PROCESS FOR REAL TIME GEOLOGICAL LOCALIZATION WITH STOCHASTIC CLUSTERING AND PATTERN MATCHING

[0001] The present invention relates to the field of geosteering and, in particular, to a process for real time geological localization with stochastic clustering and pattern matching for automating geosteering.

[0002] In a well construction process, rock destruction is guided by a drilling assembly. The drilling assembly includes sensors and actuators for biasing the trajectory and determining the heading in addition to properties of the surrounding borehole media. The intentional guiding of a trajectory to remain within the same rock or fluid and/or along a fluid boundary such as an oil/water contact or an oil/gas contact is known as geosteering.

[0003] The objective in drilling wells is to maximize the drainage of fluid in a hydrocarbon reservoir. Multiple wells placed in a reservoir are either water injector wells or producer wells. The objective is maximizing the contact of the wellbore trajectory with geological formations that: are more permeable, drill faster, contain less viscous fluid, and contain fluid of higher economical value. Furthermore, drilling more tortuous wells, slower, and out of zone add to the costs of the well.

[0004] Geosteering is drilling a horizontal wellbore that ideally is located within or near preferred rock layers. As interpretive analysis is performed while or after drilling, geosteering determines and communicates a wellbore's stratigraphic depth location in part by estimating local geometric bedding structure. Modern geosteering normally incorporates more dimensions of information, including insight from downhole data and quantitative correlation methods. Ultimately, geosteering provides explicit approximation of the location of nearby geologic beds in relationship to a wellbore and coordinate system.

[0005] Geosteering relies on mapping data acquired in the structural domain along the horizontal wellbore and into the stratigraphic depth domain. Relative Stratigraphic Depth (RSD) means that the depth in question is oriented in the stratigraphic depth direction and is relative to a geologic marker. Such a marker is typically chosen from type log data to be the top of the pay zone/target layer. The actual drilling target or “sweet spot” is located at an onset stratigraphic distance from the top of the pay zone/target layer.

[0006] In an article by H. Winkler (“Geosteering by Exact Inference on a Bayesian Network” Geophysics 82:5:D279-D291; September-October 2017), machine learning is used to solve a Bayesian network. For a sequence of log and directional survey measurements, and a pilot well log representing a geologic column, a most likely well path and geologic structure is determined.

[0007] There remains a need for autonomous geosteering processes with improved accuracy.

[0008] According to one aspect of the present invention, there is provided a method of geosteering in a wellbore construction process, the method comprising the steps of: providing an earth model defining boundaries between formation layers and petrophysical properties of the formation layers in a subterranean formation comprising data selected from the group consisting of seismic data, data from an offset well and combinations thereof; comparing sensor measurements related to the wellbore construction process to the earth model; obtaining an estimate from the earth model for a relative geometrical and geological placement of the well path with respect to a geological objective using a trained stochastic clustering and pattern matching agent; and determining an output action based on the sensor measurement for influencing a future profile of the well path with respect to the estimate.

[0012] The present invention provides a method for geosteering in a wellbore construction process. A wellbore construction process can be a wellbore drilling process. The method is advantageously conducted while drilling. The method uses a trained stochastic clustering and pattern matching (SCPM) agent. The method is a computer-implemented method.

[0013] In accordance with the present invention, an earth model is provided. The earth model defines boundaries between formation layers and petrophysical properties of the formation layers of a subterranean formation. The earth model is produced from data relating to a subterranean formation, the data selected from the group consisting of seismic data, data from an offset well and combinations thereof. Preferably, the earth model is a 3D model.

[0014] The earth model may be a static or dynamic model. Preferably, the earth model is a dynamic model that changes dynamically during the drilling process.

[0015] Sensor measurements are inputted to the earth model. The sensor measurements are obtained during the wellbore construction process. Accordingly, real-time sensor measurements are made while drilling. In a real-time drilling process, sensors are chosen based on the geological objectives. if the target reservoir and the surrounding medium can be distinguished by a particular measurement, then this measurement will be chosen. Since there is a limit of the telemetry rate, the sample frequency would also be budgeted. Preferably, the sensor measurements are provided as a streaming sequence. The sensors may be LWD sensors, MWD sensors, image logs, 2D seismic data, 3D seismic data and combinations thereof.

[0016] The LWD sensor may be selected from the group consisting of gamma-ray detectors, neutron density sensors, porosity sensors, sonic compressional slowness sensors, resistivity sensors, nuclear magnetic resonance, and combinations thereof.

[0017] The MWD sensor is selected from the group consisting of sensors for measuring mechanical properties, inclination, azimuth, roll angles, and combinations thereof.

[0018] The earth model simulates the earth and then a sensor measurement from the earth. The simulated sensor measurement is then compared to an actual sensor measurement made while drilling.

[0019] A well path is selected to reach a geological objective, such as a geological feature, such as fault, a nearby offset well, a fluid boundary and the like. Examples of fluid boundaries may be oil/water contacts, oil/gas contacts, oil/tar contacts, and the like. An estimate for the relative geometrical and geological placement of a well path to reach the geological objective is obtained using a trained SCPM agent. An output action based on the sensor measurement for influencing a future profile of the well path is determined with respect to the estimate.

[0020] In a preferred embodiment, the relative geometrical and geological placement of the well profile is determined by a relative stratigraphic depth (RSD). In this embodiment, the trained SCPM agent matches clustered sensor measurements for the relative stratigraphic depth to a reference measurement with a predetermined set of clusters to discretize the signal for the RSD. A maximum a posteriori probability discretized signal for the RSD is maximized with respect to regularization related to admissible and plausible transitions between adjacent depths and relative geological positions.

[0021] A most probable sequence of relative stratigraphic depths is solved by a sampling method selected from the group consisting of mean field, Metropolis-Hastings, Gibbs sampling, Markov chain Monte Carlo and combinations thereof. Preferably, multiple threads of solutions with different initial conditions are solved asynchronously to avoid a local minimum where the most optimal trajectory of the well path is selected.

[0022] In a preferred embodiment, the output action of the SCPM agent is determined by maximizing the placement of the well path with respect to a geological datum. An objective is maximizing the contact of the wellbore trajectory with geological formations that: are more permeable, drill faster, contain less viscous fluid, and contain fluid of higher economical value. The geological datum can be, for example, without limitation, a rock formation boundary, a geological feature, an offset well, an oil/water contact, an oil/gas contact, an oil/tar contact and combinations thereof.

[0023] The steering of the wellbore trajectories is achieved through a number of different actuation mechanisms, including, for example, rotary steerable systems (RSS) or positive displacement motors. The former contains downhole actuation, power generation feedback control and sensors, to guide the bit by either steering an intentional bend in systems known as point-the-bit or by applying a sideforce in a push-the-bit system. PDM motors contain a fluid actuated Moyno motor that converts hydraulic power to rotational mechanical power for rotating a bit. the motor contains a bend such that the axis of rotation of the bit is offset from the centerline of the drilling assembly. Curved boreholes are achieved through circulating fluid through the motor and keeping the drill-string stationary. Curved boreholes are achieved through rotating the drill string whilst circulating such that the bend cycle averages to obtain a straight borehole.

[0024] The output action can be curvature, roll angle, set points for inclination, set points for azimuth, Euler angle, rotation matrix quaternions, angle axis, position vector, position Cartesian, polar, and combinations thereof.

[0025] Referring now to FIG. 2, illustrating a work flow of one embodiment of the present invention, an initial solution is given by a proposal distribution 1. This is a joint distribution representing an initial guess of the positioning of the wellbore relative to the stratigraphy. In a non-limiting embodiment this is represented as a multivariate normal distribution.

[0026] A cost function 2 consists of a combination of: correlation with type log, deviation from position and deviation from attitude. The purpose of the cost function is to evaluate the sampled solution. A sampled solution 3, once evaluated by the cost function 2, is either accepted or rejected based on a threshold. If accepted, the parameters of the kernel, which is the joint distribution 1, is updated. A representation of the earth model is used in the objective function at 4. This is a discretized version of a 1D type log. A wellbore inclination 5, representing the heading with respect to vertical, is taken as input to the objective function. Prior knowledge of the formation dip angle is taken as input to the cost function at 6.

[0027] Preferably, the SCPM agent is trained using a simulation environment, more preferably using a simulation environment produced in accordance with the method described in “Method for Simulating a Coupled Geological and Drilling Environment” filed in the USPTO on the same day as the present application, as provisional application U.S. 62/712,490 filed 31 Jul. 2018, the entirety of which is incorporated by reference herein.

[0028] For example, the SCPM agent may be trained by (a) providing a training earth model defining boundaries between formation layers and petrophysical properties of the formation layers in a subterranean formation comprising data selected from the group consisting of seismic data, data from an offset well and combinations thereof, and producing a set of model coefficients; (b) providing a toolface input corresponding to the set of model coefficients to a drilling attitude model for determining a drilling attitude state; (c) determining a drill bit position in the subterranean formation from the drilling attitude state; (d) feeding the drill bit position to the training earth model, and determining an updated set of model coefficients for a predetermined interval and a set of signals representing physical properties of the subterranean formation for the drill bit position; (e) inputting the set of signals to a sensor model for producing at least one sensor output and determining a sensor reward from the at least one sensor output; (f) correlating the toolface input and the corresponding drilling attitude state, drill bit position, set of model coefficients, and the at least one sensor output and sensor reward in the simulation environment; and (g) repeating steps b)-f) using the updated set of model coefficients from step d).

[0029] The drilling model for the simulation environment may be a kinematic model, a dynamical system model, a finite element model, and combinations thereof.

[0030] The method of the present invention seeks to find a trajectory of a RSD such that the clustered gamma ray (according to the value of RSD) matches with the reference gamma ray, i.e., type logs. In the following, Z_t and X denote the RSD and gamma ray of the type logs, respectively, while Z_w and Y denote the estimated RSD and the observed gamma ray of the well logs, respectively.

[0031] Since X and Y are often of different lengths, their similarity cannot be measured directly. The present inventors have surprisingly found that they can overcome this problem by following method. Z_min and Z_max denote the minimum and maximum possible values of RSD, respectively, while 6 is a predetermined group width for the RSD. The set of steps in type logs and well logs are represented by S_t={1, 2, . . . , T_t} and S_w={1, 2, . . . , T_w}. Z_t⁽ⁱ⁾ is the RSD of the type logs at step i and Z_w⁽ⁱ⁾ is the estimated RSD of the well logs at step i. X_i and Y_i are the gamma ray of type logs and well logs, respectively, at step i.

[0032] The well log RSD is parameterized as follows:

Z_w⁽ⁱ⁾−Z_w^(i-1)+(ρ sin(π(a_i−90)/180)+b_i)

for i=1, 2, . . . , T_w, where ρ is a predetermined value, the so-called moving scale, and a_i and b_i are parameters. The parameter vector θ={(a₁, b₁), . . . , (a_Tw, b_Tw)} is determined through minimizing the cost function defined below.

• • [0033] 1. Group the values of X according to the value of Z_t by setting R₁={X_i: Z_min≤Z_t⁽ⁱ⁾<Z_min+δ, iϵS_t}, R₂={X_i: Z₀+δ≤Z_r⁽ⁱ⁾<Z₀+2δ, iϵS_t}, . . . , R_K={X_i: Z_max−δ≤Z_t⁽ⁱ⁾≤Z_max}. Calculate the averaged gamma ray value for all bins, and denote the average values by {dot over (X)}_b⁽¹⁾ . . . {dot over (X)}_b^(K) and {dot over (X)}_b=({dot over (X)}_b^(k₁⁾ . . . {dot over (X)}_b^(k₂⁾).
  • [0034] 2. Group the values of Y according to the value of Z_w by setting W₁={Y_i: Z_min≤Z_w⁽ⁱ⁾<Z_min+δ, iϵS_w}, W₂={Y_i: Z_min+δ≤Z_w⁽ⁱ⁾≤Z_min+2δ, iϵS_w}, . . . , W_K={Y_i: Z_max−δ≤Z_w⁽ⁱ⁾≤Z_max}. Calculate the averaged gamma ray value for all non-empty bins, and denote the average values by {dot over (Y)}_b^(k₁⁾ . . . {dot over (Y)}_b^(k₂⁾ and {dot over (Y)}_b=({dot over (Y)}_b^(k₁⁾ . . . {dot over (Y)}_b^(k₂⁾).
  • [0035] 3. Normalize {dot over (X)}_b^(k₁⁾ . . . {dot over (X)}_b^(k₂⁾ by setting

${\stackrel{\_}{X}}_{\mathrm{bn}}^{\left(k_j\right)}={\stackrel{\_}{X}}_b^{\left(k_j\right)}/\sqrt{\sum _{j=k_1}^{k_2}{\stackrel{\_}{X}}_b^{\left(j\right)}/\left(k_2-k_1+1\right)},\mathrm{for}j=k_1,\dots ,k_2.\mathrm{Let}{\stackrel{\_}{X}}_{\mathrm{bn}}=\left({\stackrel{\_}{X}}_{\mathrm{bn}}^{\left(k_1\right)},\dots ,{\stackrel{\_}{X}}_{\mathrm{bn}}^{\left(k_2\right)}\right).$

• • [0036] 4. Normalize {dot over (Y)}_b^(k₁⁾ . . . {dot over (Y)}_b^(k₂⁾ by setting

${\stackrel{\_}{Y}}_{\mathrm{bn}}^{\left(k_j\right)}={\stackrel{\_}{Y}}_b^{\left(k_j\right)}/\sqrt{\sum _{j=k_1}^{k_2}{\stackrel{\_}{Y}}_b^{\left(j\right)}/\left(k_2-k_1+1\right)},\mathrm{for}j=k_1,\dots ,k_2.\mathrm{Let}{\stackrel{\_}{Y}}_{\mathrm{bn}}=\left({\stackrel{\_}{X}}_{\mathrm{bn}}^{\left(k_1\right)},\dots ,{\stackrel{\_}{X}}_{\mathrm{bn}}^{\left(k_2\right)}\right).$

• • [0037] 5. Calculate the cosine similarity score: z_θ=0.5 log((1+r_θ)/(1−r_θ)), where r_θ=cos({dot over (X)}_b, {dot over (Y)}_b).
  • [0038] 6. Calculate the cost function

$U\left(\theta \right)=\frac{1}{2}{z}_g^2\mathrm{sign}\left(z_{\theta }\right)-\lambda \sum _{j=k_1}^{k_2}{\stackrel{\_}{X}}_{\mathrm{bn}}^{\left(j\right)}-{\stackrel{\_}{Y}}_b^{\left(j\right)}-\frac{1}{2}\sum _{i=1}^{T_w}{\left(\frac{a_i-90}{{\sigma }_1{T}_w}\right)}^2-\frac{1}{2}\sum _{i=1}^{T_w}{\left(\frac{b_i}{{\sigma }_2{T}_w}\right)}^2,\mathrm{where}\lambda ,{\sigma }_1\mathrm{and}{\sigma }_2\mathrm{are}\mathrm{tunable}\mathrm{parameters}.$

[0039] The cost function U(θ) can then be minimized by sampling from the density function

π(θ)∝exp(−U(θ)/t),

using the Stochastic Approximation Monte Carlo (SAMC) algorithm, where t is called the temperature. FIG. 1 illustrates the motivation of this method.

[0040] Sampling from high dimensional distribution is challenging due to the high likelihood of existence of multi-modes. The most popular Markov chain Monte Carlo (MCMC) sampler Metropolis-Hastings (MH) algorithm (Metropolis and Teller, “Equation of state calculations by fast computing machines” Journal of Chemical Physics, 21; 1953) and (Hastings, “Monte Carlo sampling methods using Markov chains and their applications” Biometrika, 57; 1970) is prone to becoming trapped in local mode. To overcome the local-trap problem, Liang (F. Liang and Carroll, “Stochastic approximation in Monte Carlo computation” Journal of the American Statistical Association 102; 2007) has proposed a SAMC algorithm, which is a powerful tool to effectively sample from high dimension. The basic idea of SAMC can be described as follows. Suppose that there is interest in sampling from a distribution,

ƒ(x)=cψ(x),x∈χ

where χ is the sample space and c is an unknown constant. Let E₁, . . . E_k denotes a partition of χ, and let

ω_i=∫_Eiψ(x)dx for i=1, . . . ,k.

[0041] SAMC seeks to draw samples from the trial distribution

$f_w\left(x\right)\propto \sum _{i=1}^k\frac{{\pi }_i\psi \left(x\right)}{w_i}I\left(x\in E_i\right)$

where π_i's are predetermined constants such that π_i>0 for all i and which define the desired sampling frequency for each of the subregions. If w₁, . . . w_k are known, sampling from f_w(x) will result in a random walk in the space of subregions (by regarding each subregion as a point) with each subregion being sampled with a frequency proportional to π_i. Hence, the local-trap problem can be overcome essentially, provided that the sample space is partitioned appropriately. The success of SAMC depends on whether w_i's can be well estimated. SAMC provides a systematic way to estimate w_i in an online manner. Let θ_ti denote the working estimate of log(w_i/π_i) obtained at iteration t, and let θ_t=(θ_t1, . . . , θ_tk)ϵθ, where θ denotes a compact set. Let γ_t be a positive, nondecreasing sequence satisfying

$\left(i\right)\sum _{i=1}^{\infty }{\gamma }_t-\infty ,\left(\mathrm{ii}\right)\sum _{i=1}^{\infty }{\gamma }_t^{\zeta }<\infty$

for any ζ>1. For example, one may set

${\gamma }_t=\frac{T_0}{\max \left(T_0,t\right)},t=1,2,\dots$

for some value T₀>1. Under the above setting, one iteration of SAMC consists of the following steps:

• • [0042] 1. Metropolis-Hastings (MH) sampling: simulate a sample x_t by a single MH update with the invariant distribution

$f_{{\theta }_t}\left(x\right)\propto \sum _{i=1}^k\frac{\psi \left(x\right)}{e^{{\theta }_{\mathrm{ti}}}}I\left(x\in E_i\right)$

• • [0043] 2. Weight updating: set
    • [0044] where e_t=(e_t1, . . . , e_t,k) and e_t,i=1 if x_tϵE_i and 0 otherwise. If θ*ϵθ, set θ_t+1=θ*;
    • [0045] otherwise set θ_t+1=θ*+C*, where C*=(c*, . . . , c*) can be an arbitrary vector which satisfies the condition θ*+C*ϵθ. Note that f_θ(x) is invariant to this location transformation of θ*.

[0046] A remarkable feature of SAMC is its self-adjusting mechanism, which operates based on past samples. This mechanism penalizes the over-visited subregions and rewards the under-visited subregions, and thus enables the system to escape from local traps very quickly. Mathematically, if a subregion i is visited at time t, θ_t+1,i will be updated to a larger value θ_t+1,i←θ_t,i+γ_t+1(1−π_i), such that, this subregion has a smaller probability to be visited in the next iteration. On the other hand, for those regions, j(j≠i), not visited this iteration, θ_t+1,j will decrease to a smaller value, θ_t+1,j←θ_t,j−γ_t+1(π_j), such that, the chance to visit these regions will increase in the next iteration. This mechanism enables the system to escape from local traps very quickly. This is very effective for sampling from high dimensional systems with multiple modes.

[0047] In accordance with the method of the present invention, there are two parameters, inclination angle and formation dipping angle, at each sampling step from well logs. Therefore, the number of parameters is approximate to two times of the sampling steps from well logs. With this relative high dimensional problem, SAMC is used to sample from the posterior distribution.

[0048] While preferred embodiments of the present disclosure have been described, it should be understood that various changes, adaptations and modifications can be made therein without departing from the spirit of the invention(s) as claimed below.