WO2021009471A1

WO2021009471A1 - A method of optimizing production from a hydrocarbon reservoir

Info

Publication number: WO2021009471A1
Application number: PCT/GB2019/052016
Authority: WO
Inventors: Jianhui Yang; Yingfang ZHOU
Original assignee: Total E&P Uk Limited; The University Court Of The University Of Aberdeen
Priority date: 2019-07-18
Filing date: 2019-07-18
Publication date: 2021-01-21

Abstract

Disclosed is a method for optimizing hydrocarbon recovery from a reservoir. The method comprises determining a first level set function representing the locations of pore space and solid space defined by a solid matrix within the reservoir and determining a second level set function representing the location of a wetting fluid and non-wetting fluid in the reservoir. A three-phase contact line is determined as being defined by the first level set function and second level set function. A contact angle is determined at the three-phase contact line; and used in optimizing hydrocarbon recovery from the reservoir.

Description

A method of optimizing production from a hydrocarbon reservoir

The present disclosure relates to methods for optimizing production from a hydrocarbon reservoir, and in particular for efficient determination of contact angle and wettability in reservoir analysis.

Wettability and capillary pressure a related concepts in reservoir analysis. To determine these parameters, a contact angle between a first interface between two fluids (one wetting, the other non- wetting, e.g., water and oil) with respect to a second interface between solid and void (e.g., rock and pore space). Present methods for determining this contact angle are slow, unreliable and very expensive.

It is desirable, therefore, to provide an improved method for determining this contact angle.

SUMMARY OF INVENTION

In a first aspect of the invention there is provided a method for optimizing hydrocarbon recovery from a reservoir, the method comprising: determining a first level set function representing the locations of pore space and solid space defined by a solid matrix within the reservoir; determining a second level set function representing the location of a wetting fluid and non-wetting fluid in the reservoir; determining a three-phase contact line defined by the first level set function and second level set function; calculating a contact angle at the three-phase contact line; and using the determined contact angle in optimizing hydrocarbon recovery from the reservoir.

Other aspects of the invention comprise a computer program comprising computer readable instructions which, when run on suitable computer apparatus, cause the computer apparatus to perform the method of the first aspect; and an apparatus specifically adapted to carry out all the steps of any of the method of the first aspect.

Other non-essential features of the invention are as claimed in the appended dependent claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of example only, by reference to the accompanying drawings, in which:

Figure 1 is a conceptual representation of a level set function;

Figure 2 is a conceptual representation of the first and second level set functions defined herein, and the contact angle being estimated by a method according to embodiments of the invention; and

Figure 3 is a flowchart describing a method according to an embodiment of the invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

Reservoir engineers use relative permeability and capillary pressure relationships for estimating the amount of oil and gas in a reservoir and for predicting the capacity for flow of oil, water, and gas throughout the life of the reservoir. Relative permeabilities and capillary pressure are complex functions of the structure and chemistry of the fluids and solids in a producing reservoir. As a result, they can vary from place to place in a reservoir. Capillary pressure is dependent on the contact angle, i.e., the angle of intersection of two fluids on a given surface (e.g. according to Young’s equation and later by Gibbs, modified Young’s equation). This contact angle describes wetting and non-wetting behaviours. Wettability is a key factor to reservoir characterization. Wettability can be represented through the spatial distribution of contact angle at the three-phase contact between two residing fluids and the host solid matrix. Note that contact angle distribution is not the only way of characterising wettability, although it is the most comprehensive.

Figure 1 illustrates the concept of contact angle. Figure 1 (a) shows water in a wetting phase. The water is spreading on a solid such that the contact angle Q between the water phase and gas phase is less than 90 degrees. By contrast, Figure 1(b) shows water in a non-wetting phase. The water is resting on the solid such that the contact angle Q between the water phase and gas phase is more than 90 degrees. Some systems are strongly water-wet, while others are oil-wet or neutrally wet. Mixed wettability describe systems with non-uniform wetting properties, in which portions of the solid surface are wet by one phase, and other portions are wet by the other phase.

Wettability can be inferred through indirect average measurements on centimetre-size rock samples in lab (e.g., Amott-Harvey and USBM). However, a full measurement will take a year per sample, and even then there will be no detailed wettability at pore scale thereby introducing uncertainty for simulation configurations. As an alternative, measurement of contact angle at the pore scale can be performed from micro-CT images. However, such methods provide significant challenges. Firstly, such measurements need to be done in 3D- space. The data size is typically huge, and requires subjective considerations and manual processing. Therefore the calculation is extremely time consuming (of the scale of 3 months to calculate only 150 contact values).

More automated methods for contact angle calculation has been described in“ Automatic measurement of contact angle in Pore-space images”, AlRatrout et al, Advances in Water Resources Vol. 109, Nov 2017, Pages 158-169; which is herein incorporated by reference. However, the methods described in this document use an extremely complex algorithm which comprises empirical parameters and is not mathematically well-defined. Of greater importance is that the algorithm yields mixed results at best.

To address this a method will now be described which can calculate contact angle in a much simpler way, providing a mathematically very well-defined solution. A related method for calculating curvature of the oil-water (or more generally, the wetting/non- wetting) interface is also described.

The method is based on determining a first level-set function for the wetting/non-wetting interface and a second level-set function for the solid/pore (or void) space interface. A contact line can then be defined as the surface where these interfaces meet, i.e., the line where the first level-set and second level-set are both zero (within a margin of error), i.e., where both of these level-sets have a magnitude lower than a tolerance or margin threshold close to zero. The contact angle can then be calculated from normal vectors to this contact line defined by each of the level-set functions.

A level set function F is defined as a signed normal distance function measured from an interface and is equal to zero at the interface. As such, the interface is implicitly represented by F = 0. Figure 2 illustrates the principle. Figure 2(a) shows an area comprising a first fluid 100 and a second fluid 110, defining an interface 120 therebetween. The level-set function will assign to each point a value with a magnitude dependent on the distance to the interface and a sign dependent on which side of the interface the point resides (i.e., which fluid is at that point). As such, in the specific example here, the level-set function assigns positive values to the first fluid and negative values to the second fluid, with all points on the interface being valued zero. This is illustrated by Figure 2(b). Where the area or volume is discretised (e.g., into cells or voxels), the distance to interface may be based on corresponding points within each voxel (e.g., the centre point of each voxel).

The level set function describes interfaces implicitly as the zero level set of the function F which is one dimension higher than the interface. The level set function assigns interior and exterior regions to the interface based on its sign and is allowed to move normal to itself with a velocity The motion of the level set function is governed by:

<f _t + n_h\nf \ = 0 Equation 1 where V_n is the normal component of the velocity. To maintain numerical stability the function F should be reinitialised occasionally during evolution of the level sets by Equation 1.

One such method, suitable for building a level-set function, may comprise iteratively solving Equation 1 for given initial data (0(inside fluid)<0 , 0(outside fluid)>0).

< >_t + 5(f)(|\7f |— 1) = 0 Equation 2 where the t subscript describes the iteration number and X(f) is the sign function: Equation 3

The steady-state solution of equation 2 above ensures that \F\ = 1, so that F(c) describes the shortest distance from point x to the interface.

Calculating in-situ contact angle in porous media requires detailed knowledge of the solid and void interfaces, wetting and non-wetting interface and the vector normal to the interfaces defined at the three phase contact line. It is proposed to define the first level set function f_± to represent the pore/void and solid volume locations, where f_±> 0 represents the pore space and f_±< 0 represents the solid space/matrix, such that f =0 represents the solid walls. Similarly, the second level set function f₂ is defined to represent the wetting and non-wetting fluid locations, where f₂>0 represents the wetting fluid and f₂<0 represents the non-wetting fluid, such that f₂=0 represents the fluid interfaces.

Figure 3 is a schematic illustration of this arrangement, where the shaded regions represent the solid, Q is the contact angle, the vectors np₁ and np₂ (in bold) represent the surface normals of f_± and f₂ at the pore boundary, and b is the angle between them.

According to the above definitions, it will be apparent that the contact line between the wetting/nonwetting interface and the solid/pore interface will be were f_c=0 and f₂=0. Allowing for measurement and precision inaccuracies, the contact line can be found at the line defined by:

IF₁IIF₂I < ¾ Equation 4 where e is a small threshold value indicating the interface zone (e.g., close to zero) [can you provide example values for e- ].

Once this three-phase contact line is found, the contact angle can be estimated directly using the two level set functions. More specifically, this contact angle may be found by the difference between p and the angle between the surface normals for the two level set functions at this contact line; i.e.,:

Equation 5

Furthermore, the curvature Kf of the wetting/nonwetting interface can be determined at all points away from the contact line by determining a gradient of the surface normal of the second level function at all points on the three-phase contact line where this level set function is above a second threshold value: Equation 6

All points away from the contact line may comprise all points for which \f₂ \ > e₂, where ^e2 > ^ei ·

To summarise the above, Figure 4 is a flowchart describing the steps of a proposed method of determining the in-situ contact angle at the three-phase contact between two residing fluids and a host solid matrix. The method comprises obtaining data describing the relative locations of the fluids and solid matrix 400. The data may be obtained from analysis of a suitable image such as a (e.g., segmented) micro computed tomography (CT) image of the reservoir being analysed. At step 410, a first level function is determined to represent the pore/void and solid volume locations of the solid matrix. At step 420, a second level function is determined to represent the wetting and non-wetting fluid locations of the two fluids. At step 430, the contact line between the wetting/non wetting interface and the solid/pore interface is defined at the point where the first and second level functions are both at or near zero. At step 440, the contact angle is estimated directly from the surface normals on the contact line, defined by the two level set functions. Optionally, at step 450, the curvature of the of the wetting/nonwetting interface can be calculated from the second level function away from the contact line. Finally, at step 460, a reservoir optimization ste is performed, as will now be described.

The determined contact angle and/or curvature can be used to optimize production from a hydrocarbon reservoir. In particular, capillary pressure C_p can be calculated from the contact angle Q, e.g., by the well known relationship:

2g cos Q

C_p Equation 7 where g interfacial tension, and a is the pore radius. Typically, a contact angle Q <90degrees indicates water wet and a contact angle Q >90degrees indicates oil wet, while the magnitude of the angle defines whether it is strongly or weakly water wet or oil wet.

As is known, there are very different oil recovery strategies for reservoirs for which different wetting physics dominate. For example, very different strategies may be used depending on whether a reservoir is oil wet and water wet and the degree of wetting. This is particularly relevant for waterflooding and/or enhanced oil recovery (EOR) techniques. As such, the methods herein can be used to determine the type of reservoir (oil-wet, water- wet, mixed etc.) and then to decide on a suitable recovery strategy (e.g., EOR strategy ). The determination of capillary pressure also has other well known uses, such as prediction of reservoir initial fluid saturations, displacement pressures etc..

Optimizing a production strategy based on the determined dominant wetting physics may comprise selecting from and/or optimizing one or more of: different well placements, different number of wells, different injection fluid pressures, different injection strategies, different injection fluids and/or drilling used. In particular it is known that drilling fluids can alter the wettability within a pore structure, and as such, a particular drilling fluid or type thereof may be selected based on the contact angle derivation according to methods defined herein. More specifically, the drilling fluid can penetrate into reservoir, but only in the region adjacent to well; however this will affect the production in by changing the borehole outflow performance. Optimizing hydrocarbon recovery may therefore comprise selecting one or more of said different production strategies which are determined to maximize hydrocarbon production and/or minimize production costs.

One or more steps of the methods and concepts described herein may be embodied in the form of computer readable instructions for running on suitable computer apparatus, or in the form of a computer system comprising at least a storage means for storing program instructions embodying the concepts described herein and a processing unit for performing the instructions. As is conventional, the storage means may comprise a computer memory (of any sort), and/or disk drive, optical drive or similar. Such a computer system may also comprise a display unit and one or more input/output devices.

The concepts described herein find utility in all aspects of surveillance, monitoring, optimisation and prediction of hydrocarbon reservoir and well systems, and may aid in, and form part of, methods for extracting hydrocarbons from such hydrocarbon reservoir and well systems.

It should be appreciated that the above description is for illustration only and other embodiments and variations may be envisaged without departing from the spirit and scope of the invention.

Claims

1. A method for optimizing hydrocarbon recovery from a reservoir, the method comprising: determining a first level set function representing the locations of pore space and solid space defined by a solid matrix within the reservoir; determining a second level set function representing the location of a wetting fluid and non-wetting fluid in the reservoir; determining a three-phase contact line defined by the first level set function and second level set function; calculating a contact angle at the three-phase contact line; and using the determined contact angle in optimizing hydrocarbon recovery from the reservoir.

2. A method as claimed in claim 1, wherein the contact angle comprises the angle between a first boundary defined by the first level set function and a second boundary defined by the second level set function.

3. A method as claimed in claim 1 or 2, wherein the method of calculating a contact angle comprises calculating the contact angle from the angle between: a first surface normal calculated from the first level set function at the three-phase contact line; and a second surface normal calculated from the second level set function at the three-phase contact line.

4. A method as claimed in any preceding claim, wherein the step of determining a three-phase contact line comprises determining a line defined by the first level set function and second level set function both being zero, or both having a magnitude below a first threshold value indicating an interface zone.

5. A method as claimed in any preceding claim, comprising determining the curvature of a wetting/nonwetting interface defined by the second level set function at points away from the three-phase contact line.

6. A method as claimed in claim 5, wherein said determining of the curvature of a wetting/nonwetting interface step comprises determining a gradient of the second surface normal at all points on the three-phase contact line where the second level set function is above a second threshold value.

7. A method as claimed in any preceding claim, wherein comprising reservoir data describing the relative locations of the wetting fluid, non-wetting fluid and solid matrix; and determining the first level set function and second level set function from the reservoir data.

8. A method as claimed in claim 7, wherein the reservoir data is derived from analysis of a micro computed tomography image.

9. A method as claimed in any preceding claim, comprising determining capillary pressure within the reservoir from said contact angle.

10. A method as claimed in any preceding claim, comprising performing the method to determine the dominant wetting physics within the reservoir.

11. A method as claimed in claim 10, comprising selecting and/or optimizing a production strategy based on the determined dominant wetting physics.

12. A computer program comprising computer readable instructions which, when run on suitable computer apparatus, cause the computer apparatus to perform the method of any preceding claim.

13. A computer program carrier comprising the computer program of claim 12.