INVERSION OF MULTI-CYCLE FRACTURE REOPENING PRESSURES FOR IN-SITU STRESSES

Abstract

Embodiments presented provide for a calculation and quantification of naturally occurring stresses in rock formations using inversion of multi-cycle fracture reopening pressures for in-situ stresses.

Description

FIELD OF THE DISCLOSURE

Aspects of the disclosure relate to quantification of naturally occurring stresses in underground rock. More specifically, aspects of the disclosure relate to constraining the in situ stresses using fracture reopening pressures obtained from a succession of fracture extension and pressure relaxation cycles.

BACKGROUND

Quantification of naturally occurring stresses in underground rock formations is essential for evaluating structural integrity while drilling, tunneling, or extracting resources in the subsurface. Earth stresses can be characterized by three principal stresses which are usually assumed to be the vertical stress, the maximum horizontal stress, and the minimum horizontal stress. The two horizontal stresses are generally tricky to measure; however, many techniques exist for this purpose. The most common technique, known as hydraulic fracture stress testing, involves hydraulically fracturing an isolated section of a wellbore. This is done by raising the wellbore fluid pressure until the surrounding rock fails in tension. Various attributes of the wellbore pressure are recorded as the fracture interacts with the stress field of the surrounding formation. Such attributes include the pressures at which the fracture initiates, closes when pumping ceases, and reopens when pumping resumes (i.e., the initiation, closure, and reopening pressures respectively). In a vertical well, the closure pressure usually provides the clearest indication of an in-situ stress (i.e., the minimum principal stress); however, it is often difficult to ascertain because its signature is usually obscure. A plethora of techniques for interpreting the closure pressure have been developed; however, they often produce conflicting, highly subjective results. In some cases, the closure process is slow and closure must be induced by forcibly evacuating fluid from the fracture in a procedure known as a flowback test. Flowback tests can be tricky to perform, and the fracture closure event is often difficult to discern.

The relationship between the initiation pressure and the in situ stress requires knowledge of the tensile strength of the rock, as well as assumptions about the integrity of the rock and fluid penetration into the formation prior to fracturing. The fracture initiation pressure can sometimes be difficult to detect, especially when the volume of pressurized fluid in the wellbore is large. Extracting stress information can therefore, be problematic. The peak pressure attained during pumping (sometimes referred to as the “breakdown pressure”) is often confused with the fracture initiation pressure; however, the two pressures do not always coincide. The peak pressure itself depends not only on the attributes of the rock, but also the rate of pumping, the viscosity of the fracturing fluid, and the bridging tendencies of solids being transported by this fluid.

There is a need to provide methods that are simple in procedure, depend on fewer potentially unknown rock and fluid properties and are less prone to subjectivity than conventional methods.

There is a further need to reduce economic costs of underground structural failures caused by inadequate interpretation of multi-cycle fracture pressures for in-situ stresses.

SUMMARY

So that the manner in which the above recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized below, may be had by reference to embodiments, some of which are illustrated in the drawings. It is to be noted that the drawings illustrate only typical embodiments of this disclosure and are therefore, not to be considered limiting of its scope, for the disclosure may admit to other equally effective embodiments without specific recitation. Accordingly, the following summary provides just a few aspects of the description and should not be used to limit the described embodiments to a single concept.

In one non-limiting embodiment, a method is disclosed. The method may comprise defining an interval in a borehole to be tested and establishing an apparatus in proximity to this interval. The method may also comprise creating a pressure in the test interval, and generating a fracture in the test interval, the fracture resulting from tension in the rock. The method may also comprise measuring or estimating at least one attribute of the test interval during or after pressurization, including pressures and injected fluid volumes. The method may also comprise using at least one attribute of the test interval measured during or after applying pressure to the rock formation to perform an analysis to create constrained values of the in situ stresses.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the drawings. It is to be noted; however, that the appended drawings illustrate only typical embodiments of this disclosure and are; therefore, not be considered limiting of its scope, for the disclosure may admit to other equally effective embodiments.

FIG. 1 is a schematic of fracture geometry.

FIG. 2 discloses plots of dimensionless pressure distributions inside fracture for various combinations of model parameters.

FIG. 3 discloses plots of (a) dimensionless pressure distribution inside fracture used in forward model and (b) fracture reopening pressure versus dimensionless fracture half-length computed by forward model.

FIG. 4 displays graphs of maximum versus minimum horizontal stresses when (a) both stresses are jointly inferred and (b) the minimum horizontal stress is known and the maximum horizontal stress is inferred.

FIG. 5 is a graph of data generated at the 4 dimensionless fracture lengths shown in Table 4, wherein FIG. 5(a) shows fracture reopening pressures computed using Equation (5) along with corresponding shut-in pressures from preceding cycle. FIG. 5(b) is a graph of fracture volumes at moment of shut-in computed using Equation (9).

FIG. 6 is a method of constraining in situ horizontal stresses by performing a succession of small-volume hydraulic fracture propagation cycles designed to probe the near-wellbore stress concentration sensed by short fractures of varying length.

To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures (“FIGS”). It is contemplated that elements disclosed in one embodiment may be beneficially utilized on other embodiments without specific recitation.

DETAILED DESCRIPTION

In the following, reference is made to embodiments of the disclosure. It should be understood; however, that the disclosure is not limited to specific described embodiments. Instead, any combination of the following features and elements, whether related to different embodiments or not, is contemplated to implement and practice the disclosure. Furthermore, although embodiments of the disclosure may achieve advantages over other possible solutions and/or over the prior art, whether or not a particular advantage is achieved by a given embodiment is not limiting of the disclosure. Thus, the following aspects, features, embodiments and advantages are merely illustrative and are not considered elements or limitations of the claims except where explicitly recited in a claim. Likewise, reference to “the disclosure” shall not be construed as a generalization of inventive subject matter disclosed herein and should not be considered to be an element or limitation of the claims except where explicitly recited in a claim.

Although the terms first, second, third, etc., may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms may be only used to distinguish one element, components, region, layer or section from another region, layer or section. Terms such as “first”, “second” and other numerical terms, when used herein, do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer or section discussed herein could be termed a second element, component, region, layer or section without departing from the teachings of the example embodiments.

When an element or layer is referred to as being “on,” “engaged to,” “connected to,” or “coupled to” another element or layer, it may be directly on, engaged, connected, coupled to the other element or layer, or interleaving elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly engaged to,” “directly connected to,” or “directly coupled to” another element or layer, there may be no interleaving elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed terms.

Some embodiments will now be described with reference to the figures. Like elements in the various figures will be referenced with like numbers for consistency. In the following description, numerous details are set forth to provide an understanding of various embodiments and/or features. It will be understood; however, by those skilled in the art, that some embodiments may be practiced without many of these details, and that numerous variations or modifications from the described embodiments are possible. As used herein, the terms “above” and “below”, “up” and “down”, “upper” and “lower”, “upwardly” and “downwardly”, and other like terms indicating relative positions above or below a given point are used in this description to more clearly describe certain embodiments.

Aspects of the disclosure provide a simple technique for constraining in situ stresses using fracture reopening pressures obtained from a succession of fracture extension and pressure relaxation (shut-in) cycles. These techniques exploit the fact that as the fracture propagates away from the wellbore, its exposure to the near-wellbore stress profile changes. A succession of fracture reopening pressures represents samples of this profile averaged over a portion of the fracture face. This data by itself, or in conjunction with other data derived from hydraulic fracturing, can be used to constrain in situ stresses. The fracture re-opening pressure is usually more straightforward to detect than the fracture closure pressure. It is also simpler to interpret than the fracture initiation pressure because it does not require knowledge of the tensile strength of the rock. Moreover, in contrast to the fracture initiation pressure, problems with detection of the fracture reopening pressure in large volume systems can potentially be mitigated by extending the fracture until it is sufficiently large to influence the compliance of the wellbore-fracture system.

A frequent practice within the industry has been to interpret reopening pressure using an analytical formula for predicting hydraulic fracture initiation. This formula states that the pressure, p_if, required to initiate a fracture in a vertical borehole is given by the expression

$\begin{array}{cc}{p}_{if}=3{\sigma }_h-{\sigma }_H-p_p+T_0& \left(1\right)\end{array}$

where: σ_h, σ_H, are the minimum and maximum horizontal stresses respectively, p_p, is the pore pressure, and T₀, is the tensile strength of the rock. During fracture reopening, the tensile strength is assumed to be zero and therefore, Equation (1) provides a simple constraint on the horizontal stress if p_if and p_p, are known. However, this formula assumes that prior to reopening the fracture, there is no hydraulic communication between the borehole and the fracture or intact rock surrounding it (a so-called “dry reopening”). Such a condition is more likely to exist during “sleeve reopening” whereby a packer, rather than a pressurized fluid, is used to apply stress to a wellbore wall. But during classical hydraulic fracturing, the extent of such hydraulic communication is usually not known.

An alternative approach may be used wherein the fracture reopening pressure is equated to the undisturbed in situ stress opposing the fracture plane. However, this is only correct if the fracture is in perfect hydraulic communication with the wellbore prior to reopening (so-called “wet reopening”). Moreover, to sense the undisturbed formation stress, the fracture must extend a sufficient distance from the wellbore to escape the perturbed stress zone around the wellbore, leading to an estimation of the undisturbed in situ stress. Disregarding the near-wellbore effect leads to loss of valuable information that could be used to constrain in situ stresses.

A less restrictive assumption made by some practitioners is to assume that the fracture reopening pressure in a vertical well represents an upper bound on the minimum principal stress. However, near the wellbore, a dip relative to the far-field in the magnitude of the stress, perpendicular to the fracture plane, can occur. This implies that it is theoretically possible to open a fracture when the wellbore pressure is lower than the minimum principal stress.

When stress-testing is performed over multiple cycles, a common practice is to plot reopening pressures (and other fracture diagnostics) versus the cycle number. This plot is known as a reconciliation plot and is sometimes used to determine whether the fracture has escaped the near-wellbore stress concentration. The rationale is to ensure that closure pressures selected to represent the virgin in situ stress are not influenced by the near-wellbore stress environment. The data acquired from the near-wellbore region is only used for quality control. In contrast, the current disclosure regards the near-wellbore data to be valuable in its own right. It posits that there is value in allowing the fracture to linger over multiple cycles inside the near-wellbore zone.

Dynamic simulations have been performed of hydraulic fracture propagation and closure to retrieve an estimate of the minimum horizontal stress. There was no attempt to model the fracture reopening pressure. In contrast, embodiments disclosed herein emphasize inversion of data obtained when the fracture is roughly in static equilibrium with its surroundings (at reopening and immediately after shut-in). This approach requires fewer computations and avoids having to make assumptions about dynamic properties such as the leak-off coefficient, fluid viscosity, and the fracture toughness.

Aspects of the disclosure provide a method and system to constrain the in situ stresses by performing a succession of small-volume hydraulic fracture propagation cycles designed to probe the near-wellbore stress concentration sensed by short fractures of varying length. The fracture reopening pressure prior to the commencement of each propagation cycle is measured. Simultaneous interpretation of multiple reopening pressures produces a constraint on the in situ stresses which can be used in conjunction with other data (e.g. closure pressures, injected volumes, instantaneous shut-in pressures, etc.) to further constrain these stresses.

An application of the technique to inferring the maximum and minimum horizontal stresses in a vertical well will now be described. The induced fracture is also assumed to be vertical. However the scope of the disclosure is not limited to this specific example and may be extended to wells and fractures of various orientations and to inference of other in situ stress components. Referring to FIG. 1, a plan view of a vertical borehole of radius R, containing a symmetrical two-winged hydraulic fracture of width w (x) and half-length L. A pressure p(x) acts inside the fracture where x represents distance from the wellbore wall. This pressure is opposed by the formation stress, σ_θθ, which in general varies with distance from the wellbore. The fracture is held open by the net pressure Δp(x)=p(x)−σ_θθ(x).

When the fracture is closed but on the verge of reopening, p(x) will be equal to the reopening pressure, p_reopen, at the wellbore wall and will in general decrease with increasing penetration into the fracture. The pressure inside the fracture should be greater than or equal to the pore pressure, p_p. The severity of the pressure loss inside the fracture depends upon the degree of hydraulic communication between the wellbore wall and the fracture (wet versus dry reopening). Since this is usually unknown, the following empirical expression for the pressure in the fracture will be assumed:

$\begin{array}{cc}p\left(\xi \right)=\left(p_{\mathrm{reopen}}-p_p\right)\left(1-a{\xi }^n\right)\mathrm{Exp}\left(-\frac{{\xi }^2}{{\alpha }^2}\right)+p_p& \left(2\right)\end{array}$

where: a, n, and α are empirical parameters and ξ=x/L. FIG. 2 plots this expression for various combinations of empirical parameters where:

$\begin{array}{cc}p*\left(\xi \right)=\frac{p\left(\xi \right)-p_p}{\left(p_{\mathrm{reopen}}-p_p\right)}.& \left(3\right)\end{array}$

Equation (2) should be sufficiently general to approximate any reasonable pressure loss inside the fracture, if the pressure depends only on ξ. In particular, for the case of a dry reopening, the pressure in the crack should be equal to p_reopen at the wellbore wall and equal to pore pressure elsewhere. This scenario can be approximated by using a small value of α. If there is no pressure loss, a can be set to zero and a can be set to a large value. To ensure that the pressure in the fracture decreases with ξ, but does not fall below p_p, 0≤a≤1 and n>0. More complex forms of Equation (2) can also be construed by people of ordinary skill in the art.

To estimate the reopening pressure as a function of the in situ stress, an expression for the width of the open fracture is needed. Analytical expressions exist for specific geometries. For example, for a KGB fracture, the fracture has an elliptical horizontal cross-section (as opposed to the triangular cross-section shown in FIG. 1). The width w of the fracture is given by the expression

$\begin{array}{cc}w\left(\xi \right)=\frac{2\left(1-v\right)L}{\pi G}{\int }_0^1\mathrm{Log}\left(\frac{2-{\xi }^2-s^2+2\sqrt{1-{\xi }^2}\sqrt{1-s^2}}{❘{\xi }^2-s^2❘}\right)\Delta p\left(s\right)\mathrm{ds}& \left(4\right)\end{array}$

where: v, G are the Poisson's ratio and shear modulus of the rock, respectively. The fracture reopening (or closure) pressure can be found by setting w to zero at the fracture entrance and solving for the pressure at the entrance to the fracture. Assuming the pressure distribution takes the form of Equation (2), it may be shown that:

$\begin{array}{cc}{p}_{\mathrm{reopen}}-p_p={\int }_0^{1}K\left(\xi \right)\left({\sigma }_{\theta \theta }\left(\xi \right)-p_p\right)d\xi & \left(5\right)\end{array}$ $\mathrm{where}:$ $\begin{array}{cc}K\left(\xi \right)=\frac{1}{A}\mathrm{Log}\left(\frac{2-{\xi }^2+2\sqrt{1-{\xi }^2}}{{\xi }^2}\right)& \left(6\right)\end{array}$ $\mathrm{and}$ $\begin{array}{cc}A={\int }_0^1\mathrm{Log}\left(\frac{2-{\xi }^2+2\sqrt{1-{\xi }^2}}{{\xi }^2}\right)\left(1-a{\xi }^n\right)\mathrm{Exp}\left(-\frac{{\xi }^2}{{\alpha }^2}\right)d\xi .& \left(7\right)\end{array}$

The definition of the kernel, K(ξ), given by Equations (6) and (7) is specific to the KGD fracture geometry. However, the scope of the disclosure is not restricted to this particular geometry. Alternative forms of the kernel can readily be constructed by those of ordinary skill in the art.

It should be noted that σ_θθ(ξ) will itself depend on the pressure in the wellbore and the fracture. In some formulations, it may be assumed that this stress depends only on the pressure in the wellbore, p_reopen, in which case the following analytical expression from elastic theory can be supplied for σ_θθ.

$\begin{array}{cc}{\sigma }_{\theta \theta }\left(\xi \right)={\sigma }_h+\left[\frac{1}{2}\left({\sigma }_H+{\sigma }_h\right)-p_{\mathrm{reopen}}\right]{\left(\frac{R}{L\xi +R}\right)}^2-\frac{3}{2}\left({\sigma }_H-{\sigma }_h\right){\left(\frac{R}{L\xi +R}\right)}^4& \left(8\right)\end{array}$

Equation (5) is a non-linear equation for p_reopen as a function of several potential unknowns σ_H, σ_h, L, a, n, α. The objective is to infer σ_H and σ_h. To do so, the parameters L, a, n, α must either be specified or inferred jointly with σ_h and σ_h. Many alternatives for addressing this problem are possible. For example, suppose N reopening, propagation, and closure cycles are performed. This gives rise to N values of the reopening pressure. For each value it is possible to obtain all combinations of σ_H, σ_h, L, a, n, α that satisfy the corresponding reopening pressure. This gives rise to N intervals for each of the stresses σ_H and σ_h. The intersections of these intervals provide final constraints on σ_H and On. Another possibility is as follows: For a given combination of σ_H and σ_h, compute the maximum and minimum of p_reopen over all reasonable values of L, a, n, α. If any of the observed reopening pressures fall outside these bounds, the corresponding values σ_H and σ_h are deemed to be unfeasible. Yet another option that should provide tighter constraints on σ_H and σ_h can be found by performing joint inversion of the observed reopening pressures for σ_H, σ_h, L_i, a_i, n_i, α_i where i=1, 2, . . . . N and imposing constraints on L_i, a_i, n_i, α_i. For example, it is obvious that L₁≤L₂≤L₃ . . . ≤L_N and it can further be demanded that the a_i, n_i, α_i must evolve slowly between successive cycles (i.e., they are correlated across cycles). A stronger constraint is to assume that a_i, n_i, α_i do not vary between cycles.

Further constraints are possible by using measurements of volumes injected into the fracture and “instantaneous shut-in pressures”, p_ISIP, measured at the end of each propagation stage to constrain the values of L_i. When injection of fluid into the fracture is abruptly terminated (i.e., shut-in occurs), the pressure in the fracture drops quickly to p_ISIP. At this stage, the fracture is full of fluid and the pressure inside the fracture is in quasi-static equilibrium with the opposing external stress. It is possible to relate the volume V_frac, of fluid in the fracture to p_ISISP. For example, for a KGD fracture,

$\begin{array}{cc}{V}_{\mathrm{frac}}=\frac{4\left(1-v\right)L^{2}h}{\pi G}{\int }_0^1{\int }_0^1\mathrm{Log}\left(\frac{2-{\xi }^2-s^2+2\sqrt{1-{\xi }^2}\sqrt{1-s^2}}{❘{\xi }^2-s^2❘}\right)\Delta p_{\mathrm{shut}}\left(s\right)\mathrm{ds}d\xi & \left(9\right)\end{array}$

where: h is the fracture height and Δp_shut (ξ)=p_ISISP-σ_θθ(ξ). It is assumed here that shortly after shut-in, the fracture is in good hydraulic communication with the wellbore and since the fracture is short (probing the near-wellbore region), it is reasonable to expect that the pressure inside the fracture is indistinguishable from the wellbore pressure, p_ISISP. If the formation has a low permeability, there will be negligible fluid loss from the fracture during fracture propagation and therefore, V_frac can be assessed after each of the N propagation cycles. Thus Equation (9) can provide N additional equations for the fracture lengths, L_i, which should further aid in constraining σ_H and σ_h.

An example using simulated data will now be presented to illustrate the potential of the aforementioned techniques. In the example, reopening pressures computed at 9 dimensionless fracture half-lengths (L*=L/R) will be inverted for the stresses σ_H and σ_h, the algebraic parameters, a, n, and α (assumed constant) as well as the 9 values of L*. The inversion entails solving 9 equations (one for each reopening pressure) for 14 unknown parameters and the results are expected to be non-unique. The “true” parameters used in the forward model are shown in the second row of Table 1. In addition, the pore pressure is set to 6500 psi and is assumed to be known.

TABLE 1
“True” and inferred parameters
	σh (psi)	σH (psi)	a	n	α	L*
True	11,000	12,000	0.5	1.5	20.0	1, 3, 5, 7, 9, 12, 16, 20, 24
Inferred	11,102	12,188	0.32	2.1	8.8	0.82. 2.6, 4.4, 6.2, 7.9,
Mean						10.7, 14.4, 18.4, 22.8
%	0.93	1.6	35.0	40.0	56.0	17.6, 12.3, 12.0, 12.0,
Difference						11.7, 11.1, 9.8, 7.8, 5.1
St. Dev. Of	348	1,160	0.35	1.74	8.5	0.69, 1.3, 1.9, 2.5, 3.1,
Solutions						4.0, 5.3, 6.7, 8.4

FIG. 3 shows the dimensionless pressure distribution inside the fracture and the reopening pressure produced by the “true” parameters (forward model) presented in Table 1. The reopening pressures (FIG. 3(b)) were computed using a fast numerical approximation of Equation (5) which avoids numerical integration.

The inversion proceeds by solving for combinations of 14 unknown parameters that produce an exact match to the 9 reopening pressures. In all, 532 combinations were generated. These combinations are not exhaustive but are representative of the range of existing solutions. FIG. 4(a) shows solutions for the two horizontal stresses. They appear to map out a region in σ_H and σ_h space. The mean values of the inferred stresses are illustrated on the plot along with “true” values. The inferred maximum horizontal stresses are scattered over a range of more than 7,000 psi; however, the inferred minimum horizontal stresses are much more tightly constrained. This is expected, as the reopening pressure is more sensitive to σ_h than to σ_H. Note that although fracture re-opening pressures range from 11,154 to 11,589 psi (FIG. 3(b)), it is theoretically possible to open fractures when σ_h is as high as 11735 psi (FIG. 4(a)). Therefore, as suggested previously, the fracture reopening pressure does not constitute a robust upper bound on σ_h.

The inferred mean values of σ_H and on are 11,102 psi and 12,188 psi respectively, which may be compared with the “true” values of 11,000 psi and 12,000 psi respectively (see Table 1). The corresponding percentage differences are 0.93% and 1.6% respectively (Table 1). The significant scatter observable in the solutions for σ_H (FIG. 4(a)) is reflected in their high standard deviation (1,160 psi) compared with the solutions for σ_h (standard deviation=348 psi).

Referring to FIG. 4, inverted values of the minimum (abscissa) and maximum (ordinate) horizontal stresses (On and σ_H respectively). “True” values represent values used in the forward model. Inverted values and their means are also shown: (a) σ_h and σ_H are jointly inferred; and (b) σ_h known and equal to 11,000 psi while σ_H is inferred.

The other unknown parameters are treated mainly as nuisance parameters and are therefore of secondary importance. Nonetheless, their results are presented for completeness in Table 1. As evidenced by their high standard deviations, their results show significant variability. This is to be expected, as many different combinations of fracture lengths and internal fracture pressures can produce a given set of fracture reopening pressures.

The foregoing example suggests that reopening pressures can produce reasonably well-constrained answers for σ_h, but much more variable answers for σ_H. On the other hand, if σ_h were known (e.g. from closure pressures), it is possible to utilize reopening pressures to produce fairly robust answers for σ_H. FIG. 4(b) shows the results of inversion for the same problem as the one presented in FIG. 4(a), except that the minimum horizontal stress is known (σ_h=11,000 psi). The accuracy of the inferred σ_H is in the same range as before, but the scatter in σ_H, as represented by the standard deviation, is considerably less than previously (Table 2).

TABLE 2
“True” and inferred values of the maximum horizontal stress
Max Horizontal Stress (psi)
True                  12,000
Inferred Mean         11,792
% Difference          1.7
St. Dev. of Solutions 340

As discussed earlier, a further elaboration of the embodiments disclosed herein involves jointly inverting fracture reopening pressures, instantaneous shut-in pressures, and fluid volumes inside fractures immediately after shut-in for in situ stresses. Incorporation of additional data into the inversion has the potential to improve the accuracy and reduce the uncertainty of the results. However, the disadvantage of this approach is that certain assumptions must be made about the geometry of the fracture and the elastic properties of the host rock. As can be seen from Equation (9), the fluid volume inside the fracture is a function v, G, and h, in addition to depending on L. For purposes of simplification, it will be assumed in the example that v, G, and h are known constants (Table 3). It is further assumed that a=0 and that α→∞. These assumptions produce a pressure inside the fracture that is constant and equal to the wellbore pressure at the moment of reopening (i.e., a perfect “wet” reopening). It should be emphasized that these simplifications have been made for illustrative purposes only, and do not restrict the scope of the disclosure. Table 3 shows the fixed parameters that are input to the model.

TABLE 3
Key Constants
ν	G(GPa)	h (m)	a	n	α	R(in)	pISIP	pp(psi)
0.3	10	1.0	0	N/A	20.0	4.25	12,000	0

It is now proposed to invert 4 fracture reopening pressures and the 4 injected fluid volumes and shut-in pressures that precede reopening, for the horizontal stresses σ_H, σ_h and the fracture lengths at reopening, L*₁, L*₂, L*₂, L*₄. Table 4 shows the “true” values of the unknown parameters that are input to Equations (5) and (9) to produce synthetic data. The corresponding fracture reopening pressures and fracture volumes are shown in FIG. 5.

TABLE 4
“True” and Inferred Parameters
	σh(psi)	σH(psi)	L*
	True	11,000	12,000	1, 3, 5, 7
	Inferred	11,000	12,000	1, 3, 5, 7

Referring to FIG. 5, data generated at the 4 dimensionless fracture lengths (L/R) shown in Table 4 included fracture reopening pressures computed using Equation (5). Shut-in pressures (=12,000 psi) from preceding cycle, shown for reference in FIG. 5(a).

In FIG. 5(b), fracture volumes are shown at the moment of shut-in computed using Equation (9).

Equations (5) and (9) each give rise to 4 equations so the problem consists of 8 equations and 6 unknowns. By incorporating fracture volumes into the problem, an underdetermined system of equations has been converted into an overdetermined one. There is only one exact solution and it is identical to the “true” solution. A search algorithm readily obtains it as shown in Table 4.

In this case, the algebraic parameters a, n, and α were assumed to be known. However, it is possible to treat them as unknowns and arrive at an even-determined system of equations by supplying an additional fracture reopening pressure along with the injected volume and shut-in pressure that preceded this reopening event. This would lead to a system consisting of 10 equations and 10 unknowns.

The basic technique of the disclosure is to advance the fracture in small steps so that a distribution of fracture reopening pressures that reflect the near-wellbore stress environment could be obtained. The case of a KGD fracture in a vertical well has been utilized to illustrate the techniques of this disclosure. The disclosure however, is not limited to KGD fractures. Those of ordinary skill in the art will recognize that techniques described herein can be adapted to fracture geometries of varying sophistication (including partially open fractures), a range of near-wellbore stress fields, and to deviated or horizontal wells through the use of appropriate analytical or numerical methods. Similarly, for suitably aligned wellbores and fractures, inferences can be made with respect to other stress components besides σ_h and σ_H, such as the vertical principal stress, principal stresses that are not aligned with the vertical or horizontal directions, shear stresses, and near-wellbore stresses, The effects of pressurization of the near-wellbore environment (poroelastic effects) or rock plasticity can similarly be accounted for within the scope of the current disclosure. Aspects of the disclosure cover wet reopening, where there is perfect hydraulic communication between the fracture and the wellbore. Aspects also cover dry reopening, where there is no such communication, and cases in between. Aspects further cover inversion of reopening pressure, alone, or in combination with other types of data. Aspects further cover all novel field procedures that are logically implied by the theory described herein, such as advancing the fracture in small volume steps in order to obtain a distribution of fracture diagnostics that are sensitive to the near-wellbore stress environment.

Referring to FIG. 6, a method 600 of the disclosure is disclosed. The method 600 may include, at 602, defining a downhole test interval. The method 600 may further include, at 604, establishing an apparatus in proximity to the test interval for pressurizing the borehole. The method may further include, at 606, raising the pressure in the borehole to generate a tensile fracture in the test interval. The method may further include, at 608, injecting a succession of small volumes into the test interval to propagate the fracture in small steps and shutting in the wellbore after each injection step. The method may further include, at 610, measuring at least one attribute, such as a fracture reopening pressure or other attributes that can further constrain the inferred stresses. The method may also include, at 612, inverting the measured at least one attribute of the test interval during or after creating the pressure on the test interval to perform an analysis to create constrains in situ stresses. The method may also include, at 614, displaying the inferred in situ stresses. The displaying may be done on a computer monitor. In other embodiments, the results may be stored in a non-volatile computer memory.

Specific embodiments of the disclosure, representative of the claims, but not the total disclosure, are provided below. The disclosure below does not restrict the disclosure or other possible claims as presented herein. In one non-limiting embodiment, a method is disclosed. The method may comprise defining an interval in a borehole to be tested and establishing an apparatus in proximity to this interval. The method may also comprise creating a pressure in the test interval, and generating a fracture in the test interval, the fracture resulting from tension in the rock. The method may also comprise measuring or estimating at least one attribute of the test interval during or after pressurization. The method may also comprise using at least one attribute of the test interval measured during or after applying pressure to the rock formation to perform an analysis to create constrained values of the in situ stresses

In another example embodiment, the method may be performed wherein the at least one attribute is a pressure.

In another example embodiment, the method may be performed wherein the at least one attribute is a fracture opening pressure.

In another example embodiment, the method may be performed wherein the at least one attribute is the injected fluid volume.

In another example embodiment, the method may be performed wherein the fracture is a predefined type of fracture.

In another example embodiment, the method may be performed wherein the predefined type of fracture is a KGD fracture.

In another example embodiment, the method may further comprise at least one of printing and visually representing in situ stresses.

In another example embodiment, the method may be performed wherein the visually representing the in situ stresses is on a computer monitor.

In another example embodiment, the method may be performed wherein the analysis performed uses the formula

$p_{\mathrm{reopen}}-p_p=\underset{0}{\overset{1}{\int }}K\left(\xi \right)\left({\sigma }_{\theta \theta }\left(\xi \right)-p_p\right)d\xi$

In another example embodiment, the method may be performed wherein the analysis performed uses the formula

$V_{\mathrm{frac}}=\frac{4\left(1-v\right)L^{2}h}{\pi G}{\int }_0^1{\int }_0^1\mathrm{Log}\left(\frac{2-{\xi }^2-s^2+2\sqrt{1-{\xi }^2}\sqrt{1-s^2}}{\left|{\xi }^2-s^2\right|}\right)\Delta p_{\mathrm{shut}}\left(s\right)\mathrm{dsd}\xi .$

The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.

While embodiments have been described herein, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments are envisioned that do not depart from the inventive scope. Accordingly, the scope of the present claims or any subsequent claims shall not be unduly limited by the description of the embodiments described herein.

Claims

1. A method, comprising, defining an interval in a borehole to be tested;establishing an apparatus in proximity to the interval;generating a pressure in the interval to be tested to initiate or open a fracture in the interval, the fracture opened by producing tension in the rock;propagating the fracture in small increments in order to sample the near wellbore stress concentration;measuring at least one or more fracture reopening pressures under the influence of the near-wellbore stress concentration; andusing the measured at least one fracture reopening pressure in conjunction with or without other data acquired during or after pressurization to perform an analysis to create constrained values of one or more in situ stress components.

2. The method according to claim 1, wherein the other data one or more pressures.

3. The method according to claim 1, wherein the other data is one or more instantaneous shut-in pressures.

4. The method according to claim 1, wherein the other data is one or more closure pressures.

5. The method according to claim 1, wherein the other data is one or more volumes.

6. The method according to claim 5, wherein the one or more volumes are volumes of fluid injected into the fracture.

7. The method according to claim 5, wherein the one or more volumes are estimates of the volume of the open fracture.

8. The method according to claim 1, wherein the fracture is initiated on an intact borehole wall.

9. The method according to claim 1, wherein the fracture existed prior to testing and is opened during the test.

10. The method according to claim 1, wherein the fracture is a predefined type of fracture.

11. The method according to claim 10, wherein the predefined type of fracture is a KGD fracture.

12. The method according to claim 1, further comprising: at least one of printing and visually representing one or more in situ stress components.

13. The method according to claim 12, wherein the visually representing in situ stress components is on a computer monitor.

14. The method according to claim 1, wherein the analysis performed uses the formula

15. The method according to claim 1, wherein the analysis performed uses the formula

16. The method according to claim 1, performed in vertical wells, horizontal wells, or wells of any orientation.

17. The method according to claim 1, performed on fractures of any orientation.

18. The method of claim 1 wherein the analysis is performed using models that account for plastic yielding or poroelastic effects on fracture re-opening, propagation, or closure.

19. The method of claim 1 wherein the constrained in situ stresses may comprise one or more of the following stresses: the minimum horizontal stress, the maximum horizontal stress, the vertical/overburden stress, a tilted principal stress, or a shear stress.

20. A computer readable non-volatile medium configured to perform code that is executable on a computer, the code comprising a method that enables defining an interval in a borehole to be tested; establishing an apparatus in proximity to the test interval;generating a pressure in the interval to be tested to initiate or open a fracture in the interval, the fracture opened by producing tension in the rock;propagating the fracture in small increments in order to sample the near wellbore stress concentration,measuring at least one or more fracture reopening pressures under the influence of the near-wellbore stress concentration; andusing the measured at least one fracture reopening pressure in conjunction with or without other data acquired during or after pressurization to perform an analysis to create constrained values of one or more in situ stress components.