492 T H E L E A D I N G E D G E May 2 015 Special Section: We l l g e o s te e r i n g

Uncertainty in geosteering and interpretation of horizontal wells — The necessity for constraints and geometric models

AbstractWhile geosteering or interpreting horizontal wells, engi-

neers are constantly faced with the challenge of correctly de-fining the well position with respect to the target reservoir and other geologic markers from an often incomplete set of data. Traditional petrophysical evaluation can be performed only after the geometric relationship between the well and the tar-get reservoir is interpreted. Measurements made while drilling range from a simple gamma-ray (GR) log to resistivity, appar-ent density and neutron porosities, borehole images, azimuth-al deep resistivity, and beyond. With one or a combination of these logs and other peripheral data such as well logs from off-set/pilot wells and seismic images, the question remains as to how accurate the interpreted relationship is between the well trajectory and the target reservoir. In a vertical well, an explicit geometric model of the formation is often not necessary. There is a 1D layered-earth model, either consciously or subconsciously, in people’s minds to aid the interpretation. On the other hand, because of the lateral variation of properties and thus the geo-logic complexity encountered in a horizontal well, it becomes critical to explicitly construct a formation cross-sectional model, validated in terms of its correctness and uniqueness against the available measurements and other known information. To prop-erly construct, update, and validate the formation model, the completeness of information for solving the geometric relation-ship between the well and the target reservoir is investigated. It is found that a data set with logs from the horizontal well alone is not adequate for the task. Proper constraints based on deposi-tional environments must be introduced. Well logs from offset/pilot wells define the formation sequence and add the high-res-olution details to the interpretation. Three-dimensional reser-voir models from seismic images guide the interpretation of the geologic trends along the well trajectory and the extrapolation of the model property into the volume that is not sensitive to well logs. Modeling the tool responses and understanding the under-lying response characteristics help to mitigate the interpretation uncertainty by extracting more geometric information from the physical measurements. One should also be aware of the possi-bility that the interpretation might not be unique even though a model fits the data.

IntroductionWell-log interpretation in horizontal wells still faces chal-

lenges — only a limited amount of information is acquired because of cost constraints and/or availability of technology. Furthermore, well logs from a horizontal well have different re-sponse characteristics than those from a vertical well, even in-side the same formation (Zhou, 2007, 2008).

Traditional interpretation, performed mostly in vertical wells, uses physical measurements such as gamma ray (GR),

John Zhou1

resistivity, density/neutron, and so forth to estimate petrophys-ical properties such as porosity, water saturation, and permea-bility along the well path and finishes with reserves evaluation and completion/production recommendations. On the other hand, in a horizontal well, the first priority is to understand the whereabouts of the well trajectory versus the target reservoir. The geometric interpretation answers the questions of whether the well is inside, above, or below the target and the distance to boundaries (structural and/or fluid contacts), wherever fea-sible. It is thus imperative to understand the limitation of the available information for that purpose. It is equally important to introduce proper constraints to mitigate the lack of informa-tion from well logs.

Well-placement decisions when drilling horizontal wells also require that the interpretation be done in real time. There-fore, visualization, processing, and interpretation of well logs require an efficient approach. This article reviews the workflow and illustrates proper ways of constraining the interpretation.

Before starting the analyses, let us define the data-visualization convention used here. Data and formation cross section will be pre-sented on the flattened vertical curtain defined by the well trajec-tory to facilitate the derivation of a plausible and realistic formation model. Figure 1a shows the 3D view of the well path and the verti-cal curtain (the curved yellow surface) that the well defines. Figure 1b displays the 2D cross section flattened from the vertical curtain shown in Figure 1a. Well logs along the well path are projected to true vertical depth (TVD) and lateral distance (LD) (Figure 1b).

1Maxwell Dynamics, Inc. http://dx.doi.org/10.1190/tle34050496.1.

Figure 1. Convention used in visualizing well logs acquired in a hori-zontal well. (a) Well and vertical curtain defined by the well in three dimensions. (b) The flattened vertical curtain shown in a 2D cross-sectional display, along with its projected logs.

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typically with the borehole penetrating each layer only once. The measurements at each depth point are sensitive to the physical property “around” that point and reflect the true value around the point, assuming that environmental effects are either negli-gible or correctable. These measurements are extrapolated lat-erally in one’s mind, along with the consideration of well logs available in neighboring wells.

In a horizontal-well environment, far fewer measurements (only GR or GR plus resistivity, and rarely with porosities and others) are acquired in the majority of the wells while drilling. The geometric complexity one faces, on the other hand, is orders of magnitude greater (Figure 2).

To further complicate the task, compared with the reser-voir dimension, the depths of investigation (DOI) are rela-tively shallow (within the dashed lines in Figure 2d), ranging from borehole wall to less than a few meters into the for-mation. In other words, any formation volume a few meters from the borehole is not investigated by logging tools, and its properties cannot be determined solely based on available well logs.

Another fact about the lack of the needed geometric in-formation (e.g., up and down) in a horizontal well is that con-ventional measurements (e.g., GR and resistivity logs) are omnidirectional or the measurements cannot tell whether the contribution is from above or below the sensors. For example, if the wellbore exits a target sand accidentally, one cannot tell from omnidirectional data whether it exits from the upper or lower boundary, assuming that the physical properties of the forma-tion above and below are about the same.

To overcome omnidirectionality, borehole image logs from GR or other physical parameters thus are recommended highly, and in some cases, they are absolutely neces-sary because of their geometric infor-mation content. New generations of logging-while-drilling (LWD) tools such as deep azimuthal propagation tools might also help in differenti-ating the directions. Nevertheless, these sensors still are constrained by their shallow depth of investigation. Furthermore, because of their high cost, image and/or other azimuthal-ly sensitive measurements are imple-mented less commonly in practice.

When seismic images are avail-able, they provide guidance on geo-logic trends and the approximate location of the target. However, seis-mic data cannot give the precise po-sition because of their relatively poor spatial resolution and their uncertain-ty in time-depth conversion.

The above discussion emphasizes that well logs (and other data) for well steering or interpreting the horizontal well are likely to be incomplete. To sort

For simplicity, two types of wells are mentioned in this ar-ticle, namely, the vertical well and the horizontal well. In this article, vertical well refers to any well that is vertical or close to vertical. Offset wells and/or pilot wells typically are vertical and are used as reference to facilitate the interpretation of the hori-zontal well. In the category of horizontal well, we include wells that are horizontal as well as those at high angle. The horizontal well is the one to be interpreted.

Last, because of difficulty with field data releases, the ex-amples used in this article are numerically constructed based on real-world cases to illustrate and convey the points about uncertainty in geosteering and interpreting horizontal wells and the ways of reducing interpretation ambiguity through geologic constraints.

Completeness of measurementsFor any interpretation tasks, the first question is whether the

data acquired contain the information sufficient for solving the problem posed or the completeness of the data.

To interpret a horizontal well, the problem posed is to define the geometric relationship between the well and the target res-ervoir. Let us start with the well data-acquisition and interpre-tation practices to examine the differences between vertical and horizontal well environments.

In a typical vertical well, wireline triple-combo measure-ments (formation density, neutron-porosity, deep/intermedi-ate/shallow resistivity, natural gamma radiation, hole size, and fluid temperature, all in a single logging pass) commonly are acquired. The geometric model, subconscious in many peo-ple’s minds, is more or less a 1D layered formation (Figure 2a),

Figure 2. Well and formation environments used by many well-log interpreters and geosteering engi-neers. (a) Vertical well environment where a simple 1D model is often sufficient to interpret measure-ments. (b) Horizontal well with consideration of formation heterogeneity in lateral direction, a 2D model. (c) A more challenging condition in interpreting a horizontal well in which geologic events such as faulting, pinch-outs, unconformities, and so forth might be present. (d) The volume of formation sensed by well data is a small tubular space, indicated by the dashed lines along the wellbore.

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the uncertainty caused by using an incomplete set of well data, an interpretation model should be introduced, and proper geo-logic constraints have to be applied.

Necessity for an explicit formation modelIn interpreting a vertical well, people seldom explicitly con-

struct a formation model. In many cases, “eyeball” interpretation is adequate for that purpose. For example, from the GR and re-sistivity logs in Figure 3a, one has in mind already a formation model, illustrated in Figure 3b, without having to explicitly con-struct the model. The model consists of two parts, one for physi-cal parameters (gamma ray and resistivity in red lines in this case) and the other for geometry (the parallel-layer formation on the right-hand side of Figure 3b). In short, people don’t have to build an explicit formation model to start the petrophysical evaluation in vertical wells.

On the other hand, when a horizontal well is under consid-eration, an explicit formation model becomes a necessity. Fig-ure 4a displays a set of GR and resistivity logs. The interpreted model in Figure 4b consists of sand and shale layers, which might be from a natural extension of the vertical-well interpre-tation practice in which layering is defined based on high and low values in the logs. Varying the dip angle and thickness of the formation layers, one might find a series of models “fitting” the logs. The grayed-out area in Figure 4 indicates the volume that is not sensitive to the logs.

Naturally, the question is whether the model in Figure 4b is acceptable or consistent with available well logs. For those who know the resistivity tool-response characteristics when a bore-hole crosses a layer interface at a high angle (Wu et al., 1991), it becomes apparent that the model in Figure 4c is more appro-priate than that in Figure 4b. The telltale sign is the so-called resistivity horn.

Resistivity logs vary smoothly across a bed boundary when the borehole is perpendicular to the bed boundary. The logs have a high-resistivity horn anomaly if the borehole intersects the boundary at an angle close to parallel, assuming the neigh-boring beds are also of high-resistivity contrast. The lack of a horn anomaly at LD ≈ 715 ft indicates that the borehole is closer to perpendicular to bedding than parallel to bedding. Thus, the model in Figure 4c is more appropriate than that in Figure 4b. The horn anomaly illustrated here serves as an example, and often, there are many other factors (e.g., anisot-ropy) to be considered carefully.

If one can afford a borehole image log (e.g., GR image) and/or an azimuthal propagation-resistivity image (Fig-ure 5), the model in Figure 4c can be further validated or confirmed. Through extrapolation away from the wellbore, the model in Figure 4c can be made into a 2D cross section, shown in Figure 5a.

Whatever model is derived, it also has to be verified to assess whether the model is geologically feasible. Figure 5b depicts a geologic cross section with a fault as what the model in Figure 5a might represent.

Even after the above steps, the model in Figure 5a is only one of the likely realizations because any volume a few meters from the borehole is not sensed by well logs.

Figure 3. Well logs acquired in a vertical well and the typical model in the interpreter’s mind. (a) Well logs acquired in a vertical well. (b) A typical model derived from the well logs in (a).

Figure 4. The need for a formation model consistent with the avail-able measurements and geologic understanding. (a) Logs from a hori-zontal well. (b) One of the solution models. (c) Another formation model more consistent with tool-response characteristics, although still not necessarily unique. The grayed-out area indicates the volume that is not sensitive to logs.

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As emphasized above, in a horizontal well, the geologic complexity along the well path becomes hard to comprehend without a formation model and validation against the data. The question now becomes, “What formation model is a true or ac-ceptable representation of the geology encountered?”

Constraints based on depositional environmentsOne of the main constraints comes from the depositional

environment for sedimentary rocks. In the majority of sedimen-tary rocks, stratification or lateral continuity occurs at the time of deposition. The depositional sequence is maintained mostly over geologic time, although geologic activities might give rise to more complex structures such as anticlines, faults, erosion and unconformity surfaces, and so forth.

To understand the whereabouts of the well path versus an expected geologic structure, one relies on correlating well logs between the horizontal well and its offset/pilot wells, as illus-trated in Figure 6. For good geologic continuity (Figure 6a), it is relatively easy to correlate and to determine the horizon-tal well position. However, when missing layers (because of pinch-outs or erosion surfaces, for example) and faults with large vertical offset (larger than the DOI) are present, the un-certainty in determining the whereabouts of the horizontal well increases (Figure 6b).

Let us illustrate a workflow in deriving a geologic model around and along the horizontal-well trajectory in ques-tion. When a horizontal well is designed and being drilled,

there are already good position controls from seismic images and offset wells. Figure 7 shows the geometric relationship among geologic surfaces and wells (horizontal, pilot, and off-set wells). Pilot and offset wells offer high-resolution con-straints, whereas surfaces will guide the correlation over a large lateral extent. Intersecting lines between the 3D sur-faces and the vertical curtain defined by the horizontal well are referred to here as 3D markers.

Because of the close proximity, the pilot well and its well logs are chosen to construct a formation model to guide the

Figure 5. A formation model needs to be checked against the geologic understanding when one interprets a horizontal well. (a) The interpreted cross section is validated further if image and/or azimuthal propagation-resistivity image are acquired. (b) Geologic realization corresponding to the logs measured and the model interpreted in (a).

Figure 6. In most cases, the formation sequence observed in the offset well also is observed in the horizontal well after accounting for the structural variation such as the up and down in true vertical depth. (a) This shows good continuity and is relatively easy to correlate between wells. (b) A more challenging environment for correlation.

Figure 7. Geometric relationship among horizontal well, pilot well, and offset well.

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Figure 8. Well logs and formation model built in the pilot well. Markers indicate the layers of significance and the target reservoir location.

Figure 9. Horizontal well interpretation aided by information from pilot/offset wells and 3D surfaces. (a) Well logs measured in the hori-zontal well. (b) Starting model from the pilot well. (c) Interpreted cross-sectional model.

interpretation in the horizontal well. Note that a pilot well is not always available because of its added cost, and in that case, one typically chooses the most representative offset well to start with.

Figure 8 illustrates the well logs and model built from the available well logs in the pilot well. In addition, Figure 8 shows the markers that indicate the target reservoir loca-tion and other significant layers. These markers are named as well markers, to differentiate them from the 3D markers men-tioned earlier.

The horizontal well should encounter the same or a similar sequence of formation layers as observed in the pilot well, al-though inevitably at different vertical depths. Figure 9a plots the GR and resistivity logs in the horizontal well (for clarity, only a subset of logs is displayed). In Figure 9a, there are also the GR log projected from the offset well and the 3D markers from Fig-ure 7 for reference.

For interpretation, the formation model and well logs (Fig-ure 8) from the pilot well are brought into the horizontal well (Figure 9b) as the starting model and one of the constraints. The red lines (gamma ray and resistivity) identify the model, and the green lines (GR-p and ILD-p) identify the well logs from the pilot well.

The model from the pilot certainly does not directly fit the data in the horizontal well (Figure 9b) without further edit-ing. By maintaining the layer thickness as more or less con-stant and flexing the model up and down to achieve a good fit between the model and the well logs (Figure 9c) while hon-oring the trends indicated by the 3D markers and the offset well, we arrive at the cross-sectional interpretation shown in Figure 9c.

The correctness of the interpretation is checked by the “closeness” in fitting the well logs in the horizontal well with those from the pilot/offset wells. The model can be validated further by performing a tool-response modeling with the log-ging tools moving along the well path. In Figure 9c, the well logs (GR-m and RAD2-m) are the modeled logs which overlay closely with the measured logs (GR and RAD2), especially no-table around the lateral-distance interval of 2400 ft to ~ 2600 ft. The difference between the pilot-well induction log ILD-p and the horizontal-well propagation resistivity RAD2 is caused mainly by the difference in response characteristics in a vertical well environment versus a horizontal well environment, among other contributing factors.

Effective and efficient modeling capabilities enable real-time log processing and interpretation that subsequently impact well-placement decisions. Modeling helps to extract the desired information such as the distance to fluid contacts, distance to bed boundaries, resistivity anisotropy, and apparent dip from well logs acquired in horizontal wells.

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Even with good data fitting and modeling validation, one should remember that the interpreted model in Figure 9c might not be unique. The volume a few meters from the borehole is de-rived through extrapolation from pilot/offset wells. No informa-tion is measured directly from that volume.

ConclusionsTo successfully interpret and geosteer a horizontal well, a

formation model must be constructed to account for the geologic complexity encountered along the well path. Because of cost and technology limitations, the set of logs from the horizontal well alone is generally incomplete in answering the whereabouts of the well path versus the target reservoir. Geologic constraints based on depositional environments must be applied by using the information from offset/pilot-well logs and the seismic im-ages and large-scale geologic understanding. The visualization of well logs/reservoir in a multidimensional space also becomes essential to include the geometric information between the hori-zontal well and the target formation.

Tool-response modeling/inversion and the recognition of tool-response characteristics also will help to extract the geometric

information that otherwise is not readily available to enable a more unique interpretation. It also should be noted that a model that fits the measured logs might not always be unique.

AcknowledgmentsThe author thanks Maxwell Dynamics for permission to pub-

lish this article. He is also grateful to Carlos Torres-Verdín, who reviewed and suggested improvements to the article.

Corresponding author: JohnZhou@MaxwellDynamics.com

ReferencesWu, J.-Q., M. Al Wisler, and W. C. Barnett, 1991, Bed bound-

ary detection using resistivity sensor in drilling horizontal wells: Presented at the 32nd Annual Symposium, SPWLA.

Zhou, Q., 2007, Interpreting resistivity logs from deviated wells: 69th Conference and Exhibition, EAGE, Extended Abstracts, http://dx.doi.org/10.3997/2214-4609.201401794.

Zhou, Q., 2008, Log interpretation in high-deviation wells through user-friendly tool-response processing: Presented at the 49th Annual Symposium, SPWLA.

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