FIELD

This relates to a method and apparatus for determining permeability anisotropy in a geological formation. In particular, a method and apparatus for providing a fast determination of formation permeability anisotropy in situ at a selected location within a wellbore.

BACKGROUND

In carrying out formation analysis and modelling, in order to facilitate reservoir exploration and management, a key factor is the permeability distribution of the formation. Generally, permeability can differ greatly in both the horizontal and vertical directions, therefore determining the permeability anisotropy is crucial in obtaining an accurate formation model.

Formation permeability anisotropy is the ratio of vertical permeability to horizontal permeability in a formation. Permeability anisotropy is a critical parameter for describing, defining or modelling the formation. For instance, permeability anisotropy is used when designing a well completion, is used when planning an injection strategy, and is a key input to reservoir simulations. Homogenous permeability anisotropy occurs when the vertical permeability and the horizontal permeability are the same or similar so the ratio between them is close to 1 . Heterogeneous permeability anisotropy occurs when there is large variation between vertical permeability and horizontal permeability so the ratio between them is 0.01 or lower.

Known methods of determining formation permeability include well testing, core analysis and formation vertical interference testing (VIT). Well testing can provide high level approximated and inferred data over large areas of the formation. However, it can take days or weeks to obtain data from well testing. Core analysis involves removing core samples from the formation and transporting them to a laboratory for analysis. Core analysis in a laboratory, remote from the formation, can provide detailed data relevant to the specific location in the formation from which the core sample was extracted. VIT can be carried out by interval pressure transient testing (IPTT) using a wireline or logging- while-drilling (LWD) formation tester. IPTT generally requires at least two observation probes at different depths. Fluid is drawn into the sink probe and pressure measurements are taken at the observation probes to establish a measured pressure profile. Transient analysis of the pressure profile is carried out to obtain horizontal and vertical permeabilities. Reaching communication between a vertical probe and a sink probe generally takes a number of hours, thus running such a test takes a number of hours. The analysis of the test results then provides generalised data for the portion of the formation between the sink probe and the vertical probe.

While the orientation of the probes is generally irrelevant for determining permeability in a vertical wellbore, in a horizontal or deviated wellbore the probes of known tools should be oriented parallel to the sediment bed independent of the wellbore angle and/or the dip of the sediment bed, e.g. on the horizontal plane through a crosssection of the wellbore, .in order to get accurate and comparable results, e.g. results that may be compared to results collected from other locations along the horizontal or deviated wellbore, or results collected from a vertical section of the wellbore. Rotation or orientation of the tool may be required prior to testing, to orient the probes correctly.

The known methods can be time consuming and therefore expensive. Furthermore, there can be uncertainty or inaccuracy in the results obtained from the known methods, particularly well testing and VIT. It is an object of the disclosed apparatus and method to obviate or mitigate such drawbacks.

SUMMARY

According to a first aspect there is provided an apparatus for use in determining formation permeability anisotropy, the apparatus comprising: a body; at least two probe arrangements, each probe arrangement being configured to receive fluid from the formation, and the at least two probe arrangements comprising at least one pressure sensor arrangement configured to measure the pressure of received fluid in the at least two probe arrangements, wherein at least one of the probe arrangements is shaped and/or sized to have a different angular coverage to at least one other of the probe arrangements.

Beneficially, when used in a deviated or horizontal wellbore, taking measurements using the at least two probe arrangements having different angular coverage may allow accurate and comparable horizontal permeability and vertical permeability results to be determined without the probe arrangements being oriented parallel to the sediment bed or positioned on the horizontal plane through a cross-section of the wellbore. The accurate and comparable results may be useful for assisting in the selection of preferable depths and/or locations for fluid sampling and/or pumping.

Being able to determine horizontal permeability and vertical permeability without a specific orientation of the probe arrangements may reduce the need for rotating or reorienting the apparatus in the wellbore. This may save operational time (e.g. 20 to 40 minutes per measurement station for a LWD tool depending on the depth and angle of the well) and therefore money. This may also allow the operation to be carried out using a wireline tool which generally cannot be rotated.

Being able to determine horizontal permeability and vertical permeability without requiring the probe arrangements to be specifically positioned, e.g. located on the horizontal plane, may reduce the risk of a seal between the probe arrangement and the wall of the wellbore being broken. Formations are commonly least stable on the horizontal plane due to the geomechanical stresses in the formation, therefore borehole washout is most likely to break the seal between the probe and the wall of the wellbore when the probe is positioned on the horizontal plane. Accordingly the risk of losing sealing of the probe arrangement may be reduced, for example the risk of borehole washout due to geomechanical stresses in the formation may be reduced.

The at least two probe arrangements may be arranged on the body so as to be located at the same formation depth in use. The probe arrangements may be considered to be at the same formation depth if they are located within a depth range of approximately 10cm. Preferably the probe arrangements are located within a depth range of approximately 1cm. The at least two probe arrangements located at the same depth improves the accuracy in determining the formation permeability anisotropy because the impact on the determination of fluctuations in formation properties with depth is minimised. The accurate results may be useful for assisting in the selection of preferable depths and/or locations for fluid sampling and/or pumping.

The two probe arrangements may be distributed around the body. The at least two probe arrangements may be provided on the body so as to be opposite each other on the body or 90° apart. Alternatively, the two probe arrangements may be coincident on the body. The location of the probe arrangements on the body may result in the two probes being located at the same formation depth in use.

The body may be elongate and the at least two probe arrangements may be located at the same distance along the length of the body, which may result in the two probes being located at the same formation depth in use.

The at least two probe arrangements may be co-planar on the body, e.g. on a lateral plane through the body, which may result in the two probes being located at the same formation depth in use.

Each probe arrangement may comprise one or more inlets for receiving the fluid from the formation. The different angular coverage may comprise a different angular range of the pressure measurement, or at least a different angular range over which pressure measurements by the probe arrangement have an accuracy above a threshold. The different angular coverage may comprise a different maximum sensing angle within which the probe arrangement can sense pressure. The different angular coverage may comprise a different flow regime which include the information of different contributions from vertical flow horizontal flow.

The individual inlets or the one or more inlets collectively of each probe arrangement may have a different total area and/or a different shape, i.e. the individual inlets or the one or more inlets collectively of each probe arrangement may have a different size and/or shape to the individual inlets or the one or more inlets collectively of each other probe arrangement, which may result in the different angular coverage. For example, one of the probe arrangement inlets may be more elongate than the inlets of at least one other of the probe arrangements.

The at least two probe arrangements may comprise one pressure sensor arrangement, e.g. a common pressure sensor arrangement. The common pressure sensor arrangement may be configured to measure the pressure of received fluid in each probe arrangement consecutively. Alternatively, the at least two probe arrangements may comprise at least two pressure sensor arrangements. Each pressure sensor arrangement may be associated with one or more probe arrangement of the at least two probe arrangements. Each pressure sensor arrangement may be configured to measure the pressure of received fluid in each associated probe arrangement. Each probe arrangement of the at least two probe arrangements may comprise its own pressure sensor arrangement. Each pressure sensor arrangement may measure the pressure of received fluid in the respective probe arrangement simultaneously.

As indicated above, at least one or each of the probe arrangements may comprise one or more probe inlets. Where a probe arrangement comprises one probe inlet, the probe arrangement inlet corresponds to the probe inlet. Where the inlet of a probe arrangement comprises a plurality of probe inlets, e.g. a group or cluster of probe inlets, the probe arrangement inlet corresponds to an aggregate of the plurality of probe inlets. The area/size of the probe arrangement inlet may be defined by the total combined area/size of the plurality of probe inlets for the respective probe arrangement. Each probe inlet of the plurality of probe inlets may have the same area/may be the same size. Each probe arrangement may comprise a different number of probe inlets. The total or collective area and/or size of the probe arrangement inlet may be dependent on the number of probe inlets. The shape of the probe arrangement inlet may be defined by the relative positioning of the plurality of probe inlets. Each probe arrangement may comprise at least some or all of the same probe inlets as another probe arrangement. Each respective probe inlet of one or more or each probe arrangement may be in fluid communication with a respective pressure sensor. The pressure sensor arrangement associated with one or more or each probe arrangement may comprise a plurality of pressure sensors. Each pressure sensor may be associated to a respective probe inlet. In this case, the outputs of each pressure sensor of a pressure sensor arrangement may be summed, averaged or otherwise aggregated or combined in order to obtain pressure measurements for the respective probe arrangement. Alternatively, a pressure sensor arrangement may be a single pressure sensor. Each probe inlet of the one or more probe arrangement may be associated with the pressure sensor arrangement, e.g. single pressure sensor, for that probe arrangement.

The apparatus may comprise a flow control arrangement within the body, the flow control arrangement configured to draw fluid from the formation into and/or through the inlet of each probe arrangement of the at least two probe arrangements. The flow control arrangement may be configured to record the rate of fluid flow, e.g. the volumetric flow rate, into each probe arrangement. Alternatively, the flow control arrangement may be configured to record the accumulated volume of fluid flowing into each probe arrangement. The flow control arrangement may comprise a flow rate sensor or a flow meter.

The apparatus may comprise, or be configured to communicate with, a processing system. At least part of the processing system may be comprised in the apparatus. Additionally or alternatively, at least part of the processing system may comprise a local processing system, e.g. in wired communication with the apparatus, and/or may be a remote processing system such as a cloud based system in wired or wireless communication with the apparatus. The processing system may comprise any combination of within-apparatus, local and/or remote processing system, e.g. as part of a distributed processing system. The processing system may be configured to receive pressure measurements from the/each pressure sensor arrangement. The processing system may be configured to establish a pressure profile associated with each probe arrangement of the at least two probe arrangements, e.g. based on the received pressure measurements. The pressure profile may include a drawdown pressure profile and a build-up pressure profile. The processing system may be configured to receive flow rate measurements associated with each probe arrangement from the flow control arrangement. Alternatively, the processing system may be configured to receive accumulated volume measurements associated with each probe arrangement. The processing system may be configured to establish an accumulated volume profile associated with each probe arrangement. The processing system may be configured to calculate a flow rate of fluid flowing into each probe arrangement from the accumulated volume profile associated with the probe arrangement. The processing system may be configured to establish mobility or permeability function associated with each probe arrangement from the associated pressure profile and the received or calculated flow rate data. The function may be the mobility function where viscosity is taken into account. The function may be the permeability function where viscosity is assumed to be known and a constant. The viscosity may be estimated. The mobility or permeability functions may be implemented by equations, algorithms, simulations, etc. The processing system may be configured to resolve the at least two mobility or permeability functions to determine horizontal mobility or permeability and vertical mobility or permeability at the formation depth. The processing system may be configured to calculate the permeability anisotropy at the formation depth as the ratio between the determined vertical mobility or permeability and the determined horizontal mobility or permeability. In use, the apparatus may be inserted into the wellbore such that the at least two probe arrangements are located at the same formation depth. The flow control arrangement may be configured to draw fluid from the formation at the formation depth through each of the at least two probe arrangements via the inlet of each probe arrangement. Each probe arrangement inlet having a different area or a different shape may ensure that there is a different angular pressure response for each probe arrangement, e.g. due to a different flow regime of fluid being drawn into each probe arrangement. Accordingly, the mobility or permeability function for each probe arrangement is different, and these may be simultaneously resolved to determine the unknown horizontal mobility or permeability and vertical mobility or permeability at the formation depth for which the pressure measurements are taken. The processor thus may establish the permeability anisotropy at said formation depth.

Beneficially, the apparatus is of a generally simple construction and therefore can be robust. Furthermore, many of the components of the apparatus may be off-the-shelf components. In operation, the apparatus may establish the permeability anisotropy in minutes. This testing time is reduced compared with the existing technologies and therefore testing costs may also be reduced. Furthermore, by establishing formation permeability anisotropy at a selected formation depth, characterization of the formation may be more accurate, with results comparable to core analysis results, yet with much faster calculation times. The accurate results may be used to determine a preferable depth and/or location for fluid sampling and/or pumping. This combination of speed and accuracy may allow for dynamic “on the fly” determinations, which may be useful in applications such as control of production or drilling operations, smart completion design or redesign, or groundwater management. In particular, the established permeability anisotropy may be used in decision making for reservoir strategies including perforation strategies, injection strategies and production strategies. The established permeability anisotropy data may be particularly beneficial for underbalanced drilling procedures.

Each probe arrangement inlet may be defined by an in-plane angle. The in-plane angle is the angle of the inlet along a plane. The plane may be a lateral plane through the body. In use, the plane may be horizontal and located at the selected formation depth. Thus, in use, the in-plane angle may be the horizontal angle of the probe arrangement inlet. The inlet of each probe arrangement may have a different in-plane angle. A first probe arrangement of the at least two probe arrangements may have an in-plane angle less than 10°, preferably 9°. A second probe arrangement of the at least two probe arrangements may have an in-plane angle more than 10°, preferably 20°.

Each probe arrangement inlet may be defined by an out-of-plane angle. The out- of-plane angle is the angle in the direction transverse to the plane. In use, the out-of- plane angle may be the vertical angle of the probe arrangement inlet. The inlet of each probe arrangement may have substantially the same out-of-plane angle. Beneficially, the inlet of each probe arrangement having the same out-of-plane angle reduces the risk of vertical variations in permeability introducing error into the calculations for establishing permeability anisotropy at the plane.

The at least two probe arrangements may be distributed, preferably uniformly distributed, about a periphery of the body. The at least two probe arrangements may consist of two probe arrangements. The two probe arrangements may be positioned at opposite sides of the body. Alternatively, the two probe arrangements may be positioned on the body adjacent each other, e.g. spaced 90° apart.

The two probe arrangements may be positioned on the body at the same location. The at least two probe arrangements positioned on the body at the same location improves the accuracy in determining the formation permeability anisotropy because the impact on the determination of fluctuations in formation properties is minimised. The accurate results may be useful for assisting in the selection of preferable depths and/or locations for fluid sampling and/or pumping.

The two probe arrangements may be positioned on the body in a nested configuration. A first probe arrangement may be positioned inside a second probe arrangement. The two probe arrangements may have a coincident centre point. The two probe arrangements may be concentric.

The flow control arrangement may comprise one or more pumps configured to draw fluid into the inlet of each probe arrangement of the at least two probe arrangements. The one or more pumps may be one pump. Fluid may be drawn into each probe arrangement consecutively. Beneficially, a single pump may provide a simpler apparatus. Furthermore, greater consistency and repeatability of fluid control can be achieved using a single pump. Alternatively, the one or more pumps may be at least two pumps. The one or more pumps may comprise of a pump corresponding to each probe arrangement. Each pump may be configured to draw fluid into the inlet of said corresponding probe arrangement. Fluid may be drawn into each probe arrangement simultaneously. Beneficially, a pump corresponding to each probe arrangement may reduce testing time. The at least two pumps may comprise one or more primary pumps and one or more auxiliary pumps. The one or more primary pumps may be configured to draw fluid into the at least two probe arrangements either consecutively or simultaneously. The one or more auxiliary pumps may be configured to draw fluid into the at least two probe arrangements either consecutively or simultaneously should at least one of the one or more primary pumps fail. Beneficially, the one or more auxiliary pumps provides system redundancy such that should a pump fail the apparatus does not need to be retrieved from the borehole to replace the pump.

The flow control arrangement may be configured to record the rate of fluid flow into each probe arrangement. Particularly, each pump of the one or more pumps may be configured to record the rate of fluid flow into each/a respective probe arrangement. Alternatively, each probe arrangement may additionally comprise a flow rate sensor or a flow meter configured to measure and record the rate of fluid flow into the probe arrangement or the accumulated volume of fluid flowing into the probe arrangement.

The flow control arrangement may further comprise one or more chambers configured to receive and collect fluid drawn into each probe arrangement. The apparatus may further comprise one or more sampling tanks. Each sampling tank may be fluidly connected to at least one of the one or more chambers. Each sampling tank may receive fluid from at least one of the one or more chambers. Each sampling tank may be removable from the apparatus. Beneficially, the one or more sampling tanks allow fluid samples to be retrieved from the formation. Retrieved fluid samples may be used in laboratory testing. Alternatively, the flow control arrangement may comprise one or more fluid conduit extending between the at least two probe arrangements and the borehole. The one or more fluid conduits may be configured to provide a fluid path for fluid drawn into each probe arrangement to be discharged to the wellbore.

The apparatus may further comprise a locating arrangement. The locating arrangement may comprise one or more actuators. The actuator(s) may be associated with the body, each probe arrangement or each probe inlet. The one or more actuators may be configured to rotate the body. The one or more actuators may provide a mount between the respective probe arrangement or probe inlet and the body. The one or more actuators may be configured to manoeuvre the respective probe arrangement or probe inlet into engagement with the bore wall at the selected formation depth. The one or more actuators may comprise linear actuators and/or rotary actuators. The one or more actuators may be configured to move the respective probe arrangement or probe inlet linearly along the plane. The one or more actuators may be configured to rotate the respective probe arrangement or probe inlet around the body. The one or more actuators may be configured to rotate the respective probe arrangement or probe inlet around an axis through the centre of each probe arrangement or probe inlet. Beneficially, particularly when used in a deviated or horizontal wellbore, the manipulation of the body, each probe arrangement or each probe inlet available from the locating arrangement allows each probe arrangement or probe inlet to engage the bore wall at the selected formation depth.

The locating arrangement may comprise a control system. The control system may be configured to position the body using the one or more actuator(s). The control system may be configured to automatically position the body according to preselected commands. The control system may be configured to position the body according to input commands.

The locating arrangement may comprise a position sensing arrangement. The position sensing arrangement may comprise at least one of an inclinometer, a level sensors, or other known position detecting means know in the art. The position sensing arrangement may be configured to determine the position and/or angle of at least one of the body, each probe arrangement or each probe inlet. Beneficially, the position sensing arrangement may permit the locating arrangement to determine when the probe arrangements are located at the selected formation depth. Further, when used in a deviated or horizontal wellbore, the position sensing arrangement may permit the locating arrangement to determine when the probe arrangements are located at the same formation depth.

Each probe arrangement may further comprise a sealing arrangement. The sealing arrangement may comprise a sealing element (i.e. a seal, a packer or other sealing means known in the art) circumscribing each probe inlet of the one or more probe inlets. Each sealing element may be configured to form a seal against the bore wall. Beneficially, the sealing arrangement may ensure that fluid does not leak between the formation and the apparatus, which may be detrimental to the accuracy of the test. The risk of the seal between the sealing element and the bore wall being broken, e.g. due to borehole washout, is reduced because the horizontal permeability and vertical permeability may be determined without the probe arrangements being located on the horizontal plane where the formation is least stable due to the geomechanical stresses in the formation.

Each probe inlet may further comprise a contact detection arrangement. The contact detection arrangement may be configured to detect when the sealing element associated with the probe inlet is in sealing communication with the bore wall. The contact detection arrangement may comprise one or more sensors configured to sense when the sealing element is in contact with the bore wall. The contact detection arrangement may provide feedback to the locating arrangement.

The processing system may be further configured to determine a pressure change in fluid flowing into each probe arrangement from the established pressure profile for said probe arrangement. The processing system may be further configured to calculate mobility at each probe arrangement from the respective pressure profile established for each probe arrangement and the flow rate of fluid flowing into the respective probe arrangement. The processing system may be further configured to determine permeability at each probe arrangement from the respective calculated mobility and viscosity. Viscosity may be estimated.

The apparatus may be mounted on a wireline, drill string or coiled tubing for deployment into the well bore.

According to a second aspect there is a method of collecting downhole measurements for use in determining permeability anisotropy in a formation, the method comprising: providing at least two probe arrangements comprising at least one pressure sensor arrangement, each probe arrangement comprising an inlet configured to receive fluid from the formation, and the at least one pressure sensor arrangement configured to measure the pressure of fluid received by each inlet, wherein at least one of the probe arrangements is shaped and/or sized to have a different angular coverage to at least one other of the probe arrangements; drawing formation fluid into the at least two probe arrangements; and recording the pressure of fluid drawn into each probe arrangement to establish a pressure profile associated with each probe arrangement.

Beneficially, when used in a deviated or horizontal wellbore, taking measurements using the at least two probe arrangements having different angular coverage may allow horizontal permeability and vertical permeability to be determined without the probe arrangements being oriented parallel to the sediment bed or positioned on the horizontal plane through a cross-section of the wellbore.

Being able to determine horizontal permeability and vertical permeability without a specific orientation of the probe arrangements may reduce the need for rotating or reorienting the apparatus in the wellbore. This may save operational time (e.g. 20 to 40 minutes per measurement station for a LWD tool depending on the depth and angle of the well) and therefore money. This may also allow the operation to be carried out using a wireline tool which generally cannot be rotated.

Being able to determine horizontal permeability and vertical permeability without requiring the probe arrangements to be located on the horizontal plane may reduce the risk of a seal between the probe arrangement and the wall of the wellbore being broken. Formations commonly have lowest or lower stability on the horizontal plane due to the geomechanical stresses in the formation, therefore borehole washout is most likely to break the seal between the probe and the wall of the wellbore when the probe is positioned on the horizontal plane. Accordingly the risk of losing sealing of the probe arrangement may be reduced, for example the risk of borehole washout due to geomechanical stresses in the formation may be reduced.

The method may further comprise locating the at least two probe arrangements at the same formation depth for drawing formation fluid into the at least two probe arrangements.

The method may further comprise recording the rate of flow of formation fluid drawn into each probe arrangement. The at least two probe arrangements may be comprised in the apparatus of the first aspect, i.e. the method may comprise providing the apparatus in a wellbore. The body of the apparatus may arrange the at least two probe arrangements at the same extent along the wellbore. The body of the apparatus may arrange the at least two probe arrangements at the same formation depth.

According to a third aspect of the present disclosure is a method of determining permeability anisotropy in a formation, the method comprising: receiving pressures or a pressure profile determined by at least two probe arrangements comprising at least one pressure sensor arrangement, each probe arrangement comprising an inlet configured to receive fluid from the formation, and the at least one pressure sensor arrangement configured to measure the pressure of fluid received by each inlet, wherein at least one of the probe arrangements is shaped and/or sized to have a different angular coverage to at least one other of the probe arrangements; receiving or calculating flow rates of fluid received by the inlet of each probe arrangement; and calculating permeability anisotropy for the formation depth using the pressures or pressure profiles collected by the at least two probe arrangements at that formation depth and the flow rates.

Beneficially, when used in a deviated or horizontal wellbore, taking measurements using the at least two probe arrangements having different angular coverage may allow horizontal permeability and vertical permeability to be determined without the probe arrangements being oriented parallel to the angle of the wellbore or positioned on the horizontal plane through a cross-section of the wellbore.

Being able to determine horizontal permeability and vertical permeability without a specific orientation of the probe arrangements may reduce the need for rotating or reorienting the apparatus in the wellbore. This may save operational time (e.g. 20 to 40 minutes per measurement station for a LWD tool depending on the depth and angle of the well) and therefore money. This may also allow the operation to be carried out using a wireline tool which generally cannot be rotated. Being able to determine horizontal permeability and vertical permeability without requiring the probe arrangements to be located on the horizontal plane may reduce the risk of a seal between the probe arrangement and the wall of the wellbore being broken. Formations commonly lowest or lower stability on the horizontal plane due to the geomechanical stresses in the formation, therefore borehole washout is most likely to break the seal between the probe and the wall of the wellbore when the probe is positioned on the horizontal plane. Accordingly the risk of losing sealing of the probe arrangement may be reduced, for example the risk of borehole washout due to geomechanical stresses in the formation may be reduced.

The at least two probe arrangements may be located at the same formation depth when measuring the pressures.

The method may comprise establishing a mobility or permeability function for each probe arrangement from the associated pressure profile and flow rate. The mobility or permeability functions may be implemented by equations, algorithms, simulations, etc. The method may comprise resolving the at least two mobility or permeability functions to determine horizontal mobility or permeability and vertical mobility or permeability at the formation depth. The method may comprise calculating permeability anisotropy at the formation depth as the ratio between the determined vertical mobility or permeability and the determined horizontal mobility or permeability.

The mobility or permeability function for each probe arrangement may be a function of horizontal mobility or permeability at the formation depth, vertical mobility or permeability at the formation depth, and a constant associated with said probe arrangement. The constant associated with each probe arrangement may correspond to a function of flow regime at said probe arrangement and/or inlet geometry of said probe arrangement.

The method may further comprise determining a pressure change in fluid flowing into each probe arrangement from the established pressure profile associated with said probe arrangement. The method may further comprise calculating the mobility at each probe arrangement from the associated pressure profile and the flow rate. The method may further comprise determining the permeability at each probe arrangement from the respective calculated mobility and viscosity. The method may comprise measuring the pressures or determining the pressure profiles determined by the at least two probe arrangements using the method of the second aspect.

The method may be performed by a processing apparatus that is remote from the at least two probe arrangements, e.g. the at least two probe arrangements may be configured to be located downhole in use, whereas the processing apparatus may not be downhole. The processing apparatus may be cloud based or otherwise connected via a wide area network, e.g. by wireless and/or wired communications, to the at least two probe arrangements.

According to fourth aspect is a computer program product configured such that, when implemented on a processing apparatus, causes the processing apparatus to perform the method of the third aspect.

The computer program product may be embodied on a tangible computer readable carrier medium, such as a magnetic or solid state data storage device or memory, an optical disk or other optical computer readable carrier medium, a magnetic disk or other magnetic computer readable carrier medium, quantum data storage, and/or the like.

The processing apparatus may comprise a processor, one or more data storage devices, an output device and an input device. The processing apparatus may comprise a general purpose computer or a specialist control system. The processing apparatus may comprise one or more of: a central processing unit (CPU), a field programmable gate array, an application specific integrated circuit (ASIC), a graphics processing unit (GPU), a maths co-processor, a tensor processing unit (TPU), a quantum processing device, and/or the like. The processing apparatus may be a downhole processing apparatus, e.g. comprised in or local to the apparatus with the apparatus that comprises the at least two probe arrangements. Beneficially, the processing apparatus may be a remote processing apparatus, such as a cloud based system in wired or wireless communication with the at least two probe arrangements. The processing apparatus may be configured to receive pressure measurements from the/each associated pressure sensor arrangement of the at least two probe arrangements. The processing apparatus may be configured to establish a pressure profile associated with each probe arrangement of the at least two probe arrangements, e.g. based on the received pressure measurements. The processing apparatus may be configured to receive flow rate measurements associated with each probe arrangement from the flow control arrangement. Alternatively, the processing apparatus may be configured to receive accumulated volume measurements associated with each probe arrangement. The processing apparatus may be configured to establish an accumulated volume profile associated with each probe arrangement. The processing apparatus may be configured to calculate a flow rate of fluid flowing into each probe arrangement from the accumulated volume profile associated with the probe arrangement. The processing apparatus may be configured to establish a mobility or permeability function associated with each probe arrangement from the associated pressure profile and the associated flow rate.

According to a fifth aspect is a processing apparatus configured to perform the method of the third aspect.

The processing apparatus may comprise a processor, one or more data storage devices, an output device and an input device. The processing apparatus may comprise a general purpose computer or a specialist control system. The processing apparatus may comprise one or more of: a central processing unit (CPU), a field programmable gate array, an application specific integrated circuit (ASIC), a graphics processing unit (GPU), a maths co-processor, a tensor processing unit (TPU), a quantum processing device, and/or the like. The processing apparatus may be a downhole processing apparatus, e.g. comprised in or local to the apparatus with the apparatus that comprises the at least two probe arrangements. Beneficially, the processing apparatus may be a remote processing apparatus, such as a cloud based system in wired and/or wireless communication with the at least two probe arrangements. The processing apparatus may be configured to receive pressure measurements from the/each associated pressure sensor arrangement of the at least two probe arrangements. The processing apparatus may be configured to establish a pressure profile associated with each probe arrangement of the at least two probe arrangements, e.g. based on the received pressure measurements. The processing apparatus may be configured to receive flow rate measurements associated with each probe arrangement from the flow control arrangement. Alternatively, the processing apparatus may be configured to receive accumulated volume measurements associated with each probe arrangement. The processing apparatus may be configured to establish an accumulated volume profile associated with each probe arrangement. The processing apparatus may be configured to calculate a flow rate of fluid flowing into each probe arrangement from the accumulated volume profile associated with the probe arrangement. The processing apparatus may be configured to establish mobility or permeability function associated with each probe arrangement from the associated pressure profile and the flow rate.

The above summary is intended to be merely exemplary and non-limiting. It should be understood that features defined above in accordance with any aspect of the present disclosure or below relating to any specific embodiment of the disclosure may be utilized, either alone or in combination with any other defined feature, in any other aspect or embodiment or to form a further aspect or embodiment of the disclosure.

BRIEF DESCRIPTION OF DRAWINGS

Figure 1 is a schematic cross-sectional view of an apparatus for determining permeability anisotropy in a formation;

Figure 2a is a schematic side view of a first probe arrangement of the apparatus of Figure 1 ;

Figure 2b is a schematic side view of a second probe arrangement of the apparatus of Figure 1 ;

Figure 3 is a schematic plan view of the apparatus of Figure 1 ;

Figure 4a, 4b and 4c are schematic side views of alternative probe arrangements;

Figure 5 is a graph of an exemplary pressure profile established during a formation pressure test;

Figure 6 is a flowchart illustrating a method for collecting pressure measurements using the apparatus of Figure 1 ;

Figure 7 is a flowchart illustrating a method for calculating permeability anisotropy using the measurements collected using the method of Figure 5; and Figure 8 is a schematic of a processing system used to perform the method of Figure 8.

DETAILED DESCRIPTION

Referring to Figure 1 , an apparatus 10 for determining permeability anisotropy in a formation comprises a body 12 supporting a first probe arrangement 14a and a second probe arrangement 14b. The first probe arrangement 14a and the second probe arrangement 14b are supported on opposite sides of the body 12. In alternative embodiment the first and second probe arrangements are supported on the body adjacent each other, or spaced apart but not opposite. Each probe arrangement 14a, 14b comprises an inlet 16a, 16b. The first probe arrangement 14a and the second probe arrangement 14b are supported by the body such that the inlets 16a, 16b are co-planar on a plane p. In some examples, the inlet 16a, 16b of each probe arrangement 14a, 14b is elongate and extends along the plane p, but it will be appreciated that the inlet could be other shapes, including symmetrical shapes such as square or circular. In particular, the centre of the inlet 16a of the first probe arrangement 14a is coplanar on the plane p with the centre of the inlet 16b of the second probe arrangement 14b. In an alternative embodiment, the apparatus may comprise more than two probe arrangements, in which case each of the probe arrangements are supported by the body with the inlets co-planar on the plane p and the probes are preferably but not essentially uniformly distributed around the body.

The apparatus 10 is mounted on a wireline 32 for deployment into the wellbore. Alternatively, the apparatus may be deployed into the wellbore by any other means known to the skilled person, for example on the drill string as a LWD tool. The apparatus 10 is deployed into the wellbore such that the plane p is positioned at a selected location in the formation. In a vertical wellbore, the plane p will be horizontal and positioned at the selected formation depth at which the permeability anisotropy is to be determined. In a horizontal or deviated wellbore, at least a portion of the plane will be positioned at the selected formation depth at which the permeability anisotropy is to be determined.

The apparatus 10 further comprises a flow control arrangement 18 comprising a pump 20. The pump 20 is configured to draw fluid into the apparatus 10 via the inlets 16a, 16b of each probe arrangement 14a, 14b. Each probe arrangement 14a, 14b thus functions as a sink probe, having fluid drawn into it from the formation, as will be understood by a person of skill in the art. The flow control arrangement further comprises a series of fluid conduits 24. The fluid conduits 24 provide fluid communication between each probe arrangement 14a, 14b and the pump 20. The flow control arrangement 18 further comprises a valve arrangement 22 configured to control fluid flow through the fluid conduits 24 to allow the pump 20 to draw fluid firstly into the first probe arrangement 14a and then secondly into the second probe arrangement 14b in a consecutive manner. The flow control arrangement 18 further comprises a chamber 26. The fluid conduits 24 further provide a flow path from each probe arrangement 14a, 14b to the chamber 26. The chamber 26 receives and collects the formation fluid drawn into the probe arrangements 14a, 14b by the pump 20. In an alternative embodiment (not shown), the apparatus further comprises a sampling tank in fluid communication with the chamber to receive fluid from the chamber. The sampling tank is removable from the apparatus such that fluid can be retrieved from the apparatus. In a further alternative embodiment (not shown), additional fluid conduits may be provided between the chamber and the borehole to permit fluid to be discharged from the apparatus.

Beneficially, using a single pump to draw fluid into each probe arrangement consecutively improves the consistency between the formation pressure tests for each probe arrangement, and simplifies the flow control arrangement. In an alternative embodiment, the flow control arrangement may comprise a plurality of pumps. Each pump may be associated with a corresponding probe arrangement, such that each pump is configured to draw fluid into the apparatus via the inlet of the corresponding probe arrangement. Such a pump arrangement may allow fluid to be drawn into the apparatus through each probe simultaneously. Beneficially, simultaneous testing with a plurality of pumps reduces the time required to obtain the pressure data for each probe arrangement. In a further embodiment, the described one or plural pumps are provided as primary pumps and the flow control arrangement additionally comprises one or more auxiliary pumps which can function in place of a primary pump should a primary pump fail. Beneficially, the auxiliary pump(s) provide the apparatus with redundancy so that the apparatus does not need to be returned to surface should a pump fail.

The flow control arrangement 18 further comprises a flow rate sensor (not shown) configured to record the rate of flow of fluid being drawn into each probe arrangement 14a, 14b. The flow rate sensor is integral with the pump 20. In an alternative embodiment the flow rate sensor may be replaced with a flow meter. In an alternative embodiment, the flow rate sensor or flow meter is provided as a separate component to the pump. In embodiments having plural pumps, corresponding plural flow rate sensors or flow meters may be provided.

Alternatively, a flow rate sensor or flow meter can be provided in each probe arrangement, configured to record the rate of flow of fluid being drawn into the probe arrangement or the accumulated volume of fluid flowing into the probe arrangement.

Each probe arrangement 14a, 14b further comprises a pressure sensor 28a, 28b. Each pressure sensor 28a, 28b measures the pressure of fluid being drawn into the inlet 16a, 16b of the probe arrangement 14a, 14b. In other embodiments the probe arrangements are both associated with a common pressure sensor configured to measure the pressure of received fluid in each associated probe arrangement consecutively.

In this example, the apparatus 10 further comprises a processing system 30. However, in alternative embodiments, the processing system 30 or at least part of the functionality of the processing system 30 can be provided externally from the apparatus. This may be as a separate downhole or up-hole system or most preferably as part of a remote or cloud based computing resource connected to the apparatus 10 optionally via an uphole communications relay device and a wide area network, e.g. over the internet. In this way, the apparatus 10 can signal to surface using known downhole communications methods such as electrical signal cable, fibre optic communications, acoustic communications and/or the like, and the relay device at the surface receives the communications from the apparatus 10 are transmits then via conventional digital communications techniques to the remote or cloud based computing resource.

The flow rate sensor provides the flow rate measurements for each probe arrangement 14a, 14b to the processing system 30. The pressure sensors 28a, 28b provide the pressure measurements to the processing system 30. The processing system 30 establishes a pressure profile (e.g. a profile of pressure over time) for each probe arrangement 14a, 14b from the pressure measurements received from the pressure sensor 28a, 28b of the respective probe arrangement 14a, 14b. The pressure profile includes fluid pressures during drawdown and build-up. The processing system 30 can then establish the permeability anisotropy at the selected formation depth, as will be described in greater detail below.

The apparatus 10 further comprises a locating arrangement (not shown). The locating arrangement comprises a linear actuator associated with each probe arrangement. Each linear actuator is configured to move the associated inlet 16a, 16b towards and away from the body 12 along the plane p. In use, this allows each inlet 16a, 16b to be moved into and out of engagement with the bore wall. The locating arrangement further comprises a rotary actuator configured to rotate the body 12 within the wellbore. Beneficially, in a horizontal or deviated wellbore this allows probe arrangements located on opposite sides of the body to be positioned at the same depth. The locating arrangement further comprises a control system configured to position the body 12 using the actuators to automatically position the body according to preselected commands.

In another embodiment, the locating arrangement additionally or alternatively comprises one or more rotary actuators associated with each probe arrangement. Beneficially, in use in a deviated or horizontal wellbore such a locating arrangement permits the inlets to be rotated around an axis through the centre of each inlet to bring the plane of each inlet to a horizontal orientation, and the inlets to be rotated around the body such that the plane of each inlet is located at the same depth.

Figures 2a and 2b show the first and second probe arrangements 14a, 14b respectively, in each case viewed in the direction along the plane p. The inlet 6a, 16b of each probe arrangement 14a, 14b is defined by an area. The area of the inlet 16a of the first probe arrangement 14a is preferably different to the area of the inlet 16b of the second probe arrangement 14b. In alternative embodiments having more than two probe arrangements, each inlet preferably has a different area. The inlet 16a of the first probe arrangement 14a has a different planar length l _a , to the planar length lb of the inlet 16b of the second probe arrangement 14b. The inlet 16a of the first probe arrangement 14a has the same transverse length, i.e. width w _a , as the transverse length, i.e. width Wb, of the inlet 16b of the second probe arrangement 14b. In alternative embodiments having more than two probes, each probe has a different length and the same width. The inlet geometry in the planar and transverse directions defines the flow angle of the inlet 16a, 16b in the same said directions, as will be described below. When each probe arrangement 14a, 14b is located in the wellbore adjacent a selected location of the formation, the flow angles of each inlet 16a, 16b define an envelope of the formation from which each inlet 16a, 16b will receive formation fluid when the fluid is drawn into the apparatus 10. The different inlet geometries ensure that the envelope for each probe arrangement 14a, 14b is different so that a different pressure profile is obtained for each probe arrangement 14a, 14b.

The inlet 16a, 16b of each probe arrangement 14a, 14b is defined by an out-of- plane angle z _a , Zb (see Figure 1). The out-of-plane angle z _a , Zb is the flow angle of the inlet 16a, 16b transverse to the plane p. The out-of-plane angle z _a of the inlet 16a of the first probe 14a is the same as the out-of-plane angle Zb of the inlet 16b of the second probe 14b. The centre c _a , Cb of each inlet 16a, 16b (see Figure 2) is located on the plane p, thus, when the apparatus 10 is deployed in a wellbore, for example a vertical wellbore, each inlet 16a, 16b is located at the same depth and the envelope of each inlet 16a, 16b has the same vertical range. Beneficially, this ensures that the effect of vertical variations in permeability is minimised in establishing the permeability anisotropy at the selected depth of the plane p in the formation.

Figure 3 provides a plan cross sectional view of the apparatus 10 viewed in a direction transverse to the plane p. As described above, in the present embodiment the first probe arrangement 14a and the second probe arrangement 14b are located on opposite sides of the body 12. The centre c _a of the inlet 16a of the first probe arrangement 14a is provided at a location that is 180° around the body from the centre Cb of the inlet 16b of the second probe arrangement 14b. In alternative embodiments, the centre of the inlet of the first probe arrangement may be more or less than 180° from the centre of the inlet of the second probe arrangement, e.g. the centre of the inlet of the first probe arrangement may be 90° from the centre of the inlet of the second probe arrangement.

The inlet 16a, 16b of each probe arrangement 14a, 14b is defined by an in-plane angle a _a , ab. The in-plane angle a _a , ab is the flow angle of the inlet 16a, 16b along the plane. The in-plane angle a _a of the inlet 16a of the first probe arrangement 14a is different to the in-plane angle ab of the inlet 16b of the second probe arrangement 14b. In alternative embodiments where there are more than two probe arrangements, the inplane angle of each inlet is different. The in-plane angle a _a of the inlet 16a of the first probe arrangement 14a is smaller than the in-plane angle ab of the inlet 16b of the second probe arrangement 14b. The inlet 16a of the first probe arrangement 14a has an inplane angle a _a of 9°. The inlet 16b of the second probe 14b has an in-plane angle ab of 20°. In other embodiments, any other suitable in-plane angle may be selected for each inlet, provided that in-plane angle of the inlet of each probe arrangement is not the same as the in-plane angle of the inlet of any other probe arrangement.

Referring back to Figures 2a and 2b, each probe arrangement 14a, 14b further comprises a seal arrangement 34a, 34b such as a packer surrounding the inlet 16a, 16b. The seal arrangement 34a, 34b forms a seal with the bore wall such that fluid drawn from the formation into the probe arrangement 14a, 14b does not escape between the bore wall and the apparatus 10. Beneficially, this improves the accuracy of the measurements obtained by the apparatus 10. The risk of the seal between the sealing arrangement 34a, 34b and the bore wall being broken, e.g. due to borehole washout, is reduced because the horizontal permeability and vertical permeability may be determined without the probe arrangements 14a, 14b being located on the horizontal plane where the formation is least stable due to the geomechanical stresses in the formation.

Figures 4a, 4b and 4c provide alternative probe arrangements 114a, 114b, 114c. The probe arrangements 114a, 114b, 114c each comprise a plurality of probe inlets 140. Each probe inlet 140 corresponds in form to the inlets 16a, 16b described above. However, the inlet 116a, 116b, 116c of each probe arrangement 114a, 114b, 114c corresponds to an aggregate of the probe inlets 140 of said probe arrangement 114a, 114b, 114c. The plurality of probe arrangements 114a, 114b, 114c in an apparatus each have a different number and/or arrangement of probe inlets 140, such that the flow regime of the each probe arrangement 114a, 114b, 114c is different. Figure 4a shows probe arrangement 114a comprising three probe inlets 140. The probe inlets 140 are linearly arranged such that they are co-planar along plane p. Figure 4b shows probe arrangement 114b comprising four probe inlets 140. The probe inlets 140 are arranged in a linear array in rows parallel to the plane p and columns transverse to the plane p. The number of columns of probe inlets 140 defines the in-plane angle of the probe arrangement inlet 116b. The number of rows of probe inlets 140 defines the out-of-plane angle of the probe arrangement inlet 116b. Figure 4c shows probe arrangement 114c comprising five probe inlets 140. As for probe arrangement 114a, the probe inlets 140 are linearly arranged such that they are co-planar along plane p. Numerous alternative arrangements of probe inlets can readily be envisaged by a person skilled in the art, for example the probe inlets may be arranged in a circular or triangular design to provide different flow regimes. Furthermore, in alternative embodiments, a probe arrangement may comprise 1 , 2 3, 4, 5 or more probe inlets to provide different flow regimes. Each probe arrangement 114a, 114b, 114c comprises a seal arrangement 134a, 134b, 134c. Each seal arrangement comprises a plurality of seal elements 142, each seal element 142 associated with a respective probe inlet 140. Each seal element 142 surrounds the respective probe inlet 140 so as to form a seal with the bore wall in use. The risk of the seal between the seal element 142 and the bore wall being broken, e.g. due to borehole washout, is reduced because the horizontal permeability and vertical permeability may be determined without the probe arrangements 114a, 114b, 114c being located on the horizontal plane where the formation is least stable due to the geomechanical stresses in the formation.

As mentioned above, the processor 30 can establish a pressure profile for each probe arrangement 14a, 14b from the pressure measurements taken by the pressure sensor 28a, 28b as fluid is being drawn into the probe arrangement 14a, 14b by the flow control arrangement 18. This process is referred to as a formation pressure test. An exemplary pressure profile is shown in Figure 5. From the pressure profile, the flow rate data, and a number of predetermined factors which may be stored by the processor, the processor establishes the permeability anisotropy at the formation depth, as follows.

Permeability anisotropy is the ratio of vertical permeability k _v to horizontal permeability kh. k _v Permeability anisotropy = — -h

Thus, to calculate the permeability anisotropy at the selected location in the formation of the plane p, the vertical permeability k _v to horizontal permeability kh at the selected location should be determined.

By running a formation pressure test through each probe arrangement 14a, 14b in the apparatus 10, the mobility Mdd at each probe 14a, 14b can be determined by the processor 30. During the formation pressure test, the flow rate Qdd of fluid being drawn into each the probe arrangement 14a, 14b is recorded by the flow control arrangement 18. A pressure drop APdd at each probe arrangement 14a, 14b is determined from the pressure profile for the respective probe arrangement 14a, 14b by the processor 30.

Referring to the equations presented by Moran and Kinkier for the pressure analysis during formation testing, a constant pressure at the perforation is associated with a constant flow rate during the drawdown period. For a single probe in an anisotropic formation, the relation between the pressure drop APdd and the volumetric flow rate Qdd is described by the following equation, or where P _f is the flowing pressure at the formation tester chamber, Pj is the formation pressure, APdd is the pressure drop between the formation and the chamber, p is the viscosity of the fluid, Ceff is the effective radius of a non-spherical flow region formed in the porous media towards the probe. The flow region is typically a function of the probe geometry.

For instance, the coefficient Ceff of a prolate ellipsoid shape can be expressed as, where L is the major semi-axis of the ellipsoid and R is the minor semi-axis.

The equation describing the relation between the pressure drop APdd and the volumetric flow rate Qdd can be rearranged as, where kdd is the permeability during drawdown, which is a function of vertical permeability k _v , horizontal permeability kh and flow regime factor y, kdd = F(k _v , k _h , y) Thus, mobility Mdd at each probe 14a, 14b can be calculated from the pressure drop APdd, the volumetric flow rate Qdd and a predetermined probe specific flow coefficient Ceff,

The flow coefficient for each probe is either stored in the processing system or retrievable by the processing system, for example retrievable from a database.

The mobility Mdd is equal to the ratio of permeability kdd to viscosity p,

Because each probe 14a, 14b is positioned on the same plane, i.e. at the same selected formation location, the viscosity p of the fluid being drawn into each probe 14a, 14b can be assumed to be the same. Accordingly, the permeability kdd for each probe 14a, 14b is directly proportional to the mobility Mdd for the respective probe 14a, 14b.

The permeability kdd is a function of horizontal permeability kh at the plane p, vertical permeability k _v at the plane p.

For example, according to the literature, in a spherical flow regime the relation between spherical permeability k _s , vertical permeability k _v and horizontal permeability kh is,

Also according to the literature, in a radial flow regime the relation between radial permeability k _r , vertical permeability k _v and horizontal permeability kh is, k _r = k _h k _v °

Therefore we assume that the relationship between permeability kdd, vertical permeability k _v and horizontal permeability kh can be expressed by the equation, kdd = k _h ^Y ■ k _v ^y The constant y is a function of flow regime and probe geometry, and relate the to angular coverage of the probe, thus the constant y is different for each probe arrangement 14a, 14b due to their differing inlet geometry and flow angles. In particular, the constant y is different for each probe arrangement 14a, 14b in the apparatus 10 because the inlet 16a, 16b of each probe arrangement has a different in-plane angle a _a , ab. Thus for the first probe arrangement 14a the permeability function is, and for the second probe arrangement 14a the permeability function is,

Having calculated the mobility Mdd for each probe arrangement 14a, 14b, and estimating viscosity p, the processor can resolve the two permeability functions simultaneously to determine the horizontal permeability kh and the vertical permeability k _v at the selected location of the plane p in the formation. Alternatively, it can be assumed that viscosity p is a constant (i.e. viscosity p is the same for each probe arrangement 14a, 14b and in both the horizontal and vertical directions) and a mobility function can be used in place of the permeability function for each probe. In this case, the mobility functions can be resolved to determine the horizontal mobility and the vertical mobility at the selected formation depth. The processor 30 calculates the permeability anisotropy at the selected location using the determined horizontal permeability kh and the vertical permeability k _v , as provided above (or the determined vertical mobility and determined horizontal mobility where viscosity is assumed to be constant).

Beneficially, this method of calculating the permeability anisotropy reduces testing time, and therefore also reduces cost, whilst also being capable of providing results whilst the apparatus is in-situ.

In alternative embodiments where the apparatus comprises more than two probe arrangements, for example n probe arrangements, the permeability kddn for the n probe arrangement is defined by the function, The permeability functions may be equations, algorithms, simulations, etc. The processor resolves n permeability functions simultaneously to determine the horizontal permeability kh and the vertical permeability k _v at the selected location in the formation of the plane. The processor calculates the permeability anisotropy at the location in the formation of the plane using the determined horizontal permeability kh and the vertical permeability k _v . As n increases, the accuracy of the calculated permeability anisotropy is increased.

Where core samples have been taken from the same selected formation location for which the permeability anisotropy is established, the results can be compared to core analysis of the core samples from the selected location.

Figure 6 is a flowchart illustrating a method for collecting pressure measurements using the apparatus 10. The method comprises, in step 505, providing the apparatus 10 in which at least one of the probe arrangements 14a has a different angular coverage to at least one other of the probe arrangements 14b. At least one of the probe arrangements 14a is shaped and/or sized to have a different angular coverage to at least one other of the probe arrangements 14b. In step 510, the apparatus 10 is located in the wellbore such that both of the probe arrangements 14a, 14b are located at the same formation depth. In step 515, formation fluid from the formation at that extent along the wellbore is provided to the probe arrangements 14a, 14b. In step 520, the pressure of the formation fluid received by each probe arrangement 14a, 14b from the formation at that extent along the wellbore is determined using the probe arrangements 14a, 14b.

Figure 7 is a flowchart illustrating a method for calculating permeability anisotropy using the measurements collected using the method of Figure 5. The method comprises, in step 605, receiving the pressure profile determined using the method of Figure 5. The method comprises in step 610, or calculating flow rates of fluid received by the inlet of each probe arrangement. In step 615, the method comprises calculating permeability anisotropy for the formation depth at which the pressure profiles were collected by the probe arrangements 14a, 16b. For example, this could involve establishing an permeability function for each probe arrangement 14a, 14b from the associated pressure profile and resolving the at least two permeability functions to determine, for that formation depth, horizontal permeability and vertical permeability. Thereafter, permeability anisotropy can be calculated, for that formation depth, as the ratio between the determined vertical permeability and the horizontal permeability. Figure 8 is a schematic of an example of the processing system 30 used to perform the method of Figure 7. The processing system 30 comprises a processor 705, data storage 710 such as memory, a communications system 715 for communicating over a network, one or more input devices 720 and one or more output devices 725.

The above description is intended to be merely exemplary and non-limiting. It should be understood that features defined above in accordance with any aspect of the present disclosure or relating to any specific embodiment of the disclosure may be utilized, either alone or in combination with any other defined feature, in any other aspect or embodiment or to form a further aspect or embodiment of the disclosure.

For example, although examples described above relate to a vertical wellbore, it will be appreciated that the process can also be used in deviated or other non-vertical wellbores.

Furthermore, in examples, the probe inlets have an elongate generally rectangular or a hyperellipse or superellipse form. However, other shapes could be used, such as oval, elliptical, circular, square or the like. Although probe inlets with the same extent in an out-of-plane direction and different extent in an in-plane direction are described and particularly beneficial, it will be appreciated that probes having inlets having different extents in an out-of-plane direction could be used.

Method steps of the invention can be performed by one or more programmable processors executing a computer program to perform functions of the invention by operating on input data and generating output. Method steps can also be performed by special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit) or other customised circuitry. Processors suitable for the execution of a computer program include one or more of: a central processing unit (CPU), maths co-processor (MCP), graphics processing unit (GPU), tensor processing unit (TPU) and/or the like. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks. Information carriers suitable for embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, e.g. EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in special purpose logic circuitry.

To provide for interaction with a user, the invention can be implemented on a device having a screen, e.g., a CRT (cathode ray tube), plasma, LED (light emitting diode) or LCD (liquid crystal display) monitor, for displaying information to the user and an input device, e.g., a keyboard, touch screen, a mouse, a trackball, and the like by which the user can provide input to the computer. Other kinds of devices can be used, for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input.