates material removed from (or introduced into) the domain by a sink (or a source), and the third term accounts for material accumulation in the domain.

For oil flow, the above conservation law translates as: