In-situ evaluation method of brittle plasticity of tight reservoirs

Abstract

The present invention provides an in-situ evaluation method for the brittle plasticity of a tight reservoir. The in-situ evaluation method for the brittle plasticity of a tight reservoir comprises: a parameter acquisition step: acquiring the vertical depth H and fracturing data of the tight reservoir; a first calculation step: calculating the bottom hole real volume V of the underground fracturing fluid according to the vertical depth H and the fracturing data; l , the total volume of the underground fracturing fluid and the underground proppant V t ; The second calculation step: according to the actual volume V of the bottom hole l and the total volume V t Calculation of the plasticity coefficient K of tight reservoirs p ;Evaluation steps: According to the plasticity coefficient K p The brittle plasticity evaluation index of the tight reservoir is established to evaluate the brittle plasticity of the tight reservoir. The invention solves the problem of inaccurate evaluation of the brittle plasticity of the tight reservoir in the prior art.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas development, and in particular to an in-situ evaluation method for the brittle plasticity of a dense reservoir. Background Art

[0002] With the continuous increase in oil and gas demand and the continuous decline in conventional oil and gas production, unconventional oil and gas with greater resource potential has gradually become the mainstream of development. In the process of developing tight oil and gas reservoirs, the various processes and methods used are increasingly optimized. Although a lot of work has been done in the field of fracturing and transformation technology, the evaluation of brittleness and plasticity of the formation has not been effectively solved, which seriously restricts the next step of construction design. The existing evaluation of brittleness and plasticity of tight reservoirs is mainly based on the brittleness index of rocks, mainly including the mineral composition method and the elastic modulus method. However, for large-scale and large-scale formations on site, the existing brittleness and plasticity evaluation methods still cannot achieve the goal of accurately evaluating in-situ reservoirs.

[0003] It can be seen from the above that the existing technology has the problem of inaccurate evaluation of the brittle plasticity of tight reservoirs. Summary of the invention

[0004] The main purpose of the present invention is to provide an in-situ evaluation method for the brittle plasticity of a dense reservoir, so as to solve the problem of inaccurate evaluation of the brittle plasticity of a dense reservoir in the prior art.

[0005] In order to achieve the above-mentioned object, the present invention provides an in-situ evaluation method for the brittle plasticity of a tight reservoir, comprising: a parameter acquisition step: acquiring the vertical depth H and fracturing data of the tight reservoir; a first calculation step: calculating the bottom hole real volume V of the underground fracturing fluid according to the vertical depth H and the fracturing data; l , the total volume of the underground fracturing fluid and the underground proppant V t ; The second calculation step: according to the actual volume V of the bottom hole l and the total volume V t Calculation of the plasticity coefficient K of tight reservoirs p ;Evaluation steps: According to the plasticity coefficient K p The brittle-plastic evaluation index of tight reservoirs is established to evaluate the brittle-plasticity of tight reservoirs.

[0006] Furthermore, in the parameter acquisition step, the fracturing data includes the wellhead pressure, the measured volume of the fracturing fluid injected into the ground, and the volume of the proppant injected into the ground.

[0007] Furthermore, in the first calculation step, the actual volume V of the bottom hole of the fracturing fluid injected into the ground is calculated according to the vertical depth H and the fracturing data. l Including: converting the wellhead pressure to the bottom hole pressure, and calculating the bottom hole real volume V of the underground fracturing fluid according to the measured volume of the underground fracturing fluid l .

[0008] Furthermore, in the first calculation step, the conversion formula for converting the wellhead pressure to the bottom hole pressure is:

[0009] P bt =P w +P H +P f ;

[0010] Among them, P bt is the bottom hole pressure, in MPa; P w is the wellhead pressure, in MPa; P H is the column liquid pressure, in MPa; P f is the fracturing tubing friction, in MPa.

[0011] Furthermore, in the first calculation step, the calculation formula of the column hydraulic pressure is:

[0012] P H =ρgH;

[0013] Among them, P H is the column fluid pressure, in Pa; ρ is the density of the in-ground fracturing fluid, in kg / m 3 ; g is the acceleration due to gravity 10m / s 2 ; H is the vertical depth of the tight reservoir, in meters.

[0014] Furthermore, in the first calculation step, the actual bottom hole volume V of the underground fracturing fluid is l The calculation formula is:

[0015] V l =V s (1-β(P bt -P0));

[0016] Among them, V l is the actual volume of the fracturing fluid at the bottom of the well, in m 3 ; V s is the measured volume of the underground fracturing fluid, in m 3 ; β is the volume compression coefficient of the in-ground fracturing fluid; P bt is the bottom hole pressure, in MPa; P0 is the standard atmospheric pressure, in MPa.

[0017] Furthermore, in the first calculation step, the total volume V of the underground fracturing fluid and the underground proppant is t The calculation formula is:

[0018] V t =V l +V d ;

[0019] Among them, V t is the total volume of the underground fracturing fluid and proppant, in m 3 ; V l is the actual volume of the fracturing fluid at the bottom of the well, in m 3 ; V d is the volume of the proppant inserted into the ground, in m 3 .

[0020] Furthermore, in the second calculation step, according to the actual bottom hole volume V l and the total volume V t Calculation of the plasticity coefficient K of tight reservoirs p include:

[0021] The bottom hole pressure P bt and the total volume V t After aligning the cumulative time of fracturing, V t -P bt curve, and according to V t -P bt Curve calculation of the plasticity coefficient K of tight reservoir p .

[0022] Furthermore, in the second calculation step, V t -P bt The initial segment of the curve is tangent, and the plasticity coefficient K of the tight reservoir is p The calculation formula is:

[0023]

[0024] Among them, point O is the origin of the coordinate axis; point A is V t -P bt The first peak point of the curve; Point B is the projection point of Point A on the X-axis; Point C is the intersection of the projection line of Point A onto the Y-axis and the tangent line; Point D is the projection point of Point C on the X-axis; A OAB is the lower envelope area of ​​curve OA; A OCD is the area of ​​triangle OCD.

[0025] Furthermore, in the evaluation step, according to the plasticity coefficient K p The brittle plasticity evaluation indexes for tight reservoirs include: when the plasticity coefficient K p When the plasticity coefficient K is 1, the tight reservoir is ideally brittle; p When the plasticity coefficient K is greater than 1 and less than or equal to 6, the tight reservoir is brittle plastic. p When it is greater than 6, the tight reservoir is of ideal plasticity.

[0026] By applying the technical solution of the present invention, the actual bottom hole volume V of the underground fracturing fluid is calculated by obtaining the vertical depth H of the tight reservoir and the fracturing data. l , the total volume of the underground fracturing fluid and the underground proppant V t , and according to the actual volume V l and the total volume V t Calculation of the plasticity coefficient K of tight reservoirs p Finally, according to the plasticity coefficient K p The brittle plasticity evaluation index of tight reservoirs is established to evaluate the brittle plasticity of tight reservoirs. The parameter acquisition is simple and accurate, and according to the plasticity coefficient K p The invention can accurately evaluate the brittle plasticity of the tight reservoir, thus solving the problem of inaccurate evaluation of the brittle plasticity of the tight reservoir in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The drawings constituting a part of the present application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0028] Figure 1 A flow chart showing an in-situ evaluation method of brittle plasticity of a tight reservoir in a specific embodiment of the present invention; and

[0029] Figure 2 shows a specific embodiment of the present invention V t -P bt Schematic diagram of the curve;

[0030] Figure 3 A schematic diagram of an ideal brittleness curve of a tight reservoir in a specific embodiment of the present invention is shown;

[0031] Figure 4 A schematic diagram of an ideal plasticity curve of a tight reservoir in a specific embodiment of the present invention is shown. DETAILED DESCRIPTION

[0032] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0033] It should be noted that, unless otherwise specified, all technical and scientific terms used in this application have the same meanings as commonly understood by ordinary technicians in the technical field to which this application belongs.

[0034] In the present invention, unless otherwise specified, the directional words used, such as "up, down, top, bottom", usually refer to the directions shown in the drawings, or to the components themselves in the vertical, perpendicular or gravity directions; similarly, for ease of understanding and description, "inside and outside" refer to the inside and outside relative to the outline of each component itself, but the above-mentioned directional words are not used to limit the present invention.

[0035] Obviously, the above-described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0036] In order to solve the problem of inaccurate evaluation of the brittle plasticity of tight reservoirs in the prior art, the present invention provides an in-situ evaluation method of the brittle plasticity of tight reservoirs.

[0037] like Figure 1 As shown, the in-situ evaluation method of the brittle plasticity of the tight reservoir includes: a parameter acquisition step: acquiring the vertical depth H and fracturing data of the tight reservoir; a first calculation step: calculating the bottom hole real volume V of the underground fracturing fluid according to the vertical depth H and the fracturing data l , the total volume of the underground fracturing fluid and the underground proppant V t ; The second calculation step: according to the actual volume V of the bottom hole l and the total volume V t Calculation of the plasticity coefficient K of tight reservoirs p ;Evaluation steps: According to the plasticity coefficient K p The brittle-plastic evaluation index of tight reservoirs is established to evaluate the brittle-plasticity of tight reservoirs.

[0038] The actual volume V of the bottom hole of the fracturing fluid is calculated by obtaining the vertical depth H of the tight reservoir and the fracturing data. l , the total volume of the underground fracturing fluid and the underground proppant V t , and according to the actual volume V l and the total volume V t Calculation of the plasticity coefficient K of tight reservoirs p Finally, according to the plasticity coefficient K p The brittle plasticity evaluation index of tight reservoirs is established to evaluate the brittle plasticity of tight reservoirs. In this process, the parameter acquisition is simple and accurate, and according to the plasticity coefficient K p It can accurately evaluate the brittleness and plasticity of tight reservoirs.

[0039] In this embodiment, in the parameter acquisition step, the fracturing data includes the wellhead pressure, the measured volume of the in-ground fracturing fluid, and the volume of the in-ground proppant.

[0040] In this embodiment, the volume of the underground fracturing fluid is compressed under the action of the bottom hole pressure, so it needs to be converted into the real volume of the liquid in the formation. In the first calculation step, the real bottom hole volume V of the underground fracturing fluid is calculated according to the vertical depth H and the fracturing data. l Including: converting the wellhead pressure to the bottom hole pressure, and calculating the bottom hole real volume V of the underground fracturing fluid according to the measured volume of the underground fracturing fluid l .

[0041] In this embodiment, in the first calculation step, the conversion formula for converting the wellhead pressure to the bottom hole pressure is:

[0042] P bt =P w +P H +P f ;

[0043] Among them, P bt is the bottom hole pressure, in MPa; P w is the wellhead pressure, in MPa; P H is the column liquid pressure, in MPa; P f is the fracturing tubing friction, in MPa.

[0044] In this embodiment, in the first calculation step, the fracturing oil pipe friction resistance P f The calculation formula is:

[0045] P f =7.779*10 -6 *D -4.75 *Q 1.75 *L;

[0046] Where D is the inner diameter of the fracturing tubing, in mm; Q is the displacement, in m 3 / s; L is the length of the pipe, in meters.

[0047] In this embodiment, in the first calculation step, the calculation formula of the column hydraulic pressure is:

[0048] P H =ρgH;

[0049] Among them, P H is the column fluid pressure, in Pa; ρ is the density of the in-ground fracturing fluid, in kg / m 3 ; g is the acceleration due to gravity 10m / s 2 ; H is the vertical depth of the tight reservoir, in meters.

[0050] In this embodiment, in the first calculation step, the actual bottom hole volume V of the underground fracturing fluid is l The calculation formula is:

[0051] V l =V s (1-β(P bt -P0));

[0052] Among them, V l is the actual volume of the fracturing fluid at the bottom of the well, in m 3 ; V s is the measured volume of the underground fracturing fluid, in m 3 ; β is the volume compression coefficient of the in-ground fracturing fluid; P bt is the bottom hole pressure, in MPa; P0 is the standard atmospheric pressure, in MPa.

[0053] In this embodiment, the underground proppant is generally ceramsite or quartz sand, and its volume compression can be ignored. In the first calculation step, the total volume V of the underground fracturing fluid and the underground proppant is t The calculation formula is:

[0054] V t =V l +V d ;

[0055] Among them, V t is the total volume of the underground fracturing fluid and proppant, in m 3 ; V l is the actual volume of the fracturing fluid at the bottom of the well, in m 3 ; V d is the volume of the proppant inserted into the ground, in m 3 .

[0056] In this embodiment, in the second calculation step, according to the actual bottom hole volume V l and the total volume V t Calculation of the plasticity coefficient K of tight reservoirs p Including: the bottom hole pressure P bt and the total volume V t After aligning the cumulative time of fracturing, V t -P bt curve, and according to V t -P bt Curve calculation of the plasticity coefficient K of tight reservoir p .

[0057] like Figure 2 As shown, in this embodiment, in the second calculation step, V t -P bt The initial segment of the curve is tangent, and the plasticity coefficient K of the tight reservoir is p The calculation formula is:

[0058]

[0059] Among them, point O is the origin of the coordinate axis; point A is V t -P bt The first peak point of the curve; Point B is the projection point of Point A on the X-axis; Point C is the intersection of the projection line of Point A onto the Y-axis and the tangent line; Point D is the projection point of Point C on the X-axis; A OAB is the lower envelope area of ​​curve OA; A OCD is the area of ​​triangle OCD.

[0060] It should be noted that the lower envelope area A of the curve OA OAB It refers to the area of ​​the region enclosed by the curve OA, the straight line AB and the straight line OB.

[0061] Table 1 Brittle-plastic evaluation table of tight reservoirs

[0062]

[0063] As shown in Table 1, in this embodiment, in the evaluation step, according to the plasticity coefficient K p The brittle plasticity evaluation indexes for tight reservoirs include: when the plasticity coefficient K p When the plasticity coefficient K is 1, the tight reservoir is ideally brittle; p When the plasticity coefficient K is greater than 1 and less than or equal to 5, the tight reservoir is brittle plastic. p When it is greater than 6, the tight reservoir is ideally plastic. Specifically, the plasticity coefficient K p When it is greater than 1 and less than or equal to 6, as the plasticity coefficient K p With the increase of plasticity, the tight reservoir gradually changes from low plasticity to high plasticity.

[0064] As shown in Table 1, in this embodiment, in the evaluation step, the brittle plasticity evaluation of the tight reservoir includes levels 1 to 7. When the plasticity coefficient K p When the plasticity coefficient K is 1, the brittle plasticity level is 1. p When it is greater than 1 and less than or equal to 2, the brittle plasticity level is 2. p When it is greater than 2 and less than or equal to 3, the brittle plasticity level is 3. p When it is greater than 3 and less than or equal to 4, the brittle plasticity level is 4. p When it is greater than 4 and less than or equal to 5, the brittle plasticity level is 5. p When it is greater than 5 and less than or equal to 6, the brittle plasticity level is 6. p When it is greater than 6, the brittle-ductility level is 7.

[0065] like Figure 3 As shown in Figure 2, when the tight reservoir is ideally brittle, the plasticity coefficient K pis 1. That is, A OAB and A OCD The area of ​​the ideal brittle V t -P bt In the curve graph, point A coincides with point C, and point B coincides with point D.

[0066] like Figure 4 As shown in Figure 2, when the tight reservoir is ideally brittle, the plasticity coefficient K p Greater than or equal to 6. Correspondingly, for V t -P bt The slope of the tangent line required for the initial segment of the curve gradually decreases.

[0067] In a specific embodiment, the brittle plasticity of a tight reservoir is evaluated using the in-situ evaluation method for the brittle plasticity of a tight reservoir of the present application.

[0068] First, the tight reservoir is fractured to obtain the fracturing curve.

[0069] In this embodiment, the inner diameter D of the fracturing oil pipe is 73 mm. The displacement Q can be directly read from the fracturing curve, and the displacement Q is 8m 3 / min, converted to 0.13m 3 / s. The vertical section length is 3500m, the horizontal section length is 1200m, and the pipe string length L is 4700m. f The calculation formula can be used to calculate the fracturing oil pipe friction resistance P f It is 25.80MPa.

[0070] Wellhead pressure P w It can be read directly from the fracturing curve.

[0071] The density of the underground fracturing fluid is 1000 kg / m 3 The vertical depth H of the tight reservoir is 3500m. According to the column liquid pressure P H The calculation formula can be used to calculate the column liquid pressure P H It is 35MPa.

[0072] Furthermore, the bottom hole pressure P can be calculated according to the conversion formula of wellhead pressure to bottom hole pressure. bt .

[0073] In this embodiment, the measured volume V of the in-ground fracturing fluid is s The value of is the volume of fracturing fluid pressed into the formation over time during the fracturing stage, which is obtained from the wellhead records.

[0074] Since the underground fracturing fluid is approximately pure water, the volume compression coefficient β of the underground fracturing fluid is taken as the volume compression coefficient of pure water 4.5×10 -4 MPa-1 .

[0075] According to the actual volume V of the bottom hole of the fracturing fluid l The calculation formula can be used to calculate the actual volume V of the bottom hole l .

[0076] At this time, the proppant has not been added yet, and the volume of the proppant in the ground is V d 0m 3 .

[0077] Further, according to the total volume V of the underground fracturing fluid and the underground proppant t The total volume V of the underground fracturing fluid and the underground proppant can be calculated by the calculation formula t .

[0078] The bottom hole pressure P bt and the total volume V t After aligning the cumulative time of fracturing, V t -P bt Curve. At V t -P bt In the curve, the bottom hole pressure P bt The first peak point is 119.32MPa, and the corresponding horizontal coordinate is 65.31m 3 . From this, the lower envelope area A of the curve OA in the range of the horizontal coordinate 0-65.31 is calculated OAB is 1536.45. t -P bt Find the tangent line of the initial segment of the curve, and the tangent line formula is P bt =83.49+1.16*V t On the tangent line, the bottom hole pressure P bt The first peak point of 119.32MPa corresponds to a horizontal coordinate value of 30.89, and then the envelope area under the tangent line within the horizontal coordinate range of 0-30.89 is calculated, that is, the area A of the triangle OCD OCD It is 572.52.

[0079] Finally, according to the plasticity coefficient K of the tight reservoir p The plasticity coefficient K of the tight reservoir in this embodiment is obtained by the calculation formula p It can be seen from Table 1 that the tight reservoir in this embodiment is a brittle-plastic reservoir with a brittle-plastic level of 3.

[0080] From the above description, it can be seen that the above embodiments of the present invention achieve the following technical effects: by obtaining the vertical depth H of the tight reservoir and the fracturing data, the actual bottom hole volume V of the fracturing fluid injected into the ground is calculated. l , the total volume of the underground fracturing fluid and the underground proppant V t, and according to the actual volume V l and the total volume V t Calculation of the plasticity coefficient K of tight reservoirs p Finally, according to the plasticity coefficient K p The brittle plasticity evaluation index of tight reservoirs is established to evaluate the brittle plasticity of tight reservoirs. In this process, the parameter acquisition is simple and accurate, and according to the plasticity coefficient K p It can accurately evaluate the brittleness and plasticity of tight reservoirs.

[0081] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0082] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein.

[0083] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An in-situ evaluation method for the brittle plasticity of a tight reservoir, characterized in that: include: Parameter acquisition steps: obtaining the vertical depth H of the tight reservoir and fracturing data; The first calculation step: Calculate the actual volume V of the bottom hole of the fracturing fluid according to the vertical depth H and the fracturing data l , the total volume V of the underground fracturing fluid and the underground proppant t ; The second calculation step: according to the actual volume V of the bottom hole l and the total volume V t Calculate the plasticity coefficient K of the tight reservoir p ; Evaluation steps: According to the plasticity coefficient K p Establishing a brittle-plastic evaluation index for the tight reservoir and evaluating the brittle-plasticity of the tight reservoir; In the parameter acquisition step, the fracturing data includes the wellhead pressure, the measured volume of the in-ground fracturing fluid and the volume of the in-ground proppant; In the first calculation step, the actual bottom hole volume V of the fracturing fluid injected into the ground is calculated according to the vertical depth H and the fracturing data. l include: The wellhead pressure is converted into the bottom hole pressure, and the bottom hole real volume V of the underground fracturing fluid is calculated according to the measured volume of the underground fracturing fluid. l ; In the first calculation step, the conversion formula for converting the wellhead pressure to the bottom hole pressure is: P bt =P w +P H +P f : Among them, P bt is the bottom hole pressure, in MPa; P w is the wellhead pressure, in MPa; P H is the column liquid pressure, in MPa; P f is the fracturing tubing friction, in MPa; In the second calculation step, the actual volume V of the bottom hole is calculated based on the actual volume V of the bottom hole. l and the total volume V t Calculate the plasticity coefficient K of the tight reservoir p include: The bottom hole pressure P bt and the total volume V t After aligning the cumulative time of fracturing, V t -P bt curve, and according to the V t -P bt The plasticity coefficient K of the tight reservoir is calculated by the curve p ; In the second calculation step, the V t -P bt The initial segment of the curve is tangent, and the plasticity coefficient K of the tight reservoir is p The calculation formula is: Among them, point O is the origin of the coordinate axis; point A is the V t -P bt The first peak point of the curve; Point B is the projection point of point A on the X-axis; Point C is the intersection of the projection line of point A onto the Y-axis and the tangent line; Point D is the projection point of point C on the X-axis; A OAB is the lower envelope area of ​​curve OA; A OCD is the area of ​​triangle OCD.

2. The in-situ evaluation method for brittle plasticity of a dense reservoir according to claim 1, characterized in that: In the first calculation step, the calculation formula of the column hydraulic pressure is: P H =ρgH Among them, P H is the column fluid pressure, in Pa; ρ is the density of the in-ground fracturing fluid, in kg / m 3 ; g is the acceleration due to gravity 10m / s 2 ; H is the vertical depth of the tight reservoir, in m.

3. The in-situ evaluation method for brittle plasticity of a dense reservoir according to claim 1, characterized in that: In the first calculation step, the actual bottom hole volume V of the underground fracturing fluid is l The calculation formula is: IN l =V s (1-β(P bt -P0)): Among them, V l is the actual volume of the bottom hole of the underground fracturing fluid, in m 3 ; V s is the measured volume of the in-ground fracturing fluid, in m 3 ; β is the volume compression coefficient of the in-ground fracturing fluid; P bt is the bottom hole pressure, in MPa; P0 is the standard atmospheric pressure, in MPa.

4. The in-situ evaluation method for brittle plasticity of a dense reservoir according to claim 3, characterized in that: In the first calculation step, the total volume V of the in-ground fracturing fluid and the in-ground proppant t The calculation formula is: V t =V l +V d ; Among them, V t is the total volume of the underground fracturing fluid and the underground proppant, in m 3 ; V l is the actual volume of the bottom hole of the underground fracturing fluid, in m 3 ; V d is the volume of the in-ground proppant, in m 3 .

5. The in-situ evaluation method for brittle plasticity of a tight reservoir according to any one of claims 1 to 4, characterized in that: In the evaluation step, the plasticity coefficient K p The brittle-plastic evaluation indexes for the tight reservoir include: When the plasticity coefficient K p When it is 1, the tight reservoir is ideally brittle; When the plasticity coefficient K p When it is greater than 1 and less than or equal to 6, the tight reservoir is brittle plastic; When the plasticity coefficient K p When it is greater than 6, the tight reservoir is of ideal plasticity.

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