A Decision Support System for Multi-target Geosteering

03/10/2019
by   Sergey Alyaev, et al.
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Geosteering is a sequential decision process under uncertainty. The goal of geosteering is to maximize the expected value of the well, which should be defined by an objective value-function for each operation. In this paper we present a real-time decision support system (DSS) for geosteering that aims to approximate the uncertainty with an ensemble of geo-model realizations. As the drilling operation progresses, the ensemble Kalman filter is used to sequentially update the realizations using the data from real-time logging while drilling. At every decision point a discretized dynamic programming algorithm computes all potential well trajectories until the end of the operation and the corresponding value of the well for each realization. Then, the DSS considers all immediate alternatives (continue/steer/stop) and chooses the one that gives the best predicted value across the realizations. This approach works for a variety of objectives and constraints and suggests reproducible decision under uncertainty. Moreover, it has real-time performance. The system is tested on synthetic cases in layer-cake geological environment where the target layer should be selected dynamically based on the prior(pre-drill) model and electromagnetic observations. The numerical closed-loop simulation experiments demonstrate the ability of the DSS to perform successful geosteering and landing of a well for different configurations of targets. Furthermore, the DSS allows to adjust and re-weight the objectives, making the DSS useful before fully-automated geosteering becomes reality.

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1 Introduction

According to the Norwegian Petroleum Directorate , drilling new wells is the most efficient way to increase oil recovery (Norwegian Petroleum Directorate, 2018). At the same time, well delivery and maintenance constitutes one of the major costs of oil reservoir development (Saputelli et al., 2003). To maximize value creation from each well, oil companies are continuously improving technology and procedures for optimizing the well placement to maximize production while reducing the cost of drilling and future maintenance. To place a well precisely in the best reservoir zone, operators use geosteering to adjust the well trajectory in response to real-time information acquired while drilling. The benefits of geosteering, such as higher production rates of the resulting wells, have been extensively documented in the literature (Al-Fawwaz et al., 2004; Janwadkar et al., 2012; Guevara et al., 2012; Tosi et al., 2017).

Geosteering has traditionally been dominated by manual geological interpretation and decision making, supported e.g. by visualisation of logging-while-drilling (LWD) measurements and static 3D pre-drill models, as well as real-time updates of 2D deterministic earth models. More recently, there has been a larger focus on developing strategies that include more sophisticated computer based methods both for pre-job, post-job and real-time analysis. Bashir et al. (2016) have explained how the formation tops and stratigraphic interfaces in a 3D geocellular near-well sector model were adjusted in depth during drilling. The view of the 3D model was shared among the drilling asset team stakeholders for decision support. In Constable et al. (2016) it is explained how new developments allow the deep electro-magnetic LWD-transmitter to be placed only 1.8 meters behind the bit, enabling identification of formation resistivity contrasts several meters ahead of the bit. In Antonsen et al. (2018a) 2D deep azimuthal inversion of directional resistivity measurements is used to generate 2D images in a set of planes that are perpendicular to the wellbore. Although not yet possible in real-time, a case study illustrates the importance of combining LWD measurements, ultra-deep directional resistivity inversions, surface and time-lapse seismic, and sedimentological and structural models for enabling 3D mapping of the reservoir in complex geological structures with fluid flooding resulting from production and water injection with a larger degree of certainty. The paper Antonsen et al. (2018b) discusses the importance of establishing a good understanding of how essential reservoir objects such as top reservoir and oil-water contact (OWC) are mapped by inversion of deep electromagnetic measurements in the pre-job phase of the drilling operation. In Arata et al. (2017) a case study shows how a real-time recalibration of seismic to minimize the depth discrepancy, based on LWD measurements, supports improved prediction of the reservoir structure ahead of bit.

The new workflows discussed above aim at automated inversion and interpretation of real-time measurements. However, the information extracted from data has no value unless it helps us make better decisions. Geosteering is fundamentally about making decisions to optimize outcomes such as achieving optimal production at minimal costs. Making decisions that honor all different and sometimes contradictory objectives is not intuitive and requires excessive calculations that can only be handled by a computer.

Currently there is a lack of methods, tools, and workflows that explicitly treat the uncertain nature of this decision process. To optimize the well placement under uncertainty, we should work within a probabilistic framework using a dedicated decision-analytic framework (Kullawan et al., 2014). The first step is utilization of prior data and descriptive analytics to summarize and improve our probabilistic understanding of the reservoir formation. Thereafter the real-time measurements provide information that improves our understanding of the geological and operational parameters that are crucial to optimal well placement. Finally, predictive analytics supports the continuous updating of our understanding of these parameters, and gives input to decisions on directional changes or stopping.

In this paper we present a consistent, systematic and transparent workflow for geosteering, which implements the principles above into a practical decision support system (DSS). The starting point is a probabilistic geomodel represented by multiple geomodel realizations of the possible geological scenarios which span the space of pre-drill interpretation uncertainties. The real-time measurements obtained while drilling are continuously integrated by automatically updating the realizations using an ensemble-based filtering method, similar to Chen et al. (2015); Luo et al. (2015). The real-time update of the realizations leads to a reduction in the interpretation uncertainty, providing always up-to-date predictions of the geology ahead of the bit. The update workflow is linked to the DSS. The DSS applies the probabilistic up-to-date geomodel to support geosteering decisions under uncertainty by evaluating the chosen value function for well trajectories. The value function commonly includes multiple objectives, including production potential, costs for drilling and completion, and risks associated with the operation. The trajectory optimization in the DSS is inspired by the discretized stochastic dynamic programming algorithms for geosteering that were discussed in Kullawan et al. (2017, 2018). However, the DSS presented here is specifically optimized for usage with ensemble-based update workflows which are already used on the stage of the field development planning (Hanea et al., 2015; Skjervheim et al., 2015).

The real-time update workflow was previously demonstrated for pro-active geosteering with the objective to follow the top of a reservoir (Chen et al., 2015; Luo et al., 2015). The DSS presented in this paper combines this update workflow with dynamic programming for global trajectory optimization under uncertainty. The new optimization algorithm enables a variety of practical objectives, which among other things allow to optimize well-landing in uncertain environments.

Our numerical experiments are inspired by a challenging set-up with multiple target layers from a case study presented in Hongsheng et al. (2016). Unlike an expert service required for successful geosteering in the mentioned case, the DSS delivers reproducible and good decisions under uncertainty which maximize the precise objective selected for an operation. We presented the flexibility of the DSS with respect to selection of objectives and initial tests in earlier conference proceedings (Alyaev et al., 2018a, c). Here we focus on exhaustive presentation of the features and limitations of the DSS algorithms and present statistical verification of the performance of the system.

The rest of the paper is organized as follows. Firstly, we present the ensemble-based workflow for updating of the probabilistic geomodel based on measurements. Secondly, we introduce the DSS that can utilize the up-to-date ensemble to propose the optimal decision under uncertainty. After that, the performance of the DSS is demonstrated on synthetic cases with multiple targets. Finally the main contributions of the paper are summarized in the conclusions.

2 Earth model update loop

Figure 1: Proposed geosteering workflow. The top part contains inputs to the workflow. The left part of the figure depicts the update loop. The part of the figure to the right contains the decision system that is based on the updated earth model. The ’drill ahead’ decision results in new measurements that trigger another update and complete the full loop of the workflow.

In the proposed geosteering workflow, shown in Figure 1

, real-time decision support is based on Bayesian inference from a probabilistic geomodel that is continuously updated.

2.1 Earth model

The earth model is represented as an ensemble of realizations that captures key geological uncertainties. In figure 1 the uncertainties are the positions and thicknesses of sand layers (gray) in a background shale. The pre-drill realizations are created based on a priori information drawn from seismic, logs from offset wells, production measurements and additional knowledge about geological uncertainties provided by experts.

All realizations are updated incrementally each time new measurements become available while drilling. The incremental updates of the model are performed by a statistically-sound ensemble-based method that reduces the mismatch between the measurements and the geomodel. The ensemble-based updating approach is an implementation of a Bayesian updating framework. In the rest of the section we describe the implementation of individual components of the generic update loop that was used in this study.

2.2 Measurements

By design, the ensemble-based methods perform incremental updates which can handle any number and any type of measurements simultaneously (see 1a. in figure 1). It is required however, that there is a corresponding simulation model that can transform the realizations and the measurements to a context where they can be adequately compared to compute the mismatch. The simplest way is to use a forward model that produces synthetic measurements based on the geomodel realizations (see 1b. in figure 1). The forward model should be sufficiently fast to handle hundreds of simulations at every assimilation step. For geosteering, each assimilation step should take an order of a minute to be considered real time.

Figure 2: An illustration of the depth of investigation (DOI) of the tool for the synthetic model (axes in meters). The dark red line segment to the left shows the trajectory that has been drilled; the thin red line segment shows the next proposed trajectory segment. The DOI is illustrated at the current decision point at the end of the drilled trajectory. The measurements at the highlighted location have been assimilated.

2.3 Forward modelling

The simulation methods for processing of different logs have been extensively studied by service companies (Sviridov et al., 2014; Dupuis et al., 2014; Dupuis and Denichou, 2015; Hartmann et al., 2014; Selheim et al., 2017) but are generally not available in the open domain, only as paid services. The main contribution of this paper is the DSS and not the modelling of the measurements. Therefore, we use a simple integral model for electromagnetic (EM) measurements following Chen et al. (2015). The tool set-up in that paper has a look-around capability of about 5 meters and it produces sensitivity in the up, down and side directions with the tool location placed at the drill-bit in the current prototype, see figure 2. The depth of investigation (DOI) is chosen relatively low compared to the modern tools to maintain the accuracy of the approximate integral model. However, we emphasize that this does not constrain the applicability of the workflow. For instance, in Luo et al. (2015), a similar update workflow has been tested with more advanced tools and a finite difference forward model. The tool modeled in Luo et al. (2015) provides a higher DOI that allows to see in a larger volume around the well and is expected to yield better results.

2.4 Ensemble-based update algorithm

The update loop used in this paper is compatible with a number of ensemble-based methods which have previously been implemented for reservoir data assimilation including the ensemble Kalman filter (Aanonsen et al., 2009), ensemble smoother (Skjervheim et al., 2011, 2015), the particle filter (Lorentzen et al., 2016), and more sophisticated combinations of the above, such as adaptive Gaussian mixture filter (Lorentzen et al., 2017). To demonstrate the workflow, we use the standard ensemble Kalman filter (EnKF) method (Chen et al., 2015; Luo et al., 2015) for the implementation described in this paper.

The Kalman filter (Kalman, 1960)

formulates the Bayesian update for the changes of the mean and the covariance matrix when new data is received assuming all probability distributions are Gaussian. The ensemble Kalman filter

(Evensen, 1994, 2009) is a flexible Monte Carlo implementation of the Kalman filter. When new measurements are received, they are compared to the simulated measurements generated by the corresponding forward models for each realization. The earth-model realizations used in this paper assume a layer-cake geomodel with constant resistivity in each layer. The depth of each layer boundary is represented by a series of points. The new measurements yield an incremental update of the depth values in the interfaces, which can be formulated as (Burgers et al., 1998)

(1)

where contains the updated (or posterior) ensemble representing the posterior distribution, contains the initial (or prior) ensemble representing the prior distribution, is the Kalman gain matrix, contains the perturbed measured data values111

For EnKF, a measured data value has to be perturbed with its corresponding statistics in order to avoid insufficient variance

(Burgers et al., 1998). , and contains the modelled data values corresponding to the initial ensemble. Equation (1) describes a linear combination of the prior and the measured data, which is weighted by the Kalman gain matrix . Bayes’ rule describing the relationship among the prior, likelihood, and posterior is not shown explicitly in the equation above, but it is implicitly included as the likelihood is encoded in the Kalman gain matrix and the pre-posterior is treated as a normalizing constant of the updated ensemble. A detailed description on the relationship between the formulation of the Kalman filter and the Bayesian formulation can be found in Meinhold and Singpurwalla (1983).

The incremental nature of the update removes the need of a costly joint inversion. By design the updates are also propagated ahead of the bit using the prior knowledge about the model. This provides a probabilistic prediction of the geology ahead of the bit based on the trends identified around and behind the bit. We refer the reader to Luo et al. (2015) for a more rigorous description of the update loop for geosteering.

3 Decision support system (DSS)

The update loop described above results in an always up-to-date ensemble of model realizations which contains both the prior knowledge and the latest measurements. The realizations representing the probabilistic description of relevant and material uncertainties are the input to the DSS. The DSS is based on a normative decision-making approach (Bratvold and Begg, 2010; Clemen and Reilly, 2013; Howard and Abbas, 2015) and includes optimization algorithms that take into account all realizations as well as multiple objectives, such as following the reservoir top while minimizing drilling cost and reducing the tortuosity of the well for easier completion. The objectives may be conflicting, and for each realization the algorithm calculates the well path that is optimal with respect to the weight of each objective. The objectives and the corresponding weights are defined by the user of the DSS and is the second consistent way to include expert knowledge in the workflow, see figure 1. The proposed decision for stopping or adjusting the trajectory is visualized together with the current representation of the uncertainty in the model.

The DSS presented in this paper differs from traditional decision systems that were designed for strategic decisions. In contrast, the geosteering decisions are operational, which means that they are sequential and need to be taken in a relatively short time. The presented DSS allows to tweak the weights of the objectives at all decision points and preview the outcomes in real time. That might help the user to build an understanding of how the choice of objectives influence the suggested decisions and provides a possibility to re-evaluate the trade-offs between objectives as the drilling progresses.

The logically consistent approach of the DSS allows for decisions to be transparent and reproducible. Given that the DSS is based on a normative decision quality approach, it will recommend good decisions for the decision-maker’s objectives, alternatives (following constraints), and beliefs (represented in pre-drill model).

3.1 Objectives

A natural requirement for any DSS is the possibility to take into account multiple objectives. The objectives used in modern geosteering operations include placing the well in a specific position in the reservoir, reducing costs and ensuring safety (Kullawan et al., 2016)

. For the use in a DSS the objectives need to be converted into objective functions defined on a common scale, e.g. the estimated profit in US dollars or produced-oil-barrels equivalent. To reduce conversions, we will use the stand length drilled within standard reservoir sand as the common scale in this paper. We denote each objective function as

, which depends on the trajectory () of the well and the actual sub-surface configuration (), which for now we assume known and deterministic. The profit functions are positive and costs associated with the operation are negative.

The global objective is represented as a linearly weighted sum of individual contributions from each objective function:

(2)

where is an objective weighting factor for objective where are indices of different objectives. The functions are scaled so that the initially estimated (pre-drill) profit/cost corresponding to each objective function is achieved when . The weights give the user an intuitive control to modify the priority of the objectives. corresponds to a higher priority to objective , while corresponds to a lower priority. Setting means that the objective is ignored. Changing the weights reflects an insight in how each objective contributes to the profit/cost of the well being drilled compared to originally anticipated (see the last numerical example in the next section). We will use the global objective defined by (2) as the value function in the optimization for the rest of the section.

3.2 Sequential decision optimization under uncertainty

A geosteering operation consists of a sequence of decisions . Subscript numerates decision points sequentially in time. Ensemble-based workflows represent the uncertainty in the geological interpretation as a set of realizations. Substituting different realizations instead of the deterministic model into the objective function in equation (2) might give several trajectories, where each optimal for the corresponding realizations. At the same time, the outcome of the optimization should be a single optimal decision for each decision point . In this paper we follow the optimality criterion used in robust optimization: We want to make a decision that maximizes the expected value of the well given all the available information.

Let us consider all available information at time . At each decision point the ensemble-based workflow contains up-to-date realizations representing the current understanding of the sub-surface. Moreover, in-between any two sequential decision points, new measurements are assimilated using the update loop which improves the geological understanding around and ahead of the drill-bit. The full structure of a sequential decision problem is shown in Figure 3, where denotes the decision at time , and denotes the information gathered between time and . For brevity of notation we denote all information gathered during steps to as . Generally, at the current time , the decision , that needs to be made right now, depends not only on the information that has been gathered and is contained in the sub-surface model, but also on the possibility of future learning, i.e. the information that will be gathered . Because future information is not available at time , its influence on future learning and decision-making can be modelled as uncertain events, conditioned on the current information and prior decisions.

The approach considering the full learning and decision-making structure of a sequential decision-making problem is presented in Figure 3. We call this approach ”far-sighted” as it takes into account what might happen in the future including what information will be gathered, how uncertainties will be updated using that information, and which decisions that will be made (Alyaev et al., 2018b). An implementation of the far-sighted approach using discretized stochastic dynamic programming has been described in detail for a simple geosteering problem with a single layer and updates of the boundaries by Kullawan et al. (2017, 2018).

Unfortunately the stochastic modelling required for resolution of future learning in the far-sighted approach is computationally prohibitive for real-time decision-making. First, the complexity of a problem grows exponentially as the numbers of decision points, alternatives, and the uncertainty branches increases. The phenomenon is known as the curse of dimensionality

Brown and Smith (2013). Thus, using the far-sighted approach becomes computationally prohibitive for problems with a large number of parameters. Second, the state-of-the-art methods for data assimilation (e.g., the ensemble Kalman filter used in our update loop) cannot be directly embedded into the far-sighted approach. The far-sighted approach requires storing all model realizations not only for the current decision point, but also for all future decision points, which are modified due to updates in the EnKF loop.

Figure 3: Full structure of a sequential decision problem

In this paper we present a new dynamic programming discrete optimization strategy which has real-time performance and is simple to integrate with the ensemble-based update loop. The strategy is a simplification of the far-sighted approach. It considers future decisions but omits the modelling for future learning. Instead of the modelling of the future information we optimistically assume that perfect information would be available after the current decision has been made and before the next decision is made. Thus, this approach can be classified as naive optimistic

(Alyaev et al., 2018b). It is possible to find theoretical scenarios for which this approach gives a decision recommendation that is different from the optimal choice given by the far-sighted approach (Alyaev et al., 2018b). At the same time, the naive approach is superior to myopic optimization that only considers one step ahead which was used in previous papers with ensemble-based workflows, e.g. Luo et al. (2015); Chen et al. (2015). The DSS optimizes the complete well path ahead of the bit against the currently available representation of the geological uncertainty (as represented by the set of realizations). Hence, the realizations should capture the complete and current view on the geology with uncertainties. The next subsection summarises the implementation of the algorithm.

3.3 Real-time ensemble-based optimization algorithm

For simplicity we assume near-horizontal drilling and therefore we can associate the decision points with their position along the horizontal axis . At every we discretize the trajectory alternatives by the well depth and denote the depths as for the horizontal location . The decision for step at is either to stop or to add a segment connecting to a point , where the depth , is constrained by the dogleg severity given by the user input. The optimization algorithm evaluates different trajectories that are represented as piecewise-linear curves that go through points , see figure 4. The density of points can be decided by the user and will affect the trade-off between the optimality and the computational time.

Figure 4: An example of discretization of trajectories. Vertical lines correspond to while horizontal lines correspond to (every 10th line displayed). The orange polylines are possible well trajectories that go through the decision-grid points. One can see that the well trajectories are constrained by the dog leg severity; unreachable trajectories are not considered.

For the decision at any decision point , the algorithm consists of two parts.

On the first step, a dynamic programming algorithm finds a deterministic optimal well path for each realization and for every starting point by iterating over all possible trajectories. 222 Following the principles of dynamic programming each point is evaluated only once and the results are reused Cormen et al. (2009). The result of this step is the set of optimal decisions for every point for every realization :

(3)

where the decision is expressed as a -coordinate for the point or ”none” (corresponding to the stopping decision for cases where the objective function after a certain point is always negative). In (3) the index is used to refer to horizontal locations, and for vertical locations and for the realizations respectively.

Applying equation (3) recursively one can recover key-points of the optimal trajectory for each realization

(4)

where is the starting point for the current optimization. Similarly, by substituting (4) into the objective function (2), one can calculate the predicted well value for a given scenario. The results of evaluations of equations (4) and (2) are tabularized after the first evaluations and are reused whenever necessary. Thus the reconstruction of the optimal trajectories as well as evaluation for objective function for the well is almost instantaneous.

On the second step, we need to perform a robust optimization to arrive at the single optimal decision: i.e. chose depth that gives the best outcome on average, considering all realizations. Note, it does not necessarily coincide with any of from the previous step.

To compute consider immediate permissible alternatives which are within the constraints of the dogleg severity, and choose the one that is the best on average:

(5)

where is the probability of realization . 333Note, that the evaluations for all the trajectories for individual realizations is has been already performed and cached on step one of the algorithm by applying equations (3). We emphasize that equation (5) is used exactly for one decision ahead. Thus the computational complexity of its evaluation is proportional to the number of immediate alternatives times the number of realizations and does not suffer from the curse of dimensionality. This distinguishes our optimization strategy from earlier approaches (e.g. Barros et al. (2015)), which try to optimize all future decisions neglecting the future learning.

The optimization algorithm presented in this section extends the classical robust optimization (Chen et al., 2015; Lorentzen et al., 2006; Chen et al., 2009) to include the up-to-date knowledge for the full trajectory ahead of the bit. Due to possibility of future learning, it is essential that only the first point is chosen by the robust optimization, while the rest of the trajectory is allowed to differ from realization to realization. The future learning is expected to reduce the uncertainty and improve the decision for the next decision point. The full well path joint optimization for the whole ensemble is costly and not always justifiable for a workflow where updates of the realizations are performed sequentially in time when new measurements arrive during drilling. Instead, the decision for the next step (the next decision point) is recomputed once the new measurements become available and the ensemble is updated. This strategy allows for a real-time reaction to new information while also considering the prior information at every time step. From the perspective of decision theory the strategy is equivalent to a dynamic programming with assumption of perfect information.

3.4 Visualization of the real-time modelling results

Figure 5: An illustration of the functionality of the DSS interface. To the right in the figure, individual geomodel realizations are visualized. The realization to be visualized can be selected by the user. To the top left in the figure, a ’point cloud’ view of the total ensemble of realizations is shown. The green arrows indicate how the optimal trajectory for each realization is visualized in the ’point cloud’ view. To the bottom left, a cumulative diagram of the expected value of the well (including costs and future income) is presented. It is based on the current uncertainty captured by the ensemble, with the vertical marks for (i) the mean expected value and (ii) the estimated value for a specific realization.

Adoption of any DSS requires that the system can be trusted by its users. Therefore the communication to the user of the reasoning behind the proposed decisions is essential. In the user interface, the proposed decision is visualized and the basis for the decision is explained.

The main basis for a decision is the up-to-date probabilistic earth model. In Figure 5, an earth model with two oil-bearing sand layers with high resistivities is used for the demonstration of the DSS visualization. Between these two layers there are background shales with low resistivity. High resistivity layers are indicated with a bright color, while relatively low resistivity layers appear as gray. Black layers have very low resistivity and correspond to shale. To the right in figure 5, three (out of normally a hundred) chosen realizations are shown. In the user interface any realization can be selected for examination and the realization on display can be effectively switched within milliseconds. Moreover, the uncertainty can be visualized as a ’point cloud’. That is, for each point in space we visualize the average of the resistivity value over the ensemble of realizations as shown in in figure 5. In many cases, the point cloud is an intuitive way to understand the distribution of the uncertainty within the current ensemble.

At all times the interface highlights the consequence of the immediate decision (next proposed well segment) in thick red and a written communication of the decision: an angle in degrees or ’stop’. The decision is supported by a cumulative plot of the expected value of the well based on the estimated uncertainty shown in the bottom left corner of figure 5. The plot should be interpreted as follows. For a selected value on the x-axis, the plot surface corresponds to a percentage, e.g. 20%. That means that in 20% of the realizations this value is not achieved. However, the value is exceeded in the remaining 80% of realizations.

Furthermore, the interface communicates the two-step process behind the decision optimization as explained in the previous subsection. When an individual realization is shown, the corresponding optimal trajectory resulting from optimization step one (4) is visualized (taking into account the uniquely selected next segment). At the same time the value expected from this trajectory is marked on the value plot. For convenience, the mean predicted value is also shown.444It is important to note that the mean does not necessarily coincide with a value expected from any realization. In the ’point cloud’ view, all the optimal trajectories corresponding to each realization are visualized (see figure 5). This latter display gives an intuitive understanding of the alternatives that are in reach of the current operation. The choice of alternatives for the next decision step will be updated as the realizations are updated based on new real-time measurements.

The display is fully updated with the new optimization results when the realizations are updated, or if the user adjusts the objectives. Further discussion of the flexibility of the graphical (GUI) and programming (API) interfaces of the system can be found in Alyaev et al. (2018a). In the rest of the paper we will use the point cloud view to represent uncertainty and the reachable optimal trajectories for each realization to indicate the outcomes predicted by the system.

4 Numerical examples

In this section we demonstrate the performance of the DSS on synthetic examples. In the examples we use a layer-cake earth model with two oil-bearing sand layers surrounded by background shales (see e.g. Figure 5). As in real depositional environments we allow the sands to pinch-in and out. This seemingly simple model presents a challenging setting for making decisions: the target is not predefined but should be selected dynamically based on a multi-objective value function. The value function accounts for the estimated production potential of the well versus the estimated cost of drilling. Fast and consistent evaluation of this value function while considering different alternatives under geological uncertainty is the key to good decisions. That task is nearly impossible to fulfill manually but can be solved by the DSS on a laptop within seconds.

The operation starts 15 meters above the expected reservoir top (the top is taken as zero on all figures) with a starting angle of 80 degrees commonly used before landing (Cayeux et al., 2018). To reduce the uncertainty we use unprocessed synthetic EM measurements modelled by a simple integral model as in Chen et al. (2015). The depth of investigation of the synthetic tool is about 5 meters, see figure 2.

All the tests in this section follow similar assumptions about the layered model. The layers in the model can be distinguished by their resistivity that is assumed to be known for the synthetic cases. The resestivity values are set to 10 for shale and 150 and 250 for the top and bottom sand layers respectively (all in dimensionless units). The initial ensemble of realizations is created based on the expected layer depths and the associated uncertainties. The expected boundary depths are 0, -5.3, -13.3 and -20.1 respectively. Each layer boundary is generated using an exponential variogram model (nugget=0, sill=2.5, range=350m). Furthermore, co-kriging is used to correlate the boundaries of the neighbouring layers (with correlation parameter set to 0.7), similar to Lorentzen et al. (2019). For rigorous testing, we assume that the synthetic truth is also a layer-cake model.

4.1 Optimal landing in different situations

First we want to test the DSS workflow for different geological scenarios of sub-surface. We choose the objective to stay below the reservoir roof with a distance of 1.5 meters, but the reservoir layer should be chosen based on its thickness relative to the cost of drilling to reach the layer. More precise set of objectives and constraints are sumarised in Table 1. All the decisions follow the recommendations from the DSS for the given input.

Objectives: For each location this value function outputs the reservoir thickness when drilling in the reservoir, as it should contain oil proportional to its thickness. The value is doubled in the ’sweet spot’ around 1.5 meters from a layer top ( between 0.75 and 2.25 meters form the reservoir top), which in this case would result in the best production strategy. There is a pre-set cost for drilling every meter of a well equivalent to production potential of a reservoir which is 0.3 meters thick. Constraints: The trajectory is constrained by dogleg severity of 2 degrees. The inclination is limited to 90 degrees to avoid problems with gravel packing.

Table 1: The precise list of objectives, costs and constraints for the numerical example
Figure 6: The synthetic truths for the two scenarios with the optimal trajectory (left). The final trajectories resulting from the application of the workflow in the scenarios (right). Top scenario: The well almost matches the perfect trajectory. Bottom scenario: The landing in the second layer is not perfect due to the initial uncertainty (not shown). Nevertheless the global optimization under uncertainty allows to adequately land the well in the bottom layer.

To the left in figure 6 two different alternatives for the synthetic truth are considered followed by the results of application of the workflow on the figure’s right. In the example we compare how the same set-up of the workflow operates step-by-step for these two different scenarios (everything is the same except for the truth). The truths in both scenarios contains two reservoir layers. In the top scenario the top layer is thicker and hence more profitable while in the bottom scenario the bottom layer should be prioritized. The figures of synthetic truth contain the trajectories optimized with respect to the chosen metric.

We start from an initial ensemble of realizations representing the model with uncertainty which is the same for both scenarios. The ’point cloud’ representation of the initial ensemble is depicted in the first column in figure 7. The blurry contours of the boundaries between the layers indicate the uncertainty in the layer positions and thicknesses. Initially, the global optimization foresees different decision outcomes that would result in landing in either the top or the bottom layer (the same for both scenarios). Therefore the DSS proposes the initial decision to drill with the same inclination allowing for future well landing in either of the layers.

In the next two decision steps (columns 2 and 3 in Figure 7) the look-around of measurements is insufficient to reach the reservoir layers (the sensitivity of the tool shown in pink). Therefore no update takes place and, since the pre-drill model is the same, the steering progresses similarly for both scenarios. The DSS proposes angle build-up which would allow for a better landing in the top layer which seems more promising under uncertainty. At the same time, the alternative to drill to the bottom layer is not disregarded as indicated by well paths in some realizations.

In column 4 of figure 7 the sensitivity has reached the predicted top of the layer. The uncertainty is reduced rendering the top boundary sharper on the averaged image. At that stage one can already see that the predicted top-layer thickness for the bottom-row scenario is smaller. At that stage it is still uncertain which layer will be chosen on both cases, but the objectives for the updated uncertainty representation dictate to steer downwards in the bottom scenario to be able to reach bottom layer faster, if required.

In column 5 of figure 7 the uncertainty of the top layer depth and thickness is reduced even further (notice the sharp boundary especially on the top figure). This puts more priority to landing in the top layer for the top row scenario. Contrary to that in the bottom scenario the decision is to cross the shale and drill to the bottom reservoir layer. After the update in column 6 the uncertainty for the top layer boundaries is further decreased and the landing strategies are confirmed. These decisions are consistent with our knowledge about the truth in both scenarios.

The rest of the synthetic operation is shown in figure 8. Notice that in the top scenario the well is landed in the top layer. At the same time in the first column in figure 8 the DSS estimates that it might be better to drill downwards for some realizations. This information is clearly communicated through the DSS interface.

During the decision steps described in this subsection, a complex workflow consisting of the update loop and the DSS is running behind the scenes. The measured data is generated using the described EM acquisition model from the synthetic truth with added measurement noise. Every new measurement triggers an iteration of the update loop. On a workstation with 10 cores a full model update takes about 5 seconds using early implementation that is not optimized for production. After that the DSS optimizes the trajectory of the well across all realizations and gives a result within another 10 seconds.

Figure 6 shows the final step of the operation for the considered scenarios. In both scenarios the DSS manages to land the well in the layer which is optimal with respect to the objective. We emphasize that this is possible due to the workflow where the full well trajectory is optimized against the up-to-date uncertainties.

In the scenario in the top row (figure 6), the steering is close to optimal. This can be seen by visual comparison of the actually drilled well path to the left and the optimal well path to the right. The actual well achieves value of 95.56 equivalent meters of reservoir drilled (with respect to objective from Table 1), which corresponds to 86.5% of the theoretically possible. Note that the theoretically possible value can only be reached if we have complete information of the subsurface before drilling commences, which is not possible in practice.

The bottom scenario seems less likely considering the initial representation of uncertainty (as the initial ensemble is the same as for the top-row scenario). However, as the real-time data, which indicates a thin top layer, becomes available the well path is corrected and the optimal target is reached. We note, that the new developments improving the prior model or the look-around/look-ahead capability (such as Constable et al. (2016)) would automatically improve the decision outcomes provided by DSS. Nevertheless, the well resulting from the bottom scenario has value of 44.56 equivalent meters of reservoir drilled, which is still over 52% of the theoretically possible value.

Finally, we note that for both scenarios the reservoir boundaries are automatically mapped along the well-path. The reduced uncertainty can thus benefit the further reservoir development planning.

Figure 7: Demonstration of decision support system for two synthetic scenarios. Blue dashed line indicates the unknown position of layer boundaries from the synthetic truth. The figures shows the step-by-step outputs of the DSS (as indicated by advancing bit). The initial model uncertainty is the same for both scenarios. As the operation progresses and more data is available the top layer is preferred for the top scenario and the bottom layer is preferred for the bottom scenario.
Figure 8: Continued demonstration of decision support system for two synthetic scenarios from figure 7. The figures shows the step-by-step outputs of the DSS.

4.2 Statistical analysis of the performance of the DSS

In the first numerical example we presented two situations where the DSS successfully landed the well in optimal layer despite initial uncertainty. Obviously, due to both the uncertainty of subsurface interpretation and the simplifications in the DSS ”naive” algorithms, such good results would not be achieved for all cases. In this example we investigate the statistical performance of the DSS. To do so, we generate a hundred of synthetic cases, for which we draw the synthetic truths from the same distribution as used for the the model realizations. For all 100 cases, we follow the recommendations of the DSS with the same objectives as in previous example (see Table 1).

To evaluate the results of the DSS performance, we will look at two metrics

  • Did the DSS land in the optimal layer?

  • How did the value of the well resulting from the recommendations compared to the optimal well (based on perfect information)?

Both of metrics are case-specific. Thus they are evaluated relative to the optimal well trajectory computed for the synthetic truth for each particular case. We consider the well to land in the correct layer if there are at least two drill-stands drilled in that layer (as in both cases in Figure 6).

There are two challenges related to our objectives. For cases where the top layer is optimal, coming at a low angle might result in overshooting the sweet spot. For cases where the bottom layer is preferred, the challenge is to realize early enough that the top layer is thin and drop the angle early to get good coverage of the bottom layer.

Figure 9:

The results showing the statistical performance of the DSS. The cases are grouped in bins by the percentage of the theoretical maximum value achieved. The value of a resulting well is on average higher than 60% of the theoretical maximum. The plot demonstrates a fitted Gaussian distribution for a visual reference. Good results are achieved even for scenarios where the well is landed into a suboptimal layer.

The statistics of the DSS performance is summarised on Figure 9. The pie-chart indicates that the well is landed in the optimal layer in 53% of cases. Among those, in only one of the cases the well length within the optimal layer is less than half of the best possible length.

We emphasize however, that the choice of layer was not reflected explicitly in the objective function. Thus, the value of the resulting wells should be evaluated instead, for a fair performance evaluation. The latter is summarised on the bar plot in Figure 9. The bars indicate the percentage bins of the maximum possible well value achieved by the DSS in the different cases. The bars are split by the choice of layer for the resulting well. Not surprisingly, most of the better results correspond to the wells where the drilling landed in the optimal layer. At the same time, in the challenging conditions of the chosen setup choosing the layer which is optimal could result in over 70% of maximum possible well value (see blue squares in Figure 9).

In Figure 9 one can see that the average result of the well drilled by the DSS is over 60% of the optimal value. It is reasonable to expect that achieving 100% value is almost impossible and should correspond to zero in a resulting distribution. The Gaussian fit of the resulting distribution displayed in Figure 9 gives much higher value than zero corresponding to 100% of value. Even though the results are not well fitted by a Gaussian, we believe that the statistical performance results are very convincing.

4.3 Adjusting objectives due to insights

In the final example, we want to demonstrate the flexibility of the DSS when it comes to changing weights of the different objectives. This might be important during adoption in the field, as the insights gained during an operation might change the prioritization of geosteering objectives. The main reason for changing objectives is the fact that for geosteering operations very often the objectives are simplified to ensure possibility to evaluate them in real time.

In this example we recall the operation described on the top part of figure 7. Here we consider a slightly different drilling scenario, but using the same setup including the synthetic truth. In right-most figure the bit reaches in the reservoir layer which should result in a landing as shown in figure 8. Suppose, that some of shallow log measurements that are not handled in the DSS (yet) indicate that the top reservoir layer has poor sand quality which is not good for production and the geosteering experts take a decision to prioritize the better sand, which has been the original objective. The weight of staying in the top part of the reservoir is therefore decreased to 0.3 and the weight of the sand quality objective is introduced and set to 0.7.

Figure 10: Example of how the weights of the objectives can be adjusted in the middle of the geosteering operation, in accordance with the insights gained while drilling. The ensemble of realizations is the same in both scenarios. The bottom plot compares cumulative distribution of the resulting multi-objective value functions for the choices of the weights (the vertical lines indicate mean expected value for each distribution).

The newly selected weights can be applied to the trajectory optimization in real-time. The expected outcomes are shown in Figure 10. The cumulative value diagram shown in the figure clearly indicates the reduction of the expected well value after the new value function is chosen. The alteration in the objective results in a landing in the lower reservoir layer, as shown in figure 11. Comparison of the optimal trajectories with actual outcomes in figures 6 (bottom) and 11 gives a visual proof that superior results can be achieved when the ’correct’ value function is selected at the start of an operation.

Figure 11: The final trajectory (right) for the scenario where the weights have been changed to pursue the layer with better quality sand following figure 10 (middle). For comparison, the deterministically-optimal trajectory for the metric is shown to the left. The latter is computed applying the final objectives from the start of the operation.

5 Conclusions

In this work we have presented a functioning consistent decision support system (DSS) aiming at supporting real-time geosteering decisions. The DSS provides directional drilling decision support information and recommendations. The recommendations account for real-time measurements behind and around the bit, inferred uncertainties ahead-of-the-bit, and multiple objectives. The system includes a visual display that allows the geosteering team to inspect uncertainties and immediately see the possible results of their decisions. Rather than using ”educated guesses”, about decision the DSS provides a consistent Bayesian framework for making ahead-of-the-bit inferences based on prior information and learning (from real-time data) while drilling.

The workflow implementation presented here can consistently update uncertianties ahead of the drill bit and provides a visual and interactive means to inspect the resulting multi-realization model of subsurface. However, this uncertainty quantification is not an end by itself. Rather, the objective is to make good geosteering decisions, which requires an assessment of relevant and material uncertainties. An essential part of improving the results from geosteering operations is to move the focus away from real-time data to actual decisions (Kullawan et al., 2014). The DSS uses real-time data gathering and learning-while-drilling to optimize key drilling decisions, thus ensuring the good utilization of new measurement technologies.

There is abundant research and literature demonstrating that people are exceptionally bad at making decisions in complex and uncertain environments (see e.g. Tversky and Kahneman (1974)).555The most recent Nobel Memorial Prize in Economic Sciences was given to Richard Thaler for his contributions to behavioral economics. His former collaborator, Danial Kahneman was awarded the same prize in 2002 for his work on the psychology of judgment and decision-making. The DSS embeds a consistent uncertainty quantification and a sophisticated decision-making process and is particularly advantageous for unbiased high-quality decision support when navigation in complex reservoirs with several potential targets and significant interpretation uncertainty. The real-time performance of the system is specifically important for geosteering where time for evaluation, re-consideration and decision making is scarce.

To illustrate the benefits of the DSS in this paper, we have presented synthetic cases with complex objectives, for which the full workflow consisting of the model updating and the decision recommendations was applied. The system demonstrated automatic choice of target, landing, and navigating of the well in a layer-cake geological configuration with possible pinch-outs. Good results were consistently achieved in several distinct scenarios as well as on a statistical test. Statistically, the system-recommended decisions are achieving more than 60% of the theoretically possible well value despite the uncertainty in the pre-drill geological interpretation.

Moreover, we have illustrated the flexibility of the implementation of the DSS when it comes to adjusting decision objectives. By design the DSS reacts on changes of the objectives or constraints within seconds, providing unbiased decisions for the modified choices.

The DSS builds on the existing advances of digitalization of reservoir development, formation evaluation and drilling process. It uses existing measurement and modeling tools and identifies the optimal decisions through multi-objective optimization under uncertainty. There are a number of natural future extensions of the DSS including e.g. implementation of decision criteria including risk-aversion, handling more realistic geology, application of more realistic measurements (e.g. Deep EM) with better look-ahead, integration of shallow LWD logs, and potentially surface seismic.

Acknowledgement

The authors thank Eric Cayeux and Erlend Vefring for insightful suggestions during the paper preparation.

Funding: This work was supported by the research project ’Geosteering for IOR’ (NFR-Petromaks2 project no. 268122) which is funded by the Research Council of Norway, Aker BP, Vår Energi, Equinor and Baker Hughes Norway. Aojie Hong is supported by the ’DIGIRES’ project (NFR-Petromaks2 project no. 280473) which is funded by industry partners Aker-BP, DEA, Vår Energi, Petrobras, Equinor, Lundin and VNG, Neptune Energy as well as the Research Council of Norway.

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