Patent Grant
10352162
Modeling and numerical solution of miscible contamination cleanup may be performed in association with downhole sampling of fluid from a subterranean formation.
This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify indispensable features of the claimed subject matter, nor is it intended for use as an aid in limiting the scope of the claimed subject matter.
The present disclosure introduces a method that includes operating a processing system comprising a processor and a memory to generate a proxy model by utilizing a true numerical model. The true model utilizes true model input parameters that include a pumping parameter descriptive of a pumpout time or volume of fluid to be obtained from a subterranean formation by a downhole sampling tool positioned in a wellbore extending into the subterranean formation, formation parameters descriptive of the subterranean formation, and a filtrate parameter descriptive of a drilling fluid utilized to form the wellbore. The output of the true model is contamination of the obtained fluid as a function of the pumping parameter. The proxy model utilizes proxy model input parameters each related to one or more of the true model input parameters. The output of the proxy model is the pumping parameter as a function of the contamination. Generating the proxy model includes (a) utilizing the true model to generate a plurality of true solutions for each of a plurality of different combinations of values of each of the plurality of true model input parameters, and (b) estimating fitting parameters of the proxy model utilizing the true solutions.
The present disclosure also introduces a method of evaluating performance of a downhole sampling tool in a formation traversed by a wellbore. The method includes generating a proxy model by utilizing a true numerical model of a downhole tool. The true model utilizes true model input parameters that include (i) a pumping parameter descriptive of a pumpout time or volume of fluid to be obtained from a subterranean formation by a downhole sampling tool positioned in a wellbore extending into the subterranean formation, (ii) formation parameters descriptive of the subterranean formation, and (iii) a filtrate parameter descriptive of a drilling fluid utilized to form the wellbore. The output of the true model is contamination of the obtained fluid as a function of the pumping parameter. The proxy model utilizes proxy model input parameters each related to one or more of the true model input parameters. The output of the proxy model is the pumping parameter as a function of the contamination. Generating the proxy model includes (i) utilizing the true model to generate true solutions for different combinations of values of each of the true model input parameters, and (ii) estimating fitting parameters of the proxy model utilizing the true solutions. The method also includes obtaining values of formation and filtrate input parameters representative of formation at a particular depth, and using the proxy model for the downhole tool and the values of the input parameters to evaluate performance of a downhole sampling tool by estimating pumpout time or volume required to reach desired contamination level of a sampled fluid at a particular depth in a formation. One or more aspects of the method are performed by one or more processing systems each comprising a processor and a memory.
The present disclosure also introduces a method of operating a processing system comprising a processor and a memory, including utilizing a proxy model to generate a pumping parameter as a function of contamination. The pumping parameter is descriptive of a pumpout time or volume of fluid to be obtained from a subterranean formation by a downhole sampling tool positioned in a wellbore extending into the subterranean formation. The contamination is a percentage of the fluid obtained by the downhole sampling tool that is not native to the subterranean formation. The proxy model is based on a true model. The true model utilizes true model input parameters that include the pumping parameter, formation parameters descriptive of the subterranean formation, and a filtrate parameter descriptive of a drilling fluid utilized to form the wellbore. The output of the true model is the contamination as a function of the pumping parameter. The proxy model utilizes proxy model input parameters each related to one or more of the true model input parameters.
These and additional aspects of the present disclosure are set forth in the description that follows, and/or may be learned by a person having ordinary skill in the art by reading the material herein and/or practicing the principles described herein. At least some aspects of the present disclosure may be achieved via means recited in the attached claims.
The present disclosure is understood from the following detailed description when read with the accompanying figures. It is emphasized that, in accordance with the standard practice in the industry, various features are not drawn to scale. In fact, the dimensions of the various features may be arbitrarily increased or reduced for clarity of discussion.
It is to be understood that the following disclosure provides many different embodiments, or examples, for implementing different features of various embodiments. Specific examples of components and arrangements are described below to simplify the present disclosure. These are, of course, merely examples and are not intended to be limiting. In addition, the present disclosure may repeat reference numerals and/or letters in the various examples. This repetition is for simplicity and clarity, and does not in itself dictate a relationship between the various embodiments and/or configurations discussed. Moreover, the formation of a first feature over or on a second feature in the description that follows may include embodiments in which the first and second features are formed in direct contact, and may also include embodiments in which additional features may be formed interposing the first and second features, such that the first and second features may not be in direct contact.
The present disclosure introduces one or more aspects related to parameterizing and/or approximating the solution to a mathematical model for miscible contamination cleanup, such as in relation to sampling of oil in a well drilled using oil-based drilling mud (OBM), sampling of water in a well drilled using water-based mud (WBM), and/or sampling of other subterranean formation fluids.
The present disclosure introduces methods to parameterize a mathematical model for miscible contamination cleanup for fluid sampling, approximate the model solution, and/or conduct sensitivity analyses for the input parameters, among other aspects. A low-dimensional parameterization may permit an accurate model approximation using, for example, a kriging-based proxy model. The resulting proxy model may be suitable for a variety of applications, including fast forward modeling in a tool planner workflow, as well as inverse modeling for design optimization, real-time contamination prediction, and/or closed-loop optimal control of the fluid sampling process, among other applications. The present disclosure also introduces a method that utilizes the proxy model to quantify uncertainty and identify the main sources of the uncertainty.
Downhole acquisition of fluid samples (oil, water, and/or gas) for pressure-volume-temperature (PVT) analysis using a wireline formation tester (WFT) is performed for characterizing and understanding a subterranean formation or reservoir. Knowledge of fluid type and properties may be utilized during planning of wells and surface facilities. The WFT may be equipped with one or more pumps, chambers for storing sampled fluid, and/or probes and/or packers that may be urged against a wellbore wall to establish hydraulic communication with the formation. However, oil-based mud (OBM) or water-based mud (WMB) may invade the formation during the wellbore drilling operations, thus contaminating the near-wellbore area of the formation, such that an initial or early phase of fluid sampling may include a cleanup operation to remove the contamination. Upon identification of clean formation fluid during continued pumping of fluid from the formation, the operation may switch from the cleanup phase to a sample collection phase, in which the formation fluid is diverted into one or more sample chambers of the downhole tool string, such as for subsequent fluid analysis after returning the downhole tool string to the wellsite surface. The combined cleanup and sampling operations at a single depth within the wellbore (station) may last for several hours. However, due to high rig costs, especially in offshore environments, and the risk of differential sticking of the downhole tool string, operators may seek to acquire the fluid samples as quickly as possible, while ensuring that the contamination level in the samples is sufficiently low (e.g., less than about five percent).
Accordingly, operators may perform pre-job modeling to predict cleanup times and/or select a downhole sampling tool suited for the given circumstances. For example, a three-dimensional (3D) numerical model may be utilized to describe the changing mixture of drilling fluid contamination and native formation fluid during the cleanup operation. The model may provide a prediction of the fraction of contaminant in the fluid pumped from the formation as a function of pumpout time or volume, thus permitting a prediction of the elapsed time at which a predetermined level of reduced contamination may be obtained. However, high-resolution 3D cleanup models may be computationally demanding and/or otherwise less practical for tool planner workflows, which may call for quickly evaluating multiple scenarios, such as may be due to inherent uncertainty in the formation and fluid properties.
In this context, the present disclosure introduces one or more aspects regarding approximating the numerical solutions in manners that may be both fast and accurate. The approximated solutions may then be utilized for comprehensive uncertainty analysis, such as may comprise global sensitivity analysis, and where causes of uncertainty in the predicted cleanup volume or time for a predetermined contamination level may be identified.
One or more aspects introduced in the present disclosure may find application in fast-forward modeling. For example, the proxy model described herein may be utilized to quickly evaluate parameter sensitivities, perform tool comparisons, and assess operational procedures, including where relevant to tool planner workflows and/or uncertainty quantification workflows, among other examples.
One or more aspects introduced in the present disclosure may also find application in inverse problems. For example, the proxy model described herein may be utilized in place of the true model in inverse modeling exercises, such as to speed up the optimization process. Examples may include tool design optimization and/or estimation of formation and/or fluid properties from observed cleanup data.
One or more aspects introduced in the present disclosure may also find application in real-time contamination monitoring. For example, in an application of inverse problems, as described above, the proxy model described herein may be utilized for real-time contamination monitoring by on-the-fly inversion for formation and/or fluid parameters from observed optical fluid analyzer data, and/or subsequent prediction of the cleanup time/volume remaining to reach a predetermined level of contamination.
One or more aspects introduced in the present disclosure may also find application in closed-loop optimal control of the sampling process. For example, in a combination of the above-described inverse problems and real-time contamination monitoring, the proxy model described herein may be utilized in closed-loop optimal control of the sampling process by observing contamination levels and computing real-time operational adjustments, such as changing of pump rates and/or changing of guard/sample flow split ratios for focused tools, among other examples.
One or more aspects introduced in the present disclosure pertain to the parameterization of a miscible fluid contamination cleanup model by a small (or the smallest possible) parameter set that is as complete as possible, such as parameterization that captures the variation in eight physical parameters of the contamination cleanup in three non-dimensional parameters. Such aspects may dimensionally reduce parameter space, which may facilitate the proxy model construction. One or more aspects introduced in the present disclosure may also or instead pertain to the application of kriging-based interpolation for proxy model construction, such as may be based on the parameterization described above. One or more aspects introduced in the present disclosure may also or instead pertain to the quantification of uncertainty and identification of contributors to uncertainty in the model predictions of cleanup volume and/or time.
The following description regards an example implementation of model parameterization for proxy model construction according to one or more aspects of the present disclosure.
The miscible contamination cleanup process with respect to a WFT probe may be modeled as single-phase flow with contaminant transport, as set forth below in Equations (1)-(6).
where φ is porosity, ρ is fluid mixture density, t is pumpout time, ∇ is a differential operator, u is a vector of velocities, Q is pump rate, w is contaminant mass fraction, k is a permeability tensor, μ is mixture viscosity, P is pressure, g is a vector of gravitational acceleration, Z is reservoir depth, ρ0 is density at reference pressure, e is the mathematical constant (base of the natural logarithm), cf is fluid compressibility, P0 is reference pressure, φ0 is porosity at reference pressure, cr is rock compressibility, μmf is contaminant (mud filtrate) viscosity, and μ0 is formation fluid viscosity. A linear mixing rule is suggested in Equation (6) for the mixture viscosity, but other mixing rules may also be used within the scope of the present disclosure.
A vertical well may be assumed in a non-dipping formation.
The symbol Kv is for absolute vertical permeability, but may be excluded from the model input parameters because Kh and Kv/Kh are known. It is also noted that parameters such as fluid density and compressibility are not included in Table 1 because these parameters generally do not affect miscible contamination cleanup behavior when varied within common ranges for oil sampling in OBM or water sampling in WBM.
The model represented by Equations (1)-(6) set forth above can be solved numerically by discretization in time and space. This process of numerical solution is well known in the field, and various discretization techniques and simulation codes may be utilized within the scope of the present disclosure, such as the commercial reservoir simulator ECLIPSE. In the context of the application of kriging-based interpolation for proxy model construction, the above model and its numerical solution are referred to as the true model and true solution, respectively. It is thus understood that the true solution may be a converged numerical solution, in the sense that it may be computed on a sufficiently fine grid and using sufficiently fine time intervals such that numerical approximation errors do not affect the solution.
The output from the true model may include the fraction of contaminant in the pumped formation fluid as a function of the pumped volume or, assuming a substantially constant pump rate, as a function of pumping time. For the proxy modeling, the pumped volume Vp is expressed as a function of the contaminant concentration and a vector or parameters, as set forth below in Equation (7).
Vp=Vp(w,p) (7)
where p is the vector of parameters, such as permeability, porosity, and/or others.
The proxy model is utilized to approximate the functional relationship between the pumped volume and the contaminant concentration over relevant ranges for the associated parameters.
The parameters in Table 1 set forth above are the actual physical parameters, but they do not affect the cleanup behavior independently. Thus, for the purpose of proxy model construction, the parameter set can be reduced. That is, the cleanup behavior can be considered governed by the dimensionless parameters set forth below in Equations (8)-(10).
where δ is dimensionless invasion depth, Dw is diameter of the wellbore,
In addition, for fixed values of the dimensionless parameters, the relations set forth below in Equations (11)-(14) hold.
where φa and φb denote two values of porosity, Dwa and Dwb denote two values of wellbore diameter, Qa and Qb denote two values of pump rate, and Ma and Mb denote two values of fluid mobility.
Thus, cleanup volume is not affected by mobility and pump rate, and the effects of porosity and wellbore diameter can be accounted for by simple volume corrections. Accordingly, while the proxy model may internally address variations in just the three non-dimensional parameters, it may be utilized to predict the behavior for the entire set of parameters, such as set forth above in Table 1.
It is also noted that, while the model parameterization presented above is specific to the kind of model utilized for the miscible contamination cleanup process, the approximation based on kriging interpolation described below may also be utilized for other types of cleanup models. For example, the model may be extended to include the effects of reservoir thickness, tool proximity to a bed boundary, and/or wellbore inclination, among other examples, such as by including additional parameters in the minimal complete parameter set.
The following description regards an example implementation of proxy modeling for miscible contamination cleanup according to one or more aspects of the present disclosure.
As described above, one or more aspects introduced in the present disclosure may pertain to the application of kriging-based interpolation to construct a proxy model for miscible contamination cleanup behavior. The kriging-based proxy model may be expressed as set forth below in Equation (15).
{circumflex over (V)}p(p)=αTΦ(θ,p)+βTf(p) (15)
where {circumflex over (V)}p denotes the kriging prediction of pumped volume at a given level of contamination, p denotes the vector of input parameters, T is the transpose operator, f(p) denotes a regression part of the model that includes low-order polynomials and that accounts for a global trend in the modeled data, Φ(θ, p) denotes a correlation part of the model, and α and β denote kriging model parameters that may be estimated by fitting the responses from the true model.
It may be assumed that m true model responses are given, which may be expressed as set forth below in Equation (16).
{(pi,yi=Vp(pi))}i=1m (16)
where yi is the ith of m true model responses utilizing the vector of input parameters p.
That is, the true model is evaluated in m different points in the parameter space. The regression (f(p)) and correlation (Φ(θ, p)) functions may be expressed as set forth below in Equations (17) and (18).
f(p)=[f1(p), . . . ,fq(p)]T (17)
Φ(θ,p)=[Φ1(θ,p), . . . ,Φm(θ,p)]T (18)
where Φi(θ, p)=Φi(∥Θ(p−pi)∥2) and Θ=diag(θ1, . . . , θd). Thus, the correlation function Φ(θ, p) is a function of the distance between the points in which the true model was evaluated, pi, and the current point of interest, p. The vector θ denotes scaling parameters that govern the correlation lengths in each of the parameter directions. Several different functional forms for the correlation functions were tested, and a Gaussian function of the form set forth below in Equation (19) was found to give satisfactory results. However, other Gaussian, exponential, spline, and/or other correlation functions may also be utilized within the scope of the present disclosure.
Φi=exp(−∥Θ(p−pi)∥22) (19)
For the regression functions f(p), the use of second order polynomials was found to give satisfactory results, as measured by the mean prediction error when validating the proxy model against true model responses not used during the proxy construction.
In the following description, the application of kriging-based proxy modeling to miscible contamination cleanup is demonstrated through an example cleanup using a WFT probe.
The true model may initially be evaluated at selected points in the parameter space to generate the true solutions to which the proxy model will be fitted. Example parameter ranges of interest are set forth below in Table 2.
It is noted that the minimum and maximum values in the examples of Table 2 correspond to a DOI ranging between about 2 inches (5.1 cm) and about 32 inches (81.3 cm) for a wellbore having a diameter of about 8.5 inches (21.6 cm).
A Latin Hypercube experimental design may be utilized to randomly select sixty (for example) parameter combinations, as shown in
Upon evaluation of the true model, the proxy model coefficients may be fitted by enforcing conditions by which the proxy model honors the true solutions. The methodology for fitting the coefficients is known in the art. Improved proxy accuracy may be obtained by utilizing a logarithmic transform prior to fitting the proxy, such that the actual proxy model may express the relationship between the logarithm of pumped volume/time and the input parameters (such as permeability anisotropy, viscosity ratio, and dimensionless depth-of-invasion).
The quality of the proxy model may be evaluated by validating the accuracy of its predictions for input parameter combinations not used when fitting the proxy coefficients. This validation step may also aid in validating the model parameterization by sampling in the original parameters (such as set forth above in Table 1) and evaluating the true model response using these parameters. Table 3, set forth below, lists example ranges and distributions that may be used for generating 100 random parameter combinations for which the true model is evaluated. Histograms for the 100 validation parameter sets are shown in
Accuracy of the proxy model may be most relevant in the low contamination range (such as less than about twenty percent), approaching the pumpout volume/time where fluid sample collection is initiated. The relative error in the proxy prediction of the pumped volume at five percent contamination may thus be utilized as a measure of proxy accuracy, as set forth below in Equation (20).
Example comparisons of proxy predictions and true model solutions are shown in
It is noted that, while the examples presented in this section of the disclosure concern proxy modeling of the cleanup behavior of a WFT probe, the methodology presented for proxy model construction may also be applicable or readily adaptable to cleanup by dual-packers, single-packers with multiple discrete fluid drains, as well as focused probes and packers.
The following description regards an example implementation of tool planner workflow and global sensitivity analysis according to one or more aspects of the present disclosure.
Multiple scenarios for sampling job designs may be considered during operations encountering incomplete data and/or uncertainty in reservoir and/or fluid properties. The constructed proxy model may be utilized to explore and evaluate these scenarios in almost real-time, such as by one or more of the following. First, given the available data about the reservoir, the ranges for uncertain input parameters may be sampled (perhaps exhaustively) according to assigned probability distributions. Second, statistical estimates (e.g., P05-P50-P95) for the cleanup volume pumped to reach a predetermined contamination level may be obtained utilizing the proxy model. Third, the uncertainty in the obtained estimates for the cleanup volume may be expressed via predetermined quantile ranges (e.g., P05-P95) or via standard deviation.
In the examples of
Therefore, a systematic approach may be utilized to (1) quantify and rank the main contributions to this uncertainty from the input parameters, and (2) suggest a targeted measurement program to reduce uncertainty in the identified parameters, such that the uncertainty in the predicted cleanup volume may be reduced as much as possible.
Sensitivity analysis generally quantifies the significance of input parameters in computing model predictions. In the presence of uncertainty, it may be instructive to examine a global sensitivity analysis (GSA) that quantifies the relation between uncertainties in the input parameters and uncertainty in the model outcome. Unlike traditional sensitivity analyses, such as may be based on local partial derivatives, GSA relies on variance decomposition into terms with increasing dimensionality, and explores the entire input parameter domain. This may be of particular concern for the analysis of nonlinear and non-monotonous phenomena, such as miscible cleanup processes considered in this disclosure, where traditional correlation-based methods and other commonly used approaches (such as one-at-a-time) may not be applicable.
GSA can be applied in a general problem setting with a set of uncertain input parameters, a model, and a corresponding set of model predictions. For example, let the uncertainty in the prediction of the model for Y be characterized by its variance V(Y), therefore assuming that the variance is an adequate representation of the uncertainty in Y. This assumption is often valid except for highly asymmetric probability distributions of Y. The contributions to V(Y) due to the uncertainties in the input parameters {Xi} may then be estimated.
For independent {Xi}, the Sobol' variance decomposition can be utilized to represent V(Y), as set forth below in Equation (21)
V(Y)=Σi=1NVi+Σ1≤i<j≤NVij+ . . . +V12 . . . N (21)
where Vi=V[E(Y|Xi)] are the variance in conditional expectations (E) of Y when Xi is fixed, (e.g., V(Xi)=0). Thus, Vi represent first-order contributions to the total variance V(Y). Since the true value of Xi is not known a priori, the expected value of Y when Xi is fixed (within its possible range) may be estimated, while the rest of the input parameters {Xi−1} may be varied according to their original probability distributions. Thus, Equation (22) set forth below is an estimate of the relative reduction in total variance of Y if the variance in Xi is reduced to zero.
S1i=Vi/V(Y) (22)
Similarly, Vij=V[E(Y|Xi, Xj)]−Vi−Vj is the second-order contribution to the total variance V(Y) due to interaction between Xi and Xj. The estimate of variance when both Xi and Xj are fixed simultaneously may be corrected for individual contributions Vi and Vj.
For additive models Y(X), the sum of the first-order effects S1i is equal to 1. This is not applicable for the general case of non-additive models, where second, third, and higher-order effects (e.g., interactions between two, three, or more input parameters) play a not unsubstantial role. The contribution due to higher-order effects may be estimated, however, via the total sensitivity index ST, as set forth below in Equation (23).
ST1={V(Y)−V[E(Y|X˜i)]}/V(Y), (23)
where V(Y)−V[E(Y|X˜i)] is the total variance contribution from the terms in variance decompositions that include Xi. It is also noted that STi≥S1i, and the difference between the two represents the contribution from the higher-order interaction effects that include Xi.
There are several methods available to estimate S1i and STi. For example, one may utilize an algorithm developed by Saltelli that further extends a computational approach proposed by Sobol' and Homma and Saltelli. The computational cost of calculating both S1i and STi is N(k+2), where k is a number of input parameters and N is a number of model evaluations large enough (such as between 1,000 and 10,000) to obtain an accurate estimate of conditional means and variances. With the computationally expensive true model replaced by an accurate and fast proxy model, the computational cost of GSA may become negligible.
Based on the first-order sensitivity indices shown in
The interpretation of total sensitivity indices shown in
Another illustration of the presently disclosed workflow is shown in
Results of associated GSA are shown in
The values of GSA indices and their dynamics (e.g., variation with change in contamination level) may depend on the assumed ranges of the uncertain input parameters and their assigned distributions. These assumptions may be made based on available data regarding the intended sampling interval to ensure that the GSA-based recommendations are relevant and representative.
As shown in
The drillstring 212 may be raised and lowered by turning the lifting gear with the winch, which may sometimes include temporarily unhooking the drillstring 212 from the lifting gear. In such scenarios, the drillstring 212 may be supported by blocking it with wedges in a conical recess of the rotary table 216, which is mounted on a platform 221 through which the drillstring 212 passes.
The drillstring 212 may be rotated by the rotary table 216, which engages the kelly 217 at the upper end of the drillstring 212. The drillstring 212 is suspended from the hook 218, attached to a traveling block (not shown), through the kelly 217 and the rotary swivel 219, which permits rotation of the drillstring 212 relative to the hook 218. Other example wellsite systems within the scope of the present disclosure may utilize a top drive system to suspend and rotate the drillstring 212, whether in addition to or instead of the illustrated rotary table system.
The surface system may further include drilling fluid or mud 226 stored in a pit 227 formed at the wellsite. As described above, the drilling fluid 226 may comprise OBM or WBM. A pump 229 delivers the drilling fluid 226 to the interior of the drillstring 212 via a hose or other conduit 220 coupled to a port in the swivel 219, causing the drilling fluid to flow downward through the drillstring 212 as indicated by the directional arrow 208. The drilling fluid exits the drillstring 212 via ports in the drill bit 255, and then circulates upward through the annulus region between the outside of the drillstring 212 and the wall of the wellbore 211, as indicated by the directional arrows 209. In this manner, the drilling fluid 226 lubricates the drill bit 255 and carries formation cuttings up to the surface as it is returned to the pit 227 for recirculation.
The BHA 250 may comprise one or more specially made drill collars near the drill bit 255. Each such drill collar may comprise one or more logging devices, thereby permitting downhole drilling conditions and/or various characteristic properties of the geological formation (e.g., such as layers of rock or other material) intersected by the wellbore 211 to be measured as the wellbore 211 is deepened. For example, the BHA 250 may comprise a logging-while-drilling (LWD) module 270, a measurement-while-drilling (MWD) module 280, a rotary-steerable system and motor 260, and/or the drill bit 255. Of course, other BHA components, modules, and/or tools are also within the scope of the present disclosure.
The LWD module 270 may be housed in a drill collar and may comprise one or more logging tools. More than one LWD and/or MWD module may be employed, e.g., as represented at 270A. References herein to a module at the position of 270 may mean a module at the position of 270A as well. The LWD module 270 may comprise capabilities for measuring, processing, and storing information, as well as for communicating with the surface equipment.
The MWD module 280 may also be housed in a drill collar and may comprise one or more devices for measuring characteristics of the drillstring 212 and/or drill bit 255. The MWD module 280 may further comprise an apparatus (not shown) for generating electrical power to be utilized by the downhole system. This may include a mud turbine generator powered by the flow of the drilling fluid 226. However, other power and/or battery systems may also or instead be employed. In the example shown in
At least one of the LWD modules 270/270A and/or the MWD module 280 comprises a downhole tool operable to obtain downhole a sample of fluid from the subterranean formation and perform downhole fluid analysis (DFA) to measure or estimate the composition and/or other properties of the obtained fluid sample. Such DFA may be utilized for contamination monitoring and/or cleanup prediction according to one or more aspects described elsewhere herein. The downhole fluid analyzer may then report the resulting data to the surface equipment 290.
The operational elements of the BHA 250 may be controlled by one or more electrical control systems within the BHA 250 and/or the surface equipment 290. For example, such control system(s) may include processor capability for characterization of formation fluids in one or more components of the BHA 250 according to one or more aspects of the present disclosure. Methods within the scope of the present disclosure may be embodied in one or more computer programs that run in one or more processors located, for example, in one or more components of the BHA 250 and/or the surface equipment 290. Such programs may utilize data received from one or more components of the BHA 250, for example, via mud-pulse telemetry and/or other telemetry means, and may be operable to transmit control signals to operative elements of the BHA 250. The programs may be stored on a suitable computer-usable storage medium associated with one or more processors of the BHA 250 and/or surface equipment 290, or may be stored on an external computer-usable storage medium that is electronically coupled to such processor(s). The storage medium may be one or more known or future-developed storage media, such as a magnetic disk, an optically readable disk, flash memory, or a readable device of another kind, including a remote storage device coupled over a telemetry link, among others.
The downhole tool 320 comprises an elongated body 326 encasing a variety of electronic components and modules, which are schematically represented in
One or more fluid sampling and analysis modules 332 are provided in the tool body 326. Fluids obtained from the formation and/or wellbore flow through a flowline 333, via the fluid analysis module or modules 332, and then may be discharged through a port of a pumpout module 338. Further, formation fluids in the flowline 333 may be directed to one or more fluid collecting chambers 334 for receiving and retaining the fluids obtained from the formation for transportation to the surface.
The fluid admitting assemblies, one or more fluid analysis modules, the flow path, the collecting chambers, and/or other operational elements of the downhole tool 320 may be controlled by one or more electrical control systems within the downhole tool 320 and/or the surface equipment 324. For example, such control system(s) may include processor capability for characterization of formation fluids in the downhole tool 320 according to one or more aspects of the present disclosure. Methods within the scope of the present disclosure may be embodied in one or more computer programs that run in one or more processors located, for example, in the downhole tool 320 and/or the surface equipment 324. Such programs may utilize data received from, for example, the fluid sampling and analysis module 332, via the wireline cable 322, and may be operable to transmit control signals to operative elements of the downhole tool 320. The programs may be stored on a suitable computer-usable storage medium associated with the one or more processors of the downhole tool 320 and/or surface equipment 324, or may be stored on an external computer-usable storage medium that is electronically coupled to such processor(s). The storage medium may be one or more known or future-developed storage media, such as a magnetic disk, an optically readable disk, flash memory, or a readable device of another kind, including a remote storage device coupled over a switched telecommunication link, among others.
An example downhole tool or module 400 that may be utilized in the example systems 200 and 300 of
An example downhole fluid analyzer 500 that may be used to implement DFA in the example downhole tool 400 shown in
The processing system 600 may comprise a processor 612 such as, for example, a general-purpose programmable processor. The processor 612 may comprise a local memory 614, and may execute coded instructions 632 present in the local memory 614 and/or another memory device. The processor 612 may execute, among other things, machine-readable instructions or programs to implement the methods and/or processes described herein. The programs stored in the local memory 614 may include program instructions or computer program code that, when executed by an associated processor, may permit surface equipment and/or downhole controller and/or control system to perform tasks as described herein. The processor 612 may be, comprise, or be implemented by one or more processors of various types suitable to the local application environment, and may include one or more of general-purpose computers, special-purpose computers, microprocessors, digital signal processors (“DSPs”), field-programmable gate arrays (“FPGAs”), application-specific integrated circuits (“ASICs”), and processors based on a multi-core processor architecture, as non-limiting examples. Of course, other processors from other families are also appropriate.
The processor 612 may be in communication with a main memory, such as may include a volatile memory 618 and a non-volatile memory 620, perhaps via a bus 622 and/or other communication means. The volatile memory 618 may be, comprise, or be implemented by random access memory (RAM), static random access memory (SRAM), synchronous dynamic random access memory (SDRAM), dynamic random access memory (DRAM), RAMBUS dynamic random access memory (RDRAM) and/or other types of random access memory devices. The non-volatile memory 620 may be, comprise, or be implemented by read-only memory, flash memory and/or other types of memory devices. One or more memory controllers (not shown) may control access to the volatile memory 618 and/or the non-volatile memory 620.
The processing system 600 may also comprise an interface circuit 624. The interface circuit 624 may be, comprise, or be implemented by various types of standard interfaces, such as an Ethernet interface, a universal serial bus (USB), a third generation input/output (3GIO) interface, a wireless interface, and/or a cellular interface, among others. The interface circuit 624 may also comprise a graphics driver card. The interface circuit 624 may also comprise a communication device such as a modem or network interface card to facilitate exchange of data with external computing devices via a network (e.g., Ethernet connection, digital subscriber line (“DSL”), telephone line, coaxial cable, cellular telephone system, satellite, etc.).
One or more input devices 626 may be connected to the interface circuit 624. The input device(s) 626 may permit a user to enter data and commands into the processor 612. The input device(s) 626 may be, comprise, or be implemented by, for example, a keyboard, a mouse, a touchscreen, a track-pad, a trackball, an isopoint, and/or a voice recognition system, among others.
One or more output devices 628 may also be connected to the interface circuit 624. The output devices 628 may be, comprise, or be implemented by, for example, display devices (e.g., a liquid crystal display or cathode ray tube display (CRT), among others), printers, and/or speakers, among others.
The processing system 600 may also comprise one or more mass storage devices 630 for storing machine-readable instructions and data. Examples of such mass storage devices 630 include floppy disk drives, hard drive disks, compact disk (CD) drives, and digital versatile disk (DVD) drives, among others. The coded instructions 632 may be stored in the mass storage device 630, the volatile memory 618, the non-volatile memory 620, the local memory 614, and/or on a removable storage medium 634, such as a CD or DVD. Thus, the modules and/or other components of the processing system 600 may be implemented in accordance with hardware (embodied in one or more chips including an integrated circuit such as an application specific integrated circuit), or may be implemented as software or firmware for execution by a processor. In particular, in the case of firmware or software, the embodiment can be provided as a computer program product including a computer readable medium or storage structure embodying computer program code (i.e., software or firmware) thereon for execution by the processor.
In view of the entirety of the present disclosure, including the figures and the claims, a person having ordinary skill in the art will readily recognize that the present disclosure introduces a method comprising: operating a processing system comprising a processor and a memory to generate a proxy model by utilizing a true numerical model, wherein: the true model utilizes a plurality of true model input parameters that include: (a) a pumping parameter descriptive of a pumpout time or volume of fluid to be obtained from a subterranean formation by a downhole sampling tool positioned in a wellbore extending into the subterranean formation; (b) a plurality of formation parameters descriptive of the subterranean formation; and (c) a filtrate parameter descriptive of a drilling fluid utilized to form the wellbore; the output of the true model is contamination of the obtained fluid as a function of the pumping parameter; the proxy model utilizes a plurality of proxy model input parameters each related to one or more of the true model input parameters; the output of the proxy model is the pumping parameter as a function of the contamination; and generating the proxy model comprises: (a) utilizing the true model to generate a plurality of true solutions for each of a plurality of different combinations of values of each of the plurality of true model input parameters; and (b) estimating fitting parameters of the proxy model utilizing the true solutions.
The proxy model may include a regression function that approximates the proxy model output via interpolation utilizing the true solutions. The interpolation may be kriging-based interpolation. The interpolation may approximate the proxy model output as a plurality of low-order polynomials. The low-order polynomials may be second-order polynomials. The proxy model may further include a correlation function that weights the regression-approximated proxy model output utilizing the true solutions. The correlation function may be at least one of a Gaussian function, an exponential function, and/or a spline function.
The number of proxy model input parameters may be less than the number of true model input parameters. The ones of the true model input parameters that are related to the proxy model input parameters may each independently affect a cleanup behavior of the pumped fluid, and others of the true model input parameters may not be related to the proxy model input parameters and may not independently affect the cleanup behavior. Each of the proxy model input parameters may be dimensionless, and each of the true model input parameters may not be dimensionless. For example, the true model input parameters may include at least two of porosity of the subterranean formation, absolute horizontal permeability of the subterranean formation, absolute permeability anisotropy of the subterranean formation, viscosity of the fluid to be obtained from the subterranean formation, viscosity of the contamination, depth of invasion of the contamination into the subterranean formation from the center of the wellbore, diameter of the wellbore, and the pumping parameter, and the proxy model input parameters may include at least one of a first ratio of the depth of contamination invasion to the wellbore diameter, a second ratio of the viscosity of the fluid to be obtained from the subterranean formation to the contamination viscosity, and the absolute permeability anisotropy of the subterranean formation. The true model input parameters may include each of porosity of the subterranean formation, absolute horizontal permeability of the subterranean formation, absolute permeability anisotropy of the subterranean formation, viscosity of the fluid to be obtained from the subterranean formation, viscosity of the contamination, depth of invasion of the contamination into the subterranean formation from the center of the wellbore, diameter of the wellbore, and the pumping parameter, and the proxy model input parameters may include each of a first ratio of the depth of contamination invasion to the wellbore diameter, a second ratio of the viscosity of the fluid to be obtained from the subterranean formation to the contamination viscosity, and the absolute permeability anisotropy of the subterranean formation.
The processing system, the processor, and the memory may be a first processing system, a first processor, and a first memory, respectively. The first processing system may be separate and distinct from a second processing system comprising a second processor and a second memory. The method may further comprise operating one of the first and second processing systems to evaluate each of a plurality of sampling job scenarios utilizing the proxy model. Evaluating the sampling job scenarios may comprise: randomly selecting values for each one of the proxy model input parameters that is unknown in the sampling job scenarios; utilizing the proxy model to generate a plurality of estimates of the pumping parameter at a predetermined contamination utilizing the randomly selected values for each of the unknown proxy model input parameters; and generating statistical estimates for the generated plurality of the pumping parameter estimates. The method may further comprise: applying a global sensitivity analysis to the plurality of estimated pumping parameter values; and identifying a formation or filtrate parameter that most influences the uncertainty in the estimated pumping parameter. Identifying the parameter may comprise quantifying a contribution of the parameter to the uncertainty in the estimated pumping parameter. The method may further comprise measuring the identified parameter.
The method may further comprise: obtaining values of the formation and filtrate parameters representative of the subterranean formation at a particular depth in the wellbore; and using the proxy model and the obtained values to evaluate performance of the downhole sampling tool by estimating the pumping parameter value corresponding to a predetermined level of contamination of fluid to be obtained from the subterranean formation by the downhole sampling tool at the particular depth. The method may further comprise repeating the operating and using steps for at least two downhole sampling tools. The method may further comprise repeating the operating, obtaining, and using steps for at least two different depths within the wellbore.
The present disclosure also introduces a method of evaluating performance of a downhole sampling tool in a formation traversed by a wellbore comprising: (a) generating a proxy model by utilizing a true numerical model of a downhole tool, wherein: (1) the true model utilizes a plurality of true model input parameters that include: (i) a pumping parameter descriptive of a pumpout time or volume of fluid to be obtained from a subterranean formation by a downhole sampling tool positioned in a wellbore extending into the subterranean formation; (ii) a plurality of formation parameters descriptive of the subterranean formation; and (iii) a filtrate parameter descriptive of a drilling fluid utilized to form the wellbore; (2) the output of the true model is contamination of the obtained fluid as a function of the pumping parameter; (3) the proxy model utilizes a plurality of proxy model input parameters each related to one or more of the true model input parameters; (4) the output of the proxy model is the pumping parameter as a function of the contamination; and (4) generating the proxy model comprises: (i) utilizing the true model to generate a plurality of true solutions for each of a plurality of different combinations of values of each of the plurality of true model input parameters; and (ii) estimating fitting parameters of the proxy model utilizing the true solutions; (b) obtaining values of formation and filtrate input parameters representative of formation at a particular depth; and (c) using the proxy model for the downhole tool and the values of the input parameters to evaluate performance of a downhole sampling tool by estimating pumpout time or volume required to reach desired contamination level of a sampled fluid at a particular depth in a formation; wherein steps (a) and (c) are performed by one or more processing systems each comprising a processor and a memory.
The present disclosure also introduces a method of operating a processing system comprising a processor and a memory, comprising utilizing a proxy model to generate a pumping parameter as a function of contamination, wherein: the pumping parameter is descriptive of a pumpout time or volume of fluid to be obtained from a subterranean formation by a downhole sampling tool positioned in a wellbore extending into the subterranean formation; the contamination is a percentage of the fluid obtained by the downhole sampling tool that is not native to the subterranean formation; the proxy model is based on a true model; the true model utilizes a plurality of true model input parameters that include: (i) the pumping parameter; (ii) a plurality of formation parameters descriptive of the subterranean formation; and (iii) a filtrate parameter descriptive of a drilling fluid utilized to form the wellbore; the output of the true model is the contamination as a function of the pumping parameter; and the proxy model utilizes a plurality of proxy model input parameters each related to one or more of the true model input parameters.
The proxy model may be generated by: utilizing the true model to generate a plurality of true solutions for each of a plurality of different combinations of values of each of the plurality of true model input parameters; and estimating fitting parameters of the proxy model utilizing the true solutions.
The method may further comprise operating the processing system to evaluate each of a plurality of sampling job scenarios utilizing the proxy model. Evaluating the sampling job scenarios may comprise: randomly selecting values for each one of the proxy model input parameters that is unknown in the sampling job scenarios; utilizing the proxy model to generate statistical estimates of the pumping parameter at a predetermined contamination utilizing the randomly selected values for each of the unknown proxy model input parameters; and generating uncertainties exhibited by the statistical estimates.
The foregoing outlines features of several embodiments so that a person having ordinary skill in the art may better understand the aspects of the present disclosure. A person having ordinary skill in the art should appreciate that they may readily use the present disclosure as a basis for designing or modifying other processes and structures for carrying out the same functions and/or achieving the same benefits of the embodiments introduced herein. A person having ordinary skill in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the present disclosure, and that they may make various changes, substitutions and alterations herein without departing from the spirit and scope of the present disclosure.
The Abstract at the end of this disclosure is provided to permit the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.
This application claims priority to and the benefit of U.S. Provisional Patent Application No. 62/106,978, titled “Cleanup Model Parameterization, Approximation, and Sensitivity,” filed Jan. 23, 2015, the entire disclosure of which is hereby incorporated herein by reference. This application is also related to the following references, the entire disclosures of which are hereby incorporated herein by reference: U.S. Pat. No. 9,121,263 to Zazovsky, et al.;U.S. Publication No. 2013-0110483 of Chugunov, et al.;U.S. Publication No. 2014-0278110 of Chugunov, et al.;U.S. Pat. No. 8,548,785 to Chugunov, et al.; andWIPO Publication No. WO 2014/116896 of Morton, et al.
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