Paul F. Worthington-Remembering a Technical Genius?

Paul Worthington passed away in May 2020 leaving a vast legacy of high quality petrophysical publications. In my view the breadth and quality of Paul’s papers makes him one of the greats in petrophysics, as well as being renowned for his work in Unitization & Redetermination (U&R).

My connection with Paul started in 1992 when we worked on several Syrian oil field studies, working in Damascus. This led on to collaboration on several fascinating and challenging Redetermination projects, working with both Operators and partners. I learnt a huge amount through these collaborations, both in terms of deep technical issues, but also in terms of technical strategies. Around this time I became the lead presenter of a Unitization & Redetermination course which was delivered pretty much all round the World. The last phase of Paul’s technical career focussed primarily on technical support on U&R. He became, as you would expect, the go-to-person for broad technical plus strategic U&R advice. After he retired, he constructed probably the most complete U&R course, which I helped him deliver to several clients. Linked to this course, Paul converted his Reading University Law Masters thesis into the definitive reference on the legal aspects plus regulation of Unitization (Ref-1).

Between 1992 and 2003 we travelled and worked together quite extensively. This required the adoption of some important survival strategies, for example being ready to pour oil on choppy waters when a service provider, such as a taxi driver, airline check-in or hotel reception failed to meet Paul’s high standards (something that happened quite frequently).

During a fairly long project in Norway, Paul & I would take the first flight out from Heathrow on Monday and fly back on Friday afternoon. One Monday we were on SAS but the flight was delayed, which in “Worthington world” is not really acceptable, particularly as he had just checked in for it, with his suitcase heading off to the secure zone. Having been told of the delay, after checking in, Paul was unsurprisingly upset (to put it mildly). Through not having any checked-in bag, I succeeded in transferring to the on-time BA flight but, because Paul’s bag had been checked in for the SAS flight; he was “committed”. The SAS check-in lady was having none of his protestations and walked him up & down the check-in area whilst I waited, then I went to the BA flight. She was clearly running Paul around. Just before the BA flight closed, Paul arrived all hot & sweaty. It’s best then to just sit quietly and listen to the aggrieved commentary and how many letters of complaint will be sent to all concerned. We tried not to fly on SAS, going forward. The return journey from Oslo to Heathrow was always enjoyable starting with a Bloody Mary in the airline lounge, followed by more BM’s on the flight. You can easily imagine the situation if the taxi wasn’t waiting for us at Heathrow.

Paul was very much work-focussed but not to the extent of being a workaholic. His approach to technical work (and probably everything else) encompassed thoroughness, attention to detail, calibration, or ground-truthing, as he liked to call it; adding up to consistently high quality deliverables. In terms of Petrophysics, Paul started out producing academic, or research style papers, which is typical of early career stages. As his career progressed and, I suspect, he undertook more evaluations, his second and, in my view, most significant stage, encompasses his papers on pragmatic evaluation.

His 1985 review of shaly sand water saturation models (Ref-2) beautifully summarised the legacy situation and thinking of the time. This paper is a must read for all Petrophysicists today; however, it could do with an update on developments since 1985. If, as a Petrophysicist, you decide to undertake a clastic evaluation using the Effective Porosity System then you must be able to technically justify this approach, which means demonstrating that the chosen (shaly sand) Effective Water Saturation model is correct and accurate. A few years ago I was asked to review a carbonate reservoir interpretation and was surprised to find it had used the Simandoux water saturation model together with a “clay” lithological component. The Petrophysicist was confused when I asked for the technical basis for these. Oh dear.

Paul didn’t like the Effective Porosity System because of its technical sloppiness; preferring the Total Porosity System (TPS). This is another key learning point for Petrophysicists. The EPS is, in effect, a work-around, it’s generally not a technically robust workflow because the uncertainty inherent in the estimation of Shale Volume impacts on Effective Porosity and then Effective Water Saturation. Not a good recipe for success, particularly if a single interpretation is undertaken, when all Petrophysicists should be generating pessimistic, most-likely and optimistic evaluations, as a routine.

For practical petrophysics, Paul’s 1998 paper on the use of the EPS and TPS (Ref-3) is a brilliant integration of the two approaches leading to a more robust set of results. It should be a routine workflow for all petrophysical evaluations of intergranular reservoir lithologies.

In the 1990’s I must have impressed Paul sufficiently to be honoured with presenting his latest petrophysics paper. As you’d expect I was very thoroughly briefed even to the extent of having a list of likely questions and who would probably ask them! The questions did get asked and mostly by the people Paul predicted. The medium for such presentations was 35mm slides and just to increase the complexity, Paul’s paper used two projectors. I flew up to Aberdeen the day before the presentation, studiously revising. Paul had succeeded in getting the very best slot (second on day one; not first because people will still be arriving). If you remember the Live Aid Concert in London in 1985 where Queen stole the show? You had no chance if you followed Queen’s storming set. I was very nervous; however, the first presentation didn’t go particularly well, making mine a lot easier; the opposite of Queen at Live Aid. At the Q&A on Paul’s material, I sensed people were wondering “who is this Jeremy Daines bloke, he seems to be a younger version of Paul Worthington”. Not true of course.

Paul’s petrophysical evaluation papers provide a very solid foundation, predominantly for clastic reservoirs. I don’t recall Paul doing a carbonate evaluation during the time we collaborated closely. He was commissioned to construct an Operator’s Petrophysical Evaluation Manual, which was invaluable. He was also a master of pre-emptive publishing in order to get a peer reviewed technical basis into the public domain, so that it could be used strategically.

Did Paul publish anything other than brilliant, must read papers? Only a small minority didn’t hit the spot for me, which is good because it reminds you that perfection cannot be achieved all of the time.

Paul’s 2005 paper on the Role of Cut-offs (Ref-4) has the usual excellent scene setting and invaluable review of legacy papers on cut-offs; making it an essential read. He also proposes a standard terminology, which if adopted across the discipline would be very beneficial. He discusses the need for cut-offs to be fit for purpose and shows the complexity of trying to define dynamic cut-offs. But, his emphasis is predominantly on clastics and the Effective Porosity System. In terms of the technical basis for these reservoirs, the paper is spot-on, which is why it is a must-read, see Figure-1.

Figure-1

But I’d be surprised if many (or any) Petrophysicists have followed his workflow for dynamic cut-offs, even though it is technically correct (rigorous). There has been a long, ongoing discussion around cut-offs; however, with the arrival of 3D modelling where continuous logs are provided for upscaling, a second branch of the cut-off dichotomy arrived. Where zonal property summations are required Petrophysicists should really provide zonal gross averages where no cut-offs have been applied. This provides the reference point for the petrophysical interpretation; you could say, the Base Case from which the estimated Net zonal properties are derived via fully substantiated cut-offs following Paul’s workflow.

Paul was keenly aware of technical uncertainty; however the vast majority of his evaluation-related papers focussed on deterministic estimates. But he hated the term “determined”, for example “the Free Water Level depth was determined at 8500 ft tvdss”. Very little in Petrophysics, Geoscience or Reservoir Engineering is actually determined; virtually every parameter has uncertainty and therefore is an estimate. He would readily agree that all petrophysical estimates should include a range of uncertainty, but he didn’t go into print on how best to go about this, unless I’m mistaken? The manual he wrote for an Operator entitled: “Manual of Effective Deterministic Petrophysical Interpretation” reflects this.

I mentioned earlier that Paul was a master of getting technical papers published so that he could then refer to them for strategic purposes. I’ll leave you to see if you can spot any such papers. His 2002 paper on how to know whether you have enough core data (Ref-5) might have been a strategic paper. The paper’s premise is to provide a criterion as to whether a petrofacies is sufficiently described by the existing core data, or not. This isn’t the more traditional value of information approach; it’s purely technical, attempting to “contribute to the attainment of a balance between technical uncertainty and operating costs…” As you’d expect the technical basis is well established; however, I can’t see the approach being routinely adopted. If you have cut core you would include core analysis, otherwise why obtain the core? You cannot generally be definitive that obtaining core will give you the same petrofacies that are already established. Have a read and see what you think?

I, as you’d expect when working with a guru, picked up Paul’s technical themes and then ran with some of them; sometimes going further than Paul chose to. I concluded that petrophysical evaluations should not be single deterministic ones, because the range of uncertainty can be significant even if you implement, for example, Paul’s rigorous workflows. A small change in a Shale Volume (Vsh) log can feed into a significant change in net reservoir thickness, together with a small change in Effective Porosity and moderate change in Effective Water Saturation. Factor in the uncertainty in the depth of the Free Water Level, plus saturation-height function and it is easy to create what appears to be a technically robust deterministic interpretation but which could lie in the P10 to P30 (i.e. optimistic), or P70 to P90 (i.e. pessimistic) cumulative probability windows.

Paul’s evaluation papers tend to focus on achieving the best possible deterministic estimates. The problem is that an uncertainty analysis is required to place these estimates with respect to pessimistic, most-likely and optimistic estimates.

Possibly one of the most significant elements that Paul published on was the importance of establishing correlations and predictive functions at the scale of application. Traditional petrophysics didn’t respect this. For example, core plug capillary pressure (Pc), water saturation (Sw) data (even for specific petrofacies) is not scale compatible with log-derived water saturation estimates and definitely not compatible with a reservoir unit application. But the traditional core plug Pc/Sw workflow is still routinely and incorrectly applied today. Paul demonstrated that permeability is a scale dependent parameter, and a very crucial one (Ref-6). See Appendix-1 for an extract from his 2002 SPE Distinguished Lecture paper. As a simple illustration, a function derived directly from core plug porosity and permeability data is not scale compatible with wireline or LWD logs. The core plug data should be transposed to the log scale, following Paul’s recommended workflows and functions derived at the same scale as they are planned to be applied. When peer reviewing or simply reading papers, I’ve yet to see this being undertaken!

So, Paul addressed the technically dodgy Effective Porosity System, then inherent pitfalls in predicting permeability (Ref-6) followed by, in 2002, a big parameter: Saturation Height Functions (Ref-7). This paper is another must read, not only for Petrophysicists but also Geoscientists (particularly Geomodellers) and Reservoir Engineers undertaking simulation modelling. This extract from Reference-7 sums up the key technical take-away on height function application:

“The choice of saturation-height function usually has been driven by petrophysical preference, with too little regard for the subsequent incorporation of the resulting Sw values into volumetric calculations. An overriding principle of contemporary petrophysics is that an empirical relationship should be applied only at the scale for which it has been established. This principle already has been emphasized in the case of predictive algorithms for permeability. It is frequently violated in practice.

A detailed analysis of the impact of scale on saturation-height functions is beyond the scope of this paper. Let it suffice to say that if a function is established at the core scale, it should be applied strictly only at the core scale. If agreement between core and log-derived saturations can be demonstrated, the function can be extrapolated to the log scale. However, geologic mapping operates at the scale of stratigraphic zones or their constituent petrofacies units. If, therefore, a saturation-height function is to be applied at the petrofacies scale, it should be established at that scale. Cross-scale application or the introduction of hybrid functions from a scale perspective can cause significant degradation of the resulting evaluation of hydrocarbon saturation.”

So, constructing a core plug-based Leverett-J function and applying this in a static or dynamic model really isn’t technically supportable; like the Effective Porosity System isn’t really supportable.

A final must-read is Paul’s 2014 paper with Shane Hattingh: Optimizing the Value of Reservoir Simulation Through Quality-assured Initialization (Ref-8).

It’s worth noting a paragraph of the author’s introduction to this paper:

“It is a prerequisite that the reservoir description be realistic and representative, and that its conditioning for simulation be carried out in a manner that retains reservoir character in a workable format. These requirements are rarely satisfied in practice. Shortcomings can be traced to ambiguous terminology, inconsistent definitions of reservoir properties, inappropriate parameter selection, incomplete data sampling, inconsistent upscaling, cross-scale misapplication of interpretative algorithms, erroneous identification of net reservoir, unrepresentative fluid analyses and incorrect application of software options.”

The 2014 paper provides the ultimate end-point, in terms of reservoir dynamic modelling, for the Petrophysicist, whilst also providing the recommended technical framework for Geoscientists plus Reservoir Engineers working on static and dynamic models. If your petrophysical work is feeding into a static then dynamic model I highly recommend you share Paul’s 2014 paper with your team before any serious work kicks-off.

In the 2000s Paul gradually moved away from petrophysics, preferring to build wide expertise in Unitization and Redetermination. I worked with him on two large field redeterminations which both ended successfully for the clients. Around this time I became the lead presenter of a 3 day U&R training course, which took me to some exotic places including Vietnam, Nigeria and Sarawak.

So, prior to Paul’s retirement from Gaffney, Cline & Associates and then during his final stint of consulting via his own company; he provided huge U&R value to multiple clients. I assisted him in reviewing his bespoke new U&R course (Figure-2) before assisting him presenting it in Europe.

Figure-2

If you know Paul you won’t be surprised to find out the course was very detailed and actually quite difficult to present in his preferred two-day format. I failed to persuade him to reduce the course intensity and introduce practical sessions, spread over three days.

Lastly, if you’re involved in U&R and particularly within a National Oil Company then I recommend Paul’s treatise on the Law on Petroleum Unitization (Ref-1, available through Amazon!) and, if you’re a Petrophysicist, experienced or otherwise; I highly recommend reading the other papers referenced below and implementing his excellent technical insights in your future work.

Paul’s pragmatic evaluation publications provide the best source of technical literature for aspiring and experienced Petrophysicists, Geoscientists, Reservoir Engineers plus Technical/Subsurface Managers. If you have a peer assist or peer review role, Paul’s material provides a very solid foundation to work from.

Feel free to contact me on technical or U&R matters. Also get in touch if you are struggling accessing the referenced papers.

Jeremy Daines

Oleum Khaos Ltd

W: www.oleumkhaos.com

T: +44 (0)1252 416396

E: [email protected]

References

1.     Worthington P.F. 2020. The Law on Petroleum Unitization Legislating for Effective Regulatory Governance. Elgar Energy Law & Practice

2.     Worthington, P.F. 1985. The Evolution of Shaly-Sand Concepts in Reservoir Evaluation. The Log Analyst, 26(1), 23-40.

3.     Worthington, P.F. 1998. Conjunctive Interpretation of Core and Log Data Through Association of the Effective and Total Porosity Models.   In: Core-log Integration (P.K. Harvey & M.A. Lovell: Eds.), Geological Society of London Special Publication, 136, 213-223.

4.     Worthington, P.F and Cosentino, L. 2005. The Role of Cut-offs in Integrated Reservoir Studies. Society of Petroleum Engineers, SPE84387.

5.     Worthington, P.F. 2002. A Validation Criterion to Optimize Core Sampling for the Characterization of Petrophysical Facies. PETROPHYSICS 43(6), 477-493.

6.     Worthington, P.F. 2004. The Effect of Scale on the Petrophysical Estimation of Intergranular Permeability. PETROPHYSICS, 45(1), 59-72.

7.     Worthington, P.F. 2002. Application of Saturation-height Functions in Integrated Reservoir Description. In: Geological Applications of Well Logs (M. Lovell & N. Parkinson: Eds): AAPG Methods in Exploration No. 13, 75-89.

8.     Worthington, P.F and Hattingh, S.K.F. 2014. Optimizing the Value of Reservoir Simulation Through Quality-assured Initialization. Petroleum Geoscience, 20, 283-301.

Appendix-1

Extract from Paul’s 2001 SPE Distinguished Lecturer paper on "Maximizing the Effectiveness of Integrated Reservoir Studies: Some Practical Approaches to Improving the Process and Results":

“Scale Effects.

All predictive algorithms that have an empirical foundation are scale-dependent. They should only be applied at the scale at which they were established. These statements are especially pertinent in the case of permeability estimation. If they are not heeded, predicted permeability can be seriously in error.

Figure-1, below illustrates this point. It relates to a set of core data from a sequence of sandstone intervals separated by shales. The data show a cyclic distribution of porosity with a six-inch core sampling interval. The relationship of core porosity Phi to core permeability K is of the form:

log K = C + B log Phi

A Y-on-X regression in bilogarithmic space furnished values for the coefficient B and intercept C as indicated in Figure-1. The data were then subjected to a five-point running mean, which transposed them to a notional scale of two feet along the axis of the cored well. The regression was repeated on the transposed data. The resulting values of B and C changed (Figure-1). The process was repeated with a nine-point running mean (a four-foot moving average) and finally using averages at the interval scale, in this case over about eight feet. These subsequent values of B and C continued to change, but less markedly. At this point four different relationships had been established, each of which related to a notional scale of "measurement" along the well axis. Figure-1 also indicates the permeability that would be predicted using each of these relationships for an input porosity of 0.25, a value that lies within the ranges of the data used to establish all the algorithms. It can be seen that the permeability predicted at the interval scale is more than double that predicted at the core scale.

Figure-1

If a relationship that has been established at the core scale is applied at the interval scale, the predicted permeability will be an underestimate, and this outcome is a consequence of scale abuse. This is one of the reasons why static predictions of permeability are often less than those inferred from well test analysis, even in reservoirs where intergranular flow is known to predominate. The importance of honoring scale cannot be overemphasized. Another reason for disparity between static predictions of permeability and those interpreted from well tests is the use of inappropriate methods of averaging core permeability over the test interval.”