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

Abstract

A computer implemented method that enables reservoir characterization is described. The method includes obtaining bottom-hole pressure data and bottom-hole temperature data as an 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 method includes determining a mass rate of the injection fluid based on, at least in part, a wellhead fluid model and wellhead flow rate. The method includes determining bottom-hole flow rate data corresponding to wellhead flow rate data based on, at least in part, the mass rate and the bottom-hole fluid model.

Description

TECHNICAL FIELD

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

BACKGROUND

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.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows a pressure transient analysis workflow.

FIG. 2A shows a conversion of a surface flow rate to an equivalent bottom-hole flow rate.

FIG. 2B shows a source in a flow domain Ω bounded by a surface Γ.

FIG. 3 shows pressures for a water-alternating-CO2 injection-falloff test.

FIG. 4 shows temperatures for a water-alternating-CO2 injection-falloff test.

FIG. 5 shows injection rates for a water-alternating-CO2 injection-falloff test.

FIG. 6 is a log-log plot comparing the pressure difference and the pressure derivative of selected flow periods.

FIG. 7 shows equivalent total flow rate for conventional PTA and PTA according to the present techniques.

FIG. 8 is a log-log plot comparing the pressure difference and the pressure derivative of selected flow periods.

FIG. 9 is a process flow diagram of a method that enables estimating reservoir properties from falloff tests conducted with thermally sensitive injection fluids.

FIG. 10 illustrates hydrocarbon production operations that include both one or more field operations and one or more computational operations, which exchange information and control exploration for the production of hydrocarbons.

FIG. 11 is a schematic illustration of an example controller (or control system) for that enables estimating reservoir properties from falloff tests conducted with thermally sensitive injection fluids.

DETAILED DESCRIPTION

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.

FIG. 1 shows a pressure transient analysis (PTA) workflow 100. In the example of FIG. 1, the particular PTA executed by FIG. 1 is 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:

B                     Formation volume factor, bbl/stb
c                     Fluid component
cf                    Rock compressibility, psi−1
cg                    Gas compressibility, psi−1
co                    Oil compressibility, psi−1
cw                    Water compressibility, psi−1
ct                    Total compressibility, psi−1
k                     Permeability, md
{circumflex over (n)} Outward unit normal
p                     Pressure, psia
{dot over (q)}        Subsurface flow rate, bbl
qt                    Total subsurface flow rate, bbl
qtsc                  Total surface flow rate, stb
q                     Mass flow rate, lbm/hr
R                     Solubility, vol/vol
Rs                    Solution gas-oil ratio, scf/stb
Rw                    Solution gas-water ratio, scf/stb
Ry                    Volatilized oil-gas ratio, stb/scf
t                     Time, hr
S                     Saturation, fraction
u                     Flow velocity, ft/hr
ug                    Gas flow velocity, ft/hr
uo                    Oil flow velocity, ft/hr
uw                    Water flow velocity, ft/hr
V                     Fluid volume, cuft
Vc, sc                Volume of dissolved component at standard condition, cuft
Vp, sc                Volume of dissolving fluid phase at standard condition, cuft
∇                     nabla/del operator
ρ                     Fluid density, lbm/cuft
ρsc                   Fluid density at standard condition, lbm/cuft
μ                     Fluid viscosity, cp
ϕ                     Porosity, fraction
Γ                     Surface/boundary
Ω                     Domain

Subscripts
α   Fluid phase
c   Fluid component
f   Rock
g   Gas at reservoir condition
gsc Gas at standard condition
gwc Gas at wellhead condition
o   Oil at reservoir condition
osc Oil at standard condition
owc Oil at wellhead condition
ref Reference
sc  Standard condition
t   Total
p   Fluid phase
v   Volatilized oil
w   Water at wellhead condition
wc  Wellhead condition
wsc Water at standard condition
wwc Water at wellhead condition

Referring again to FIG. 1, at block 102 input 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 104, 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 106. At block 108, 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 110, 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 block 108 includes 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_surface) to the volume it occupies at bottom-hole (V_reservoir) through the following expression:

$\begin{array}{cc}B=\frac{V_{reservoir}}{V_{\mathrm{surface}}}& \left(1\right)\end{array}$

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

$\begin{array}{cc}B=\frac{{\rho }_{\mathrm{surface}}}{{\rho }_{reservoir}}& \left(2\right)\end{array}$

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:

$\begin{array}{cc}R=\frac{V_{c,\mathrm{sc}}}{V_{p,\mathrm{sc}}}& \left(3\right)\end{array}$

V_c,sc is the volume of the dissolved fluid (component c) and V_p,sc is 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. FIG. 2A 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 FIG. 2A, wellhead flow rate (q_wc) (202) is combined with wellhead density (ρ_wc) (204) to estimate the mass rate of fluid injected (206). 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 (206) is used together with bottom-hole density (ρ) (208) to obtain the bottom-hole flow rate (q) (210). The attendant bottom-hole density (ρ) (208) is obtained from the fluid model anchored on bottom-hole pressure and temperature condition.

As shown FIG. 2A, the conversion of a surface flow rate to an equivalent bottom-hole flow rate ultimately yields a bottom-hole flow rate given by

$\begin{array}{cc}q=q_{\mathrm{wc}}\frac{{\rho }_{\mathrm{wc}}}{\rho }& \left(4\right)\end{array}$

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),

$\begin{array}{cc}q=q_{\mathrm{wc}}\frac{{\rho }_{\mathrm{wc}}}{{\rho }_{\mathrm{sc}}}\frac{{\rho }_{\mathrm{sc}}}{\rho }& \left(5\right)\end{array}$

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

$\begin{array}{cc}q=q_{\mathrm{wc}}\frac{1}{B_{\mathrm{wc}}}B& \left(6\right)\end{array}$ $q=\frac{q_{\mathrm{wc}}}{B_{\mathrm{wc}}}B$

Note that the divisor (B_wc) first translates the wellhead flow rate (q_wc) 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_wc=1, simplifying Eq. (6) to

$\begin{array}{cc}q=q_{wc}B& \left(7\right)\end{array}$

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,

$\begin{array}{cc}{q}_t=\frac{q_{\mathrm{owc}}}{B_{\mathrm{owc}}}{B}_o+\frac{q_{\mathrm{gwc}}}{B_{\mathrm{gwc}}}{B}_g+\frac{q_{\mathrm{wwc}}}{B_{\mathrm{wwc}}}{B}_w& \left(8\right)\end{array}$

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:

$\begin{array}{cc}{q}_t=\frac{q_{\mathrm{owc}}}{B_{\mathrm{owc}}}\left(\frac{B_o-R_s{B}_g}{1-R_s{R}_v}\right)+\frac{q_{\mathrm{gwc}}}{B_{\mathrm{gwc}}}\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)+\frac{q_{\mathrm{wwc}}}{B_{\mathrm{wwc}}}\left[B_w-R_w\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\right]& \left(9\right)\end{array}$

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

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

$\begin{array}{cc}{q}_{\mathrm{tsc}}=\frac{q_t}{B_{\mathrm{ref}}}& \left(10\right)\end{array}$ $q_t=q_{\mathrm{tsc}}{B}_{\mathrm{ref}}$

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

$\begin{array}{cc}{q}_{\mathrm{tsc}}{B}_{\mathrm{ref}}=\frac{q_{\mathrm{owc}}}{B_{\mathrm{owc}}}\left(\frac{B_o-R_s{B}_g}{1-R_s{R}_v}\right)+\frac{q_{\mathrm{gwc}}}{B_{\mathrm{gwc}}}\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)+\frac{q_{wwc}}{B_{wwc}}\left[B_w-R_w\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\right]& \left(11\right)\end{array}$

The above rate conversion expressions have a firm theoretical underpinning; the proof is described with respect to FIG. 2B. FIG. 2B shows a source in a flow domain Ω bounded by a surface Γ. FIG. 2B 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:

$\begin{array}{cc}\left[\begin{array}{c}\mathrm{Net}\mathrm{mass}\\ \mathrm{throughput}\mathrm{rate}\end{array}\right]-\left[\begin{array}{c}\mathrm{Net}\mathrm{mass}\mathrm{rate}\\ \mathrm{withdrawn}\mathrm{by}\mathrm{sink}\end{array}\right]=\left[\begin{array}{c}\mathrm{Rate}\mathrm{of}\mathrm{mass}\\ \mathrm{accumulation}\end{array}\right]& \left(12\right)\end{array}$

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:

$\begin{array}{cc}& \left(13\right)\end{array}$ $-{\int }_{\Gamma }\left({\rho }_o{u}_o+\frac{R_v{\rho }_{\mathrm{osc}}}{B_g}{u}_g\right)·\hat{n}d\Gamma -{\int }_{\Omega }{\dot{q}}_{o}d\Omega =\frac{\partial }{\partial t}{\int }_{\Omega }\varphi \left({\rho }_o{S}_o+\frac{R_v{\rho }_{\mathrm{osc}}{S}_g}{B_g}\right)d\Omega$

For gas flow,

$\begin{array}{cc}-{\int }_{\Gamma }\left({\rho }_g{u}_g+\frac{R_s{\rho }_{\mathrm{gsc}}}{B_o}{u}_o+\frac{R_w{\rho }_{\mathrm{gsc}}}{B_w}{u}_w\right)·\hat{n}d\Gamma -{\int }_{\Omega }{\dot{q}}_{g}d\Omega =\frac{\partial }{\partial t}{\int }_{\Omega }\varphi \left({\rho }_g{S}_g+\frac{R_s{\rho }_{\mathrm{gsc}}{S}_o}{B_o}+\frac{R_w{\rho }_{\mathrm{gsc}}{S}_w}{B_w}\right)d\Omega & \left(14\right)\end{array}$

For water flow,

$\begin{array}{cc}-{\int }_{\Gamma }\left({\rho }_w{u}_w\right)·\hat{n}d\Gamma -{\int }_{\Omega }{\dot{q}}_{w}d\Omega =\frac{\partial }{\partial t}{\int }_{\Omega }\left(\varphi {\rho }_w{S}_w\right)d\Omega & \left(15\right)\end{array}$

In Eq. (13) through (15), assume a modified black-oil fluid formulation where both gas and oil are mutually soluble, gas is further soluble in water, and water is insoluble in both oil and gas. Using the divergence theorem of Gauss, the boundary integrals in Eq. (13) through (15) can be converted to domain integral respectively thus:

$-{\int }_{\Omega }\nabla ·\left({\rho }_o{u}_o+\frac{R_v{\rho }_{osc}}{B_g}{u}_g\right)d\Omega -{\int }_{\Omega }{\dot{q}}_{o}d\Omega =\frac{\partial }{\partial t}{\int }_{\Omega }\varphi \left({\rho }_o{S}_o+\frac{R_v{\rho }_{osc}{S}_g}{B_g}\right)d\Omega$ $-{\int }_{\Omega }\nabla ·\left({\rho }_g{u}_g+\frac{R_s{\rho }_{gsc}}{B_o}{u}_o+\frac{R_w{\rho }_{gsc}}{B_w}{u}_w\right)d\Omega -{\int }_{\Omega }{\dot{q}}_{g}d\Omega =\frac{\partial }{\partial t}{\int }_{\Omega }\varphi \left({\rho }_g{S}_g+\frac{R_s{\rho }_{gsc}{S}_o}{B_o}+\frac{R_w{\rho }_{gsc}{S}_w}{B_w}\right)d\Omega$ $-{\int }_{\Omega }\nabla ·\left({\rho }_w{u}_w\right)d\Omega -{\int }_{\Omega }{\stackrel{.}{q}}_{w}d\Omega =\frac{\partial }{\partial t}{\int }_{\Omega }\left(\varphi {\rho }_w{S}_w\right)d\Omega$

which simplifies as

$\begin{array}{cc}{\int }_{\Omega }\left\{-\nabla ·\left({\rho }_0{u}_o+\frac{R_v{\rho }_{osc}}{B_g}{u}_g\right)-{\dot{q}}_o-\frac{\partial }{\partial t}\left[\varphi \left({\rho }_o{S}_o+\frac{R_v{\rho }_{osc}{S}_g}{B_g}\right)\right]\right\}d\Omega =0& \left(16\right)\end{array}$ $\begin{array}{cc}{\int }_{\Omega }\left\{-\nabla ·\left({\rho }_g{u}_g+\frac{R_s{\rho }_{gsc}}{B_o}{u}_o+\frac{R_w{\rho }_{gsc}}{B_w}{u}_w\right)-{\dot{q}}_g-\frac{\partial }{\partial t}\left[\varphi \left({\rho }_g{S}_g+\frac{R_s{\rho }_{gsc}{S}_o}{B_o}+\frac{R_w{\rho }_{gsc}{S}_w}{B_w}\right)\right]\right\}d\Omega =0& \left(17\right)\end{array}$ $\begin{array}{cc}{\int }_{\Omega }\left\{-\nabla ·\left({\rho }_w{u}_w\right)-{\dot{q}}_w-\frac{\partial }{\partial t}\left(\varphi {\rho }_w{S}_w\right)\right\}d\Omega -0& \left(18\right)\end{array}$

Since the choice of the domain (as well as its geometry) is arbitrary and the integral in each of Eq. (16) though (18) vanishes, the integral is possible if and only if its integrand vanishes. That is,

$\begin{array}{cc}-\nabla ·\left({\rho }_o{u}_o+\frac{R_v{\rho }_{osc}}{B_g}{u}_g\right)-{\dot{q}}_o=\frac{\partial }{\partial t}\left[\varphi \left({\rho }_o{S}_o+\frac{R_v{\rho }_{osc}{S}_g}{B_g}\right)\right]& \left(19\right)\end{array}$ $\begin{array}{cc}-\nabla ·\left({\rho }_g{u}_g+\frac{R_s{\rho }_{gsc}}{B_o}{u}_o+\frac{R_w{\rho }_{gsc}}{B_w}{u}_w\right)-{\dot{q}}_g=\frac{\partial }{\partial t}\left[\varphi \left({\rho }_g{S}_g+\frac{R_s{\rho }_{gsc}{S}_o}{B_o}+\frac{R_w{\rho }_{gsc}{S}_w}{B_w}\right)\right]& \left(20\right)\end{array}$ $\begin{array}{cc}-\nabla ·\left({\rho }_w{u}_w\right)-{\dot{q}}_w=\frac{\partial }{\partial t}\left(\varphi {\rho }_w{S}_w\right)& \left(21\right)\end{array}$

Darcy's law is used as the momentum principle. Neglecting gravity and capillary effects and assuming an isotropic system, the law dictates the flow of fluid phase α according to the following rule:

$\begin{array}{cc}{u}_{\alpha }=-\frac{k_{\alpha }}{{\mu }_{\alpha }}\nabla p& \left(22\right)\end{array}$

Incorporating Eq. (22) in Eq. (19) through (21) yields,

$\begin{array}{cc}\nabla ·\left[\left({\rho }_o\frac{k_o}{{\mu }_o}+\frac{R_v{\rho }_{osc}}{B_g}\frac{k_g}{{\mu }_g}\right)\nabla p\right]-{\dot{q}}_o=\frac{\partial }{\partial t}\left[\varphi \left({\rho }_o{S}_o+\frac{R_v{\rho }_{osc}{S}_g}{B_g}\right)\right]& \left(23\right)\end{array}$ $\begin{array}{cc}\nabla ·\left[\left({\rho }_g\frac{k_g}{{\mu }_g}+\frac{R_s{\rho }_{gsc}}{B_o}\frac{k_o}{{\mu }_o}+\frac{R_w{\rho }_{gsc}}{B_w}\frac{k_w}{{\mu }_w}\right)\nabla p\right]-{\dot{q}}_g=\frac{\partial }{\partial t}\left[\varphi \left({\rho }_g{S}_g+\frac{R_s{\rho }_{gsc}{S}_o}{B_o}+\frac{R_w{\rho }_{gsc}{S}_w}{B_w}\right)\right]& \left(24\right)\end{array}$ $\begin{array}{cc}\nabla ·\left[\left({\rho }_w\frac{k_w}{{\mu }_w}\right)\nabla p\right]-{\dot{q}}_w=\frac{\partial }{\partial t}\left(\varphi {\rho }_w{S}_w\right)& \left(25\right)\end{array}$

Substituting in the fluid-model relationship in Eq. 2 and applying the chain rule of differentiation on the RHS of Eq. (23) through (25) leads to:

$\begin{array}{cc}\nabla ·\left[\left(\frac{1}{B_o}\frac{k_o}{{\mu }_o}+\frac{R_v}{B_g}\frac{k_g}{{\mu }_g}\right)\nabla p\right]-\frac{{\dot{q}}_o}{{\rho }_{osc}}=\frac{\partial }{\partial p}\left[\varphi \left(\frac{S_o}{B_o}+\frac{R_v{S}_g}{B_g}\right)\right]\frac{\partial p}{\partial t}& \left(26\right)\end{array}$ $\begin{array}{cc}\nabla ·\left[\left(\frac{1}{B_g}\frac{k_g}{{\mu }_g}+\frac{R_s}{B_o}\frac{k_o}{{\mu }_o}+\frac{R_w}{B_w}\frac{k_w}{{\mu }_w}\right)\nabla p\right]-\frac{{\dot{q}}_g}{{\rho }_{gsc}}=\frac{\partial }{\partial p}\left[\varphi \left(\frac{S_g}{B_g}+\frac{R_s{S}_o}{B_o}+\frac{R_w{S}_w}{B_w}\right)\right]\frac{\partial p}{\partial t}& \left(27\right)\end{array}$ $\begin{array}{cc}\nabla ·\left[\left(\frac{1}{B_w}\frac{k_w}{{\mu }_w}\right)\nabla p\right]-\frac{{\dot{q}}_w}{{\rho }_{wsc}}=\frac{\partial }{\partial p}\left(\varphi \frac{S_w}{B_w}\right)\frac{\partial p}{\partial t}& \left(28\right)\end{array}$

Multiplying Eq. (26), (27), and (28) by (B_o−R_sB_g), (B_g−R_vB_o), and [B_w(1−R_vR_s)−R_w(B_g−R_vB_o)] respectively and adding the resultants up while recognizing the following saturation constraint,

S_o+S_g+S_w=1  (29)

the resultant is,

$\begin{array}{cc}\nabla ·\left[\left(\frac{k_o}{{\mu }_o}+\frac{k_g}{{\mu }_g}+\frac{k_w}{{\mu }_w}\right)\nabla p\right]-\left(\frac{B_o-R_s{B}_g}{1-R_s{R}_v}\right)\frac{{\stackrel{.}{q}}_o}{{\rho }_{\mathrm{osc}}}-\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\frac{{\stackrel{.}{q}}_g}{{\rho }_{\mathrm{gsc}}}-\left[B_w-R_w\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\right]\frac{{\stackrel{.}{q}}_w}{{\rho }_{\mathrm{wsc}}}=\frac{\partial \varphi }{\partial p}\frac{\partial p}{\partial t}-\frac{\varphi S_o}{B_o}\left[\frac{\partial B_o}{\partial p}-\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\frac{\partial R_s}{\partial p}\right]\frac{\partial p}{\partial t}-\frac{\varphi S_g}{B_g}\left[\frac{\partial B_g}{\partial p}-\left(\frac{B_o-R_s{B}_g}{1-R_s{R}_v}\right)\frac{\partial R_v}{\partial p}\right]\frac{\partial p}{\partial t}-\frac{\varphi S_w}{B_w}\left[\frac{\partial B_w}{\partial p}-\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\frac{\partial R_w}{\partial p}\right]\frac{\partial p}{\partial t}& \left(30\right)\end{array}$

Eq. (30) assumes that pressure and saturation gradients are small. This holds approximately true for buildup/falloff events where fluid withdrawal/injection has ceased and the fluid front advance in the reservoir is negligibly small.

Surface flow rate (q_asc) for each fluid phase is α given by:

$\begin{array}{cc}{q}_{asc}=\frac{{\dot{q}}_a}{{\rho }_{\alpha \mathrm{sc}}}& \left(31\right)\end{array}$

Also note the following compressibility terms:

$\begin{array}{cc}{c}_f=\frac{1}{\varphi }\frac{\partial \varphi }{\partial p}& \left(32\right)\end{array}$ $\begin{array}{cc}{c}_o=-\frac{1}{B_o}\left[\frac{\partial B_o}{\partial p}-\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\frac{\partial R_s}{\partial p}\right]& \left(33\right)\end{array}$ $\begin{array}{cc}{c}_g=-\frac{1}{B_g}\left[\frac{\partial B_g}{\partial p}-\left(\frac{B_o-R_s{B}_g}{1-R_s{R}_v}\right)\frac{\partial R_v}{\partial p}\right]& \left(34\right)\end{array}$ $\begin{array}{cc}{c}_w=-\frac{1}{B_w}\left[\frac{\partial B_w}{\partial p}-\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\frac{\partial R_w}{\partial p}\right]& \left(35\right)\end{array}$

Substituting Eq. (31) through (35) into (30),

$\begin{array}{cc}\nabla ·\left[\left(\frac{k_o}{{\mu }_o}+\frac{k_g}{{\mu }_g}+\frac{k_w}{{\mu }_w}\right)\nabla p\right]-\left(\frac{B_o-R_s{B}_g}{1-R_s{R}_v}\right)q_{osc}-\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)q_{gsc}-\left[B_w-R_w\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\right]q_{wsc}=\varphi \left(c_f+S_o{c}_o+S_g{c}_g+S_w{c}_w\right)\frac{\partial p}{\partial t}& \left(36\right)\end{array}$

Setting the following expressions for total mobility, total compressibility, and total subsurface rate respectively,

$\begin{array}{cc}{\left(\frac{k}{\mu }\right)}_t=\frac{k_o}{{\mu }_o}+\frac{k_g}{{\mu }_g}+\frac{k_w}{{\mu }_w}& \left(37\right)\end{array}$ $\begin{array}{cc}{c}_t=c_f+S_o{c}_o+S_g{c}_g+S_w{c}_w& \left(38\right)\end{array}$ $\begin{array}{cc}{q}_t=q_{osc}\left(\frac{B_o-R_s{B}_g}{1-R_s{R}_v}\right)+q_{gsc}\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)+q_{wsc}\left[B_w-R_w\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\right]& \left(39\right)\end{array}$

The total subsurface rate given by Eq. (39) can be converted to surface rate by introducing the formation volume factor, B_ref, of the reference fluid phase (that is, the primary reservoir fluid phase) thus:

$\begin{array}{cc}{q}_{\mathrm{tsc}}=\frac{q_t}{B_{ref}}& \left(40\right)\end{array}$ $q_t=q_{\mathrm{tsc}}{B}_{ref}$

Substituting Eq. (40) into (39), the formula for equivalent total rate becomes:

$\begin{array}{cc}{q}_{\mathrm{tsc}}{B}_{ref}=q_{osc}\left(\frac{B_o-R_s{B}_g}{1-R_s{R}_v}\right)+q_{gsc}\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)+q_{wsc}\left[B_w-R_w\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\right]& \left(41\right)\end{array}$

Substituting Eq. (37) through (41) into (36) yields,

$\begin{array}{cc}\nabla ·\left[{\left(\frac{k}{\mu }\right)}_t\nabla p\right]]-q_{\mathrm{tsc}}{B}_{ref}=\varphi c_t\frac{\partial p}{\partial t}& \left(42\right)\end{array}$

Assuming total mobility is constant, then Eq. (42) simplifies as,

$\begin{array}{cc}\nabla ·\left(\nabla p\right)-\frac{q_{\mathrm{tsc}}{B}_{ref}}{{\left(k/\mu \right)}_t}=\frac{\varphi c_t}{{\left(k/\mu \right)}_t}\frac{\partial p}{\partial t}& \left(43\right)\end{array}$ ${\nabla }^{2}p-\frac{q_{\mathrm{tsc}}{B}_{ref}}{{\left(k/\mu \right)}_t}=\frac{\varphi c_t}{{\left(k/\mu \right)}_t}\frac{\partial p}{\partial t}$

Eq. (43) is the diffusivity equation for multiphase flow similar to the diffusivity equation for single-phase flow. It is driven by an equivalent total rate, Eq. (41), computed using a fluid model referenced to standard temperature. This is valid when the wellhead temperature is at or near standard temperature. In following, is a mechanism for handling non-standard surface temperatures.

The equivalent total rate expression of Eq. (41) assumes that the individual phase surface rates were measured at standard condition (sc). If the rates are measured at other wellhead conditions (wc), then they are be corrected to standard condition as shown below.

$\begin{array}{cc}{q}_{\mathrm{osc}}=\frac{q_{\mathrm{owc}}}{B_{\mathrm{owc}}}& \left(44\right)\end{array}$ $\begin{array}{cc}{q}_{\mathrm{gsc}}=\frac{q_{\mathrm{gwc}}}{B_{\mathrm{gwc}}}& \left(45\right)\end{array}$ $\begin{array}{cc}{q}_{\mathrm{wsc}}=\frac{q_{\mathrm{wwc}}}{B_{\mathrm{wwc}}}& \left(46\right)\end{array}$

Substituting Eq. (44) through (46) into (41), the equivalent total rate for non-standard surface temperature flow is therefore given by:

$\begin{array}{cc}{q}_{\mathrm{tsc}}{B}_{ref}=\frac{q_{owc}}{B_{owc}}\left(\frac{B_o-R_s{B}_g}{1-R_s{R}_v}\right)+\frac{q_{gwc}}{B_{gwc}}\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)+\frac{q_{wwc}}{B_{wwc}}\left[B_w-R_w\left(\frac{B_g-R_v{B}_o}{1-R_s{R}_v}\right)\right]& \left(47\right)\end{array}$

Referring again to FIG. 1, at block 108, flow events are selected for analysis after bottom-hole equivalents are determined. Transient analysis is pursued to estimate well parameters and reservoir properties. This is achieved by first selecting a flow event of interest. In examples, the flow event is a delineable portion of the well-test data, such as an injection event or a shut-in event. A selected period corresponding to the flow event is characterized by good quality data and long enough to reveal reservoir properties. The rate and pressure data for the event are then rendered on a log-log diagnostic plot where pertinent flow regimes are identified. In some embodiments, rendering rate and pressure data on a log-log plot is used to automatically diagnose flow regimes accessed by a well test. Knowledge of these regimes yields well and reservoir parameters. For past data, the log-log rendering is fixed; new pressure and rate data, however, can be rendered automatically on the log-log plot as they become available without human intervention. Well/reservoir parameters are obtained from each regime by application of appropriate specialized flow-regime calculations. The attendant total mobility and total compressibility informing the analysis is computed according to Eq. (37) and (38) respectively.

Analysis may be repeated for other flow events present in the dataset. Ideally, the results for all flow events should agree with one another; any discrepancy would be a cause for investigation, which may include improving the fluid models or further quality-checking the input transient data. Agreement here implies that analysis of each flow event yields similar reservoir parameters (e.g. flow capacity, flow barriers, vertical anisotropy, reservoir extent in the case of a finite system) as the others, provided that all input data are correct. Deviations from this expectation may be caused by an incorrect fluid model or errors in certain sections of the input flow data (pressure, temperature, and/or rate). In some embodiments, when the models do not agree, a manual review of the fluid model is performed to ensure the fluid model is descriptive of the fluid's behavior. For example, manual review includes inputting laboratory data points into a predetermined fluid modeling routine and using them as a constraint to identify and fit the right fluid property correlation. Also, since certain fluid properties have functional dependence, for instance formation volume factor and compressibility, an analyst ensures this dependence is not violated. In examples, the predetermined fluid modeling routine is pre-packaged with a fluid PVT module. The predetermined fluid modeling routine is used to define a representative fluid model for driving PTA analysis. Laboratory PVT data, if available, are entered in the module to constrain the fluid model and provide a ground-truth to the fluid model.

FIGS. 3, 4, and 5 show the pressures, temperatures, and injection rate for a water-alternating-CO2 injection-falloff test. FIGS. 3, 4, and 5 represent real world actions associated with the workflow 100 of FIG. 1 using field test data. Observe that all the data categories have both wellhead and bottom-hole counterparts, except flow rate which is only reported at wellhead. Observe that water injection/falloff dominate the first three-quarters of the test period, and CO2 injection/falloff the rest quarter of the test.

The first task is to quality-check the data and eliminate any anomalies and noises that may impact transient analysis. Also recommended is ensuring the datasets are synchronized, as misalignment affects the eventual log-log diagnosis, especially the early time. The data for this example has been cleaned and are ready for use.

Observe in FIG. 5 that the injected CO2 is liquid at wellhead; its temperature is essentially 12° F. during injection (as reported in FIG. 4). This temperature condition is much different than the standard temperature of 60° F. In conventional PTA, total flow rate is computed by linearly combining the water rate and the liquid CO2 rate based on the assumption that liquid CO2 density is the same order of magnitude as water density. The resultant is used as an equivalent water rate to drive analysis. For the present demonstration, the water and the CO2 falloff events (highlighted in FIG. 3 through FIG. 5) are selected for analysis on a log-log plot (FIG. 6).

FIG. 6 compares the pressure difference and the pressure derivative of the selected flow periods. Various interpretation results/parameters can be drawn from this plot, including skin characterization, hydraulic fracture inducement post CO2 injection, etc. but these are secondary in this demonstration. Of primary interest is the fact that the derivative plateau accessed by the two flow periods do not agree; the water-falloff derivative indicates better reservoir quality than the CO2-falloff derivative. This discrepancy is caused by the “equal density” assumption which informed the total rate computation: it fails to account for CO2 phase change between the wellhead and bottom-hole. Based on the surface and subsurface conditions, the injected CO2 transitions from liquid at wellhead to supercritical at bottom-hole, experiencing a volume change in the process. This volume change is ignored in conventional PTA.

The present techniques resolve the reservoir-quality discrepancies that occur using conventional PTA. Eq. (9) is applied to the water and CO2 rate history of FIG. 5 to recover a rigorous equivalent total rate, as shown in FIG. 7. This computation indeed reveals a volume expansion as depicted by the differential between the linear and the rigorous equivalent total rates, especially within the injection period directly preceding the CO2 falloff event. The log-log diagnostic plot is generated but, this time, based on the rigorous equivalent total rate. This is shown in FIG. 8. In FIG. 8, both the water-falloff and the CO2-falloff derivative plateaus agree.

FIG. 9 is a process flow diagram of a method that enables estimating reservoir properties from falloff tests conducted with thermally sensitive injection fluids.

At block 902, bottom-hole pressure, and bottom-hole temperature are obtained from at least one downhole gauges. In examples, the bottom-hole pressure and bottom-hole temperature are captured as 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.

At block 904, a mass rate of an injection fluid is determined based on, at least in part, wellhead density and wellhead flow rate.

At block 906, the mass rate and the bottom-hole density are used to determine the 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.

At block 908, the well is tied back into the production stream, wherein the well is managed in the production stream according to the operating strategy in force. In examples, the operating strategy is a remediation action that is planned for the well should PTA analysis confirm significant well performance impairment caused by near-wellbore formation damage. Other PTA results provide information for planning field development and guiding reservoir management. The rigorous computation of the bottom-hole flow rate as described herein duly accounts for fluid volume change between wellhead and bottom-hole through material balance considerations. This guarantees that accurate flow rate is used to drive reservoir engineering calculations.

FIG. 10 illustrates hydrocarbon production operations 1000 that include both one or more field operations 1010 and one or more computational operations 1012, which exchange information and control exploration for the production of hydrocarbons. In some implementations, outputs of techniques of the present disclosure can be performed before, during, or in combination with the hydrocarbon production operations 1000, specifically, for example, either as field operations 1010 or computational operations 1012, or both.

Examples of field operations 1010 include forming/drilling a wellbore, reservoir characterization, hydraulic fracturing, producing through the wellbore, injecting fluids (such as water) through the wellbore, to name a few. In some implementations, methods of the present disclosure can trigger or control the field operations 1010. For example, the methods of the present disclosure can generate data from hardware/software including sensors and physical data gathering equipment (e.g., seismic sensors, well logging tools, flow meters, and temperature and pressure sensors). The methods of the present disclosure can include transmitting the data from the hardware/software to the field operations 1010 and responsively triggering the field operations 1010 including, for example, generating plans and signals that provide feedback to and control physical components of the field operations 1010. Alternatively or in addition, the field operations 1010 can trigger the methods of the present disclosure. For example, implementing physical components (including, for example, hardware, such as sensors) deployed in the field operations 1010 can generate plans and signals that can be provided as input or feedback (or both) to the methods of the present disclosure.

Examples of computational operations 1012 include one or more computer systems 1020 that include one or more processors and computer-readable media (e.g., non-transitory computer-readable media) operatively coupled to the one or more processors to execute computer operations to perform the methods of the present disclosure. The computational operations 1012 can be implemented using one or more databases 1018, which store data received from the field operations 1010 and/or generated internally within the computational operations 1012 (e.g., by implementing the methods of the present disclosure) or both. For example, the one or more computer systems 1020 process inputs from the field operations 1010 to assess conditions in the physical world, the outputs of which are stored in the databases 1018. For example, seismic sensors of the field operations 1010 can be used to perform a seismic survey to map subterranean features, such as facies and faults. In performing a seismic survey, seismic sources (e.g., seismic vibrators or explosions) generate seismic waves that propagate in the earth and seismic receivers (e.g., geophones) measure reflections generated as the seismic waves interact with boundaries between layers of a subsurface formation. The source and received signals are provided to the computational operations 1012 where they are stored in the databases 1018 and analyzed by the one or more computer systems 1020.

In some implementations, one or more outputs 1022 generated by the one or more computer systems 1020 can be provided as feedback/input to the field operations 1010 (either as direct input or stored in the databases 1018). The field operations 1010 can use the feedback/input to control physical components used to perform the field operations 1010 in the real world.

For example, the computational operations 1012 can process the seismic data to generate three-dimensional (3D) maps of the subsurface formation. The computational operations 1012 can use these 3D maps to provide plans for locating and drilling exploratory wells. In some operations, the exploratory wells are drilled using logging-while-drilling (LWD) techniques which incorporate logging tools into the drill string. LWD techniques can enable the computational operations 1012 to process new information about the formation and control the drilling to adjust to the observed conditions in real-time.

The one or more computer systems 1020 can update the 3D maps of the subsurface formation as information from one exploration well is received and the computational operations 1012 can adjust the location of the next exploration well based on the updated 3D maps. Similarly, the data received from production operations can be used by the computational operations 1012 to control components of the production operations. For example, production well and pipeline data can be analyzed to predict slugging in pipelines leading to a refinery and the computational operations 1012 can control machine operated valves upstream of the refinery to reduce the likelihood of plant disruptions that run the risk of taking the plant offline.

In some implementations of the computational operations 1012, customized user interfaces can present intermediate or final results of the above-described processes to a user. Information can be presented in one or more textual, tabular, or graphical formats, such as through a dashboard. The information can be presented at one or more on-site locations (such as at an oil well or other facility), on the Internet (such as on a webpage), on a mobile application (or app), or at a central processing facility.

The presented information can include feedback, such as changes in parameters or processing inputs, that the user can select to improve a production environment, such as in the exploration, production, and/or testing of petrochemical processes or facilities. For example, the feedback can include parameters that, when selected by the user, can cause a change to, or an improvement in, drilling parameters (including drill bit speed and direction) or overall production of a gas or oil well. The feedback, when implemented by the user, can improve the speed and accuracy of calculations, streamline processes, improve models, and solve problems related to efficiency, performance, safety, reliability, costs, downtime, and the need for human interaction.

In some implementations, the feedback can be implemented in real-time, such as to provide an immediate or near-immediate change in operations or in a model. The term real-time (or similar terms as understood by one of ordinary skill in the art) means that an action and a response are temporally proximate such that an individual perceives the action and the response occurring substantially simultaneously. For example, the time difference for a response to display (or for an initiation of a display) of data following the individual's action to access the data can be less than 1 millisecond (ms), less than 1 second(s), or less than 5 s. While the requested data need not be displayed (or initiated for display) instantaneously, it is displayed (or initiated for display) without any intentional delay, taking into account processing limitations of a described computing system and time required to, for example, gather, accurately measure, analyze, process, store, or transmit the data.

Events can include readings or measurements captured by downhole equipment such as sensors, pumps, bottom hole assemblies, or other equipment. The readings or measurements can be analyzed at the surface, such as by using applications that can include modeling applications and machine learning. The analysis can be used to generate changes to settings of downhole equipment, such as drilling equipment. In some implementations, values of parameters or other variables that are determined can be used automatically (such as through using rules) to implement changes in oil or gas well exploration, production/drilling, or testing. For example, outputs of the present disclosure can be used as inputs to other equipment and/or systems at a facility. This can be especially useful for systems or various pieces of equipment that are located several meters or several miles apart, or are located in different countries or other jurisdictions.

FIG. 11 is a schematic illustration of an example controller 1100 (or control system) for that enables estimating reservoir properties from falloff tests conducted with thermally sensitive injection fluids. For example, the controller 1100 may be operable according to the workflow 100 of FIG. 1 or the process 900 of FIG. 9. In some embodiments, the controller 1100 is the same as or similar to the computer systems 1020 of FIG. 10. The controller 1100 is intended to include various forms of digital computers, such as printed circuit boards (PCB), processors, digital circuitry, or otherwise parts of a system for supply chain alert management. Additionally the system can include portable storage media, such as, Universal Serial Bus (USB) flash drives. For example, the USB flash drives may store operating systems and other applications. The USB flash drives can include input/output components, such as a wireless transmitter or USB connector that may be inserted into a USB port of another computing device.

The controller 1100 includes a processor 1110, a memory 1120, a storage device 1130, and an input/output interface 1140 communicatively coupled with input/output devices 1160 (for example, displays, keyboards, measurement devices, sensors, valves, pumps). Each of the components 1110, 1120, 1130, and 1140 are interconnected using a system bus 1150. The processor 1110 is capable of processing instructions for execution within the controller 1100. The processor may be designed using any of a number of architectures. For example, the processor 1110 may be a CISC (Complex Instruction Set Computers) processor, a RISC (Reduced Instruction Set Computer) processor, or a MISC (Minimal Instruction Set Computer) processor.

In one implementation, the processor 1110 is a single-threaded processor. In another implementation, the processor 1110 is a multi-threaded processor. The processor 1110 is capable of processing instructions stored in the memory 1120 or on the storage device 1130 to display graphical information for a user interface on the input/output interface 1140.

The memory 1120 stores information within the controller 1100. In one implementation, the memory 1120 is a computer-readable medium. In one implementation, the memory 1120 is a volatile memory unit. In another implementation, the memory 1120 is a nonvolatile memory unit.

The storage device 1130 is capable of providing mass storage for the controller 1100. In one implementation, the storage device 1130 is a computer-readable medium. In various different implementations, the storage device 1130 may be a floppy disk device, a hard disk device, an optical disk device, or a tape device.

The input/output interface 1140 provides input/output operations for the controller 1100. In one implementation, the input/output devices 1160 includes a keyboard and/or pointing device. In another implementation, the input/output devices 1160 includes a display unit for displaying graphical user interfaces.

There can be any number of controllers 1100 associated with, or external to, a computer system containing controller 1100, with each controller 1100 communicating over a network. Further, the terms “client,” “user,” and other appropriate terminology can be used interchangeably, as appropriate, without departing from the scope of the present disclosure. Moreover, the present disclosure contemplates that many users can use one controller 1100 and one user can use multiple controllers 1100.

Embodiments/Examples

According to some non-limiting embodiments or examples, provided is a computer-implemented method that enables estimating reservoir properties, comprising: obtaining, using at least one hardware processor, bottom-hole pressure data, a bottom-hole fluid model, and bottom-hole temperature data as an 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; determining, using the at least one hardware processor, a mass rate of the injection fluid based on, at least in part, a wellhead fluid model and wellhead flow rate; and determining, using the at least one hardware processor, bottom-hole flow rate data corresponding to wellhead flow rate data based on, at least in part, the mass rate and the bottom-hole fluid model.

According to some non-limiting embodiments or examples, provided is an apparatus comprising a non-transitory, computer readable, storage medium that stores instructions that, when executed by at least one processor, cause the at least one processor to perform operations comprising: obtaining bottom-hole pressure data, a bottom-hole fluid model, and bottom-hole temperature data as an 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; determining a mass rate of the injection fluid based on, at least in part, a wellhead fluid model and wellhead flow rate; and determining bottom-hole flow rate data corresponding to wellhead flow rate data based on, at least in part, the mass rate and the bottom-hole fluid model.

According to some non-limiting embodiments or examples, provided is a system, comprising: one or more memory modules; one or more hardware processors communicably coupled to the one or more memory modules, the one or more hardware processors configured to execute instructions stored on the one or more memory modules to perform operations comprising: obtaining bottom-hole pressure data, a bottom-hole fluid model, and bottom-hole temperature data as an 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; determining a mass rate of the injection fluid based on, at least in part, a wellhead fluid model and wellhead flow rate; and determining bottom-hole flow rate data corresponding to wellhead flow rate data based on, at least in part, the mass rate and the bottom-hole fluid model.

Further non-limiting aspects or embodiments are set forth in the following numbered embodiments:

Embodiment 1: A computer-implemented method that enables estimating reservoir properties, including: obtaining, using at least one hardware processor, bottom-hole pressure data, a bottom-hole fluid model, and bottom-hole temperature data as an 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; determining, using the at least one hardware processor, a mass rate of the injection fluid based on, at least in part, a wellhead fluid model and wellhead flow rate; and determining, using the at least one hardware processor, bottom-hole flow rate data corresponding to wellhead flow rate data based on, at least in part, the mass rate and the bottom-hole fluid model.

Embodiment 2: The computer implemented method of any preceding embodiment, wherein the injection fluid is a thermally-sensitive injection fluid.

Embodiment 3: The computer implemented method of any preceding embodiment, wherein input data is automatically rendered on a log-log plot to realize at least one flow regime.

Embodiment 4: The computer implemented method of any preceding embodiment, wherein the bottom-hole flow rate and obtained bottom-hole pressure are used to characterize the host reservoir.

Embodiment 5: The computer implemented method of any preceding embodiment, wherein characterizing the host reservoir includes determining a size of the host reservoir, a shape of the host reservoir, an ability of the host reservoir to produce fluids, or any combinations thereof.

Embodiment 6: The computer implemented method of any preceding embodiment, including synchronizing the bottom-hole pressure, the bottom-hole flow rate, and the bottom-hole temperature to enhance log-log diagnostics.

Embodiment 7: The computer implemented method of any preceding embodiment, wherein the bottom-hole pressure and the bottom-hole temperature are obtained from at least one downhole gauge.

Embodiment 8: The computer implemented method of any preceding embodiment, including automatically tying the well into a production stream based on the determined bottom-hole flow rate, wherein the well is managed in the production stream according to the bottom-hole flow rate.

Embodiment 9: An apparatus including a non-transitory, computer readable, storage medium that stores instructions that, when executed by at least one processor, cause the at least one processor to perform operations including: obtaining bottom-hole pressure data, a bottom-hole fluid model, and bottom-hole temperature data as an 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; determining a mass rate of the injection fluid based on, at least in part, a wellhead fluid model and wellhead flow rate; and determining bottom-hole flow rate data corresponding to wellhead flow rate data based on, at least in part, the mass rate and the bottom-hole fluid model.

Embodiment 10: The apparatus of any preceding embodiment, wherein the injection fluid is a thermally-sensitive injection fluid.

Embodiment 11: The apparatus of any preceding embodiment, wherein input data is automatically rendered on a log-log plot to realize at least one flow regime.

Embodiment 12: The apparatus of any preceding embodiment, wherein the bottom-hole flow rate and obtained bottom-hole pressure are used to characterize the host reservoir.

Embodiment 13: The apparatus of any preceding embodiment, wherein characterizing the host reservoir includes determining a size of the host reservoir, a shape of the host reservoir, an ability of the host reservoir to produce fluids, or any combinations thereof.

Embodiment 14: The apparatus of any preceding embodiment, including synchronizing the bottom-hole pressure, the bottom-hole flow rate, and the bottom-hole temperature to enhance log-log diagnostics.

Embodiment 15: The apparatus of any preceding embodiment, wherein the bottom-hole pressure and the bottom-hole temperature are obtained from at least one downhole gauge.

Embodiment 16: A system, including: one or more memory modules; one or more hardware processors communicably coupled to the one or more memory modules, the one or more hardware processors configured to execute instructions stored on the one or more memory modules to perform operations including: obtaining bottom-hole pressure data, a bottom-hole fluid model, and bottom-hole temperature data as an 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; determining a mass rate of the injection fluid based on, at least in part, a wellhead fluid model and wellhead flow rate; and determining bottom-hole flow rate data corresponding to wellhead flow rate data based on, at least in part, the mass rate and the bottom-hole fluid model.

Embodiment 17: The system of any preceding embodiment, wherein the injection fluid is a thermally-sensitive injection fluid.

Embodiment 18: The system of any preceding embodiment, wherein input data is automatically rendered on a log-log plot to realize at least one flow regime.

Embodiment 19: The system of any preceding embodiment, wherein the bottom-hole flow rate and obtained bottom-hole pressure are used to characterize the host reservoir.

Embodiment 20: The system of any preceding embodiment, wherein characterizing the host reservoir includes determining a size of the host reservoir, a shape of the host reservoir, an ability of the host reservoir to produce fluids, or any combinations thereof.

Implementations of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Software implementations of the described subject matter can be implemented as one or more computer programs. Each computer program can include one or more modules of computer program instructions encoded on a tangible, non-transitory, computer-readable computer-storage medium for execution by, or to control the operation of, data processing apparatus. Alternatively, or additionally, the program instructions can be encoded in/on an artificially generated propagated signal. The example, the signal can be a machine-generated electrical, optical, or electromagnetic signal that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus. The computer-storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of computer-storage mediums.

The terms “data processing apparatus,” “computer,” and “electronic computer device” (or equivalent as understood by one of ordinary skill in the art) refer to data processing hardware. For example, a data processing apparatus can encompass all kinds of apparatus, devices, and machines for processing data, including by way of example, a programmable processor, a computer, or multiple processors or computers. The apparatus can also include special purpose logic circuitry including, for example, a central processing unit (CPU), a field programmable gate array (FPGA), or an application specific integrated circuit (ASIC). In some implementations, the data processing apparatus or special purpose logic circuitry (or a combination of the data processing apparatus or special purpose logic circuitry) can be hardware- or software-based (or a combination of both hardware- and software-based). The apparatus can optionally include code that creates an execution environment for computer programs, for example, code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of execution environments. The present disclosure contemplates the use of data processing apparatuses with or without conventional operating systems, for example, LINUX, UNIX, WINDOWS, MAC OS, ANDROID, or IOS.

A computer program, which can also be referred to or described as a program, software, a software application, a module, a software module, a script, or code, can be written in any form of programming language. Programming languages can include, for example, compiled languages, interpreted languages, declarative languages, or procedural languages. Programs can be deployed in any form, including as stand-alone programs, modules, components, subroutines, or units for use in a computing environment. A computer program can, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, for example, one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files storing one or more modules, sub programs, or portions of code. A computer program can be deployed for execution on one computer or on multiple computers that are located, for example, at one site or distributed across multiple sites that are interconnected by a communication network. While portions of the programs illustrated in the various figures may be shown as individual modules that implement the various features and functionality through various objects, methods, or processes, the programs can instead include a number of sub-modules, third-party services, components, and libraries. Conversely, the features and functionality of various components can be combined into single components as appropriate. Thresholds used to make computational determinations can be statically, dynamically, or both statically and dynamically determined.

The methods, processes, or logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The methods, processes, or logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, for example, a CPU, an FPGA, or an ASIC.

Computers suitable for the execution of a computer program can be based on one or more of general and special purpose microprocessors and other kinds of CPUs. The elements of a computer are a CPU for performing or executing instructions and one or more memory devices for storing instructions and data. Generally, a CPU can receive instructions and data from (and write data to) a memory. A computer can also include, or be operatively coupled to, one or more mass storage devices for storing data. In some implementations, a computer can receive data from, and transfer data to, the mass storage devices including, for example, magnetic, magneto optical disks, or optical disks. Moreover, a computer can be embedded in another device, for example, a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a global positioning system (GPS) receiver, or a portable storage device such as a universal serial bus (USB) flash drive.

Computer readable media (transitory or non-transitory, as appropriate) suitable for storing computer program instructions and data can include all forms of permanent/non-permanent and volatile/non-volatile memory, media, and memory devices. Computer readable media can include, for example, semiconductor memory devices such as random access memory (RAM), read only memory (ROM), phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and flash memory devices. Computer readable media can also include, for example, magnetic devices such as tape, cartridges, cassettes, and internal/removable disks. Computer readable media can also include magneto optical disks and optical memory devices and technologies including, for example, digital video disc (DVD), CD ROM, DVD+/−R, DVD-RAM, DVD-ROM, HD-DVD, and BLURAY. The memory can store various objects or data, including caches, classes, frameworks, applications, modules, backup data, jobs, web pages, web page templates, data structures, database tables, repositories, and dynamic information. Types of objects and data stored in memory can include parameters, variables, algorithms, instructions, rules, constraints, and references. Additionally, the memory can include logs, policies, security or access data, and reporting files. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

Implementations of the subject matter described in the present disclosure can be implemented on a computer having a display device for providing interaction with a user, including displaying information to (and receiving input from) the user. Types of display devices can include, for example, a cathode ray tube (CRT), a liquid crystal display (LCD), a light-emitting diode (LED), and a plasma monitor. Display devices can include a keyboard and pointing devices including, for example, a mouse, a trackball, or a trackpad. User input can also be provided to the computer through the use of a touchscreen, such as a tablet computer surface with pressure sensitivity or a multi-touch screen using capacitive or electric sensing. Other kinds of devices can be used to provide for interaction with a user, including to receive user feedback including, for example, sensory feedback including visual feedback, auditory feedback, or tactile feedback. Input from the user can be received in the form of acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to, and receiving documents from, a device that is used by the user. For example, the computer can send web pages to a web browser on a user's client device in response to requests received from the web browser.

The term “graphical user interface,” or “GUI,” can be used in the singular or the plural to describe one or more graphical user interfaces and each of the displays of a particular graphical user interface. Therefore, a GUI can represent any graphical user interface, including, but not limited to, a web browser, a touch screen, or a command line interface (CLI) that processes information and efficiently presents the information results to the user. In general, a GUI can include a plurality of user interface (UI) elements, some or all associated with a web browser, such as interactive fields, pull-down lists, and buttons. These and other UI elements can be related to or represent the functions of the web browser.

Implementations of the subject matter described in this specification can be implemented in a computing system that includes a back end component, for example, as a data server, or that includes a middleware component, for example, an application server. Moreover, the computing system can include a front-end component, for example, a client computer having one or both of a graphical user interface or a Web browser through which a user can interact with the computer. The components of the system can be interconnected by any form or medium of wireline or wireless digital data communication (or a combination of data communication) in a communication network. Examples of communication networks include a local area network (LAN), a radio access network (RAN), a metropolitan area network (MAN), a wide area network (WAN), Worldwide Interoperability for Microwave Access (WIMAX), a wireless local area network (WLAN) (for example, using 802.11 a/b/g/n or 802.20 or a combination of protocols), all or a portion of the Internet, or any other communication system or systems at one or more locations (or a combination of communication networks). The network can communicate with, for example, Internet Protocol (IP) packets, frame relay frames, asynchronous transfer mode (ATM) cells, voice, video, data, or a combination of communication types between network addresses.

The computing system can include clients and servers. A client and server can generally be remote from each other and can typically interact through a communication network. The relationship of client and server can arise by virtue of computer programs running on the respective computers and having a client-server relationship. Cluster file systems can be any file system type accessible from multiple servers for read and update. Locking or consistency tracking may not be necessary since the locking of exchange file system can be done at application layer. Furthermore, Unicode data files can be different from non-Unicode data files.

While this specification contains many specific implementation details, these should not be construed as limitations on the scope of what may be claimed, but rather as descriptions of features that may be specific to particular implementations. Certain features that are described in this specification in the context of separate implementations can also be implemented, in combination, in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations, separately, or in any suitable sub-combination. Moreover, although previously described features may be described as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can, in some cases, be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.

Particular implementations of the subject matter have been described. Other implementations, alterations, and permutations of the described implementations are within the scope of the following claims as will be apparent to those skilled in the art. While operations are depicted in the drawings or claims in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed (some operations may be considered optional), to achieve desirable results. In certain circumstances, multitasking or parallel processing (or a combination of multitasking and parallel processing) may be advantageous and performed as deemed appropriate.

Moreover, the separation or integration of various system modules and components in the previously described implementations should not be understood as requiring such separation or integration in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

Accordingly, the previously described example implementations do not define or constrain the present disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of the present disclosure.

Furthermore, any claimed implementation is considered to be applicable to at least a computer-implemented method; a non-transitory, computer-readable medium storing computer-readable instructions to perform the computer-implemented method; and a computer system comprising a computer memory interoperably coupled with a hardware processor configured to perform the computer-implemented method or the instructions stored on the non-transitory, computer-readable medium.

Particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results. As one example, some processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results.

Claims

1. A computer-implemented method that enables estimating reservoir properties, comprising:

obtaining, using at least one hardware processor, bottom-hole pressure data, a bottom-hole fluid model, and bottom-hole temperature data as an 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;

determining, using the at least one hardware processor, a mass rate of the injection fluid based on, at least in part, a wellhead fluid model and wellhead flow rate; and

determining, using the at least one hardware processor, bottom-hole flow rate data corresponding to wellhead flow rate data based on, at least in part, the mass rate and the bottom-hole fluid model.

2. The computer implemented method of claim 1, wherein the injection fluid is a thermally-sensitive injection fluid.

3. The computer implemented method of claim 1, wherein input data is automatically rendered on a log-log plot to realize at least one flow regime.

4. The computer implemented method of claim 1, wherein the bottom-hole flow rate and obtained bottom-hole pressure are used to characterize the host reservoir.

5. The computer implemented method of claim 4, wherein characterizing the host reservoir comprises determining a size of the host reservoir, a shape of the host reservoir, an ability of the host reservoir to produce fluids, or any combinations thereof.

6. The computer implemented method of claim 1, comprising synchronizing the bottom-hole pressure, the bottom-hole flow rate, and the bottom-hole temperature to enhance log-log diagnostics.

7. The computer implemented method of claim 1, wherein the bottom-hole pressure and the bottom-hole temperature are obtained from at least one downhole gauge.

8. The computer implemented method of claim 1, comprising tying the well into a production stream, wherein the well is managed in the production stream according to the operating strategy in force.

9. An apparatus comprising a non-transitory, computer readable, storage medium that stores instructions that, when executed by at least one processor, cause the at least one processor to perform operations comprising:

obtaining bottom-hole pressure data, a bottom-hole fluid model, and bottom-hole temperature data as an 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;

determining a mass rate of the injection fluid based on, at least in part, a wellhead fluid model and wellhead flow rate; and

determining bottom-hole flow rate data corresponding to wellhead flow rate data based on, at least in part, the mass rate and the bottom-hole fluid model.

10. The apparatus of claim 9, wherein the injection fluid is a thermally-sensitive injection fluid.

11. The apparatus of claim 9, wherein input data is automatically rendered on a log-log plot to realize at least one flow regime.

12. The apparatus of claim 9, wherein the bottom-hole flow rate and obtained bottom-hole pressure are used to characterize the host reservoir.

13. The apparatus of claim 12, wherein characterizing the host reservoir comprises determining a size of the host reservoir, a shape of the host reservoir, an ability of the host reservoir to produce fluids, or any combinations thereof.

14. The apparatus of claim 9, comprising synchronizing the bottom-hole pressure, the bottom-hole flow rate, and the bottom-hole temperature to enhance log-log diagnostics.

15. The apparatus of claim 9, wherein the bottom-hole pressure and the bottom-hole temperature are obtained from at least one downhole gauge.

16. A system, comprising:

one or more memory modules;

one or more hardware processors communicably coupled to the one or more memory modules, the one or more hardware processors configured to execute instructions stored on the one or more memory modules to perform operations comprising:

obtaining bottom-hole pressure data, a bottom-hole fluid model, and bottom-hole temperature data as an 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;

determining a mass rate of the injection fluid based on, at least in part, a wellhead fluid model and wellhead flow rate; and

determining bottom-hole flow rate data corresponding to wellhead flow rate data based on, at least in part, the mass rate and the bottom-hole fluid model.

17. The system of claim 16, wherein the injection fluid is a thermally-sensitive injection fluid.

18. The system of claim 16, wherein input data is automatically rendered on a log-log plot to realize at least one flow regime.

19. The system of claim 16, wherein the bottom-hole flow rate and obtained bottom-hole pressure are used to characterize the host reservoir.

20. The system of claim 19, wherein characterizing the host reservoir comprises determining a size of the host reservoir, a shape of the host reservoir, an ability of the host reservoir to produce fluids, or any combinations thereof.